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@@ -0,0 +1,908 @@
+1
+00:00:21,530 --> 00:00:25,710
+بسم الله الرحمن الرحيم لازلنا في موضوع الـ
+
+2
+00:00:25,710 --> 00:00:29,410
+Integral domain الذي ابتدأناه قبل ذلك، واليوم
+
+3
+00:00:29,410 --> 00:00:33,930
+نكمل على نفس الموضوع. وصلنا المرة اللي فاتت إلى
+
+4
+00:00:33,930 --> 00:00:38,130
+النظرية اللي أمامنا، التي نصفها كما يلي: every
+
+5
+00:00:38,130 --> 00:00:44,070
+finite integral domain is a field. يعني نحن تكون
+
+6
+00:00:44,070 --> 00:00:48,930
+عندنا Integral domain، وهذا الـ Integral domain عدد
+
+7
+00:00:48,930 --> 00:00:55,520
+عناصره محدود. إن حدث ذلك، يبقى هذا الكلام يكون فيه
+
+8
+00:00:55,520 --> 00:00:59,900
+لأ، طيب الفرق بين الـ integral والـ domain، الـ
+
+9
+00:00:59,900 --> 00:01:04,640
+integral domain والـ field شغلة واحدة، كل واحد ميزته
+
+10
+00:01:04,640 --> 00:01:09,660
+بثلاث شغلات، اثنتان مشتركتان فيما بينهما، وهي
+
+11
+00:01:09,660 --> 00:01:14,280
+commutative ring with unity، والشغلة الثالثة أن
+
+12
+00:01:14,280 --> 00:01:18,480
+الـ integral domain ما فيهِ zero divisors، لكن الـ
+
+13
+00:01:18,480 --> 00:01:25,050
+field، كل عنصر غير صفري يكون له معكوس. يبقى every non
+
+14
+00:01:25,050 --> 00:01:29,950
+zero element is a unit أو has a multiplicative
+
+15
+00:01:29,950 --> 00:01:35,890
+inverse. نعم، كويس. نجي نفرض، صحّح هذا الكلام، يبقى
+
+16
+00:01:35,890 --> 00:01:44,230
+بأجي أقول: let R = {a1, a2, ..., an} a finite integral domain
+
+17
+00:01:44,230 --> 00:01:57,320
+with
+
+18
+00:01:57,320 --> 00:02:01,560
+...
+
+19
+00:02:01,560 --> 00:02:12,300
+حيث ai ≠ aj  for i ≠ j
+
+20
+00:02:18,860 --> 00:02:23,200
+يبدو أن افترضنا أنّ العناصر a1, a2, ...
+
+21
+00:02:23,200 --> 00:02:28,060
+و an finite integral domain. يبدو هذا
+
+22
+00:02:28,060 --> 00:02:34,220
+integral domain عدد عناصره محدود، ويساوي n من
+
+23
+00:02:34,220 --> 00:02:40,140
+العناصر. تمام. و ليش واحد فيهم زي الثاني؟ كان بإمكاني
+
+24
+00:02:40,140 --> 00:02:45,840
+أصوغها وأقول: are with distinct elements. يبقى عناصر
+
+25
+00:02:45,840 --> 00:02:51,540
+منفصلة عن بعضها تماماً، ولا عنصر يساوي الثاني، لأنّ
+
+26
+00:02:51,540 --> 00:02:57,420
+فرضنا أنّ R هي العناصر، ولا عنصر فيهم يساوي الثاني، لكلّ i
+
+27
+00:02:57,420 --> 00:03:06,240
+≠ j. أحاول أثبت أنّ هذا is a field. طيب الآن
+
+28
+00:03:06,240 --> 00:03:18,020
+R is a commutative ring
+
+29
+00:03:19,630 --> 00:03:26,750
+with unity. واحد
+
+30
+00:03:26,750 --> 00:03:37,370
+مثلاً يبقى one. افترضنا أنّ الـ unity اعتبرناه هو
+
+31
+00:03:37,370 --> 00:03:44,410
+الواحد. إيش باقي علينا نثبت؟ أنّ كل عنصر من هذا غير
+
+32
+00:03:44,410 --> 00:03:50,700
+صفر يكون unit. يبقى فلياً أقول: افترض أنّ الـ a
+
+33
+00:03:50,700 --> 00:04:01,420
+موجود في الـ ring R بحيث أنّ الـ a ≠ 0. يبقى
+
+34
+00:04:01,420 --> 00:04:06,960
+الـ a عنصر غير صفري موجود في الـ R. يبقى الـ a هذا
+
+35
+00:04:06,960 --> 00:04:12,620
+قد يكون الـ a1، وقد يكون الـ a2، وقد يكون الـ a3، وقد
+
+36
+00:04:12,620 --> 00:04:19,210
+يكون الـ an. يبقى أي عنصر من هذه العناصر. الآن
+
+37
+00:04:19,210 --> 00:04:28,790
+هذا الـ set اللي هي a في R. إيش يعني؟ يعني بدي أضرب الـ
+
+38
+00:04:28,790 --> 00:04:33,350
+element غير الصفري في الـ set R. يعني بدي أضربه في
+
+39
+00:04:33,350 --> 00:04:38,210
+كل العناصر من عناصر الـ ring اللي عندنا. يبقى بده يصير
+
+40
+00:04:38,210 --> 00:04:45,910
+a a1، و a a2، ونظل ماشيين لـ a an.
+
+41
+00:04:49,960 --> 00:04:55,340
+طيب، هذه الـ set صارت فيها عناصر جديدة. ممكن اثنان
+
+42
+00:04:55,340 --> 00:05:00,880
+يساويا بعض؟ لأ، ربما لأ، ممكن يحصل، ممكن يحصل.
+
+43
+00:05:00,880 --> 00:05:06,720
+لكن أنا بدي أثبت أنّ ولا واحد فيهم بده يساوي
+
+44
+00:05:06,720 --> 00:05:11,400
+الثاني. يعني هدول كذلك are distinct. ولا واحد زي
+
+45
+00:05:11,400 --> 00:05:17,380
+الثاني خالص، نهائياً. يبقى بأجي بقول: the set aR هذه
+
+46
+00:05:17,380 --> 00:05:26,680
+العناصر هذه has distinct elements
+
+47
+00:05:26,680 --> 00:05:32,760
+because
+
+48
+00:05:32,760 --> 00:05:37,240
+أنا
+
+49
+00:05:37,240 --> 00:05:43,900
+أَدّعي الآن أنّ هذه العناصر ولا واحد زي الثاني، طبعاً
+
+50
+00:05:43,900 --> 00:05:48,400
+بدنا نشوف هل الادعاء هذا اللي أنا بقوله صحيح، والله
+
+51
+00:05:48,400 --> 00:05:59,300
+غير صحيح because if مثلاً a ai = a aj، و i ≠ j. افترض أنّ اثنين منهم
+
+52
+00:05:59,300 --> 00:06:10,120
+كان متساويين، مين ما يكون i ومين ما يكون j، بس المهم
+
+53
+00:06:10,120 --> 00:06:15,620
+هما ما يتساووش. افترضت أنّ اثنين متساويين، لمن؟ للـ i
+
+54
+00:06:15,620 --> 00:06:21,750
+لا يساوي الـ j. بتشوف هذا الفرض لوين بده يوصلني.
+
+55
+00:06:21,750 --> 00:06:27,250
+إذا وصلني إلى نتيجة صحيحة، بيكون كلامي هذا باطل.
+
+56
+00:06:27,890 --> 00:06:32,670
+وإذا وصلني إلى نتيجة خاطئة، بصير كلامي هذا، بصير هذا
+
+57
+00:06:33,050 --> 00:06:39,650
+كلامي صحيح. لأنّ هدول distinct، ولا واحد زي الثاني، إلا
+
+58
+00:06:39,650 --> 00:06:44,070
+افترضت أنّ اثنين سوا بعض. على عكس ما قلنا فوق، بدي
+
+59
+00:06:48,800 --> 00:06:55,420
+أشوف هذا وين بده يوصلني. يبقى بأقدر أقول: a ai − a aj = 0 باستخدام الـ
+
+60
+00:06:55,420 --> 00:07:02,420
+distributive law. بأقدر أقول هذا الكلام: a(ai − aj) = 0. هذا إيش
+
+61
+00:07:02,420 --> 00:07:09,000
+معناه؟ هذا معناه أنّ a = 0 أو أنّ ai
+
+62
+00:07:09,000 --> 00:07:15,120
+− aj = 0. لكن أنا فرضت أنّ a لن
+
+63
+00:07:15,120 --> 00:07:23,970
+يساوي 0. يبقى هنا بعدين بقول: since بما أنّ a
+
+64
+00:07:38,250 --> 00:07:49,210
+لا يساوي 0، we have أنّ ai − aj =
+
+65
+00:07:49,210 --> 00:07:56,230
+اللي بده يساوي 0. هذا إيش معناه؟ معناه أنّ ai بده
+
+66
+00:07:56,230 --> 00:08:03,030
+يساوي aj. على عكس الكلام اللي احنا فرضناه من الأساس.
+
+67
+00:08:03,030 --> 00:08:12,150
+يبقى هذا this is a contradiction. هذا تناقض.
+
+68
+00:08:15,900 --> 00:08:20,680
+يناقض مين؟ يناقض العبارة اللي قلناها هذه، أنّ ai
+
+69
+00:08:20,680 --> 00:08:26,200
+لا يساوي aj. فلنقل أنّ ai يساوي aj، إذا هذا كلام
+
+70
+00:08:26,200 --> 00:08:32,240
+خطأ. من أين أتى الخطأ؟ من الفرض الخاطئ اللي أنا
+
+71
+00:08:32,240 --> 00:08:37,440
+فرضته. يبقى فعلاً هذول are distinct، ولا واحد زي
+
+72
+00:08:37,440 --> 00:08:43,820
+الثاني. يبقى هنا الـ a
+
+73
+00:08:55,140 --> 00:09:02,320
+a a1، و a a2، و a an
+
+74
+00:09:02,320 --> 00:09:12,640
+are distinct. يبقى ولا واحد فيهم زي الثاني. تمام. طيب
+
+75
+00:09:12,640 --> 00:09:18,220
+كويس. يبقى أخذنا معلومة أنّ هذه العناصر منفصلة عن
+
+76
+00:09:18,220 --> 00:09:25,220
+بعضها تماماً، ما في تساوي بين أي عنصرين. السؤال هو: طيب
+
+77
+00:09:25,220 --> 00:09:30,220
+هل R closed under multiplication؟ ولا لا؟ لأنّ
+
+78
+00:09:30,220 --> 00:09:34,100
+عملية الضرب is a binary operation. يبقى a في
+
+79
+00:09:34,100 --> 00:09:40,240
+a، وعناصر موجودة where؟ في الـ ring a، و a في
+
+80
+00:09:40,240 --> 00:09:40,780
+a2
+
+81
+00:09:47,270 --> 00:09:58,410
+يبقى اللي بقوله: since بما أنّ R is closed under
+
+82
+00:09:58,410 --> 00:10:01,490
+multiplication
+
+83
+00:10:13,450 --> 00:10:20,470
+إنّ الـ R العناصر هذه كلها ai ai ai ai ai ai ai ai ai
+
+84
+00:10:20,470 --> 00:10:23,290
+ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai
+
+85
+00:10:23,290 --> 00:10:24,210
+ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai
+
+86
+00:10:24,210 --> 00:10:26,490
+ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai
+
+87
+00:10:26,490 --> 00:10:26,670
+ai ai ai ai ai ai ai ai ai ai ai ai ai ai ai
+
+88
+00:10:26,670 --> 00:10:33,630
+ai ai ai
+
+89
+00:10:33,630 --> 00:10:41,990
+ai ai ai ai ai ai ai
+
+90
+00:10:41,990 --> 00:10:48,300
+نبدأ مع عنصر ring. إحنا هنا قلنا R integral domain
+
+91
+00:10:48,300 --> 00:10:52,280
+الـ integral domain يحتوي على unity. ولا لا؟ يبقى
+
+92
+00:10:52,280 --> 00:10:57,980
+معناته واحد فيهم بده يساوي الـ unity، صح ولا لا؟ يبقى
+
+93
+00:10:57,980 --> 00:11:08,040
+بأجي بقول: نعم، الواحد موجود في R because R is
+
+94
+00:11:08,040 --> 00:11:10,440
+an integral
+
+95
+00:11:13,890 --> 00:11:19,630
+domain. يبقى الواحد لازم يساوي، طبعاً اللي هو الـ
+
+96
+00:11:19,630 --> 00:11:25,430
+unity. الواحد هذا لازم يساوي واحد من هذه العناصر.
+
+97
+00:11:25,430 --> 00:11:32,250
+يبقى هذا بدي يعطيك أنّ a في a، مثلاً، بده يساوي
+
+98
+00:11:32,250 --> 00:11:40,470
+اللي هي الـ unity، one. إيش تفسيرك لهذا الكلام؟ أنّ الـ
+
+99
+00:11:40,470 --> 00:11:46,930
+a is a unit، صح؟ لأنّه ما أخذناه بيساوي 0، صح؟ يبقى
+
+100
+00:11:46,930 --> 00:11:59,250
+this means that هذا يعني أنّ a is a unit. يبقى
+
+101
+00:11:59,250 --> 00:12:07,250
+every non-zero element is a unit. يبقى هنا: every
+
+102
+00:12:08,610 --> 00:12:18,790
+non-zero element element
+
+103
+00:12:18,790 --> 00:12:28,430
+of R is a unit. therefore
+
+104
+00:12:28,430 --> 00:12:32,950
+ولهذا
+
+105
+00:12:32,950 --> 00:12:37,710
+R is a field.
+
+106
+00:12:48,980 --> 00:12:57,280
+السؤال: بدنا نعمل العكس. هل field integral domain؟ هل
+
+107
+00:12:57,280 --> 00:13:03,440
+كل field يكون integral domain؟ عملية عكسية؟
+
+108
+00:13:03,440 --> 00:13:09,640
+السؤال هو: الـ field فيه zero divisor؟ لأ، لأنّ كل عنصر
+
+109
+00:13:09,640 --> 00:13:14,380
+عبارة عن unit، صح ولا لا؟  كل عنصر، يبقى لا
+
+110
+00:13:14,380 --> 00:13:19,820
+يمكن للـ unit أن يكون zero divisor. يعني ما فيها
+
+111
+00:13:19,820 --> 00:13:24,000
+zero divisor، بيبقى إيش صارت؟ Integral domain. يبقى
+
+112
+00:13:24,000 --> 00:13:29,020
+any field is an integral domain، لكن العكس ليس
+
+113
+00:13:29,020 --> 00:13:35,640
+بالضرورة صحيحاً. يعني مش كل integral domain هو field.
+
+114
+00:13:36,430 --> 00:13:42,590
+لكن إذا كان الـ Integral domain  finite، حسب نصّ
+
+115
+00:13:42,590 --> 00:13:48,030
+النظرية، بيكون هو field. تمام؟ يبقى الـ Integral
+
+116
+00:13:48,030 --> 00:13:52,650
+domain لازم أحط عليه شرط مشان يصير field، لكن الـ
+
+117
+00:13:52,650 --> 00:13:57,310
+field ما بحطّ عليه ولا شرط مشان يصير Integral domain.
+
+118
+00:13:57,310 --> 00:14:06,840
+طيب ننتقل الآن إلى نتيجة على هذه النظرية. الآن
+
+119
+00:14:06,840 --> 00:14:11,820
+Corollary. الـ Corollary
+
+120
+00:14:11,820 --> 00:14:21,080
+بتقول: معناته for every prime p، for every prime p
+
+121
+00:14:21,080 --> 00:14:33,240
+Zp، Zp اللي هي the ring of integers
+
+122
+00:14:34,820 --> 00:14:50,100
+modulo p. modulo p. الـ p شفناها
+
+123
+00:14:50,100 --> 00:14:54,160
+قبل،  كتبناها في المحاضرة الماضية، وإيش قلنا
+
+124
+00:14:54,160 --> 00:15:00,660
+عليها؟ Integral domain، صح ولا لأ؟ يبقى هنا بقولوا: we
+
+125
+00:15:00,660 --> 00:15:14,870
+know that إحنا بنعرف أنّ Zp is an integral domain. من
+
+126
+00:15:14,870 --> 00:15:21,150
+وين هذا الكلام؟ مثال سابق، هي بيصِف example في
+
+127
+00:15:21,150 --> 00:15:27,010
+المحاضرة السابقة، مش بعيد يعني. تمام؟ يبقى هذا
+
+128
+00:15:27,010 --> 00:15:33,030
+integral domain. السؤال هو: finite ولا لأ؟ قداش عدد
+
+129
+00:15:33,030 --> 00:15:41,810
+العناصر فيه؟ قداش؟  p − 1، العنصر الأخير
+
+130
+00:15:41,810 --> 00:15:47,330
+فيه p − 1. لكن أول عنصر قداش؟ 0. إذا عدد
+
+131
+00:15:47,330 --> 00:15:54,050
+العناصر فيه يبقى الـ Zp
+
+132
+00:15:54,050 --> 00:16:01,370
+has p elements.
+
+133
+00:16:05,520 --> 00:16:11,020
+that is p
+
+134
+00:16:11,020 --> 00:16:19,400
+elements. يبقى p من العناصر. يعني it is p finite.
+
+135
+00:16:19,400 --> 00:16:33,480
+يبقى by the above theorem، بالنظرية
+
+136
+00:16:33,480 --> 00:16:42,840
+السابقة، Zp is a field. لو
+
+137
+00:16:42,840 --> 00:16:49,860
+جيبت لك سؤال في الامتحان، وقلت لك: اثبت لي أنّ Zp is a field،
+
+138
+00:16:49,860 --> 00:16:57,180
+بتقدر تثبت لي أولاً أنّه integral domain، تمام؟ اللي
+
+139
+00:16:57,180 --> 00:17:00,800
+هو من النظريات السابقة، وأضيف عليه الكلمتين
+
+140
+00:17:00,800 --> 00:17:28,870
+هذول: أنّه finite وبالتالي بصير a field. طيب
+
+141
+00:17:28,870 --> 00:17:29,770
+example
+
+142
+00:17:37,820 --> 00:17:49,240
+مثل Z3[i]، اللي هي على الصيغة: كل العناصر a
+
+143
+00:17:49,240 --> 00:18:02,620
++ bi، such that a و b belongs to Z3. من
+
+144
+00:18:02,620 --> 00:18:08,990
+العناصر هذه اللي هي تساوي 0 و 1 و 2،
+
+145
+00:18:08,990 --> 00:18:16,890
+والـ i، والـ 1 + i، والـ 2 + i، والـ 2i،
+
+146
+00:18:16,890 --> 00:18:27,050
+والـ 1 + 2i، والـ 2 + 2i is a
+
+147
+00:18:27,050 --> 00:18:27,490
+field.
+
+148
+00:18:39,650 --> 00:18:43,590
+الـ Z3[i]. طبعاً الـ Z3 هم العناصر اللي هي
+
+149
+00:18:43,590 --> 00:18:48,990
+0، و 1، و 2 فقط. غير ثلاثة عناصر.
+
+150
+00:18:48,990 --> 00:18:55,290
+العناصر بتبقى Z[i] على صيغة إيش؟ زي a + bi، في
+
+151
+00:18:55,290 --> 00:19:00,830
+الـ a والـ b موجودة في Z3. يعني الـ a والـ b يا إمّا
+
+152
+00:19:00,830 --> 00:19:05,970
+0 يا إمّا 1 يا إمّا 2. ما عدا ذلك، ما فيش
+
+153
+00:19:05,970 --> 00:19:10,670
+عناصر فيه. تمام؟ طيب هذه لو جيت أدوّر على عناصرها
+
+154
+00:19:10,670 --> 00:19:15,730
+بلاقي: 0، 1، و 2. بلاقي i، 1 + i، 2 + i،
+
+155
+00:19:15,730 --> 00:19:21,810
+2i، 1 + 2i، و
+
+156
+00:19:21,810 --> 00:19:27,450
+2 + 2i. خلصنا. هي العناصر. عدّهم، بتلاقيهم
+
+157
+00:19:27,450 --> 00:19:33,750
+تسعة عناصر. هذا الـ ring فيه تسعة عناصر.
+
+158
+00:19:33,750 --> 00:19:42,710
+طبعاً هذا commutative ring with unity. من هنا one
+
+159
+00:19:42,710 --> 00:19:54,830
+يبقى هذا because Z3[i] is a commutative
+
+160
+00:19:54,830 --> 00:19:58,130
+ring
+
+161
+00:19:58,130 --> 00:20:09,710
+with unity، اللي هم الواحد اللي بيساوي 1 +
+
+162
+00:20:09,710 --> 00:20:18,210
+0 في i، اللي موجود في Z3[i]. يبقى 1 هو
+
+163
+00:20:18,210 --> 00:20:22,630
+الـ unity. هذا موجود في Z3 لأنّ ابتدى الاقتباس
+
+164
+00:20:22,630 --> 00:20:27,150
+على الصيغة 1 + 0 في i، والـ 1 والـ 0
+
+165
+00:20:27,150 --> 00:20:33,410
+موجود في Z3. هذا كلام مظبوط. ضلّ علينا أثبت أنّه
+
+166
+00:20:33,410 --> 00:20:37,900
+ما فيهِ zero divisors. يبقى إيه؟ بعدي عن الـ 0
+
+167
+00:20:37,900 --> 00:20:43,820
+تعالى لباقي العناصر. هل ممكن تظهر أي اثنين
+
+168
+00:20:43,820 --> 00:20:52,620
+فيهم يطلع 0؟ لأنّ كل واحد فيهم عبارة عن unit، تمام؟
+
+169
+00:20:52,620 --> 00:21:04,400
+يبقى this ring has no zero divisors.
+
+170
+00:21:06,840 --> 00:21:11,840
+ما في عندي ضرب، كل عنصر عبارة عن إيش؟ عبارة عن
+
+171
+00:21:11,840 --> 00:21:17,600
+unit. طيب ما بنلاقِ فيه zero divisor، لأنّه لا يمكن
+
+172
+00:21:17,600 --> 00:21:23,620
+أضرب عنصرين غير صفرين يطلع 0. خذ أي اثنين
+
+173
+00:21:23,620 --> 00:21:28,620
+واضربهم، لا يمكن يطلع صفر. يبقى this ring has no zero
+
+174
+00:21:28,620 --> 00:21:41,940
+divisor. Z3[i] is a finite integral
+
+175
+00:21:41,940 --> 00:21:46,340
+domain. ليش؟
+
+176
+00:21:46,340 --> 00:21:52,860
+إنّ فيه كم عنصر؟ تسعة عناصر. تسعة عناصر، يبقى finite
+
+177
+00:21:52,860 --> 00:22:00,140
+و integral domain. يبقى is a field. يبقى هذا بيعطينا أنّ Z
+
+
+223
+00:27:14,670 --> 00:27:23,300
+هو Q جذر إثنين، شكل يعني هذا اللي هو كل العناصر اللي
+
+224
+00:27:23,300 --> 00:27:29,840
+على صيغة a زائد b جذر إثنين، بحيث الـ a والـ b are
+
+225
+00:27:29,840 --> 00:27:44,520
+rational numbers. هذه is a commutative ring with
+
+226
+00:27:44,520 --> 00:27:46,460
+unity.
+
+227
+00:27:52,880 --> 00:27:59,200
+One، معقول؟ أه، هذه الكميوتة تبقى with unity one.
+
+228
+00:27:59,200 --> 00:28:06,820
+مثلاً واحد زائد صفر في جذر إثنين، يبقى هذا
+
+229
+00:28:06,820 --> 00:28:10,940
+هو الـ unity في الـ set اللي عندنا هذا، وهذه الكميوتة
+
+230
+00:28:10,940 --> 00:28:14,820
+تبقى لأنها عملية ضرب الـ rational numbers عملية
+
+231
+00:28:14,820 --> 00:28:21,480
+إبدالية، يقول ماعندنا مشكلة فيها، مش ضايلة لها. فيها
+
+232
+00:28:21,480 --> 00:28:28,540
+Zero Divisors؟ مش فيها Zero Divisors بالمرة لأن
+
+233
+00:28:28,540 --> 00:28:34,200
+any two rational numbers لا يمكن أن يعطينا Zero
+
+234
+00:28:34,200 --> 00:28:39,660
+بشرط أن ولا واحد فيهم يساوي Zero، تمام؟ إذا ما عنديش
+
+235
+00:28:39,660 --> 00:28:46,740
+rational numbers ما عنديش units فيها، ما عنديش Zero
+
+236
+00:28:46,740 --> 00:28:51,310
+Divisors جدًا، بقيت إثنين. Is it finite ولا
+
+237
+00:28:51,310 --> 00:28:56,870
+infinite؟ Infinite. يبقى هذا السؤال مش على النظرية،
+
+238
+00:28:56,870 --> 00:29:04,090
+هذا السؤال يعتبر سؤال خارجي. يبقى أنا أَدّعي أن هذا
+
+239
+00:29:04,090 --> 00:29:09,230
+الآن is ايه فيه. يبقى النظرية صحيحة، عشان أَشْرَع أن الـ
+
+240
+00:29:09,230 --> 00:29:14,270
+commutative ring with unity. تمام؟ أظل أُثبت والله
+
+241
+00:29:14,270 --> 00:29:19,820
+إذا كان كل عنصر له معكوس تحت عملية الضرب، يعني
+
+242
+00:29:19,820 --> 00:29:24,400
+multiplicative inverse، بتبقى المفروض بصورة أن أدي
+
+243
+00:29:24,400 --> 00:29:32,000
+اسم ايه فيه، تمام؟ بقدر أروح أقوله I want to show
+
+244
+00:29:32,000 --> 00:29:35,400
+أن
+
+245
+00:29:35,400 --> 00:29:50,140
+الهدف أن نبين أن أي عنصر غير صفري  any non-zero element of Q of
+
+246
+00:29:50,140 --> 00:30:01,460
+جذر إثنين has a multiplicative
+
+247
+00:30:01,460 --> 00:30:06,520
+inverse. بدأت
+
+248
+00:30:06,520 --> 00:30:14,260
+أن أي عنصر غير صفري له معكوس. لذلك بعدين بقوله افترض
+
+249
+00:30:14,260 --> 00:30:25,810
+أن الـ a زائد b جذر إثنين لا يساوي صفر، بروح
+
+250
+00:30:25,810 --> 00:30:31,010
+بقول Z multiplicative
+
+251
+00:30:31,010 --> 00:30:35,710
+inverse
+
+252
+00:30:35,710 --> 00:30:47,820
+of الـ a زائد b جذر إثنين is من ذاك الرقم اللي لو
+
+253
+00:30:47,820 --> 00:30:52,200
+ضربته في هذا العنصر بدي يعطيني الـ unity اللي هو
+
+254
+00:30:52,200 --> 00:31:01,800
+واحد. مين؟ واحد على هذا المقدار، تمام؟ واحد على ايه
+
+255
+00:31:01,800 --> 00:31:08,780
+لقيت فيه جذر إثنين. السؤال: هل العنصر هذا موجود في الـ
+
+256
+00:31:08,780 --> 00:31:15,940
+Q جذر إثنين؟ يعني هذا العنصر هل مكتوب على صيغة
+
+257
+00:31:15,940 --> 00:31:21,810
+ثابت زائد ثابت في جذر إثنين؟ لأ، مش مكتوب
+
+258
+00:31:21,810 --> 00:31:30,090
+وبالتالي يمكن نَقْدَر نَقْتُلُه ويمكن ما نَقْدَرْش. إذا قدرنا
+
+259
+00:31:30,090 --> 00:31:33,970
+نقتله بيصير كلامنا صحيح وخلصنا من المسألة، إذا
+
+260
+00:31:33,970 --> 00:31:38,890
+ما قدرناش بيصير ادعائنا هذا غير صحيح، بيصير هذا معكوس
+
+261
+00:31:38,890 --> 00:31:42,230
+لكن هذا القلم اللي جِبْتُه من الشارع أنا ما جِبْتُوش من
+
+262
+00:31:42,230 --> 00:31:48,800
+الـ ring اللي عندي، تمام؟ يبقى إذا قدرت أثبت أن هذا
+
+263
+00:31:48,800 --> 00:31:54,040
+على الصيغة ثابت زائد ثابت في جذر إثنين،
+
+264
+00:31:54,040 --> 00:31:59,000
+بيصير موجود في الـ Q فعلاً، يكون هذا هو المعقول، لذلك
+
+265
+00:31:59,000 --> 00:32:03,640
+إذا قُلْت ضَبَطْت في ذاكرتي أن قِصَّة الـ element هذا هو الـ
+
+266
+00:32:03,640 --> 00:32:12,700
+element هذا لأيش؟ هو هذا أنا أدعي أنه موجود في
+
+267
+00:32:12,700 --> 00:32:27,150
+الـ Q of جذر إثنين. ليش؟ لأن واحد على a زائد
+
+268
+00:32:27,150 --> 00:32:33,970
+b جذر إثنين بده يساوي واحد على a زائد b جذر
+
+269
+00:32:33,970 --> 00:32:40,950
+إثنين، لو ضربته في مرافق المقام فبيصير عندنا ايه
+
+270
+00:32:40,950 --> 00:32:48,090
+ناقص b جذر إثنين على ا² ناقص b² جذر إثنين بهذا
+
+271
+00:32:48,090 --> 00:32:54,130
+الشكل. المقام مش هو تحليل الفرق بين مربعين، بدي
+
+272
+00:32:54,130 --> 00:32:58,730
+أرجعه إلى أصله، يبقى رجعناه إلى أصله بيصير
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c64c26e67e50b2707016dd7f79e1e8d3a55f4e84
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_postprocess.srt
@@ -0,0 +1,1088 @@
+1
+00:00:21,530 --> 00:00:25,710
+بسم الله الرحمن الرحيم لازلنا في موضوع الـ
+
+2
+00:00:25,710 --> 00:00:29,410
+Integral domain اللي ابتدأناه قبل ذلك و اليوم
+
+3
+00:00:29,410 --> 00:00:33,930
+بنكمل على نفس الموضوع وصلنا المرة اللي فاتت إلى
+
+4
+00:00:33,930 --> 00:00:38,130
+النظرية اللي أمامنا اللي بنصفها كما يلي every
+
+5
+00:00:38,130 --> 00:00:44,070
+finite integral domain is a field يعني احنا بتكون
+
+6
+00:00:44,070 --> 00:00:48,930
+عندنا Integral domain وهذا ال Integral domain عدد
+
+7
+00:00:48,930 --> 00:00:55,520
+العناصر محدودإن حدث ذلك يبقى هذا الكلام يكون فيه
+
+8
+00:00:55,520 --> 00:00:59,900
+لأ طب الفرق بين ال integral و ال domain ال
+
+9
+00:00:59,900 --> 00:01:04,640
+integral domain و ال field شغلة واحدة كل واحد ميزه
+
+10
+00:01:04,640 --> 00:01:09,660
+ب ثلاث شغلات تنتين مشتركة فيما بينهما و هي
+
+11
+00:01:09,660 --> 00:01:14,280
+communicative ring with unity و الشغلة التالتة ان
+
+12
+00:01:14,280 --> 00:01:18,480
+ال integral domain مافيش فيه zero divisors لكن ال
+
+13
+00:01:18,480 --> 00:01:25,050
+fieldكل عنصر غير صفري يكون له معكوش يبقى every non
+
+14
+00:01:25,050 --> 00:01:29,950
+zero element is a unit أو has a multiplicative
+
+15
+00:01:29,950 --> 00:01:35,890
+inverse نعم كويس بنجي نفرض صحيك هذا اي كلام يبقى
+
+16
+00:01:35,890 --> 00:01:44,230
+بداجي اقول let L R تساوي و اي واحد و اتنى و لغاية
+
+17
+00:01:44,230 --> 00:01:57,320
+A N D Afinite field finite integral domain
+
+18
+00:01:57,320 --> 00:02:01,560
+with
+
+19
+00:02:01,560 --> 00:02:12,300
+ال a i لا تسوى a g for i لا تسوى g
+
+20
+00:02:18,860 --> 00:02:23,200
+يبدو ان افترض الارة اللي عناصر و اي واحد و اي
+
+21
+00:02:23,200 --> 00:02:28,060
+اتنين و اي ان finite integral domain يبدو هذا
+
+22
+00:02:28,060 --> 00:02:34,220
+integral domain عدد العناصر محدود و يساوي n من
+
+23
+00:02:34,220 --> 00:02:40,140
+العناصر تمام و ليش واحد فيهم زي التاني كان بإمكاني
+
+24
+00:02:40,140 --> 00:02:45,840
+أصيخة و أقول are with distinct elements يبقى عناصر
+
+25
+00:02:45,840 --> 00:02:51,540
+منفصلة عن بعضها تماما ولا عنصريساوي الثاني لأن لا
+
+26
+00:02:51,540 --> 00:02:57,420
+فرض R هي العلاصر ولا عنصر فيهم يساوي الثاني لكل I
+
+27
+00:02:57,420 --> 00:03:06,240
+لا تساوي G بتحاول أثبت أن هذه is a field طيب الآن
+
+28
+00:03:06,240 --> 00:03:18,020
+ال R is ال R is commutative ring
+
+29
+00:03:19,630 --> 00:03:26,750
+with unity واحد
+
+30
+00:03:26,750 --> 00:03:37,370
+مثل يبقى one three افترض ان ال unity اعتبرنا هو
+
+31
+00:03:37,370 --> 00:03:44,410
+الواحد ايش ضايل علينا نثبر ان كل عنصر من هذا غير
+
+32
+00:03:44,410 --> 00:03:50,700
+صفر يكون united يبقى فتاليا اقول افترضإن الـ A
+
+33
+00:03:50,700 --> 00:04:01,420
+موجود في الـ ring R بحيث أن الـ A لا يقل لـ 0 يبقى
+
+34
+00:04:01,420 --> 00:04:06,960
+الـ A عنصر غير صفري موجود في الـ R يبقى الـ A هذا
+
+35
+00:04:06,960 --> 00:04:12,620
+قد يكون الـ A1 وقد يكون الـ A2 وقد يكون الـ A3 وقد
+
+36
+00:04:12,620 --> 00:04:19,210
+وقد يكون الـ A N يبقى أي عنصر من هذه العناصرالان
+
+37
+00:04:19,210 --> 00:04:28,790
+ده set اللي هي A في R ايش يعني؟ يعني بدي اضرب ال
+
+38
+00:04:28,790 --> 00:04:33,350
+element غير الصفري في ال set R يعني بدي اضربه في
+
+39
+00:04:33,350 --> 00:04:38,210
+كل عناصر من عناصر ال ring اللي عندنا يبقى بده يصير
+
+40
+00:04:38,210 --> 00:04:45,910
+A A1 و A A2 ونظل ماشينا غير A A N
+
+41
+00:04:49,960 --> 00:04:55,340
+طيب الست هذه صار فيها عناصر جديدة ممكن يتنين
+
+42
+00:04:55,340 --> 00:05:00,880
+يساويوا بعض؟ لأ لأ ربما لأ لأ ممكن يحصل ممكن يحصل
+
+43
+00:05:00,880 --> 00:05:06,720
+لكن انا ها ها بدي اثبت ان ولا واحد فيهم بدي يساوي
+
+44
+00:05:06,720 --> 00:05:11,400
+التاني يعني هدول كذلك are destined ولا واحد زي
+
+45
+00:05:11,400 --> 00:05:17,380
+التاني خالص نهائي يبقى باجي بقوله the set ar هاي
+
+46
+00:05:17,380 --> 00:05:26,680
+العناصر هذهhas distinct elements
+
+47
+00:05:26,680 --> 00:05:32,760
+because
+
+48
+00:05:32,760 --> 00:05:37,240
+أنا
+
+49
+00:05:37,240 --> 00:05:43,900
+أدعي الآن أن هذه العناصر ولا واحد زي التاني طبعاً
+
+50
+00:05:43,900 --> 00:05:48,400
+بدنا نشوف هل الادعاء هذا اللي أنا بقوله صحيهوالله
+
+51
+00:05:48,400 --> 00:05:59,300
+غير صحيح because if مثلا ال a في ال ai بده ساوي ال
+
+52
+00:05:59,300 --> 00:06:10,120
+a في ال aj والi لا تساوي الجي افترض ان اتنين منهم
+
+53
+00:06:10,120 --> 00:06:15,620
+كان متساويين مين مايكون i ومين مايكون j بس من
+
+54
+00:06:15,620 --> 00:06:21,750
+همالهم مايتساووشافترضت ان اثنين متساوين لمين لل I
+
+55
+00:06:21,750 --> 00:06:27,250
+لا يساوي ال J. بتشوف هذا الفرض لوين بده يوصلني.
+
+56
+00:06:27,890 --> 00:06:32,670
+إذا وصلني إلى نتيجة صحيحة بيكون كلامي هذا باطل.
+
+57
+00:06:33,050 --> 00:06:39,650
+وإذا وصلني إلى نتيجة خاطئة بصير كلامي هذا بصير هذا
+
+58
+00:06:39,650 --> 00:06:44,070
+كلامي صحيح. لأن هدول دسن ولا واحد زي التاني. الا
+
+59
+00:06:44,070 --> 00:06:48,800
+افترضت ان اثنين سوا بعض.على عكس ما نجيه الفوق بدي
+
+60
+00:06:48,800 --> 00:06:55,420
+أشوف هذا وين بدي أوصيك يبقى ذنب بقدر أقول ال a في
+
+61
+00:06:55,420 --> 00:07:02,420
+ال a i نقص ال a في ال a j بده ساوي زير باستخدام ال
+
+62
+00:07:02,420 --> 00:07:09,000
+distributive law بقدر أقول هذا الكلام a في ال a i
+
+63
+00:07:09,000 --> 00:07:15,120
+نقص ال a j بده ساوي مين؟ بده ساوي زيره هذا أيش
+
+64
+00:07:15,120 --> 00:07:23,970
+معناه؟هذا معناه ان ال a بده يساوي zero او ال ai
+
+65
+00:07:23,970 --> 00:07:30,970
+ناقص ال aj بده يساوي zero لكن انا فارغ ان ال a لن
+
+66
+00:07:30,970 --> 00:07:38,250
+يساوي zero يبقى هنا بعدين بقوله since بما ان ال a
+
+67
+00:07:38,250 --> 00:07:49,210
+لا يساوي zero we have ان ال aiالـ AI ناقص ال AJ هو
+
+68
+00:07:49,210 --> 00:07:56,230
+اللي بده يسوى Z هذا إيش معناه؟ معناه إن ال AI بده
+
+69
+00:07:56,230 --> 00:08:03,030
+يسوى مين؟ AJ على عكس الكلام أحنا فرضينه من الأساس
+
+70
+00:08:03,030 --> 00:08:12,150
+يبقى هذا this is contradiction هذا تناقض
+
+71
+00:08:15,900 --> 00:08:20,680
+يناقض مين؟ يناقض العبارة اللي قلناها هذه ان ال AI
+
+72
+00:08:20,680 --> 00:08:26,200
+لا يسوى ال AJ فلعلنا ال AI يسوى AJ، إذا هذا كلام
+
+73
+00:08:26,200 --> 00:08:32,240
+خطأ، من أين أجا الخطأ؟ من الفرض الخطأ اللي أنا
+
+74
+00:08:32,240 --> 00:08:37,440
+فرضته، يبقى فعلا هذول are distinct ولا واحد زي
+
+75
+00:08:37,440 --> 00:08:43,820
+التاني، يبقى هنا ال A
+
+76
+00:08:55,140 --> 00:09:02,320
+الـ A في الـ A1 والـ A في الـ A2 والـ A في الـ AN
+
+77
+00:09:02,320 --> 00:09:12,640
+are distinct يبقى ولا واحد فيهم زي التاني تمامطيب
+
+78
+00:09:12,640 --> 00:09:18,220
+كويس يبقى أخدنا معلومة أن هذه العناصر منفصلة عن
+
+79
+00:09:18,220 --> 00:09:25,220
+بعضها تماما مافيش تساوي بين أي عنصرية السؤال هو طب
+
+80
+00:09:25,220 --> 00:09:30,220
+هي ال R closed under multiplication ولا لا؟ لأن
+
+81
+00:09:30,220 --> 00:09:34,100
+عملية الطرق is a binary operational يبقى ال A في
+
+82
+00:09:34,100 --> 00:09:40,240
+ال A وعناصر موجود where؟ في ال ring A و ال A في ال
+
+83
+00:09:40,240 --> 00:09:40,780
+A2
+
+84
+00:09:47,270 --> 00:09:58,410
+يبقى بالي بقوله since بما ان ال R is closed under
+
+85
+00:09:58,410 --> 00:10:01,490
+multiplication
+
+86
+00:10:13,450 --> 00:10:20,470
+إن الار العناصر هذه كلها اي اي اي اي اي اي اي اي
+
+87
+00:10:20,470 --> 00:10:23,290
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+88
+00:10:23,290 --> 00:10:24,210
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+89
+00:10:24,210 --> 00:10:26,490
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+90
+00:10:26,490 --> 00:10:26,670
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+91
+00:10:26,670 --> 00:10:33,630
+اي اي اي اي
+
+92
+00:10:33,630 --> 00:10:41,990
+اي اي اي اي اي اي اي اي اي
+
+93
+00:10:41,990 --> 00:10:48,300
+ابدأ مع نصر رنج احنا هنا قلنا ال R integral domain
+
+94
+00:10:48,300 --> 00:10:52,280
+ال integral domain يحتاج ولا ال unity ولا لا يبقى
+
+95
+00:10:52,280 --> 00:10:57,980
+معناته واحد فيهم بده يساوي ال unity صح ولا لا يبقى
+
+96
+00:10:57,980 --> 00:11:08,040
+ماجي بقوله نعم الواحد موجود في R because ال R is
+
+97
+00:11:08,040 --> 00:11:10,440
+an integral
+
+98
+00:11:13,890 --> 00:11:19,630
+domain يبقى الواحد لازم يساوي طبعا اللي هو ال
+
+99
+00:11:19,630 --> 00:11:25,430
+unity الواحد هذا لازم يساوي واحد من هذه العناصر
+
+100
+00:11:25,430 --> 00:11:32,250
+يبقى هذا بدي يعطيك ان ال a في ال a كمثلا بدي أساوي
+
+101
+00:11:32,250 --> 00:11:40,470
+اللي هي ال unity one إيش تفسيرك لهذا الكلام؟ان ال
+
+102
+00:11:40,470 --> 00:11:46,930
+a is a unit صح لان ماخد ال a بسويش ال zero صح يبقى
+
+103
+00:11:46,930 --> 00:11:59,250
+this means that هذا يعني ان ال a is a unit يبقى
+
+104
+00:11:59,250 --> 00:12:07,250
+every non zero element is a unit يبقى هنا سا every
+
+105
+00:12:08,610 --> 00:12:18,790
+non-zero element element
+
+106
+00:12:18,790 --> 00:12:28,430
+of R is a unit therefore
+
+107
+00:12:28,430 --> 00:12:32,950
+ولهذا
+
+108
+00:12:32,950 --> 00:12:37,710
+الـ R is a field
+
+109
+00:12:48,980 --> 00:12:57,280
+السؤال بدعمل العكس هل ال field integral domain؟ هل
+
+110
+00:12:57,280 --> 00:13:03,440
+كل field يكون integral domain عملية العكسية؟
+
+111
+00:13:03,440 --> 00:13:09,640
+السؤال هو ال field في zero divisor؟ لأ لأن كل أنصر
+
+112
+00:13:09,640 --> 00:13:14,380
+عبارة عن unitصح ولا لا؟ مدين كل أنصار من يبقى لا
+
+113
+00:13:14,380 --> 00:13:19,820
+يمكن لل unit أن يكون zero divisor يعني مش فيها
+
+114
+00:13:19,820 --> 00:13:24,000
+zero divisor، بيبقى ايش صارت؟ Integral domain يبقى
+
+115
+00:13:24,000 --> 00:13:29,020
+any field is an integral domain لكن العكس ليس
+
+116
+00:13:29,020 --> 00:13:35,640
+بالضرورة صحيحا يعني مش كل integral domain هو field
+
+117
+00:13:36,430 --> 00:13:42,590
+لكن إذا كان الـ Integral domain finite حسب نص
+
+118
+00:13:42,590 --> 00:13:48,030
+النظرية بيكون هو field تمام؟ يبقى الـ Integral
+
+119
+00:13:48,030 --> 00:13:52,650
+domain لازم أحط عليه شرط مشان يصير field لكن ال
+
+120
+00:13:52,650 --> 00:13:57,310
+field بحطش عليه ولا شرط مشان يصير Integral domain
+
+121
+00:13:57,310 --> 00:14:06,840
+طيب ننتقل الآن إلى نتيجة على هذه النظريةالان
+
+122
+00:14:06,840 --> 00:14:11,820
+كرولري الكرولري
+
+123
+00:14:11,820 --> 00:14:21,080
+بتقول معناته for every prime P for every prime P
+
+124
+00:14:21,080 --> 00:14:33,240
+ال ZP ال ZP اللي هي the range of integers
+
+125
+00:14:34,820 --> 00:14:50,100
+موديولو P موديولو P ال P شوفناها
+
+126
+00:14:50,100 --> 00:14:54,160
+قبل ما كتبناها في المحاضرة الماضية و إيش قلنا
+
+127
+00:14:54,160 --> 00:15:00,660
+عليها Integral domain صح ولا لأ يبقى هنا بقولوا we
+
+128
+00:15:00,660 --> 00:15:14,870
+know thatاحنا بنعرف ان ZP is an integral domain من
+
+129
+00:15:14,870 --> 00:15:21,150
+وين هذا الكلام مثال سابق هي بيصف example في
+
+130
+00:15:21,150 --> 00:15:27,010
+المحاضرة السابقة مش بعيد يعني تمام؟ يبقى هذا
+
+131
+00:15:27,010 --> 00:15:33,030
+integral domain السؤال هو finite ولا لأ؟قداش عدد
+
+132
+00:15:33,030 --> 00:15:41,810
+العناصر في ايه؟ كداش؟ في ناقص واحد العنصر الأخير
+
+133
+00:15:41,810 --> 00:15:47,330
+فيه ناقص واحد لكن أول عنصر كداش؟ Zero إذا عدد
+
+134
+00:15:47,330 --> 00:15:54,050
+العناصر فيه يبقى الـLZP
+
+135
+00:15:54,050 --> 00:16:01,370
+has finite elements
+
+136
+00:16:05,520 --> 00:16:11,020
+that is P
+
+137
+00:16:11,020 --> 00:16:19,400
+elements يبقى P من العناصر يعني it is P finite
+
+138
+00:16:19,400 --> 00:16:33,480
+يبقى by the by the above theorem بالنظرية
+
+139
+00:16:33,480 --> 00:16:42,840
+السابقةZP is AP فلو
+
+140
+00:16:42,840 --> 00:16:49,860
+جيبتك سؤال في الامتحان و قولتك اثبتيلي ان ZP is AP
+
+141
+00:16:49,860 --> 00:16:57,180
+بتقدرش تثبتيلي اولا انه integral domain تمام اللي
+
+142
+00:16:57,180 --> 00:17:00,800
+هو القرآن تبع المرأة الماضية و اضيف عليه الكلمتين
+
+143
+00:17:00,800 --> 00:17:28,870
+هدولإنه finite وبالتالي بصير as a field طيب
+
+144
+00:17:28,870 --> 00:17:29,770
+example
+
+145
+00:17:37,820 --> 00:17:49,240
+زي التلاتة on I اللي هي على الصيرة كل العناصر A
+
+146
+00:17:49,240 --> 00:18:02,620
+زائد B في I such that ال A و ال B belongs to D3 من
+
+147
+00:18:02,620 --> 00:18:08,990
+العناصر هذه اللي هي تساويالـ zero والواحد والاتنين
+
+148
+00:18:08,990 --> 00:18:16,890
+وال I والواحد زائد I والاتنين زائد I والاتنين I
+
+149
+00:18:16,890 --> 00:18:27,050
+وواحد زائد اتنين I والاتنين زائد اتنين I is a
+
+150
+00:18:27,050 --> 00:18:27,490
+field
+
+151
+00:18:39,650 --> 00:18:43,590
+الـ Z3 of I طبعا الـ Z3 همين العلاصة اللي ربنا
+
+152
+00:18:43,590 --> 00:18:48,990
+ناقصها؟ Zero واحد و اتنين فقط لغير ثلاثة علاصة
+
+153
+00:18:48,990 --> 00:18:55,290
+العلاصة بتبقى Z of I على صيغة إيه زي الـ Bi في حد
+
+154
+00:18:55,290 --> 00:19:00,830
+الـ A والـ B موجودة في Z3 يعني الـ A والـ B يا إما
+
+155
+00:19:00,830 --> 00:19:05,970
+Zero يا إما واحد يا إما اتنين ما خلال ذلك مانيش
+
+156
+00:19:05,970 --> 00:19:10,670
+علاقة فيه تمام؟طيب هذه لو جيت ادور على عناصرها
+
+157
+00:19:10,670 --> 00:19:15,730
+بلاقي zero واحد و اتنين بلاقي I واحد زايد I اتنين
+
+158
+00:19:15,730 --> 00:19:21,810
+زايد I stop بتروحلى الاتنين I واحد زايد اتنين I و
+
+159
+00:19:21,810 --> 00:19:27,450
+اتنين زايد اتنين I خلصنا هى العناصر عديهم بتلاقيهم
+
+160
+00:19:27,450 --> 00:19:33,750
+هاش تسعة عناصر يجي هذا ring فيهاش الا تسعة عناصر
+
+161
+00:19:33,750 --> 00:19:42,710
+طبعا هذه commutative ringwith unity من هنا one
+
+162
+00:19:42,710 --> 00:19:54,830
+يبقى هذه because Z of تلاتة I is a commutative
+
+163
+00:19:54,830 --> 00:19:58,130
+ring
+
+164
+00:19:58,130 --> 00:20:09,710
+with unity اللي همينالواحد اللى بيساوي واحد زائد
+
+165
+00:20:09,710 --> 00:20:18,210
+زيرو في I اللى موجود في Z تلاتة او I يبقى واحد هو
+
+166
+00:20:18,210 --> 00:20:22,630
+ال unity هذا موجود في Z تلاتة لإن ابتدى الاقتبال
+
+167
+00:20:22,630 --> 00:20:27,150
+على الصيغة واحد زائد زيرو في I والواحد والزيرو
+
+168
+00:20:27,150 --> 00:20:33,410
+موجود في Z تلاتة هذا كلام مظبوط ضليش عندي اثبت انه
+
+169
+00:20:33,410 --> 00:20:37,900
+مافيهاش Zero divisorsيبقى ايه بعدي عن ال zero
+
+170
+00:20:37,900 --> 00:20:43,820
+تعالى لباقي التامة العناصر هل ممكن تظهر بأي اتنين
+
+171
+00:20:43,820 --> 00:20:52,620
+فيهم يطلع zero لأن كل واحد فيهم عبارة عن unit تمام
+
+172
+00:20:52,620 --> 00:21:04,400
+يبقى this ring has no zero divisors
+
+173
+00:21:06,840 --> 00:21:11,840
+مافيش عندى بالماضى كل أنصر عبارة عن ايش عبارة عن
+
+174
+00:21:11,840 --> 00:21:17,600
+unit طيب مابنامفش فيها zero divider لانه لايمكن
+
+175
+00:21:17,600 --> 00:21:23,620
+اضرب أنصرين غير صفرين ابدا عن zero خدي اي اتنين
+
+176
+00:21:23,620 --> 00:21:28,620
+وضربهم لايمكن يطلع صفر ديبجى this ring has no zero
+
+177
+00:21:28,620 --> 00:21:41,940
+divisor سزد تلاتة of Iis a finite finite integral
+
+178
+00:21:41,940 --> 00:21:46,340
+domain ليش
+
+179
+00:21:46,340 --> 00:21:52,860
+ان فيه كام عنصر تسعة عناصر تسعة عناصر يبقى finite
+
+180
+00:21:52,860 --> 00:22:00,140
+وintegral domain يبقى is AP يبقى هذا بتيعطينا ان Z
+
+181
+00:22:00,140 --> 00:22:03,000
+تلاتة of I
+
+182
+00:22:10,660 --> 00:22:18,740
+مشان يكون فيل كل عنصر بد يكون unit صح؟ فلينا نتاكد
+
+183
+00:22:18,740 --> 00:22:25,660
+هل فعلا كل عنصر عبارة عن unit هيسبنا zero الواحد
+
+184
+00:22:25,660 --> 00:22:33,100
+لو ضربت في واحد واحد is a unitإتنين لو ضربته في
+
+185
+00:22:33,100 --> 00:22:37,980
+اتنين يطلع أربعة في زي التلاتة بسيب تلاتة بيبقى
+
+186
+00:22:37,980 --> 00:22:44,820
+الجداش يبقى اتنين is a unit تمام نيجي لل I و اتنين
+
+187
+00:22:44,820 --> 00:22:51,600
+I العنصر هذا مع العنصر هذا لو ضربنهم في بعض بيصير
+
+188
+00:22:51,600 --> 00:22:58,760
+I كده اضبه في اتنين I يبقى اتنين في سالب واحد اللي
+
+189
+00:22:58,760 --> 00:23:04,670
+هو سالب اتنينماعنديش شريك Z3 سالب اتنين لكن سالب
+
+190
+00:23:04,670 --> 00:23:11,390
+اتنين يكافئ عمصر موجود في Z3 مين هو هذا العمصر
+
+191
+00:23:11,390 --> 00:23:18,030
+يبقى سالب اتنين زائد تلاتة لما اضيف تلاتة ومضاعفة
+
+192
+00:23:18,030 --> 00:23:23,210
+تلاتة تؤثر على العمصر يبقى مين بيطلع ال unity اللي
+
+193
+00:23:23,210 --> 00:23:29,200
+هو الواحد يبقى اتحاصر ضرب الاتنين سوا ال unityيبقى
+
+194
+00:23:29,200 --> 00:23:36,460
+هذا يخلّي ان ال I و 2 I are units يبقى هذا يخلّي
+
+195
+00:23:36,460 --> 00:23:46,960
+ان ال I و 2 I are units طيب لو مسكت ضرب تمين ضربت
+
+196
+00:23:46,960 --> 00:23:54,580
+ال واحد زائد I تمين في ال اتنين زائد ال I نشوف ايش
+
+197
+00:23:54,580 --> 00:24:01,560
+بيعطيه واحد في اتنين باتنينوحد في I ب I I في اتنين
+
+198
+00:24:01,560 --> 00:24:10,160
+ب اتنين I I في I بسالب واحد تمام سالب واحد واتنين
+
+199
+00:24:10,160 --> 00:24:17,060
+يصير واحد زائد تلاتة I تلاتة I يبقى دياشر Zero
+
+200
+00:24:17,060 --> 00:24:22,740
+يبقى الجواب يساوي واحد يبقى حاصل ضربهم يساوي واحد
+
+201
+00:24:22,740 --> 00:24:28,260
+يبقى اتنين هدول are units يبقى هدف يعطينا مينإن
+
+202
+00:24:28,260 --> 00:24:38,840
+الواحد زائد I وكذلك الاتنين زائد I are units أظن
+
+203
+00:24:38,840 --> 00:24:43,380
+مش لا ألغى الأخر اتنين كلهم
+
+204
+00:24:43,380 --> 00:24:48,000
+ضربناهم ما عدا مين ما عدا أخر اتنين يبقى لو جيت
+
+205
+00:24:48,000 --> 00:24:56,240
+هنا and رحت أخد واحد زائد اتنين I في مينفى اتنين
+
+206
+00:24:56,240 --> 00:25:03,360
+زائد اتنين I ويسار واحد فى اتنين باتنين زائد اتنين
+
+207
+00:25:03,360 --> 00:25:16,260
+I زائد اربعة I زائد اربعة I ناقص اربعة تمام ؟ طيب
+
+208
+00:25:16,260 --> 00:25:23,160
+هذا الكلام ناقص اربعة و اتنين بيظل ناقص اتنين و
+
+209
+00:25:23,160 --> 00:25:31,210
+هدول كدهشزائد ستة I التلاتة ب zero يبقى الستة كمان
+
+210
+00:25:31,210 --> 00:25:37,330
+ب zero يبقى ناتج يسوى نقص اتنين زائد تلاتة اللي هو
+
+211
+00:25:37,330 --> 00:25:42,570
+الواحد اللي هو ال unity يبقى هنا سواء واحد زائد
+
+212
+00:25:42,570 --> 00:25:53,330
+اتنين I وكذلك اتنين زائد اتنين I هدول are units
+
+213
+00:25:54,840 --> 00:26:02,700
+يبقى صار every non zero element في zi unit يبقى
+
+214
+00:26:02,700 --> 00:26:10,360
+thus و هكذا every every
+
+215
+00:26:10,360 --> 00:26:21,800
+non zero element in z3
+
+216
+00:26:21,800 --> 00:26:34,480
+of iis YOLO لذلك هذا field كما زعمنا قبل قليل طبعا
+
+217
+00:26:34,480 --> 00:26:39,960
+في الكتاب عندك راح عامل جدولة ضرب لكل العناصر
+
+218
+00:26:39,960 --> 00:26:45,320
+التسعة اللي عندك بمجالك تطلع إلى جدولة ضرب في
+
+219
+00:26:45,320 --> 00:26:51,300
+الكتاب حصل ضرب هذه العناصر مع بعضها البعض
+
+220
+00:26:56,370 --> 00:27:03,670
+طيب هذا كان مثال رقم واحد نروح لمثال رقم اتنين for
+
+221
+00:27:03,670 --> 00:27:07,830
+example اتنين
+
+222
+00:27:07,830 --> 00:27:14,670
+هذا ست اللي
+
+223
+00:27:14,670 --> 00:27:23,300
+هو Q جذر اتنين شكل يعني هذااللي هو كل العناصر اللي
+
+224
+00:27:23,300 --> 00:27:29,840
+ع صيغة a زائد b جدري اتنين بحيث ال a و ال b are
+
+225
+00:27:29,840 --> 00:27:44,520
+rational number هذه is a commutative ring with
+
+226
+00:27:44,520 --> 00:27:46,460
+unity
+
+227
+00:27:52,880 --> 00:27:59,200
+One، معقول؟ أه، هذه الكميوتة تبقى with unity one
+
+228
+00:27:59,200 --> 00:28:06,820
+لغة ساوية واحد زائد زيرو في جذري اتنين، يبقى هذا
+
+229
+00:28:06,820 --> 00:28:10,940
+هو ال unity في الست اللي عندنا هذا، وهذه الكميوتة
+
+230
+00:28:10,940 --> 00:28:14,820
+تبقى لإنها عملية ضرب ال rational number لعملية
+
+231
+00:28:14,820 --> 00:28:21,480
+إبداعية، يقول ماعنا مشكلة فيها، مش ضايلة لها.فيها
+
+232
+00:28:21,480 --> 00:28:28,540
+Zero Divisors؟ مش فيها Zero Divisors بالمرة لإنه
+
+233
+00:28:28,540 --> 00:28:34,200
+any two rational number لايمكن انه يعطينا Zero
+
+234
+00:28:34,200 --> 00:28:39,660
+بشرط ان ولا واحد فيهم يسوي Zero تمام؟ إذا ماعنديش
+
+235
+00:28:39,660 --> 00:28:46,740
+rational number ماعنديش units فيها، ماعنديش Zero
+
+236
+00:28:46,740 --> 00:28:51,310
+Divisors جدًا، بقيت اتنينIs it finite ولا
+
+237
+00:28:51,310 --> 00:28:56,870
+infinite؟ Infinite يبقى هذا السؤال مش على النظرية،
+
+238
+00:28:56,870 --> 00:29:04,090
+هذا السؤال يعتبر سؤال خارجي. يبقى أنا أدعي انه هذا
+
+239
+00:29:04,090 --> 00:29:09,230
+الآن is ايه فيه. يبقى النظرية صحيه عشان شجع ان ال
+
+240
+00:29:09,230 --> 00:29:14,270
+computer can ring with unity. تمام؟ أظل أثبت والله
+
+241
+00:29:14,270 --> 00:29:19,820
+إذا كان كل عنصرالو معكوز تحت عملية الضرر يعني
+
+242
+00:29:19,820 --> 00:29:24,400
+multiplicative inverse بتبني المفروض بصي ان ادي
+
+243
+00:29:24,400 --> 00:29:32,000
+اسم ايه فيه تمام؟ بقدر اروح اقوله I want to show
+
+244
+00:29:32,000 --> 00:29:35,400
+ان
+
+245
+00:29:35,400 --> 00:29:50,140
+الروح انبين ذات انه any none zero element ofEq of
+
+246
+00:29:50,140 --> 00:30:01,460
+جدر اتنين has a multiplicative
+
+247
+00:30:01,460 --> 00:30:06,520
+inverse.بدأت
+
+248
+00:30:06,520 --> 00:30:14,260
+انه اي عنصر غير صحي له معكس.لذلك بعدين بقوله افترض
+
+249
+00:30:14,260 --> 00:30:25,810
+ان ال a زائد bجادر اتنين لا يساوي Z بروح
+
+250
+00:30:25,810 --> 00:30:31,010
+بقول Z multiplicative
+
+251
+00:30:31,010 --> 00:30:35,710
+inverse
+
+252
+00:30:35,710 --> 00:30:47,820
+of ال A زائد B جادر اتنين is من ذاك الرقماللي لو
+
+253
+00:30:47,820 --> 00:30:52,200
+ضربته في هذا العنصر بدي أعطيه ال unity اللي هو
+
+254
+00:30:52,200 --> 00:31:01,800
+واحد مين؟ واحد على هذا المقدار تمام؟ واحد على إيه
+
+255
+00:31:01,800 --> 00:31:08,780
+لقيت بيه جذر إتنى السؤال هل العنصر هذا موجود في ال
+
+256
+00:31:08,780 --> 00:31:15,940
+IQ جذر إتنى؟ يعني هذا العنصر هل مكتوب على صيغة
+
+257
+00:31:15,940 --> 00:31:21,810
+constantزائد كنستان في جدرتنا؟ لأ مش مكتوب
+
+258
+00:31:21,810 --> 00:31:30,090
+وبالتالي يمكن نقدر نقتله ويمكن مايمكنش إذا قدرنا
+
+259
+00:31:30,090 --> 00:31:33,970
+نقتله بصير كلامنا صحيح وخلصنا من المسألة إذا
+
+260
+00:31:33,970 --> 00:31:38,890
+ماقدرناش بصير إدعائنا هذا غير صحيح بصير هذا معكس
+
+261
+00:31:38,890 --> 00:31:42,230
+لكن هذا القلم اللي جبته من الشارع أنا ماجبتوش من
+
+262
+00:31:42,230 --> 00:31:48,800
+ال ring اللي عندي تمام؟ يبقىإذا جدرت أثبت إن هذا
+
+263
+00:31:48,800 --> 00:31:54,040
+على الصيغة constant زائد constant في جذر اتنين
+
+264
+00:31:54,040 --> 00:31:59,000
+بصير موجود في الـQ فعلاً يكون هذا هو المعقول لذلك
+
+265
+00:31:59,000 --> 00:32:03,640
+إذا قُلت ضبطت في ذكرة إن غصوب ال element هذا هو ال
+
+266
+00:32:03,640 --> 00:32:12,700
+element هذا لأيش؟ هو هذا أنا أدعي أنه موجود في
+
+267
+00:32:12,700 --> 00:32:27,150
+الـQ ofof جذر اتنين cents ليش؟ لأن واحد على ا زائد
+
+268
+00:32:27,150 --> 00:32:33,970
+بيه جذر اتنين بده يساوي واحد على ا زائد بيه جذر
+
+269
+00:32:33,970 --> 00:32:40,950
+اتنين لو ضربته في مرافق المقام فبصير عند مين ايه
+
+270
+00:32:40,950 --> 00:32:48,090
+ناقص بيه جذر اتنينعلى إيه ناقص بيه جذري اتنين بهذا
+
+271
+00:32:48,090 --> 00:32:54,130
+الشكل المقام مش هو تحليل الفرق بين المراد عين بدي
+
+272
+00:32:54,130 --> 00:32:58,730
+أرجعه إلى أصله يبقى رجعناه إلى أصله بيصير
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c1da0c46635bf9b2751fd9891bfb1380fd6ec9ee
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_raw.json
@@ -0,0 +1 @@
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0.805908203125}, {"start": 851.82, "end": 852.26, "word": " بتقول", "probability": 0.6318359375}, {"start": 852.26, "end": 852.94, "word": " معناته", "probability": 0.7064615885416666}, {"start": 852.94, "end": 853.24, "word": " for", "probability": 0.89697265625}, {"start": 853.24, "end": 853.54, "word": " every", "probability": 0.79931640625}, {"start": 853.54, "end": 854.08, "word": " prime", "probability": 0.86328125}, {"start": 854.08, "end": 854.58, "word": " P", "probability": 0.3896484375}, {"start": 854.58, "end": 855.24, "word": " for", "probability": 0.7080078125}, {"start": 855.24, "end": 857.44, "word": " every", "probability": 0.77490234375}, {"start": 857.44, "end": 859.72, "word": " prime", "probability": 0.931640625}, {"start": 859.72, "end": 861.08, "word": " P", "probability": 0.9677734375}, {"start": 861.08, "end": 862.3, "word": " ال", "probability": 0.8388671875}, {"start": 862.3, "end": 863.6, "word": " ZP", "probability": 0.875244140625}, {"start": 863.6, "end": 864.68, "word": " ال", "probability": 0.60546875}, {"start": 864.68, "end": 865.62, "word": " ZP", "probability": 0.923583984375}, {"start": 865.62, "end": 867.3, "word": " اللي", "probability": 0.921142578125}, {"start": 867.3, "end": 867.62, "word": " هي", "probability": 0.8271484375}, {"start": 867.62, "end": 868.16, "word": " the", "probability": 0.315673828125}, {"start": 868.16, "end": 869.64, "word": " range", "probability": 0.431396484375}, {"start": 869.64, "end": 871.5, "word": " of", "probability": 0.958984375}, {"start": 871.5, "end": 873.24, "word": " integers", "probability": 0.94677734375}], "temperature": 1.0}, {"id": 30, "seek": 90352, "start": 874.82, "end": 903.52, "text": "موديولو P موديولو P ال P شوفناها قبل ما كتبناها في المحاضرة الماضية و إيش قلنا عليها Integral domain صح ولا لأ يبقى هنا بقولوا we know that", "tokens": [2304, 2407, 16254, 12610, 2407, 430, 3714, 2407, 16254, 12610, 2407, 430, 2423, 430, 13412, 38688, 8315, 11296, 12174, 36150, 19446, 9122, 2655, 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0.913818359375}, {"start": 890.7, "end": 890.9, "word": " ما", "probability": 0.134521484375}, {"start": 890.9, "end": 891.5, "word": " كتبناها", "probability": 0.757275390625}, {"start": 891.5, "end": 891.62, "word": " في", "probability": 0.50146484375}, {"start": 891.62, "end": 892.18, "word": " المحاضرة", "probability": 0.775665283203125}, {"start": 892.18, "end": 892.92, "word": " الماضية", "probability": 0.9773763020833334}, {"start": 892.92, "end": 893.68, "word": " و", "probability": 0.70849609375}, {"start": 893.68, "end": 893.84, "word": " إيش", "probability": 0.625732421875}, {"start": 893.84, "end": 894.16, "word": " قلنا", "probability": 0.9518229166666666}, {"start": 894.16, "end": 894.8, "word": " عليها", "probability": 0.978271484375}, {"start": 894.8, "end": 896.16, "word": " Integral", "probability": 0.56121826171875}, {"start": 896.16, "end": 896.58, "word": " domain", "probability": 0.7861328125}, {"start": 896.58, "end": 897.36, "word": " صح", "probability": 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{"start": 931.25, "end": 931.53, "word": " ولا", "probability": 0.9677734375}, {"start": 931.53, "end": 932.13, "word": " لأ؟", "probability": 0.7278645833333334}], "temperature": 1.0}, {"id": 32, "seek": 96137, "start": 932.19, "end": 961.37, "text": "قداش عدد العناصر في ايه؟ كداش؟ في ناقص واحد العنصر الأخير فيه ناقص واحد لكن أول عنصر كداش؟ Zero إذا عدد العناصر فيه يبقى الـLZP has finite elements", "tokens": [28543, 33599, 6225, 3215, 3215, 18863, 8315, 9381, 2288, 8978, 1975, 1829, 3224, 22807, 9122, 3215, 33599, 22807, 8978, 8717, 995, 4587, 9381, 36764, 24401, 18863, 1863, 9381, 2288, 16247, 9778, 13546, 8978, 3224, 8717, 995, 4587, 9381, 36764, 24401, 44381, 5551, 12610, 18871, 9381, 2288, 9122, 3215, 33599, 22807, 17182, 11933, 15730, 6225, 3215, 3215, 18863, 8315, 9381, 2288, 8978, 3224, 7251, 3555, 4587, 7578, 2423, 39184, 43, 57, 47, 575, 19362, 4959], "avg_logprob": -0.2916666618982951, "compression_ratio": 1.609271523178808, "no_speech_prob": 0.0, "words": [{"start": 932.19, 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"end": 942.75, "word": " ناقص", "probability": 0.995361328125}, {"start": 942.75, "end": 943.03, "word": " واحد", "probability": 0.996826171875}, {"start": 943.03, "end": 944.03, "word": " لكن", "probability": 0.6669921875}, {"start": 944.03, "end": 944.45, "word": " أول", "probability": 0.70166015625}, {"start": 944.45, "end": 944.85, "word": " عنصر", "probability": 0.9773763020833334}, {"start": 944.85, "end": 945.67, "word": " كداش؟", "probability": 0.8671875}, {"start": 945.67, "end": 946.41, "word": " Zero", "probability": 0.716796875}, {"start": 946.41, "end": 946.79, "word": " إذا", "probability": 0.5919189453125}, {"start": 946.79, "end": 947.33, "word": " عدد", "probability": 0.9041341145833334}, {"start": 947.33, "end": 948.43, "word": " العناصر", "probability": 0.8758544921875}, {"start": 948.43, "end": 949.47, "word": " فيه", "probability": 0.9052734375}, {"start": 949.47, "end": 950.83, "word": " يبقى", "probability": 0.9476318359375}, {"start": 950.83, "end": 954.05, "word": " الـLZP", "probability": 0.4382568359375}, {"start": 954.05, "end": 955.51, "word": " has", "probability": 0.75537109375}, {"start": 955.51, "end": 956.99, "word": " finite", "probability": 0.982421875}, {"start": 956.99, "end": 961.37, "word": " elements", "probability": 0.72412109375}], "temperature": 1.0}, {"id": 33, "seek": 99422, "start": 965.52, "end": 994.22, "text": "that is P elements يبقى P من العناصر يعني it is P finite يبقى by the by the above theorem بالنظرية السابقة", "tokens": [6780, 307, 430, 4959, 7251, 3555, 4587, 7578, 430, 9154, 18863, 8315, 9381, 2288, 37495, 22653, 309, 307, 430, 19362, 7251, 3555, 4587, 7578, 538, 264, 538, 264, 3673, 20904, 20666, 1863, 19913, 2288, 10632, 21136, 16758, 28671], "avg_logprob": -0.24038461309212905, "compression_ratio": 1.2566371681415929, "no_speech_prob": 0.0, "words": [{"start": 965.52, "end": 966.18, "word": "that", "probability": 0.489501953125}, {"start": 966.18, "end": 966.98, "word": " is", "probability": 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"word": " by", "probability": 0.90234375}, {"start": 981.2, "end": 983.2, "word": " the", "probability": 0.79541015625}, {"start": 983.2, "end": 985.44, "word": " by", "probability": 0.5078125}, {"start": 985.44, "end": 986.78, "word": " the", "probability": 0.9404296875}, {"start": 986.78, "end": 988.36, "word": " above", "probability": 0.94140625}, {"start": 988.36, "end": 990.28, "word": " theorem", "probability": 0.326904296875}, {"start": 990.28, "end": 993.48, "word": " بالنظرية", "probability": 0.9044921875}, {"start": 993.48, "end": 994.22, "word": " السابقة", "probability": 0.9827473958333334}], "temperature": 1.0}, {"id": 34, "seek": 102122, "start": 994.68, "end": 1021.22, "text": "ZP is AP فلو جيبتك سؤال في الامتحان و قولتك اثبتيلي ان ZP is AP بتقدرش تثبتيلي اولا انه integral domain تمام اللي هو القرآن تبع المرأة الماضية و اضيف عليه الكلمتين هدول", "tokens": [57, 47, 307, 5372, 6156, 1211, 2407, 10874, 1829, 3555, 2655, 4117, 8608, 33604, 6027, 8978, 2423, 10943, 2655, 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3615, 995, 29538, 800, 325, 1166, 4875], "avg_logprob": -0.23437499296008132, "compression_ratio": 2.0476190476190474, "no_speech_prob": 0.0, "words": [{"start": 1147.99, "end": 1148.33, "word": "طيب", "probability": 0.69970703125}, {"start": 1148.33, "end": 1148.61, "word": " هذه", "probability": 0.356689453125}, {"start": 1148.61, "end": 1148.77, "word": " لو", "probability": 0.96142578125}, {"start": 1148.77, "end": 1149.07, "word": " جيت", "probability": 0.82861328125}, {"start": 1149.07, "end": 1149.59, "word": " ادور", "probability": 0.7288411458333334}, {"start": 1149.59, "end": 1149.91, "word": " على", "probability": 0.677734375}, {"start": 1149.91, "end": 1150.67, "word": " عناصرها", "probability": 0.9078369140625}, {"start": 1150.67, "end": 1151.15, "word": " بلاقي", "probability": 0.6565755208333334}, {"start": 1151.15, "end": 1151.51, "word": " zero", "probability": 0.1912841796875}, {"start": 1151.51, "end": 1152.05, "word": " واحد", "probability": 0.874755859375}, 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"probability": 0.927001953125}, {"start": 1164.59, "end": 1164.77, "word": " هى", "probability": 0.4510498046875}, {"start": 1164.77, "end": 1165.37, "word": " العناصر", "probability": 0.9078369140625}, {"start": 1165.37, "end": 1166.21, "word": " عديهم", "probability": 0.80126953125}, {"start": 1166.21, "end": 1167.45, "word": " بتلاقيهم", "probability": 0.81341552734375}, {"start": 1167.45, "end": 1167.77, "word": " هاش", "probability": 0.418212890625}, {"start": 1167.77, "end": 1168.49, "word": " تسعة", "probability": 0.9488932291666666}, {"start": 1168.49, "end": 1169.65, "word": " عناصر", "probability": 0.9871419270833334}, {"start": 1169.65, "end": 1170.59, "word": " يجي", "probability": 0.6231282552083334}, {"start": 1170.59, "end": 1170.89, "word": " هذا", "probability": 0.93701171875}, {"start": 1170.89, "end": 1171.21, "word": " ring", "probability": 0.7626953125}, {"start": 1171.21, "end": 1171.81, "word": " فيهاش", "probability": 0.9348958333333334}, {"start": 1171.81, "end": 1172.15, "word": " الا", "probability": 0.72607421875}, {"start": 1172.15, "end": 1172.97, "word": " تسعة", "probability": 0.9895833333333334}, {"start": 1172.97, "end": 1173.75, "word": " عناصر", "probability": 0.98974609375}, {"start": 1173.75, "end": 1174.59, "word": " طبعا", "probability": 0.9766845703125}, {"start": 1174.59, "end": 1175.31, "word": " هذه", "probability": 0.46728515625}, {"start": 1175.31, "end": 1176.41, "word": " commutative", "probability": 0.6238606770833334}, {"start": 1176.41, "end": 1177.07, "word": " ring", "probability": 0.978515625}], "temperature": 1.0}, {"id": 40, "seek": 120521, "start": 1177.49, "end": 1205.21, "text": "with unity من هنا one يبقى هذه because Z of تلاتة I is a commutative ring with unity اللي همين", "tokens": [11820, 18205, 9154, 34105, 472, 7251, 3555, 4587, 7578, 29538, 570, 1176, 295, 6055, 1211, 9307, 3660, 286, 307, 257, 800, 325, 1166, 4875, 365, 18205, 13672, 1829, 8032, 2304, 9957], "avg_logprob": -0.2080078162252903, 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1190.49, "word": " I", "probability": 0.9560546875}, {"start": 1190.49, "end": 1191.51, "word": " is", "probability": 0.83349609375}, {"start": 1191.51, "end": 1192.43, "word": " a", "probability": 0.9765625}, {"start": 1192.43, "end": 1194.83, "word": " commutative", "probability": 0.94189453125}, {"start": 1194.83, "end": 1198.13, "word": " ring", "probability": 0.9697265625}, {"start": 1198.13, "end": 1200.65, "word": " with", "probability": 0.93115234375}, {"start": 1200.65, "end": 1203.01, "word": " unity", "probability": 0.9775390625}, {"start": 1203.01, "end": 1204.71, "word": " اللي", "probability": 0.767578125}, {"start": 1204.71, "end": 1205.21, "word": " همين", "probability": 0.8310546875}], "temperature": 1.0}, {"id": 41, "seek": 123527, "start": 1205.87, "end": 1235.27, "text": "الواحد اللى بيساوي واحد زائد زيرو في I اللى موجود في Z تلاتة او I يبقى واحد هو ال unity هذا موجود في Z تلاتة لإن ابتدى الاقتبال على الصيغة واحد زائد زيرو في I والواحد والزيرو موجود في Z تلاتة هذا 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"word": "الواحد", "probability": 0.8072916666666666}, {"start": 1207.17, "end": 1207.79, "word": " اللى", "probability": 0.67578125}, {"start": 1207.79, "end": 1208.45, "word": " بيساوي", "probability": 0.86748046875}, {"start": 1208.45, "end": 1209.15, "word": " واحد", "probability": 0.95703125}, {"start": 1209.15, "end": 1209.71, "word": " زائد", "probability": 0.8961588541666666}, {"start": 1209.71, "end": 1210.23, "word": " زيرو", "probability": 0.6793212890625}, {"start": 1210.23, "end": 1210.49, "word": " في", "probability": 0.87060546875}, {"start": 1210.49, "end": 1210.99, "word": " I", "probability": 0.70556640625}, {"start": 1210.99, "end": 1211.91, "word": " اللى", "probability": 0.97021484375}, {"start": 1211.91, "end": 1212.59, "word": " موجود", "probability": 0.9900716145833334}, {"start": 1212.59, "end": 1212.91, "word": " في", "probability": 0.89501953125}, {"start": 1212.91, "end": 1213.35, "word": " Z", "probability": 0.71484375}, {"start": 1213.35, "end": 1214.67, 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تلاتة", "probability": 0.9444580078125}, {"start": 1221.39, "end": 1221.65, "word": " لإن", "probability": 0.7718098958333334}, {"start": 1221.65, "end": 1222.11, "word": " ابتدى", "probability": 0.4508056640625}, {"start": 1222.11, "end": 1222.63, "word": " الاقتبال", "probability": 0.564422607421875}, {"start": 1222.63, "end": 1222.87, "word": " على", "probability": 0.8505859375}, {"start": 1222.87, "end": 1223.33, "word": " الصيغة", "probability": 0.9384765625}, {"start": 1223.33, "end": 1223.69, "word": " واحد", "probability": 0.98388671875}, {"start": 1223.69, "end": 1224.29, "word": " زائد", "probability": 0.9705403645833334}, {"start": 1224.29, "end": 1225.07, "word": " زيرو", "probability": 0.8080240885416666}, {"start": 1225.07, "end": 1225.21, "word": " في", "probability": 0.87841796875}, {"start": 1225.21, "end": 1225.51, "word": " I", "probability": 0.9658203125}, {"start": 1225.51, "end": 1226.41, "word": " والواحد", "probability": 0.721435546875}, {"start": 1226.41, "end": 1227.15, "word": " والزيرو", "probability": 0.8015625}, {"start": 1227.15, "end": 1227.65, "word": " موجود", "probability": 0.9900716145833334}, {"start": 1227.65, "end": 1227.81, "word": " في", "probability": 0.88134765625}, {"start": 1227.81, "end": 1228.03, "word": " Z", "probability": 0.95947265625}, {"start": 1228.03, "end": 1228.93, "word": " تلاتة", "probability": 0.9664306640625}, {"start": 1228.93, "end": 1229.29, "word": " هذا", "probability": 0.8681640625}, {"start": 1229.29, "end": 1229.91, "word": " كلام", "probability": 0.967529296875}, {"start": 1229.91, "end": 1230.75, "word": " مظبوط", "probability": 0.780859375}, {"start": 1230.75, "end": 1231.81, "word": " ضليش", "probability": 0.4669596354166667}, {"start": 1231.81, "end": 1232.31, "word": " عندي", "probability": 0.864013671875}, {"start": 1232.31, "end": 1233.09, "word": " اثبت", "probability": 0.89794921875}, {"start": 1233.09, "end": 1233.41, "word": " انه", "probability": 0.77001953125}, {"start": 1233.41, "end": 1233.91, "word": " مافيهاش", "probability": 0.794189453125}, {"start": 1233.91, "end": 1234.35, "word": " Zero", "probability": 0.51025390625}, {"start": 1234.35, "end": 1235.27, "word": " divisors", "probability": 0.72021484375}], "temperature": 1.0}, {"id": 42, "seek": 126440, "start": 1235.62, "end": 1264.4, "text": "يبقى ايه بعدي عن ال zero تعالى لباقي التامة العناصر هل ممكن تظهر بأي اتنين فيهم يطلع zero لأن كل واحد فيهم عبارة عن unit تمام يبقى this ring has no zero divisors", "tokens": [1829, 3555, 4587, 7578, 1975, 1829, 3224, 45030, 16254, 18871, 2423, 4018, 37279, 6027, 7578, 5296, 3555, 995, 38436, 16712, 10943, 3660, 18863, 8315, 9381, 2288, 8032, 1211, 3714, 43020, 6055, 19913, 3224, 2288, 4724, 10721, 1829, 1975, 2655, 1863, 9957, 8978, 16095, 7251, 9566, 1211, 3615, 4018, 5296, 33456, 28242, 36764, 24401, 8978, 16095, 6225, 3555, 9640, 3660, 18871, 4985, 46811, 10943, 7251, 3555, 4587, 7578, 341, 4875, 575, 572, 4018, 25974, 830], "avg_logprob": 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"probability": 0.865966796875}, {"start": 1241.04, "end": 1241.6, "word": " ممكن", "probability": 0.990478515625}, {"start": 1241.6, "end": 1242.18, "word": " تظهر", "probability": 0.8677978515625}, {"start": 1242.18, "end": 1243.06, "word": " بأي", "probability": 0.6537679036458334}, {"start": 1243.06, "end": 1243.82, "word": " اتنين", "probability": 0.9443359375}, {"start": 1243.82, "end": 1244.28, "word": " فيهم", "probability": 0.900390625}, {"start": 1244.28, "end": 1244.76, "word": " يطلع", "probability": 0.961669921875}, {"start": 1244.76, "end": 1245.24, "word": " zero", "probability": 0.64453125}, {"start": 1245.24, "end": 1247.84, "word": " لأن", "probability": 0.413818359375}, {"start": 1247.84, "end": 1248.5, "word": " كل", "probability": 0.84716796875}, {"start": 1248.5, "end": 1249.22, "word": " واحد", "probability": 0.997314453125}, {"start": 1249.22, "end": 1250.14, "word": " فيهم", "probability": 0.957275390625}, {"start": 1250.14, "end": 1250.9, "word": " عبارة", "probability": 0.980712890625}, {"start": 1250.9, "end": 1251.2, "word": " عن", "probability": 0.9931640625}, {"start": 1251.2, "end": 1251.66, "word": " unit", "probability": 0.9658203125}, {"start": 1251.66, "end": 1252.62, "word": " تمام", "probability": 0.6781005859375}, {"start": 1252.62, "end": 1254.32, "word": " يبقى", "probability": 0.850830078125}, {"start": 1254.32, "end": 1255.68, "word": " this", "probability": 0.72802734375}, {"start": 1255.68, "end": 1257.94, "word": " ring", "probability": 0.93017578125}, {"start": 1257.94, "end": 1260.4, "word": " has", "probability": 0.81005859375}, {"start": 1260.4, "end": 1262.24, "word": " no", "probability": 0.85546875}, {"start": 1262.24, "end": 1263.22, "word": " zero", "probability": 0.884765625}, {"start": 1263.22, "end": 1264.4, "word": " divisors", "probability": 0.929443359375}], "temperature": 1.0}, {"id": 43, "seek": 129380, "start": 1266.84, "end": 1293.8, "text": "مافيش عندى بالماضى كل أنصر عبارة عن ايش عبارة عن unit طيب 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inverse بتبني المفروض بصي ان ادي اسم ايه فيه تمام؟ بقدر اروح اقوله I want to show ان الروح انبين ذات انه any none zero element of", "tokens": [6027, 2407, 20449, 4117, 2407, 11622, 6055, 33753, 6225, 42213, 10632, 6024, 114, 2288, 2288, 37495, 22653, 17596, 1166, 17340, 39894, 3555, 22653, 9673, 5172, 32887, 11242, 4724, 9381, 1829, 16472, 1975, 16254, 24525, 2304, 1975, 1829, 3224, 8978, 3224, 46811, 10943, 22807, 4724, 28543, 2288, 1975, 32887, 5016, 1975, 39648, 3224, 286, 528, 281, 855, 16472, 2423, 32887, 5016, 16472, 3555, 9957, 29910, 9307, 16472, 3224, 604, 6022, 4018, 4478, 295], "avg_logprob": -0.4105308284498241, "compression_ratio": 1.387434554973822, "no_speech_prob": 0.0, "words": [{"start": 1756.84, "end": 1757.32, "word": "الو", "probability": 0.3785400390625}, {"start": 1757.32, "end": 1758.2, "word": " معكوز", "probability": 0.7413330078125}, {"start": 1758.2, "end": 1758.54, "word": " تحت", "probability": 0.988525390625}, {"start": 1758.54, "end": 1759.06, "word": " 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مين ايه ناقص بيه جذر اتنين", "tokens": [2670, 10874, 8848, 2288, 1975, 2655, 1863, 9957, 14941, 32239, 8592, 22807, 5296, 33456, 36764, 24401, 15844, 1975, 30767, 16373, 3215, 4724, 1829, 3224, 10874, 8848, 2288, 1975, 2655, 1863, 9957, 47525, 3224, 7251, 3794, 995, 45865, 36764, 24401, 15844, 1975, 30767, 16373, 3215, 4724, 1829, 3224, 10874, 8848, 2288, 1975, 2655, 1863, 9957, 45164, 48812, 25513, 47395, 8978, 3714, 23557, 5172, 4587, 9673, 4587, 10943, 6156, 3555, 9381, 13546, 43242, 3714, 9957, 1975, 1829, 3224, 8717, 995, 4587, 9381, 4724, 1829, 3224, 10874, 8848, 2288, 1975, 2655, 1863, 9957], "avg_logprob": -0.17050138050383265, "compression_ratio": 1.9236111111111112, "no_speech_prob": 0.0, "words": [{"start": 1935.31, "end": 1936.57, "word": "of", "probability": 0.6083984375}, {"start": 1936.57, "end": 1937.43, "word": " جذر", "probability": 0.7090657552083334}, {"start": 1937.43, "end": 1938.61, "word": " اتنين", "probability": 0.8984375}, {"start": 1938.61, "end": 1940.61, "word": " cents", "probability": 0.6826171875}, {"start": 1940.61, "end": 1943.09, "word": " ليش؟", "probability": 0.6411946614583334}, {"start": 1943.09, "end": 1944.59, "word": " لأن", "probability": 0.82373046875}, {"start": 1944.59, "end": 1945.23, "word": " واحد", "probability": 0.940185546875}, {"start": 1945.23, "end": 1946.01, "word": " على", "probability": 0.830078125}, {"start": 1946.01, "end": 1946.39, "word": " ا", "probability": 0.5732421875}, {"start": 1946.39, "end": 1947.15, "word": " زائد", "probability": 0.81396484375}, {"start": 1947.15, "end": 1947.69, "word": " بيه", "probability": 0.714111328125}, {"start": 1947.69, "end": 1948.33, "word": " جذر", "probability": 0.99169921875}, {"start": 1948.33, "end": 1948.97, "word": " اتنين", "probability": 0.9764404296875}, {"start": 1948.97, "end": 1949.61, "word": " بده", "probability": 0.5291748046875}, {"start": 1949.61, "end": 1950.17, "word": " يساوي", "probability": 0.8599853515625}, {"start": 1950.17, "end": 1951.25, "word": " واحد", "probability": 0.884521484375}, {"start": 1951.25, "end": 1951.61, "word": " على", "probability": 0.84814453125}, {"start": 1951.61, "end": 1952.07, "word": " ا", "probability": 0.81396484375}, {"start": 1952.07, "end": 1952.85, "word": " زائد", "probability": 0.9664713541666666}, {"start": 1952.85, "end": 1953.31, "word": " بيه", "probability": 0.9962565104166666}, {"start": 1953.31, "end": 1953.97, "word": " جذر", "probability": 0.9969075520833334}, {"start": 1953.97, "end": 1954.55, "word": " اتنين", "probability": 0.9886474609375}, {"start": 1954.55, "end": 1955.39, "word": " لو", "probability": 0.94921875}, {"start": 1955.39, "end": 1955.99, "word": " ضربته", "probability": 0.9288736979166666}, {"start": 1955.99, "end": 1956.25, "word": " في", "probability": 0.92236328125}, {"start": 1956.25, "end": 1957.01, "word": " مرافق", "probability": 0.9884033203125}, {"start": 1957.01, "end": 1958.39, "word": " المقام", "probability": 0.99267578125}, {"start": 1958.39, "end": 1959.49, "word": " فبصير", "probability": 0.80987548828125}, {"start": 1959.49, "end": 1959.77, "word": " عند", "probability": 0.302734375}, {"start": 1959.77, "end": 1960.25, "word": " مين", "probability": 0.764892578125}, {"start": 1960.25, "end": 1960.95, "word": " ايه", "probability": 0.7138671875}, {"start": 1960.95, "end": 1961.61, "word": " ناقص", "probability": 0.913818359375}, {"start": 1961.61, "end": 1962.09, "word": " بيه", "probability": 0.98876953125}, {"start": 1962.09, "end": 1962.77, "word": " جذر", "probability": 0.99609375}, {"start": 1962.77, "end": 1963.43, "word": " اتنين", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 67, "seek": 197873, "start": 1963.67, "end": 1978.73, "text": "على إيه ناقص بيه جذري اتنين بهذا الشكل المقام مش هو تحليل الفرق بين المراد عين بدي أرجعه إلى أصله يبقى رجعناه إلى أصله بيصير", "tokens": [3615, 23942, 11933, 1829, 3224, 8717, 995, 4587, 9381, 4724, 1829, 3224, 10874, 8848, 16572, 1975, 2655, 1863, 9957, 39627, 15730, 25124, 28820, 9673, 4587, 10943, 37893, 31439, 6055, 5016, 20292, 1211, 27188, 2288, 4587, 49374, 9673, 2288, 18513, 6225, 9957, 4724, 16254, 5551, 47341, 3615, 3224, 30731, 5551, 36520, 3224, 7251, 3555, 4587, 7578, 12602, 7435, 3615, 8315, 3224, 30731, 5551, 36520, 3224, 4724, 1829, 9381, 13546], "avg_logprob": -0.29846014319986536, "compression_ratio": 1.6592592592592592, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1963.67, "end": 1964.23, "word": "على", "probability": 0.862548828125}, {"start": 1964.23, "end": 1964.63, "word": " إيه", "probability": 0.818115234375}, {"start": 1964.63, "end": 1965.35, "word": " ناقص", "probability": 0.8704833984375}, {"start": 1965.35, "end": 1966.05, "word": " بيه", "probability": 0.7413736979166666}, {"start": 1966.05, "end": 1966.67, "word": " جذري", "probability": 0.6376953125}, {"start": 1966.67, "end": 1967.39, "word": " اتنين", "probability": 0.9166259765625}, {"start": 1967.39, "end": 1968.09, "word": " بهذا", "probability": 0.5545654296875}, {"start": 1968.09, "end": 1968.69, "word": " الشكل", "probability": 0.98291015625}, {"start": 1968.69, "end": 1970.47, "word": " المقام", "probability": 0.7999674479166666}, {"start": 1970.47, "end": 1970.91, "word": " مش", "probability": 0.58056640625}, {"start": 1970.91, "end": 1971.09, "word": " هو", "probability": 0.6015625}, {"start": 1971.09, "end": 1971.63, "word": " تحليل", "probability": 0.9351806640625}, {"start": 1971.63, "end": 1971.99, "word": " الفرق", "probability": 0.8561197916666666}, {"start": 1971.99, "end": 1972.23, "word": " بين", "probability": 0.94189453125}, {"start": 1972.23, "end": 1972.75, "word": " المراد", "probability": 0.7459309895833334}, {"start": 1972.75, "end": 1973.23, "word": " عين", "probability": 0.70751953125}, {"start": 1973.23, "end": 1974.13, "word": " بدي", "probability": 0.614990234375}, {"start": 1974.13, "end": 1974.91, "word": " أرجعه", "probability": 0.86669921875}, {"start": 1974.91, "end": 1975.17, "word": " إلى", "probability": 0.60888671875}, {"start": 1975.17, "end": 1975.95, "word": " أصله", "probability": 0.8761393229166666}, {"start": 1975.95, "end": 1976.51, "word": " يبقى", "probability": 0.57940673828125}, {"start": 1976.51, "end": 1977.67, "word": " رجعناه", "probability": 0.6337890625}, {"start": 1977.67, "end": 1977.87, "word": " إلى", "probability": 0.8212890625}, {"start": 1977.87, "end": 1978.37, "word": " أصله", "probability": 0.919921875}, {"start": 1978.37, "end": 1978.73, "word": " بيصير", "probability": 0.82470703125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1978.82775, "duration_after_vad": 1887.9799999999943}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6a44734b52e7ce879ea52fad3345c7608ceb5740
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_postprocess.srt
@@ -0,0 +1,1812 @@
+1
+00:00:20,860 --> 00:00:26,560
+بسم الله الرحمن الرحيم احنا المرة اللي فاتت لم
+
+2
+00:00:26,560 --> 00:00:32,840
+نصور المحاضرة الماضية وذلك بسبب سوء الأحوال
+
+3
+00:00:32,840 --> 00:00:39,500
+الأرضية من قطع كهربا أو غيره فانعتدر للطلب الذين
+
+4
+00:00:39,500 --> 00:00:46,600
+يشاهدوننا على مستوى العالم وانتم منهم فتم يطأ
+
+5
+00:00:46,600 --> 00:00:51,220
+المحاضرة بدون تصويراليوم احنا بنكمل على المحاضرة،
+
+6
+00:00:51,220 --> 00:00:56,800
+المحاضرة لم نعطيها إلا نظرية واحدة وهي ال RDOS
+
+7
+00:00:56,800 --> 00:01:01,160
+Quality Test، تمام؟ وما بدني أظهر ليهم الذاكرين
+
+8
+00:01:01,160 --> 00:01:06,980
+هولا لأ، لإن بتعطي كمان إدارة عالية، تمام؟ ال ..
+
+9
+00:01:06,980 --> 00:01:12,200
+حد من ذاكره ما هو نقص النظرية؟ برهناه هنا اللي
+
+10
+00:01:12,200 --> 00:01:20,150
+واحنا ايوة؟أنا بقى أحكي بلدي مش مشكلة إذا
+
+11
+00:01:20,150 --> 00:01:34,570
+كان النفس
+
+12
+00:01:34,570 --> 00:01:41,150
+كالثالث أخذ القلعوم F of X موجودة في Z of X يعني
+
+13
+00:01:41,150 --> 00:01:47,760
+المعاملات كلهاأعداد صحيحة تمام روحنا أخدنا فيه
+
+14
+00:01:47,760 --> 00:01:56,760
+prime وشوفنا إيش هل ال F bar irreducible في ZP ولا
+
+15
+00:01:56,760 --> 00:02:03,380
+لأ إذا كانت F bar irreducible في ZP وفي نفس الوقت
+
+16
+00:02:03,380 --> 00:02:07,440
+كان ال degree لل F هي نفس ال degree لل F bar
+
+17
+00:02:07,440 --> 00:02:13,380
+نستنتجإن ال F of X الأصلية is irreducible على مين
+
+18
+00:02:13,380 --> 00:02:18,080
+على ست of rational numbers اللي هي مين اللي هي D
+
+19
+00:02:18,080 --> 00:02:23,840
+cubed هذا كان نص النظرية لما نعطي مثال كمان على
+
+20
+00:02:23,840 --> 00:02:30,920
+نفس النظرية هذه كتارة يبقى example three example
+
+21
+00:02:30,920 --> 00:02:37,160
+three show
+
+22
+00:02:37,160 --> 00:02:49,870
+thatshow that بينونا ان ال F of X التي تساعد X5
+
+23
+00:02:49,870 --> 00:02:58,810
+زيدي 2X زيدي الأربعة is irreducible
+
+24
+00:02:58,810 --> 00:03:05,590
+irreducible over اللي هو ال Q
+
+25
+00:03:20,810 --> 00:03:25,730
+الان لما نطلع على المعاملات بتاعة البرانوميل كلها
+
+26
+00:03:25,730 --> 00:03:32,590
+أعداد صحيحة إذا هذه موجودة وين؟ في Z of X يبقى ال
+
+27
+00:03:32,590 --> 00:03:43,910
+F of X موجودة في Z of X حيث نقطلوني بنروح أخد عدد
+
+28
+00:03:43,910 --> 00:03:54,480
+Prime وشوف ال F bar في ZPيبقى let في مثلا تساوي
+
+29
+00:03:54,480 --> 00:04:03,020
+تلاتة then بدي ال f bar ال f bar of x بدي أحسبها
+
+30
+00:04:03,020 --> 00:04:10,500
+في z تلاتة يبقى x plus خمسة كما هي 2x كما هي
+
+31
+00:04:10,500 --> 00:04:15,600
+الأربعة في z تلاتة عبارة عن إيش؟ عن واحد هذه
+
+32
+00:04:15,600 --> 00:04:23,070
+موجودة في zبelongs to z تلاتة of x يبقى دي belongs
+
+33
+00:04:23,070 --> 00:04:32,710
+في z تلاتة of x تمام الان بدي اشوف هل هذه بقدر
+
+34
+00:04:32,710 --> 00:04:39,750
+احللها الى عوامل والله بقدرش وين في z بيه تعالوا
+
+35
+00:04:39,750 --> 00:04:48,540
+نشوف نشوف ال F bar of zeroلنشتغل ولا بلات احنا في
+
+36
+00:04:48,540 --> 00:04:53,180
+Z تلاتة بدنا نشتغل ال Z تلاتة فيها تلاتة ناصر Zero
+
+37
+00:04:53,180 --> 00:04:59,220
+واحد و اتنين بتاع لو أخدت ال F bar of Zero يبقى ال
+
+38
+00:04:59,220 --> 00:05:06,960
+Zero Zero بضل قداش واحد بدنا ال F bar of واحد واحد
+
+39
+00:05:06,960 --> 00:05:12,660
+واحد اتنين و اتنين اربعة في Z تلاتة بواحد صحيح
+
+40
+00:05:12,660 --> 00:05:18,510
+بدنا ال F bar of اتنينإثنين و أصفر فليه بإتنين و
+
+41
+00:05:18,510 --> 00:05:23,630
+تلاتين شيل منهم تلاتين اللي هو مضاعفات التلاتة
+
+42
+00:05:23,630 --> 00:05:29,610
+بيبقى لنا جداش اتنين اتنين في اتنين باربع و اتنين
+
+43
+00:05:29,610 --> 00:05:33,870
+ستة مضاعفات التلاتة شيلهم بيبقى لنا جداش بقى
+
+44
+00:05:33,870 --> 00:05:39,450
+الواحد بقعد الكلام بدي أساوي واحد معناه هذا الكلام
+
+45
+00:05:39,450 --> 00:05:51,440
+ان ال F bar has no zerosنزد تلاتة كويس؟ No zeros
+
+46
+00:05:51,440 --> 00:05:56,740
+يعني في factor of linear degree أو of degree one
+
+47
+00:05:56,740 --> 00:06:02,720
+مش إمكانية لأنه لو كان هناك zero بقول X ناقص هذا
+
+48
+00:06:02,720 --> 00:06:07,920
+الرقم هو أحد ال factors لهذه ال polynomial يبقى ال
+
+49
+00:06:07,920 --> 00:06:14,000
+F bar has no zeros in Z تلاتة يبقى باجي بقوله ال F
+
+50
+00:06:14,000 --> 00:06:14,520
+bar
+
+51
+00:06:20,320 --> 00:06:27,600
+no linear factor او no factor
+
+52
+00:06:27,600 --> 00:06:34,960
+of first degree طب
+
+53
+00:06:34,960 --> 00:06:40,120
+اذا مافيش فيه factor of first degree فيه factor of
+
+54
+00:06:40,120 --> 00:06:45,280
+fourth degree لأ لأنه بدنا نضرب ال first في ال
+
+55
+00:06:45,280 --> 00:06:50,520
+fourth بطلع اكسوس خمسةيبقى كمان مستبعد تبقى من ال
+
+56
+00:06:50,520 --> 00:06:59,060
+degree رقم 4 يبقى هذا بيدهي يعطينا ان ال F با of X
+
+57
+00:06:59,060 --> 00:07:12,040
+has no factor of degree 4 يبقى ايش ليلتنا؟ يا
+
+58
+00:07:12,040 --> 00:07:18,180
+اتنين يا تلاتينبدي افترض ان في عندي factor of
+
+59
+00:07:18,180 --> 00:07:25,600
+second degree وش هو الشي اللي بده يصير يبقى هنا ال
+
+60
+00:07:25,600 --> 00:07:36,920
+F bar of X may have ربما يكون فيها factor of
+
+61
+00:07:36,920 --> 00:07:42,160
+second degree
+
+62
+00:07:43,810 --> 00:07:53,350
+من الدرجة الثانية in the form مثلًا X تربية زي AX
+
+63
+00:07:53,350 --> 00:08:04,150
+زي B هك صح ولا أقول AX تربية زي B X زي C؟ معامل
+
+64
+00:08:04,150 --> 00:08:09,190
+واحد يبقى .. انسى الموضوع هنا بتكون المعامل واحد
+
+65
+00:08:09,190 --> 00:08:15,150
+يبقى X تربية زي AX زي B السؤال هوفي زد ثلاث كم
+
+66
+00:08:15,150 --> 00:08:25,510
+احتمال بيجيبلي يعني؟ نين، ثلاثة، خمسة، ستة، كداش؟
+
+67
+00:08:25,510 --> 00:08:30,390
+تسعة احتمالات. بدنا نشوف ما هي الاحتمالات التسعة.
+
+68
+00:08:31,250 --> 00:08:39,190
+يبقى هنا sum for this factor
+
+69
+00:08:46,180 --> 00:08:52,040
+nine nine possibilities
+
+70
+00:08:52,040 --> 00:08:59,320
+نشوف
+
+71
+00:08:59,320 --> 00:09:06,320
+منهم التسعة دول احتمال هذا يكون TX تربيع بس الشريف
+
+72
+00:09:06,320 --> 00:09:16,180
+واحتمال يكون X تربيع زائد Xو احتمال يكون x تربيع
+
+73
+00:09:16,180 --> 00:09:26,940
+زائد 2x واحتمال يكون x تربيع زائد 2 واحتمال يكون x
+
+74
+00:09:26,940 --> 00:09:36,040
+تربيع زائد 2x زائد 1 1 2 3 4 5 واحتمال يكون x
+
+75
+00:09:36,040 --> 00:09:45,180
+تربيع زائد x زائد 1 واحتمال يكونX تربيع زائد واحد
+
+76
+00:09:45,180 --> 00:09:53,820
+واحتمال يكون X تربيع زائد X زائد اتنين والاحتمال
+
+77
+00:09:53,820 --> 00:09:59,600
+الاخير X تربيع زائد اتنين X زائد اتنين شوفيلي اذا
+
+78
+00:09:59,600 --> 00:10:03,520
+بتلاقي احتمال عاشر قوليلي يا عزيزي معاكي من هنا
+
+79
+00:10:03,520 --> 00:10:09,140
+لنهاية الفصل مش اليوم راحتك احنا بشغل في Z3 ه
+
+80
+00:10:09,490 --> 00:10:12,490
+معاملة الـ Zero، واحد واثنين، مانتعداش اتنين
+
+81
+00:10:12,490 --> 00:10:17,370
+ومابنزلش على الـ Zero. تمام؟ طيب، هاي كل احتمالات
+
+82
+00:10:17,370 --> 00:10:22,910
+الممكنة. طب تمسك كل واحد فيهم. احنا ايش قولنا هناك
+
+83
+00:10:22,910 --> 00:10:28,630
+و هناك؟ الـ F bar has no factor of first degree.
+
+84
+00:10:29,430 --> 00:10:34,250
+يعني لا يمكن يكون عندي معامل من الدرجة الأولى
+
+85
+00:10:34,250 --> 00:10:41,350
+نهائيًا. طب تعالى شوف هذا إيش بتسويه.هذه x في x،
+
+86
+00:10:41,350 --> 00:10:46,670
+هل ليس حصل ضرب معاملين من الدرجة الأولى؟ طيب، هذا
+
+87
+00:10:46,670 --> 00:10:52,950
+احتمال يكون x في x زائد واحد، حصل ضرب عاملين من
+
+88
+00:10:52,950 --> 00:10:59,270
+الدرجة الأولى، هذا بدي يعطينا x في x زائد اتنين،
+
+89
+00:10:59,270 --> 00:11:04,210
+حصل ضرب عاملين من الدرجة الأولى، هذا بدي يعطينا
+
+90
+00:11:05,590 --> 00:11:12,650
+يتحلل و الله لا يتحلل فعالي نشوف X زائد واحد X
+
+91
+00:11:12,650 --> 00:11:21,310
+زائد اتنين معقول؟ X في X ب X تربية زائد X و زائد
+
+92
+00:11:21,310 --> 00:11:26,610
+اتنين X زائد تلاتة X زد ثلاثة Zero فتبقى واحد في
+
+93
+00:11:26,610 --> 00:11:34,230
+اتنين باتنين هاي هذا عادي جدا X زائد واحد X زائد
+
+94
+00:11:34,230 --> 00:11:41,410
+واحدهذا ما بدري قداشى أبصر قداشى حاصر ضرب فو سيم
+
+95
+00:11:41,410 --> 00:11:49,950
+يبقى هنا X وهنا X ايش رايك نقول زائد اتنين وهنا
+
+96
+00:11:49,950 --> 00:11:56,130
+زائد اتنين بمشي الحال كحال الجو هي X تربية زائد
+
+97
+00:11:56,130 --> 00:12:02,090
+اتنين X زائد اتنين X زائد اربعة اكشلي تلاتة بضل
+
+98
+00:12:02,090 --> 00:12:07,410
+زائد X هي اتنين في اتنينأربعة شيلتلات اه و نصلي ال
+
+99
+00:12:07,410 --> 00:12:13,490
+100 المين طب كل واحد من هدول بده يساوي Zero و احنا
+
+100
+00:12:13,490 --> 00:12:20,290
+قلنا هنا مفيش Zero's الأفبار مالهاش Zero's صح ولا
+
+101
+00:12:20,290 --> 00:12:26,110
+لا؟ بمعنى كل احتمال من هذه الاحتمال هذه لا موجودة
+
+102
+00:12:26,110 --> 00:12:30,990
+لاو لأن من فوق قلنا مالهاش Zero's طب هذه بتساوي
+
+103
+00:12:30,990 --> 00:12:37,550
+Zero اه بتساوي Zeroهذه بتساوي zero at x يساوي zero
+
+104
+00:12:37,550 --> 00:12:44,330
+هذه بتساوي zero at x يساوي zero و ال x يساوي اتنين
+
+105
+00:12:44,330 --> 00:12:52,130
+حط x ب اتنين واحد تلاتة يبقى هاي zero راحة طب نمسك
+
+106
+00:12:52,130 --> 00:12:59,430
+هذه كده تساوي zero عند x يساوي zero او ال x يساوي
+
+107
+00:12:59,430 --> 00:13:04,860
+واحدحط واحد بصيرها تلاتة زيرو وحط زيرو بصير زيرو
+
+108
+00:13:04,860 --> 00:13:12,280
+هنا هذه بدها تساوي زيرو ال X يساوي اتنين وال X
+
+109
+00:13:12,280 --> 00:13:17,460
+يساوي واحد اتنين بصير زيرو واحد بصير الجثة ده زيرو
+
+110
+00:13:17,460 --> 00:13:24,400
+هذا الكلام بده يساوي زيرو ال X يساوي اتنين فقط
+
+111
+00:13:24,400 --> 00:13:30,110
+لإنه حط اتنين وواحد تلاتة اتنين وواحد تلاتةهذه
+
+112
+00:13:30,110 --> 00:13:38,150
+كمان بدها تساوي zero at x يساوي واحد تمام؟ يبقى
+
+113
+00:13:38,150 --> 00:13:44,870
+هذا الكلام كله ايه مسكي؟ هذا كله possible ولا
+
+114
+00:13:44,870 --> 00:13:52,690
+impossible؟ impossible ليش؟ يعني لا يمكن ان تكون
+
+115
+00:13:52,690 --> 00:13:55,990
+المعادلة من الدرجة التانية او ال factor اللي من
+
+116
+00:13:55,990 --> 00:14:01,450
+الدرجة التانيةيكون على أي صيغة من هذه الصيغة الستة
+
+117
+00:14:01,450 --> 00:14:05,550
+لإنه كل واحدة من الصيغة الستة بتجيب له zero واحنا
+
+118
+00:14:05,550 --> 00:14:13,150
+قولنا مافيش zeros في Z3 تمام؟ يبقى هذا الكلام كله
+
+119
+00:14:13,150 --> 00:14:19,410
+impossible on
+
+120
+00:14:19,410 --> 00:14:21,070
+Z3
+
+121
+00:14:22,810 --> 00:14:28,810
+يعنيش؟ يعني ال F bar has no zeros هذا الكلام مش
+
+122
+00:14:28,810 --> 00:14:32,590
+ممكن يحصل، إيش يعني مش ممكن يحصل؟ يعني لا يمكن
+
+123
+00:14:32,590 --> 00:14:36,790
+للمعادلة من الضرورية التانية أن تكون على أي شكل من
+
+124
+00:14:36,790 --> 00:14:40,910
+الأشكال الستة لأنه أي شكل من الأشكال الستة بدي
+
+125
+00:14:40,910 --> 00:14:45,990
+يزيني zeros وهذا يناقض الشغل اللي حسبناها حساب
+
+126
+00:14:45,990 --> 00:14:51,190
+بدينا، مالجيناش ولا zeros لل F bar على مين؟ على Z3
+
+127
+00:14:51,590 --> 00:14:57,750
+يبقى هذا كله غير ممكن، شو ضايل عندنا؟ تلاتة، طب
+
+128
+00:14:57,750 --> 00:15:03,390
+بتاجنا التلاتة هدول، بدي أعمللهم division أو long
+
+129
+00:15:03,390 --> 00:15:08,670
+division، قسمة مطولة، بدي أجسم هذه على هذا، وهذه
+
+130
+00:15:08,670 --> 00:15:13,630
+على التانية، وهذه على التالتة، هل تتم القسمة بدون
+
+131
+00:15:13,630 --> 00:15:18,130
+باقي، والله بيكون فيه باقي، في التلات حالات فيه
+
+132
+00:15:18,130 --> 00:15:23,090
+باقي، أنا والله جسمتها بيدي،كنت بدى أجرب أتأكد
+
+133
+00:15:23,090 --> 00:15:28,770
+هالكلام صح ولا مش صح؟ لجيته كله فيه باقي، مدى فيه
+
+134
+00:15:28,770 --> 00:15:35,690
+باقي يبقى ولا factor من الدرجة الثانية ومن ثم من
+
+135
+00:15:35,690 --> 00:15:39,970
+الدرجة التالتة بيكون أحد عوامل للإفبار يبقى
+
+136
+00:15:39,970 --> 00:15:48,210
+الإفبار is a radius على 63، مظبوط؟ يبقى هنا بقى
+
+137
+00:15:49,960 --> 00:16:02,420
+long by long division بالقسمة
+
+138
+00:16:02,420 --> 00:16:13,040
+المطولة any one of ال X تربية زي 1 او ال X تربية
+
+139
+00:16:13,040 --> 00:16:24,050
+زي X او 2 او ال X تربية زي 2x زائد اتنين is a
+
+140
+00:16:24,050 --> 00:16:41,290
+factor of any of هؤلاء is not a factor of
+
+141
+00:16:41,290 --> 00:16:52,200
+f of x يسوى x أص خمسة زائد اتنين xزائد واحد معناته
+
+142
+00:16:52,200 --> 00:17:00,420
+ايش Irreducible كل التسعة استبعداهم يبقى هنا ف ال
+
+143
+00:17:00,420 --> 00:17:10,780
+F bar of X is Irreducible over
+
+144
+00:17:10,780 --> 00:17:23,680
+33 and وزيادة على ذلكال degree لل F هي نفس ال
+
+145
+00:17:23,680 --> 00:17:32,580
+degree لل F bar اللي تساوي خمسة تمام؟ لما اتحققت
+
+146
+00:17:32,580 --> 00:17:36,680
+شروط النظرية نظرية
+
+147
+00:17:36,680 --> 00:17:40,920
+الكتبناها المرة اللي فاتت و رهنناها مدام تحققت
+
+148
+00:17:40,920 --> 00:17:45,660
+شروط النظرية يعني معناته ال F of X الأصلي is
+
+149
+00:17:45,660 --> 00:17:54,120
+irreducibleعلى الـ Q بروحيله و بقوله Y D above
+
+150
+00:17:54,120 --> 00:18:05,580
+theorem بالنظرية أعلى ال F of X اللي تساوي X أُس
+
+151
+00:18:05,580 --> 00:18:16,940
+خمسة زي اتنين X زائد أربعة is irreducible of Rلكن
+
+152
+00:18:16,940 --> 00:18:25,080
+هو هو المفروض يروحلك في أسلة في التمريين بشكل هذا
+
+153
+00:18:25,080 --> 00:18:28,820
+يمكن تلاقي درجة الرابعة، يمكن خمسة، يمكن درجة
+
+154
+00:18:28,820 --> 00:18:34,060
+تالتة، برضه زيك، بتاخدليك P prime، اتنين، تلاتة،
+
+155
+00:18:34,060 --> 00:18:38,420
+خمسة، سبعة، حسب طبيعة المثلة، و تشوف هل إلها zeros
+
+156
+00:18:38,420 --> 00:18:43,520
+ولا لا، ماطلعش zeros، بحط الاحتمالات الممكنة و
+
+157
+00:18:43,520 --> 00:18:48,660
+بشتغلها، عنسينا نقول شغلها يا بناتيبقى by division
+
+158
+00:18:48,660 --> 00:18:54,680
+algorithm هذه كلها is not a factor of ذلك ضايل
+
+159
+00:18:54,680 --> 00:18:58,840
+علينا ايش؟ ضايل علينا ان احنا خدنا من الدرجة
+
+160
+00:18:58,840 --> 00:19:03,840
+الثانية برضه there is no factor of third degree
+
+161
+00:19:03,840 --> 00:19:08,600
+لإن التانية هي بتكملي التالتة حصل الدرجة بيعطينا
+
+162
+00:19:08,600 --> 00:19:17,010
+105 هذه لسينا تقول يا بنات بدنا نحو هىبدنا نحطها
+
+163
+00:19:17,010 --> 00:19:36,790
+هنا وهي also وكذلك there is no factor of degree 3
+
+164
+00:19:36,790 --> 00:19:40,670
+نيجي
+
+165
+00:19:40,670 --> 00:19:43,050
+للنظرية اللي عندنا فعلا
+
+166
+00:20:06,080 --> 00:20:15,140
+موجودة أين؟ في Z of X if there is a prime K F
+
+167
+00:20:15,140 --> 00:20:23,160
+there is a prime P
+
+168
+00:20:28,910 --> 00:20:40,290
+بحيث ان ال P لا تقسم ال AN P لا تقسم ال AN ولكن ال
+
+169
+00:20:40,290 --> 00:20:55,470
+P تقسم ال AN-1 وP تقسم ال AN وP تقسم ال ANالـP
+
+170
+00:20:55,470 --> 00:21:04,150
+تربية لا تقسم الـA نوت الـP تربية لا تقسم الـA
+
+171
+00:21:04,150 --> 00:21:15,510
+نوت، ثم الـF of X ثم الـF of X is irreducible
+
+172
+00:21:15,510 --> 00:21:20,550
+over الـQ
+
+173
+00:21:35,260 --> 00:21:41,920
+إذا احنا الآن بهذه النظرية جيبنا شغلة ثانية للحكم
+
+174
+00:21:41,920 --> 00:21:46,880
+على ال polynomial بأنها irreducible المرة اللي
+
+175
+00:21:46,880 --> 00:21:52,680
+فاتت حطينا الشروط و من خلالها أثبتنا ان ال F of X
+
+176
+00:21:52,680 --> 00:21:58,660
+is irreducible فكان عندي بدي ال F of X موجودة في Z
+
+177
+00:21:58,660 --> 00:22:05,890
+of X بدي أدور على prime P تماموالاقى ان ال F bar
+
+178
+00:22:05,890 --> 00:22:12,030
+of X هه is irreducible على Z بيه وضرية ال F كانت
+
+179
+00:22:12,030 --> 00:22:16,430
+ضرية ال F bar ان حدث ذلك تبقى ال F of X تبقى
+
+180
+00:22:16,430 --> 00:22:20,750
+irreducible على Q الآن جيبنا طريقة تانية طريقة
+
+181
+00:22:20,750 --> 00:22:26,650
+تانية تتلخص في النظرية التالية ال F of X هي موجودة
+
+182
+00:22:26,650 --> 00:22:31,930
+في Z of X نفس المعطيات اللى موجودة في النظرية
+
+183
+00:22:31,930 --> 00:22:38,700
+السادسةقال إذا قدرت ألاقي prime P مش for any if
+
+184
+00:22:38,700 --> 00:22:45,200
+various إذا قدرنا نوجد a prime P بحيث ال PS لا
+
+185
+00:22:45,200 --> 00:22:53,200
+يقسم المعامل تبع XM لكنه يقسم جميع المعاملات
+
+186
+00:22:53,200 --> 00:22:59,820
+الأخرى لل Polynomial وموجعه لا يقسم العامل الأخر
+
+187
+00:22:59,820 --> 00:23:05,390
+اللي هو كل من تبع ال Polynomialإن حدث ذلك يبقى ال
+
+188
+00:23:05,390 --> 00:23:10,390
+F of X تبقى irreducible كذلك على مين؟ على ال IQ
+
+189
+00:23:10,390 --> 00:23:16,950
+.ماشي برهنة المرة اللي فاتت؟ التناقض صح ولا لا؟ و
+
+190
+00:23:16,950 --> 00:23:21,530
+الشبتر هذا غالب البرهين كلها بال contradiction. و
+
+191
+00:23:21,530 --> 00:23:26,370
+هذه كمان بينان برهنها بال contradiction بالتلاعب.
+
+192
+00:23:26,770 --> 00:23:29,270
+يبقى ال proof التالي ما هو المطلوب
+
+193
+00:23:33,990 --> 00:23:38,290
+إن ال F of X is irreducible عليكم، بتروح أفترضها
+
+194
+00:23:38,290 --> 00:23:47,870
+reducible يا جمالي بيقول ال F of X موجودة في Z of
+
+195
+00:23:47,870 --> 00:23:59,570
+X and ال F of X is reducible over
+
+196
+00:23:59,570 --> 00:24:06,360
+ال Qطب انا انا خدنا اللغية في هذا الشام طب ال
+
+197
+00:24:06,360 --> 00:24:10,640
+reducibility على ال Q بصحبها على مين؟ على ال Z
+
+198
+00:24:10,640 --> 00:24:19,900
+يبقى هنا بقول هذا بده يعطينا ان ال F of X is
+
+199
+00:24:19,900 --> 00:24:32,540
+reducible over Z هذا من وين ال previous theorem
+
+200
+00:24:33,320 --> 00:24:40,640
+هذه نظرية سابعة تجمعنا هذا الكلام ان ال F of X
+
+201
+00:24:40,640 --> 00:24:48,140
+بقدر اكتبها على الشكل G of X في 100 ال H of X طب
+
+202
+00:24:48,140 --> 00:24:57,540
+ال G و ال H وين موجودة؟ ال Z of X وين حيث ال G of
+
+203
+00:24:57,540 --> 00:25:05,800
+X و ال H of Xموجودة في Z of X مش حاجات دايكو بس
+
+204
+00:25:05,800 --> 00:25:12,780
+هذول بدهم يكونوا of lower degree than مين لأن ال F
+
+205
+00:25:12,780 --> 00:25:24,490
+يبقى and ال degree لل G و ال degree لمين لل Hأكبر
+
+206
+00:25:24,490 --> 00:25:30,130
+من او تساوي الواحد وأقل من ال degree تبع تلفر هي
+
+207
+00:25:30,130 --> 00:25:36,930
+كده؟ N أعلى أس عندى موجود N يبقى هذه ال polynomial
+
+208
+00:25:36,930 --> 00:25:44,270
+من الضغط النولية تمام طبعى كويس يبقى أنا صار عندى
+
+209
+00:25:44,270 --> 00:25:50,270
+F of X هي حاصل ضرب two polynomialsخلّيني أضع لكل
+
+210
+00:25:50,270 --> 00:25:55,130
+واحدة منهم شكل ونشوف إيش اللي بده يصير معانا يبقى
+
+211
+00:25:55,130 --> 00:26:03,130
+لو جيت قلت هنا لأ ال G of X بده يساوي ال PR X أُس
+
+212
+00:26:03,130 --> 00:26:11,270
+R PR minus ال one X أُس R minus ال one زائد P one
+
+213
+00:26:11,270 --> 00:26:22,060
+X زائد ال P نوع and ال H of Xcs x to the power s
+
+214
+00:26:22,060 --> 00:26:30,040
+cs minus ال 1 x to the power s minus ال 1 زائد
+
+215
+00:26:30,040 --> 00:26:39,140
+زائد اللي هو c1x زائد c0 فاحنا
+
+216
+00:26:39,140 --> 00:26:46,480
+عندنا f of x يساوي حاصل ضربهماإذا الحد فيكم بيقدر
+
+217
+00:26:46,480 --> 00:26:52,440
+يعرفلي قداش حاصل الضرب أخر تيرم في حاصل الضرب إيش
+
+218
+00:26:52,440 --> 00:26:57,860
+بيكون؟ P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+219
+00:26:57,860 --> 00:27:02,620
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+220
+00:27:02,620 --> 00:27:03,240
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+221
+00:27:03,240 --> 00:27:09,780
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P
+
+222
+00:27:14,000 --> 00:27:19,900
+5 خواش في صمم الموضوع ال P بتقسم ايه ال P بتقسم ال
+
+223
+00:27:19,900 --> 00:27:24,520
+A نوت تبقى ال P هتقسم ال B نوت C نوت صحيح ولا لأ
+
+224
+00:27:24,520 --> 00:27:35,200
+ال P بتقسم ال A نوت ال A نوت هو B نوت C نوت هذا
+
+225
+00:27:35,200 --> 00:27:43,470
+imply ان ال P بتقسم ال B نوت C نوتيبقى ال P يابدها
+
+226
+00:27:43,470 --> 00:27:50,230
+تقسم الأول يابدها تقسم الثاني يبقى هذا بدي أعطيكوا
+
+227
+00:27:50,230 --> 00:27:57,790
+ان P يابدها تقسم ال P نوت او ال P يابدها تقسم ال C
+
+228
+00:27:57,790 --> 00:28:06,470
+نوت إذا لو أخدناها تقسم أحدهما لن تقسم الآخر
+
+229
+00:28:06,470 --> 00:28:18,680
+مظبوط؟ أيوة يبقى هناsuppose that افترضوا ان ال P
+
+230
+00:28:18,680 --> 00:28:31,620
+بتقسم ال B نوت then ال P لا تقسم ال C نوت تقسموه و
+
+231
+00:28:31,620 --> 00:28:38,140
+ال P بتقسم ال B نوت ايه
+
+232
+00:28:38,140 --> 00:28:48,230
+يعنيصارت ال P تقسم ال P نوت ولا تقسم ال C نوت لا
+
+233
+00:28:48,230 --> 00:28:55,090
+ممكن اضيف شغلة مما يعزز ان ال P لا تقسم ال C نوت
+
+234
+00:28:55,090 --> 00:29:01,130
+ان ال P تربية لا تقسم ال A نوت ال P تربية لا تقسم
+
+235
+00:29:01,130 --> 00:29:06,370
+ال A نوت يعني لابدها تقسم ال P نوت ولا تقسم ال C
+
+236
+00:29:06,370 --> 00:29:12,120
+نوتلكن لما كان ال P بتقسم ال B نوت بصير الاحتمال
+
+237
+00:29:12,120 --> 00:29:19,640
+الاقوى ان P تربيع لا تقسم ال C نوت او ال P لا تقسم
+
+238
+00:29:19,640 --> 00:29:25,660
+ال C نوت مش مشكلة مش مشكلة كتير طبعا اذا ال P لا
+
+239
+00:29:25,660 --> 00:29:30,900
+تقسم ال B نوت شو رايك احنا روحنا جيبنا اخر تير في
+
+240
+00:29:30,900 --> 00:29:36,640
+حاصل الضرب السؤال هو شو رايك في اول تير من حاصل
+
+241
+00:29:36,640 --> 00:29:48,370
+الضربإيش بيكون؟ A N بده يساوي مين؟ P R C S صحيح؟
+
+242
+00:29:48,370 --> 00:30:00,170
+يبقى هنا ورصة وكذلك ال A N بده يساوي P R في C S
+
+243
+00:30:00,170 --> 00:30:07,480
+طيب إيش مواطعيننا؟إن ال P لا تقسم ال AN إذا لن
+
+244
+00:30:07,480 --> 00:30:14,840
+تقسم هذه لأن لن تقسم حاصل الضرب هذا يبقى since بما
+
+245
+00:30:14,840 --> 00:30:27,880
+أن ال P لا تقسم ال AN we have إن ال P لا تقسم ال
+
+246
+00:30:27,880 --> 00:30:30,400
+PR في ال CS
+
+247
+00:30:35,140 --> 00:30:41,460
+مافيش تفسيرك لهذه الأجازة لا تقسم الأول ولا تقسم
+
+248
+00:30:41,460 --> 00:30:49,780
+التاني طيب هذا بده يعطينا ان ال P لا تقسم ال PR
+
+249
+00:30:49,780 --> 00:31:02,020
+and ال P لا تقسم ال CS اخو خديلي هذا ال
+
+250
+00:31:02,020 --> 00:31:11,350
+P لا تقسم ال PRطبعا إذا ال P ممكن تقسم اللي بعده
+
+251
+00:31:11,350 --> 00:31:16,350
+تبقى للكلام اللي احنا جايلينه هنا صحيح ولا لأ إذا
+
+252
+00:31:16,350 --> 00:31:22,230
+ال P ممكن تقسم اللي هو الكل القيم اللي بعده يعني
+
+253
+00:31:22,230 --> 00:31:26,410
+PR minus ال one PR minus ال two لغاية P one و
+
+254
+00:31:26,410 --> 00:31:33,250
+لغاية P none صحيح ولا لأ طيب ال PR هذا الرقم
+
+255
+00:31:35,280 --> 00:31:43,060
+مظبوط؟ رقم الرقم هذا يمكن اه يمكن بدينا نعد من
+
+256
+00:31:43,060 --> 00:31:49,100
+عنده ويمكن قبل ويمكن بعده لإنه حاصر الضرر تبع هذا
+
+257
+00:31:49,100 --> 00:31:57,200
+ال G و ال S هل عدد العلاصر التانوس اللي هنا جد عدد
+
+258
+00:31:57,200 --> 00:32:03,110
+علاصر التانوس اللي هنا؟ ماحدش جال هيكواللي لو كان
+
+259
+00:32:03,110 --> 00:32:06,630
+اكيد كان بدل ما قولنا R و S خلينا أقولها R و
+
+260
+00:32:06,630 --> 00:32:11,030
+خلاصنا أو أقولها S و خلاصنا يبقى يمكن المعادلة
+
+261
+00:32:11,030 --> 00:32:15,570
+الأولى أو ال polynomial يكون فيها عشرة عناصر
+
+262
+00:32:15,570 --> 00:32:20,390
+مجموعة التاني يكون فيها ستة صحيح ولا لأ؟ يبقى
+
+263
+00:32:20,390 --> 00:32:28,570
+بجاني أخد رقم بحيث من عنده يبدأ العدل اللي هو تكون
+
+264
+00:32:28,570 --> 00:32:36,280
+ال PR لا تساوي Zeroيبقى بالدالي أقول له let T be
+
+265
+00:32:36,280 --> 00:32:43,100
+the smallest positive
+
+266
+00:32:43,100 --> 00:32:47,500
+integer
+
+267
+00:32:47,500 --> 00:32:50,520
+such
+
+268
+00:32:50,520 --> 00:32:55,840
+that بحيث
+
+269
+00:32:55,840 --> 00:33:06,180
+أن ال P لا تقسمفي ال B T في
+
+270
+00:33:06,180 --> 00:33:11,900
+ال R أنا مش عارف ان هي 8 بقول تخوض T هو أصغر رقم
+
+271
+00:33:11,900 --> 00:33:20,040
+من عنده ال P لا تقسم مين في ال B T تمام يبقى بتقسم
+
+272
+00:33:20,040 --> 00:33:28,260
+مين اللي بقعده صحيح ولا لأ يبقى هذه ممتازة يبقى ال
+
+273
+00:33:28,260 --> 00:33:35,070
+P بدها تقسم اللي بعدهاطيب ال VET هذا مش بده يقابله
+
+274
+00:33:35,070 --> 00:33:42,090
+واحد اسمه CT واتنين بده يقابلهم في حاصر الضرب واحد
+
+275
+00:33:42,090 --> 00:33:48,490
+اسمه ET لأن ال ET نتجت من حاصر الضرب هذا، صحيح ولا
+
+276
+00:33:48,490 --> 00:33:52,450
+لأ؟ طيب الان خليني أعرف مين هي ET هذا
+
+277
+00:34:11,960 --> 00:34:20,340
+قبل ما رأيت خضرسة هو T هادي أكبر من N ولا أصغر؟
+
+278
+00:34:20,340 --> 00:34:27,040
+ممكن تسويها؟ لأ يبقى هو أصغر من N صحيح ولا لأ؟ طيب
+
+279
+00:34:27,040 --> 00:34:33,900
+الآن consider وديلي
+
+280
+00:34:33,900 --> 00:34:43,370
+AT مين هي AT؟ وحاصل ضاربمعاملات من جيه ومعاملة من
+
+281
+00:34:43,370 --> 00:34:48,750
+اتش وبنجمعهم بيعطيني هذا المعامل اللي هو مين لو
+
+282
+00:34:48,750 --> 00:34:56,150
+روحتي قولتلك بي تي سي نوت زائد بي تي ماينوس الوان
+
+283
+00:34:56,150 --> 00:35:04,530
+سي وان زائد زائد ال بي وان سي تي ماينوس الوان زائد
+
+284
+00:35:04,530 --> 00:35:12,490
+ال بي نوت سي تيطبعا أخدنا أول مبدئ ال polynomial
+
+285
+00:35:12,490 --> 00:35:18,090
+حاصل ضرب two polynomials وكيف بنجيب المعامل تبع كل
+
+286
+00:35:18,090 --> 00:35:24,010
+x os n x os n minus one x os n minus two يبقى هذا
+
+287
+00:35:24,010 --> 00:35:29,090
+الشكل ال 80 طيب
+
+288
+00:35:29,090 --> 00:35:40,480
+الآن نجي لغاية السؤال هو هلالـP تقسم الـAT تقسم
+
+289
+00:35:40,480 --> 00:35:43,360
+الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ
+
+290
+00:35:43,360 --> 00:35:44,980
+تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم
+
+291
+00:35:44,980 --> 00:35:45,780
+الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ
+
+292
+00:35:45,780 --> 00:35:48,640
+تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم
+
+293
+00:35:48,640 --> 00:35:49,180
+الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ
+
+294
+00:35:49,180 --> 00:35:50,460
+تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم
+
+295
+00:35:50,460 --> 00:35:59,440
+الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ
+
+296
+00:35:59,440 --> 00:36:03,400
+تقسم الـAT لأ تقسم الـAT ل
+
+297
+00:36:08,130 --> 00:36:18,950
+الـP بتقسم من الـAT السبب لأن T أقل من N لكن لو
+
+298
+00:36:18,950 --> 00:36:25,070
+كانت تسوى N، هنسفش جسمها بالمرة، هي مايكونش جسمه
+
+299
+00:36:25,070 --> 00:36:30,170
+نصيف زي ما بيقولوا، يبقى هنا هتجسمهم كلهم، مافيش
+
+300
+00:36:30,170 --> 00:36:37,590
+فائزة، يبقى P بتقسم من الـAT السبب لأن T أقل من N
+
+301
+00:36:38,000 --> 00:36:46,180
+تمام؟ خيب كويس الان قلنا هنا ال P لا تقسم ال P
+
+302
+00:36:46,180 --> 00:36:56,980
+تقسمين اللي بعده يبقى هنا also وكذلك ال P لا تقسم
+
+303
+00:36:56,980 --> 00:37:04,760
+ال P تي but ال P تقسم او divides
+
+304
+00:37:08,970 --> 00:37:16,410
+قول بي تي ماينوس ال one و بي تي ماينوس ال two و بي
+
+305
+00:37:16,410 --> 00:37:25,150
+one و بي نوت هذا بده يعطيلي ان ال P divide بدها
+
+306
+00:37:25,150 --> 00:37:33,470
+تقسم ايه بدها تقسم مثلا ال بي نوت CT
+
+307
+00:37:37,550 --> 00:37:54,130
+الـ V1 CT-1 زائد انظل للآخر انظل BT-1 C1 طبعا؟
+
+308
+00:37:54,130 --> 00:38:03,130
+طيب، الآن P بتقسم الـ AT وP بتقسم هدول إذا الفيب
+
+309
+00:38:03,130 --> 00:38:11,760
+تقسم الفرق بينهما ولا لايبقى هنا ساعة ال P بتقسم
+
+310
+00:38:11,760 --> 00:38:24,840
+ال AT minus B not CT B not CT زائد B1 CT minus ال
+
+311
+00:38:24,840 --> 00:38:34,630
+1 زائد زائد BT minus ال 1 C1 بالشكل اللي عندهاإذاً
+
+312
+00:38:34,630 --> 00:38:41,750
+ال P بتقسم و لل AT هي فوق بدي أشيلها و أحط القيم
+
+313
+00:38:41,750 --> 00:38:56,970
+تبعتها يبقى BTC0 زائد BT-1C1 زائد زائد B1CT زائد
+
+314
+00:38:56,970 --> 00:39:03,390
+CT-1 زائد B0CT
+
+315
+00:39:04,260 --> 00:39:09,940
+ناقص إذا انت خلّي على كل واحدة من هدول يبقى ناقص B
+
+316
+00:39:09,940 --> 00:39:22,140
+non CT ناقص B one CT minus ال one ناقص ناقص B T
+
+317
+00:39:22,140 --> 00:39:31,600
+minus ال one C one طب أطلع هذه موجبة وهذه سالمة مع
+
+318
+00:39:31,600 --> 00:39:38,410
+السلامةو هذه موجبة و هذه سالبة غير ما نصوف عليها و
+
+319
+00:39:38,410 --> 00:39:44,150
+نظل ماشيين هذه موجبة و هذه سالبة إذا لن يلقى إلا
+
+320
+00:39:44,150 --> 00:39:52,990
+من إلا ترم الأول يبقى بصيرها إن في تقسم ال BTC
+
+321
+00:39:52,990 --> 00:40:01,670
+نقطة يبقى فيه تقسم و أخد منها صح؟ يبقى هذا معناه
+
+322
+00:40:01,670 --> 00:40:11,250
+إن فيهبتقسم ال بي تي or ال بي بتقسم السي نوت فاحنا
+
+323
+00:40:11,250 --> 00:40:15,830
+حاطين ان ال بي ممنوع تقسم السي نوت يبقى ال بي
+
+324
+00:40:15,830 --> 00:40:24,970
+هتقسم ال بي تي لإن هذا بده يعطينا ان ال بي بتقسم
+
+325
+00:40:24,970 --> 00:40:34,720
+ال بي تي because السبب لإن ال بيلأ تقسم الـC not
+
+326
+00:40:34,720 --> 00:40:44,260
+طب استنى شوية طلعيلي هذه وطلعيلي لهذه هنا تقسم
+
+327
+00:40:44,260 --> 00:40:49,220
+الـB T وهنا بيبقى تقسم ال contradiction ولا لأ
+
+328
+00:40:49,220 --> 00:40:56,700
+يبقى this is a contradict that
+
+329
+00:41:01,710 --> 00:41:08,790
+هذا يناقض ان ال P لا تقسم ال B T طب ايش جاب
+
+330
+00:41:08,790 --> 00:41:14,970
+التناقض؟ جاب التناقض الفرض اللى فرضنا هذا صح هذا
+
+331
+00:41:14,970 --> 00:41:22,110
+يبقى الفرض اللى فرضنا غلط وعكسه هو الصح يبقى بس
+
+332
+00:41:22,110 --> 00:41:29,150
+وهكذا ال F of X is irreducible
+
+333
+00:41:30,680 --> 00:41:40,440
+over the cube هو المظهر نعطيك مثال توضيحي مباشر
+
+334
+00:41:40,440 --> 00:41:47,200
+مثال على
+
+335
+00:41:47,200 --> 00:41:57,140
+كيفية استخدام هذه النظرية مثلًا بيقول شهداد
+
+336
+00:41:57,140 --> 00:42:00,040
+الكوروناوية شهداد
+
+337
+00:42:01,390 --> 00:42:12,230
+that the polynomial which
+
+338
+00:42:12,230 --> 00:42:24,710
+is f of x to the seventh ثلاثة اكس وخمسة زائد
+
+339
+00:42:24,710 --> 00:42:26,830
+خمستاشر
+
+340
+00:42:32,460 --> 00:42:44,240
+عشرين X تكريم زائد عشرة X زائد عشرين اللي موجودة
+
+341
+00:42:44,240 --> 00:42:53,820
+في Z of X معناه هذه is irreducible
+
+342
+00:42:53,820 --> 00:42:58,460
+irreducible
+
+343
+00:42:58,460 --> 00:43:08,650
+of Rالكيموز. قال لي ولكن قال لي بييل لي ان كثيرة
+
+344
+00:43:08,650 --> 00:43:14,090
+الحدود اللي على الشكل هذا المعاملات كلهم انتجة زي
+
+345
+00:43:14,090 --> 00:43:19,250
+ما موجودة في Z of X is irreducible عالميا على
+
+346
+00:43:19,250 --> 00:43:25,010
+الكيموز. إذن بدنا نروح نختار ال prime number. نطلع
+
+347
+00:43:25,010 --> 00:43:31,200
+من ال prime number المناسب.أطلعيلي هنا في ال 15
+
+348
+00:43:31,200 --> 00:43:35,940
+ولا 20 ولا 10 ولا 20 مين ال prime number اللي
+
+349
+00:43:35,940 --> 00:43:42,220
+بيقسمهم كلهم خمسة بيقسم التلاتة 100% يفجأة بدي
+
+350
+00:43:42,220 --> 00:43:54,120
+أقوله هنا take the prime number بيتساوي
+
+351
+00:43:54,120 --> 00:44:03,220
+خمسة الآن الخمسةلا تقسم التلاتة يعني الخمسة لا
+
+352
+00:44:03,220 --> 00:44:11,500
+تقسم الان لكن الخمسة بتقسم اللي هو الخمستاشر
+
+353
+00:44:11,500 --> 00:44:20,460
+والخمسة بتقسم ناقص عشرين والخمسة بتقسم العشر
+
+354
+00:44:20,460 --> 00:44:29,030
+والخمسة بتقسم العشرين and الخمسة تربية مين هي
+
+355
+00:44:29,030 --> 00:44:36,510
+المناسبة؟ لا، ساقس من العشرين. اوش البرنامج
+
+356
+00:44:36,510 --> 00:44:42,150
+الموجودة في Zip Code X واتحققت شروط النظرية كلها.
+
+357
+00:44:42,490 --> 00:44:48,750
+يبقى بالنظرية ترد يوسف وخلصنا، دون شروط. يبقى هنا
+
+358
+00:44:48,750 --> 00:44:54,490
+بروح اقوله I The Above The.
+
+359
+00:44:57,450 --> 00:45:04,450
+by the above theorem ال F of X اللي عندها .. اللي
+
+360
+00:45:04,450 --> 00:45:13,270
+هي تلاتة X أُس خمسة زائد خمستاشر X أُس أربعة ناقص
+
+361
+00:45:13,270 --> 00:45:25,730
+عشرة X زائد عشرين is irreducible over
+
+362
+00:45:27,160 --> 00:45:32,000
+لكيوك أظن هذه نظرية سهل التعامل معاها مش زي اللي
+
+363
+00:45:32,000 --> 00:45:37,620
+قبلها برهانة صحيح أصعب من اللي قبلها لكن الشغل
+
+364
+00:45:37,620 --> 00:45:43,380
+ابقى بسيط لدى الان في نتيجة على هذه النظرية
+
+365
+00:45:43,380 --> 00:45:46,200
+النتيجة كانت تانية
+
+366
+00:45:57,850 --> 00:46:06,530
+طبعاً اكتشافها راحت يقولون الـ EIS, ENST,
+
+367
+00:46:08,090 --> 00:46:21,030
+EIN criteria هذا
+
+368
+00:46:21,030 --> 00:46:25,770
+توفى هو سنة 1850
+
+369
+00:46:26,500 --> 00:46:31,860
+واتكشفها سنة الف تمانية وتبانية واربعين قبل ميمون
+
+370
+00:46:31,860 --> 00:46:38,600
+بسنتين وكان هناك مدرس وبعدين طلعوا الشغل هذه الى
+
+371
+00:46:38,600 --> 00:46:46,060
+الوجود وهي موجودة في غالب كتب الجدد. تقول ما يكوّر
+
+372
+00:46:46,060 --> 00:46:54,000
+أي crime فيه. يبقى هذا أي crime مش شغل محدد.
+
+373
+00:46:57,840 --> 00:47:07,100
+is cyclotomic cyclotomic
+
+374
+00:47:07,100 --> 00:47:15,680
+polynomial في
+
+375
+00:47:15,680 --> 00:47:23,580
+اليابان اللي هي Phi P of X Phi P of X في X to the
+
+376
+00:47:23,580 --> 00:47:30,580
+power P ناقص واحدعلى x ناقص واحد يتساوي x بي ناقص
+
+377
+00:47:30,580 --> 00:47:38,740
+واحد x بي ناقص اتنين انضال زائد x زائد واحد is
+
+378
+00:47:38,740 --> 00:47:41,900
+irreducible
+
+379
+00:47:41,900 --> 00:47:53,300
+is irreducible over a q irreducible على مين على a
+
+380
+00:47:53,300 --> 00:47:53,500
+q
+
+381
+00:48:30,090 --> 00:48:37,310
+خلّى بقى كده بيقوللي اثبت ان هذه البراناية بدى على
+
+382
+00:48:37,310 --> 00:48:42,530
+الشكل هذا irreducible على مين؟ على ال F يقولوا
+
+383
+00:48:42,530 --> 00:48:52,050
+تعالى شوف بدي اخد F of X يبقى هنا let F of X
+
+384
+00:48:52,050 --> 00:48:59,950
+بيساوي Phi P of X plus 1هذه بده تجيبها من وين بده
+
+385
+00:48:59,950 --> 00:49:05,890
+تجيبها من هنا إذا نحشيل كل X وحط مكانها X plus one
+
+386
+00:49:05,890 --> 00:49:12,290
+يبقى هذه بيصير X plus one to the power of P ناقص
+
+387
+00:49:12,290 --> 00:49:19,150
+واحد X زائد واحد ناقص واحد يبقى الشيلة شيلنا كل X
+
+388
+00:49:19,150 --> 00:49:26,450
+وحطينا مكانها X زائد واحد هذه يا بناة هي لغوية ذات
+
+389
+00:49:26,450 --> 00:49:37,410
+الحدينبدي افكر لو فكتها يبقى X و P زي توفيق P من
+
+390
+00:49:37,410 --> 00:49:46,510
+الأشياء المخوذة اتنين يبقاش بصير زي P فبين في X و
+
+391
+00:49:46,510 --> 00:49:53,570
+P ناقص واحد اللي بعده P في P ناقص واحد على مضروب
+
+392
+00:49:53,570 --> 00:49:58,640
+الثاني اتنين في واحد اللي بعدهزائد P في P ناقص
+
+393
+00:49:58,640 --> 00:50:03,180
+واحد في P ناقص اتنين على مضغوب التلاتة زائد الى
+
+394
+00:50:03,180 --> 00:50:08,980
+اخرين ما علينا بيهمنيش كتير بيهمني اظل ماشي لغاية
+
+395
+00:50:08,980 --> 00:50:16,680
+مين لغاية P في X زائد واحد وعنده ناقص واحد زايد و4
+
+396
+00:50:16,680 --> 00:50:25,870
+وهذه كلها مقسمة على مين على Xالان زائد واحد و ناقص
+
+397
+00:50:25,870 --> 00:50:33,090
+واحد مالها مع السلامة يبقى هذه بدها تساوي X أس P
+
+398
+00:50:33,090 --> 00:50:42,070
+ناقص الواحد زائد P X أس P ناقص اتنين زائد زائد P
+
+399
+00:50:42,070 --> 00:50:51,330
+هذا كله مين؟ Phi P of X زائد واحد لو بدها تساوي
+
+400
+00:50:51,330 --> 00:51:00,730
+المين؟الـ F of X يبقى هاي كثيرة حدود و الـ Prime
+
+401
+00:51:00,730 --> 00:51:07,190
+هو P مضي أخد الـ Prime هو P فهذا الـ Prime P من
+
+402
+00:51:07,190 --> 00:51:14,970
+مكان يكون كدهش المعامل هنا الـ P تقسم الواحد لأ كل
+
+403
+00:51:14,970 --> 00:51:21,500
+حد من هذه الحدود يحتوي على P P في P ناقص واحدP في
+
+404
+00:51:21,500 --> 00:51:26,540
+P نقص واحد في P نقص اتنين لغاية اخر حد اللي هو P
+
+405
+00:51:26,540 --> 00:51:33,760
+وكل واحد منهم يقبل القسمة على P ما عدا مين؟ ما عدا
+
+406
+00:51:33,760 --> 00:51:42,800
+الاول اتنين العناصر كلهم هدول موجودة في Z of
+
+407
+00:51:42,800 --> 00:51:52,360
+X هدى ال polynomial موجودة في Z of Xإن كل المعاملة
+
+408
+00:51:52,360 --> 00:51:58,960
+أرقام صحية Integers تمام؟ طيب إذا المعلومة الأولى
+
+409
+00:51:58,960 --> 00:52:06,380
+اتحققت، المعلومة الثانية ال P ليه تقسم ال A N اللي
+
+410
+00:52:06,380 --> 00:52:18,140
+هي بواحد؟ الآن ال P تقسم ال A N تقسم ال A ال minus
+
+411
+00:52:18,140 --> 00:52:24,630
+ال one اللي هي Pبتقسم نفسها تمام؟ وذا وضلنا ماشي
+
+412
+00:52:24,630 --> 00:52:39,190
+ال P بتقسم ال A ناضله P and ال P ترفيع لا تقسم ال
+
+413
+00:52:39,190 --> 00:52:45,370
+A ناضله بساوي ال P في ترفيع بتقسم ال P بدون باقية
+
+414
+00:52:45,370 --> 00:52:51,890
+أبعادها إذا انت حققت مين؟الشروط النظرية مدام تحققت
+
+415
+00:52:51,890 --> 00:52:56,970
+شروط النظرية يبقى ال F of X لأنها irreducible
+
+416
+00:52:56,970 --> 00:53:05,090
+عالميا عالميا يبقى هذا بالتوافق فينا F of X اللي
+
+417
+00:53:05,090 --> 00:53:16,190
+هي بدها تساوي 5P of X زي واحد is irreducible over
+
+418
+00:53:18,580 --> 00:53:27,840
+Lithium وهذا المطلوب؟ لأ مش انا هذه 5PX زي 1 احنا
+
+419
+00:53:27,840 --> 00:53:33,980
+بدنا 5P of X صح ولا لأ؟ واحنا في هذا ال chapter
+
+420
+00:53:33,980 --> 00:53:39,240
+كلنا الحمد لله ماشيين الفراهين بالتناقض اذا انا
+
+421
+00:53:39,240 --> 00:53:46,740
+بروح اختار ان هذه Reducible وشوف وين بتوصل الدنيا
+
+422
+00:53:47,120 --> 00:53:52,780
+مظبوط، إذا وصلت لتناقض، مقناته عكسه هو الصحيح،
+
+423
+00:53:52,780 --> 00:53:59,260
+مظبوط؟ طيب، الان وصلنا إلى ماتي، تحققت كل شروط
+
+424
+00:53:59,260 --> 00:54:04,520
+فضرية، ال graph of x بفعي P of x هو irreducible
+
+425
+00:54:04,520 --> 00:54:10,760
+على K، مش هذا اللي بدي أثبته، أنا بدي أثبت أن فعي
+
+426
+00:54:10,760 --> 00:54:15,760
+P of x هي ال irreducible على K، اللي بدي أفترض
+
+427
+00:54:15,760 --> 00:54:25,730
+العكس،هروح اقول هنا I assume افترض انه Phi P of X
+
+428
+00:54:25,730 --> 00:54:41,530
+is irreducible over ال Q then شو اللي بده يصير Phi
+
+429
+00:54:41,530 --> 00:54:51,670
+P of X بده يساوي ال G of Xالـ H of X والـ
+
+430
+00:54:51,670 --> 00:55:00,450
+degree أو الـ G of X والـ H of X موجودة في الـ Q
+
+431
+00:55:00,450 --> 00:55:11,790
+of X والـ degree للـ G للـ G والـ degree للـ H أقل
+
+432
+00:55:11,790 --> 00:55:26,090
+من مين؟ أقل من ال degreeلـ Phi P of X أقل
+
+433
+00:55:26,090 --> 00:55:35,010
+من Phi P of X مافيش
+
+434
+00:55:35,010 --> 00:55:39,010
+رأيك؟ لو شيلت الـ X و حطيت بدالها X زائد واحد،
+
+435
+00:55:39,010 --> 00:55:45,110
+بتغير؟ هذي اللينية لو هذي اللينيةيبقى هذا بدي يقيل
+
+436
+00:55:45,110 --> 00:55:51,910
+فاي P of X زائد واحد بدي يسوي ال GX زائد واحد بال
+
+437
+00:55:51,910 --> 00:55:59,710
+HX زائد واحد يبقى هذا معناته ان فاي P of X زائد
+
+438
+00:55:59,710 --> 00:56:06,070
+واحد is reducible صحيح ولا لا؟ اذا احنا ايش قلنا
+
+439
+00:56:06,070 --> 00:56:16,190
+هنا؟ is reducible، مصر تناقض؟ تناقضيبقى هنا this
+
+440
+00:56:16,190 --> 00:56:19,890
+is contradiction
+
+441
+00:56:19,890 --> 00:56:26,750
+اللي فرضنا .. اللي فرضنا هو الغلط اللي جاب ال
+
+442
+00:56:26,750 --> 00:56:31,830
+contradiction ان الفرض هذه irreducible يبقى sir
+
+443
+00:56:31,830 --> 00:56:44,370
+phi P of X is irreducible over liquidبحب أشير إلى
+
+444
+00:56:44,370 --> 00:56:50,950
+ما يكتب الكلام اللي كتبته هنا هو حل سؤال خمسة عندك
+
+445
+00:56:50,950 --> 00:56:58,790
+في الكتاب رقم C خمسة A وB وC وD الرقم C هيحله
+
+446
+00:56:58,790 --> 00:57:07,380
+قدامك عندهم بس هناك محطش واحد حطه Ux زائد Cيبقى
+
+447
+00:57:07,380 --> 00:57:10,920
+مكان الـC احنا حاطينه واحد الحل هيو قدامك علّه
+
+448
+00:57:10,920 --> 00:57:16,040
+احتباط سواء خمسة C هو هو لم يتغير بال
+
+449
+00:57:16,040 --> 00:57:20,120
+contradiction نمرأيه بال contradiction نمرأيه بال
+
+450
+00:57:20,120 --> 00:57:23,800
+contradiction نمرأي الـC بال contradiction كذلك
+
+451
+00:57:23,800 --> 00:57:29,100
+كلهم التلاتة بال contradiction ونفس التكتيك اللي
+
+452
+00:57:29,100 --> 00:57:35,220
+تبقى هو نفسه إلى هنا انتهت هذه المحاضرة ونكمل ان
+
+453
+00:57:35,220 --> 00:57:39,020
+شاء اللهالمحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b37d528138e94d37ce002906dcc62cb674db8077
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4858, "start": 20.86, "end": 48.58, "text": "بسم الله الرحمن الرحيم احنا المرة اللي فاتت لم نصور المحاضرة الماضية وذلك بسبب سوء الأحوال الأرضية من قطع كهربا أو غيره فانعتدر للطلب الذين يشاهدوننا على مستوى العالم وانتم منهم فتم يطأ المحاضرة بدون تصوير", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 1975, 5016, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 32767, 8717, 9381, 13063, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 4032, 8848, 23275, 4724, 35457, 3555, 8608, 2407, 38207, 16247, 5016, 2407, 6027, 16247, 43042, 10632, 9154, 12174, 9566, 3615, 9122, 3224, 25513, 995, 34051, 32771, 13546, 3224, 6156, 7649, 34268, 3215, 2288, 24976, 9566, 46152, 32545, 9957, 7251, 8592, 40294, 3215, 11536, 8315, 15844, 3714, 14851, 2407, 7578, 18863, 45340, 4032, 7649, 39237, 9154, 16095, 6156, 39237, 7251, 9566, 10721, 9673, 5016, 46958, 25720, 47525, 11536, 6055, 9381, 2407, 13546], "avg_logprob": -0.09528186201464896, "compression_ratio": 1.913265306122449, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 20.86, "end": 20.98, "word": "بسم", "probability": 0.93310546875}, {"start": 20.98, "end": 21.22, "word": " الله", "probability": 0.97119140625}, {"start": 21.22, "end": 21.7, "word": " الرحمن", "probability": 0.9811197916666666}, {"start": 21.7, "end": 22.28, "word": " الرحيم", "probability": 0.98583984375}, {"start": 22.28, "end": 24.82, "word": " احنا", "probability": 0.8629557291666666}, {"start": 24.82, "end": 25.14, "word": " المرة", "probability": 0.947998046875}, {"start": 25.14, "end": 25.38, "word": " اللي", "probability": 0.75341796875}, {"start": 25.38, "end": 26.32, "word": " فاتت", "probability": 0.99169921875}, {"start": 26.32, "end": 26.56, "word": " لم", "probability": 0.9716796875}, {"start": 26.56, "end": 27.18, "word": " نصور", "probability": 0.9765625}, {"start": 27.18, "end": 28.18, "word": " المحاضرة", "probability": 0.9814453125}, {"start": 28.18, "end": 29.74, "word": " الماضية", "probability": 0.9879557291666666}, {"start": 29.74, "end": 30.88, "word": " وذلك", "probability": 0.81884765625}, {"start": 30.88, "end": 31.52, "word": " بسبب", "probability": 0.9930013020833334}, {"start": 31.52, "end": 31.92, "word": " سوء", "probability": 0.9921875}, {"start": 31.92, "end": 32.84, "word": " الأحوال", "probability": 0.952392578125}, {"start": 32.84, "end": 34.04, "word": " الأرضية", "probability": 0.9938151041666666}, {"start": 34.04, "end": 34.6, "word": " من", "probability": 0.81591796875}, {"start": 34.6, "end": 35.02, "word": " قطع", "probability": 0.9659830729166666}, {"start": 35.02, "end": 35.88, "word": " كهربا", "probability": 0.9200439453125}, {"start": 35.88, "end": 36.24, "word": " أو", "probability": 0.7216796875}, {"start": 36.24, "end": 36.8, "word": " غيره", "probability": 0.9236653645833334}, {"start": 36.8, "end": 38.16, "word": " فانعتدر", "probability": 0.75107421875}, {"start": 38.16, "end": 39.0, "word": " للطلب", "probability": 0.955078125}, {"start": 39.0, "end": 39.5, "word": " الذين", "probability": 0.879638671875}, {"start": 39.5, "end": 40.6, "word": " يشاهدوننا", "probability": 0.9772135416666666}, {"start": 40.6, "end": 41.02, "word": " على", "probability": 0.9658203125}, {"start": 41.02, "end": 42.32, "word": " مستوى", "probability": 0.9228515625}, {"start": 42.32, "end": 43.08, "word": " العالم", "probability": 0.99658203125}, {"start": 43.08, "end": 44.3, "word": " وانتم", "probability": 0.822265625}, {"start": 44.3, "end": 45.36, "word": " منهم", "probability": 0.99609375}, {"start": 45.36, "end": 46.12, "word": " فتم", "probability": 0.95361328125}, {"start": 46.12, "end": 46.6, "word": " يطأ", "probability": 0.5589192708333334}, {"start": 46.6, "end": 47.26, "word": " المحاضرة", "probability": 0.99072265625}, {"start": 47.26, "end": 47.9, "word": " بدون", "probability": 0.990478515625}, {"start": 47.9, "end": 48.58, "word": " تصوير", "probability": 0.9630126953125}], "temperature": 1.0}, {"id": 2, "seek": 7295, "start": 49.02, "end": 72.96, "text": "اليوم احنا بنكمل على المحاضرة، المحاضرة لم نعطيها إلا نظرية واحدة وهي ال RDOS Quality Test، تمام؟ وما بدني أظهر ليهم الذاكرين هولا لأ، لإن بتعطي كمان إدارة عالية، تمام؟ ال .. حد من ذاكره ما هو نقص النظرية؟ برهناه هنا اللي واحنا ايوة؟", "tokens": [6027, 1829, 20498, 1975, 5016, 8315, 44945, 24793, 1211, 15844, 9673, 5016, 46958, 25720, 12399, 9673, 5016, 46958, 25720, 32767, 8717, 3615, 9566, 1829, 11296, 11933, 15040, 8717, 19913, 2288, 10632, 36764, 24401, 3660, 37037, 1829, 2423, 49488, 4367, 28892, 9279, 12399, 46811, 10943, 22807, 4032, 15042, 47525, 22653, 5551, 19913, 3224, 2288, 32239, 16095, 32545, 995, 37983, 9957, 8032, 12610, 995, 5296, 10721, 12399, 5296, 28814, 1863, 39894, 3615, 9566, 1829, 9122, 2304, 7649, 11933, 3215, 9640, 3660, 6225, 6027, 10632, 12399, 46811, 10943, 22807, 2423, 4386, 11331, 3215, 9154, 29910, 995, 37983, 3224, 19446, 31439, 8717, 4587, 9381, 28239, 19913, 2288, 10632, 22807, 4724, 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61.16, "end": 61.44, "word": " هولا", "probability": 0.5084635416666666}, {"start": 61.44, "end": 61.66, "word": " لأ،", "probability": 0.683837890625}, {"start": 61.66, "end": 61.84, "word": " لإن", "probability": 0.7948404947916666}, {"start": 61.84, "end": 62.32, "word": " بتعطي", "probability": 0.8814697265625}, {"start": 62.32, "end": 62.64, "word": " كمان", "probability": 0.9069010416666666}, {"start": 62.64, "end": 63.14, "word": " إدارة", "probability": 0.494873046875}, {"start": 63.14, "end": 63.9, "word": " عالية،", "probability": 0.68597412109375}, {"start": 63.9, "end": 65.42, "word": " تمام؟", "probability": 0.9855143229166666}, {"start": 65.42, "end": 65.72, "word": " ال", "probability": 0.375244140625}, {"start": 65.72, "end": 66.98, "word": " ..", "probability": 0.82421875}, {"start": 66.98, "end": 67.34, "word": " حد", "probability": 0.770263671875}, {"start": 67.34, "end": 67.52, "word": " من", "probability": 0.736328125}, {"start": 67.52, "end": 68.06, "word": " ذاكره", "probability": 0.65673828125}, {"start": 68.06, "end": 68.22, "word": " ما", "probability": 0.92041015625}, {"start": 68.22, "end": 68.52, "word": " هو", "probability": 0.94873046875}, {"start": 68.52, "end": 69.0, "word": " نقص", "probability": 0.733642578125}, {"start": 69.0, "end": 70.26, "word": " النظرية؟", "probability": 0.845458984375}, {"start": 70.26, "end": 71.6, "word": " برهناه", "probability": 0.617333984375}, {"start": 71.6, "end": 71.84, "word": " هنا", "probability": 0.9658203125}, {"start": 71.84, "end": 72.2, "word": " اللي", "probability": 0.81201171875}, {"start": 72.2, "end": 72.42, "word": " واحنا", "probability": 0.5989583333333334}, {"start": 72.42, "end": 72.96, "word": " ايوة؟", "probability": 0.749072265625}], "temperature": 1.0}, {"id": 3, "seek": 10273, "start": 74.05, "end": 102.73, "text": "أنا بقى أحكي بلدي مش مشكلة إذا كان النفس كالثالث أخذ القلعوم F of X موجودة في Z of X يعني المعاملات كلها", "tokens": [10721, 8315, 4724, 4587, 7578, 5551, 5016, 4117, 1829, 4724, 1211, 16254, 37893, 37893, 28820, 3660, 11933, 15730, 25961, 28239, 36178, 9122, 6027, 12984, 6027, 12984, 5551, 9778, 8848, 25062, 1211, 3615, 20498, 479, 295, 1783, 3714, 29245, 23328, 3660, 8978, 1176, 295, 1783, 37495, 22653, 9673, 3615, 10943, 1211, 9307, 28242, 11296], "avg_logprob": -0.3492476769067623, "compression_ratio": 1.3692307692307693, "no_speech_prob": 0.0, "words": [{"start": 74.05, "end": 74.41, "word": "أنا", "probability": 0.4517822265625}, {"start": 74.41, "end": 74.61, "word": " بقى", "probability": 0.7467447916666666}, {"start": 74.61, "end": 74.91, "word": " أحكي", "probability": 0.92724609375}, {"start": 74.91, "end": 75.29, "word": " بلدي", "probability": 0.9801432291666666}, {"start": 75.29, "end": 75.49, "word": " مش", "probability": 0.82861328125}, {"start": 75.49, "end": 75.93, "word": " مشكلة", "probability": 0.9835611979166666}, {"start": 75.93, "end": 80.15, "word": " إذا", "probability": 0.624755859375}, {"start": 80.15, "end": 80.93, "word": " كان", "probability": 0.6875}, {"start": 80.93, "end": 94.57, "word": " النفس", "probability": 0.2724609375}, {"start": 94.57, "end": 95.75, "word": " كالثالث", "probability": 0.738720703125}, {"start": 95.75, "end": 96.41, "word": " أخذ", "probability": 0.6493326822916666}, {"start": 96.41, "end": 97.17, "word": " القلعوم", "probability": 0.380340576171875}, {"start": 97.17, "end": 97.73, "word": " F", "probability": 0.51904296875}, {"start": 97.73, "end": 98.09, "word": " of", "probability": 0.203369140625}, {"start": 98.09, "end": 98.41, "word": " X", "probability": 0.97509765625}, {"start": 98.41, "end": 99.53, "word": " موجودة", "probability": 0.932861328125}, {"start": 99.53, "end": 99.81, "word": " في", "probability": 0.95458984375}, {"start": 99.81, "end": 100.39, "word": " Z", "probability": 0.59228515625}, {"start": 100.39, "end": 100.69, "word": " of", "probability": 0.91748046875}, {"start": 100.69, "end": 100.99, "word": " X", "probability": 0.98828125}, {"start": 100.99, "end": 101.15, "word": " يعني", "probability": 0.7685546875}, {"start": 101.15, "end": 101.99, "word": " المعاملات", "probability": 0.97998046875}, {"start": 101.99, "end": 102.73, "word": " كلها", "probability": 0.986083984375}], "temperature": 1.0}, {"id": 4, "seek": 12882, "start": 103.12, "end": 128.82, "text": "أعداد صحيحة تمام روحنا أخدنا فيه prime وشوفنا إيش هل ال F bar irreducible في ZP ولا لأ إذا كانت F bar irreducible في ZP وفي نفس الوقت كان ال degree لل F هي نفس ال degree لل F bar نستنتج", "tokens": [10721, 22488, 18513, 20328, 5016, 1829, 5016, 3660, 46811, 10943, 12602, 2407, 5016, 8315, 5551, 9778, 3215, 8315, 8978, 3224, 5835, 4032, 8592, 38688, 8315, 11933, 1829, 8592, 8032, 1211, 2423, 479, 2159, 16014, 769, 32128, 8978, 1176, 47, 49429, 5296, 10721, 11933, 15730, 25961, 2655, 479, 2159, 16014, 769, 32128, 8978, 1176, 47, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 25961, 2423, 4314, 24976, 479, 39896, 8717, 36178, 2423, 4314, 24976, 479, 2159, 8717, 14851, 29399, 7435], "avg_logprob": -0.23397943528392648, "compression_ratio": 1.6023391812865497, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 103.12, "end": 104.06, "word": "أعداد", "probability": 0.691650390625}, {"start": 104.06, "end": 104.92, "word": " صحيحة", "probability": 0.90166015625}, {"start": 104.92, "end": 105.68, "word": " تمام", "probability": 0.78515625}, {"start": 105.68, "end": 106.72, "word": " روحنا", "probability": 0.8017578125}, {"start": 106.72, "end": 107.3, "word": " أخدنا", "probability": 0.7774658203125}, {"start": 107.3, "end": 107.76, "word": " فيه", "probability": 0.5948486328125}, {"start": 107.76, "end": 108.38, "word": " prime", "probability": 0.56103515625}, {"start": 108.38, "end": 110.16, "word": " وشوفنا", "probability": 0.921875}, {"start": 110.16, "end": 110.6, "word": " إيش", "probability": 0.5789388020833334}, {"start": 110.6, "end": 111.34, "word": " هل", "probability": 0.89794921875}, {"start": 111.34, "end": 111.56, "word": " ال", "probability": 0.9404296875}, {"start": 111.56, "end": 112.06, "word": " F", "probability": 0.60986328125}, {"start": 112.06, "end": 112.86, "word": " bar", "probability": 0.7744140625}, {"start": 112.86, "end": 115.56, "word": " irreducible", "probability": 0.69830322265625}, {"start": 115.56, "end": 115.96, "word": " في", "probability": 0.97607421875}, {"start": 115.96, "end": 116.5, "word": " ZP", "probability": 0.77001953125}, {"start": 116.5, "end": 116.76, "word": " ولا", "probability": 0.71630859375}, {"start": 116.76, "end": 117.08, "word": " لأ", "probability": 0.90673828125}, {"start": 117.08, "end": 117.4, "word": " إذا", "probability": 0.8203125}, {"start": 117.4, "end": 117.86, "word": " كانت", "probability": 0.938720703125}, {"start": 117.86, "end": 118.14, "word": " F", "probability": 0.908203125}, {"start": 118.14, "end": 118.56, "word": " bar", "probability": 0.8876953125}, {"start": 118.56, "end": 119.94, "word": " irreducible", "probability": 0.9755859375}, {"start": 119.94, "end": 120.26, "word": " في", "probability": 0.9765625}, {"start": 120.26, "end": 121.52, "word": " ZP", "probability": 0.977294921875}, {"start": 121.52, "end": 122.42, "word": " وفي", "probability": 0.92236328125}, {"start": 122.42, "end": 122.78, "word": " نفس", "probability": 0.99853515625}, {"start": 122.78, "end": 123.38, "word": " الوقت", "probability": 0.9788411458333334}, {"start": 123.38, "end": 123.92, "word": " كان", "probability": 0.97412109375}, {"start": 123.92, "end": 124.14, "word": " ال", "probability": 0.69677734375}, {"start": 124.14, "end": 124.56, "word": " degree", "probability": 0.9970703125}, {"start": 124.56, "end": 124.88, "word": " لل", "probability": 0.76708984375}, {"start": 124.88, "end": 125.3, "word": " F", "probability": 0.935546875}, {"start": 125.3, "end": 125.54, "word": " هي", "probability": 0.131591796875}, {"start": 125.54, "end": 125.86, "word": " نفس", "probability": 0.99755859375}, {"start": 125.86, "end": 126.08, "word": " ال", "probability": 0.90478515625}, {"start": 126.08, "end": 126.38, "word": " degree", "probability": 0.99462890625}, {"start": 126.38, "end": 126.68, "word": " لل", "probability": 0.93701171875}, {"start": 126.68, "end": 127.06, "word": " F", "probability": 0.96337890625}, {"start": 127.06, "end": 127.44, "word": " bar", "probability": 0.87451171875}, {"start": 127.44, "end": 128.82, "word": " نستنتج", "probability": 0.85223388671875}], "temperature": 1.0}, {"id": 5, "seek": 15772, "start": 129.02, "end": 157.72, "text": "إن ال F of X الأصلية is irreducible على مين على ست of rational numbers اللي هي مين اللي هي D cubed هذا كان نص النظرية لما نعطي مثال كمان على نفس النظرية هذه كتارة يبقى example three example three show that", "tokens": [28814, 1863, 2423, 479, 295, 1783, 16247, 9381, 1211, 10632, 307, 16014, 769, 32128, 15844, 3714, 9957, 15844, 8608, 2655, 295, 15090, 3547, 13672, 1829, 39896, 3714, 9957, 13672, 1829, 39896, 413, 36510, 23758, 25961, 8717, 9381, 28239, 19913, 2288, 10632, 5296, 15042, 8717, 3615, 9566, 1829, 50113, 6027, 9122, 2304, 7649, 15844, 8717, 36178, 28239, 19913, 2288, 10632, 29538, 9122, 2655, 9640, 3660, 7251, 3555, 4587, 7578, 1365, 1045, 1365, 1045, 855, 300], "avg_logprob": -0.3316666674613953, "compression_ratio": 1.5549738219895288, "no_speech_prob": 0.0, "words": [{"start": 129.02, "end": 129.34, "word": "إن", "probability": 0.642578125}, {"start": 129.34, "end": 129.54, "word": " ال", "probability": 0.72998046875}, {"start": 129.54, "end": 129.9, "word": " F", "probability": 0.466064453125}, {"start": 129.9, "end": 130.26, "word": " of", "probability": 0.68798828125}, {"start": 130.26, "end": 130.62, "word": " X", "probability": 0.974609375}, {"start": 130.62, "end": 131.36, "word": " الأصلية", "probability": 0.71893310546875}, {"start": 131.36, "end": 131.68, "word": " is", "probability": 0.77490234375}, {"start": 131.68, "end": 132.66, "word": " irreducible", "probability": 0.92919921875}, {"start": 132.66, "end": 133.06, "word": " على", "probability": 0.90869140625}, {"start": 133.06, "end": 133.38, "word": " مين", "probability": 0.493499755859375}, {"start": 133.38, "end": 133.98, "word": " على", "probability": 0.60400390625}, {"start": 133.98, "end": 134.36, "word": " ست", "probability": 0.75146484375}, {"start": 134.36, "end": 134.52, "word": " of", "probability": 0.1287841796875}, {"start": 134.52, "end": 134.9, "word": " rational", "probability": 0.919921875}, {"start": 134.9, "end": 135.7, "word": " numbers", "probability": 0.449951171875}, {"start": 135.7, "end": 136.2, "word": " اللي", "probability": 0.711669921875}, {"start": 136.2, "end": 136.4, "word": " هي", "probability": 0.9423828125}, {"start": 136.4, "end": 136.8, "word": " مين", "probability": 0.6634521484375}, {"start": 136.8, "end": 137.22, "word": " اللي", "probability": 0.791015625}, {"start": 137.22, "end": 137.64, "word": " هي", "probability": 0.96142578125}, {"start": 137.64, "end": 138.08, "word": " D", "probability": 0.102783203125}, {"start": 138.08, "end": 138.48, "word": " cubed", "probability": 0.34814453125}, {"start": 138.48, "end": 139.04, "word": " هذا", "probability": 0.6865234375}, {"start": 139.04, "end": 139.36, "word": " كان", "probability": 0.97607421875}, {"start": 139.36, "end": 139.64, "word": " نص", "probability": 0.724609375}, {"start": 139.64, "end": 140.28, "word": " النظرية", "probability": 0.9483642578125}, {"start": 140.28, "end": 140.96, "word": " لما", "probability": 0.77490234375}, {"start": 140.96, "end": 141.78, "word": " نعطي", "probability": 0.8765869140625}, {"start": 141.78, "end": 142.56, "word": " مثال", "probability": 0.936279296875}, {"start": 142.56, "end": 143.48, "word": " كمان", "probability": 0.8719075520833334}, {"start": 143.48, "end": 143.84, "word": " على", "probability": 0.93994140625}, {"start": 143.84, "end": 144.36, "word": " نفس", "probability": 0.996337890625}, {"start": 144.36, "end": 145.1, "word": " النظرية", "probability": 0.9776611328125}, {"start": 145.1, "end": 145.58, "word": " هذه", "probability": 0.68212890625}, {"start": 145.58, "end": 146.88, "word": " كتارة", "probability": 0.736328125}, {"start": 146.88, "end": 147.5, "word": " يبقى", "probability": 0.9322509765625}, {"start": 147.5, "end": 148.08, "word": " example", "probability": 0.4794921875}, {"start": 148.08, "end": 148.86, "word": " three", "probability": 0.1865234375}, {"start": 148.86, "end": 150.92, "word": " example", "probability": 0.75927734375}, {"start": 150.92, "end": 153.42, "word": " three", "probability": 0.9140625}, {"start": 153.42, "end": 157.16, "word": " show", "probability": 0.87109375}, {"start": 157.16, "end": 157.72, "word": " that", "probability": 0.9423828125}], "temperature": 1.0}, {"id": 6, "seek": 18559, "start": 159.03, "end": 185.59, "text": "show that بينونا ان ال F of X التي تساعد X5 زيدي 2X زيدي الأربعة is irreducible irreducible over اللي هو ال Q", "tokens": [34436, 300, 4724, 1829, 1863, 2407, 8315, 16472, 2423, 479, 295, 1783, 38392, 6055, 3794, 995, 22488, 1783, 20, 30767, 1829, 16254, 568, 55, 30767, 1829, 16254, 16247, 25513, 27884, 307, 16014, 769, 32128, 16014, 769, 32128, 670, 13672, 1829, 31439, 2423, 1249], "avg_logprob": -0.44282670454545453, "compression_ratio": 1.208, "no_speech_prob": 0.0, "words": [{"start": 159.03, "end": 159.71, "word": "show", "probability": 0.2734375}, {"start": 159.71, "end": 161.17, "word": " that", "probability": 0.82080078125}, {"start": 161.17, "end": 163.25, "word": " بينونا", "probability": 0.59169921875}, {"start": 163.25, "end": 164.15, "word": " ان", "probability": 0.59130859375}, {"start": 164.15, "end": 164.53, "word": " ال", "probability": 0.305419921875}, {"start": 164.53, "end": 164.99, "word": " F", "probability": 0.29736328125}, {"start": 164.99, "end": 165.59, "word": " of", "probability": 0.7255859375}, {"start": 165.59, "end": 166.17, "word": " X", "probability": 0.9501953125}, {"start": 166.17, "end": 167.15, "word": " التي", "probability": 0.87646484375}, {"start": 167.15, "end": 168.15, "word": " تساعد", "probability": 0.6466064453125}, {"start": 168.15, "end": 169.87, "word": " X5", "probability": 0.45220947265625}, {"start": 169.87, "end": 171.35, "word": " زيدي", "probability": 0.651611328125}, {"start": 171.35, "end": 172.47, "word": " 2X", "probability": 0.89453125}, {"start": 172.47, "end": 173.49, "word": " زيدي", "probability": 0.9345703125}, {"start": 173.49, "end": 174.49, "word": " الأربعة", "probability": 0.798828125}, {"start": 174.49, "end": 175.65, "word": " is", "probability": 0.80078125}, {"start": 175.65, "end": 178.81, "word": " irreducible", "probability": 0.8933919270833334}, {"start": 178.81, "end": 181.71, "word": " irreducible", "probability": 0.7855631510416666}, {"start": 181.71, "end": 183.03, "word": " over", "probability": 0.8486328125}, {"start": 183.03, "end": 184.57, "word": " اللي", "probability": 0.82666015625}, {"start": 184.57, "end": 184.99, "word": " هو", "probability": 0.97900390625}, {"start": 184.99, "end": 185.19, "word": " ال", "probability": 0.1927490234375}, {"start": 185.19, "end": 185.59, "word": " Q", "probability": 0.7578125}], "temperature": 1.0}, {"id": 7, "seek": 22953, "start": 200.81, "end": 229.53, "text": "الان لما نطلع على المعاملات بتاعة البرانوميل كلها أعداد صحيحة إذا هذه موجودة وين؟ في Z of X يبقى ال F of X موجودة في Z of X حيث نقطلوني بنروح أخد عدد Prime وشوف ال F bar في ZP", "tokens": [6027, 7649, 5296, 15042, 8717, 9566, 1211, 3615, 15844, 9673, 3615, 10943, 1211, 9307, 39894, 995, 27884, 2423, 26890, 7649, 20498, 26895, 28242, 11296, 5551, 22488, 18513, 20328, 5016, 1829, 5016, 3660, 11933, 15730, 29538, 3714, 29245, 23328, 3660, 4032, 9957, 22807, 8978, 1176, 295, 1783, 7251, 3555, 4587, 7578, 2423, 479, 295, 1783, 3714, 29245, 23328, 3660, 8978, 1176, 295, 1783, 11331, 1829, 12984, 8717, 47432, 1211, 11536, 1829, 44945, 32887, 5016, 5551, 9778, 3215, 6225, 3215, 3215, 9655, 4032, 8592, 38688, 2423, 479, 2159, 8978, 1176, 47], "avg_logprob": -0.27864584426085154, "compression_ratio": 1.5401069518716577, "no_speech_prob": 0.0, "words": [{"start": 200.81, "end": 201.39, "word": "الان", "probability": 0.80322265625}, {"start": 201.39, "end": 202.25, "word": " لما", "probability": 0.728271484375}, {"start": 202.25, "end": 202.79, "word": " نطلع", "probability": 0.6845703125}, {"start": 202.79, "end": 202.99, "word": " على", "probability": 0.499267578125}, {"start": 202.99, "end": 204.01, "word": " المعاملات", "probability": 0.94970703125}, {"start": 204.01, "end": 204.35, "word": " بتاعة", "probability": 0.8351236979166666}, {"start": 204.35, "end": 205.19, "word": " البرانوميل", "probability": 0.6837890625}, {"start": 205.19, "end": 205.73, "word": " كلها", "probability": 0.910888671875}, {"start": 205.73, "end": 206.23, "word": " أعداد", "probability": 0.8849283854166666}, {"start": 206.23, "end": 206.97, "word": " صحيحة", "probability": 0.9146484375}, {"start": 206.97, "end": 207.47, "word": " إذا", 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{"start": 317.09, "end": 317.43, "word": " أصفر", "probability": 0.66119384765625}, {"start": 317.43, "end": 317.85, "word": " فليه", "probability": 0.6825358072916666}, {"start": 317.85, "end": 318.37, "word": " بإتنين", "probability": 0.67021484375}, {"start": 318.37, "end": 318.51, "word": " و", "probability": 0.7880859375}, {"start": 318.51, "end": 319.35, "word": " تلاتين", "probability": 0.97314453125}, {"start": 319.35, "end": 320.37, "word": " شيل", "probability": 0.6640625}, {"start": 320.37, "end": 320.95, "word": " منهم", "probability": 0.80615234375}, {"start": 320.95, "end": 321.85, "word": " تلاتين", "probability": 0.94189453125}, {"start": 321.85, "end": 322.03, "word": " اللي", "probability": 0.85546875}, {"start": 322.03, "end": 322.25, "word": " هو", "probability": 0.86962890625}, {"start": 322.25, "end": 323.15, "word": " مضاعفات", "probability": 0.885546875}, {"start": 323.15, "end": 323.63, "word": " التلاتة", "probability": 0.951904296875}, {"start": 323.63, "end": 323.83, "word": " بيبقى", "probability": 0.7470703125}, {"start": 323.83, "end": 324.07, "word": " لنا", "probability": 0.76953125}, {"start": 324.07, "end": 324.71, "word": " جداش", "probability": 0.8050130208333334}, {"start": 324.71, "end": 325.71, "word": " اتنين", "probability": 0.801513671875}, {"start": 325.71, "end": 326.61, "word": " اتنين", "probability": 0.80584716796875}, {"start": 326.61, "end": 326.73, "word": " في", "probability": 0.5791015625}, {"start": 326.73, "end": 327.83, "word": " اتنين", "probability": 0.9459228515625}, {"start": 327.83, "end": 328.75, "word": " باربع", "probability": 0.6588134765625}, {"start": 328.75, "end": 329.01, "word": " و", "probability": 0.83935546875}, {"start": 329.01, "end": 329.61, "word": " اتنين", "probability": 0.95068359375}, {"start": 329.61, "end": 330.73, "word": " ستة", "probability": 0.8966471354166666}, {"start": 330.73, "end": 331.35, "word": " مضاعفات", "probability": 0.9517578125}, {"start": 331.35, "end": 331.93, "word": " التلاتة", "probability": 0.98291015625}, {"start": 331.93, "end": 332.29, "word": " شيلهم", "probability": 0.7552083333333334}, {"start": 332.29, "end": 332.57, "word": " بيبقى", "probability": 0.89599609375}, {"start": 332.57, "end": 332.71, "word": " لنا", "probability": 0.73876953125}, {"start": 332.71, "end": 333.23, "word": " جداش", "probability": 0.9827473958333334}, {"start": 333.23, "end": 333.87, "word": " بقى", "probability": 0.433349609375}, {"start": 333.87, "end": 334.63, "word": " الواحد", "probability": 0.9210611979166666}, {"start": 334.63, "end": 335.53, "word": " بقعد", "probability": 0.41656494140625}, {"start": 335.53, "end": 336.17, "word": " الكلام", "probability": 0.96044921875}, {"start": 336.17, "end": 336.55, "word": " بدي", "probability": 0.70166015625}, {"start": 336.55, "end": 336.93, "word": " أساوي", "probability": 0.584716796875}, {"start": 336.93, "end": 337.41, "word": " واحد", "probability": 0.939697265625}, {"start": 337.41, "end": 338.27, "word": " معناه", "probability": 0.8650716145833334}, {"start": 338.27, "end": 338.71, "word": " هذا", "probability": 0.91943359375}, {"start": 338.71, "end": 339.45, "word": " الكلام", "probability": 0.9847005208333334}, {"start": 339.45, "end": 339.95, "word": " ان", "probability": 0.398193359375}, {"start": 339.95, "end": 340.27, "word": " ال", "probability": 0.93994140625}, {"start": 340.27, "end": 340.69, "word": " F", "probability": 0.6455078125}, {"start": 340.69, "end": 341.57, "word": " bar", "probability": 0.479248046875}, {"start": 341.57, "end": 342.37, "word": " has", "probability": 0.87451171875}, {"start": 342.37, "end": 343.23, "word": " no", "probability": 0.93505859375}, {"start": 343.23, "end": 345.13, "word": " zeros", "probability": 0.93994140625}], "temperature": 1.0}, {"id": 12, "seek": 37452, "start": 346.22, "end": 374.52, "text": "نزد تلاتة كويس؟ No zeros يعني في factor of linear degree أو of degree one مش إمكانية لأنه لو كان هناك zero بقول X ناقص هذا الرقم هو أحد ال factors لهذه ال polynomial يبقى ال F bar has no zeros in Z تلاتة يبقى باجي بقوله ال F bar", "tokens": [1863, 11622, 3215, 6055, 1211, 9307, 3660, 9122, 45865, 3794, 22807, 883, 35193, 37495, 22653, 8978, 5952, 295, 8213, 4314, 34051, 295, 4314, 472, 37893, 11933, 2304, 41361, 10632, 5296, 33456, 3224, 45164, 25961, 34105, 4117, 4018, 4724, 39648, 1783, 8717, 995, 4587, 9381, 23758, 34892, 4587, 2304, 31439, 5551, 24401, 2423, 6771, 46740, 24192, 2423, 26110, 7251, 3555, 4587, 7578, 2423, 479, 2159, 575, 572, 35193, 294, 1176, 6055, 1211, 9307, 3660, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 2423, 479, 2159], "avg_logprob": -0.31555316777064885, "compression_ratio": 1.4954128440366972, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 346.21999999999997, "end": 347.2, "word": "نزد", "probability": 0.3339742024739583}, {"start": 347.2, "end": 347.88, "word": " تلاتة", "probability": 0.8785400390625}, {"start": 347.88, "end": 350.4, "word": " كويس؟", 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363.28, "end": 363.52, "word": " هو", "probability": 0.8623046875}, {"start": 363.52, "end": 364.08, "word": " أحد", "probability": 0.9052734375}, {"start": 364.08, "end": 364.68, "word": " ال", "probability": 0.92138671875}, {"start": 364.68, "end": 365.28, "word": " factors", "probability": 0.974609375}, {"start": 365.28, "end": 365.84, "word": " لهذه", "probability": 0.870849609375}, {"start": 365.84, "end": 366.04, "word": " ال", "probability": 0.888671875}, {"start": 366.04, "end": 366.6, "word": " polynomial", "probability": 0.62939453125}, {"start": 366.6, "end": 367.76, "word": " يبقى", "probability": 0.942138671875}, {"start": 367.76, "end": 367.92, "word": " ال", "probability": 0.8251953125}, {"start": 367.92, "end": 368.22, "word": " F", "probability": 0.6943359375}, {"start": 368.22, "end": 368.54, "word": " bar", "probability": 0.67041015625}, {"start": 368.54, "end": 368.92, "word": " has", "probability": 0.8212890625}, {"start": 368.92, "end": 369.3, "word": " no", "probability": 0.9248046875}, {"start": 369.3, "end": 369.8, "word": " zeros", "probability": 0.8876953125}, {"start": 369.8, "end": 370.24, "word": " in", "probability": 0.4423828125}, {"start": 370.24, "end": 370.56, "word": " Z", "probability": 0.65966796875}, {"start": 370.56, "end": 371.46, "word": " تلاتة", "probability": 0.8992919921875}, {"start": 371.46, "end": 372.36, "word": " يبقى", "probability": 0.974609375}, {"start": 372.36, "end": 372.82, "word": " باجي", "probability": 0.8307291666666666}, {"start": 372.82, "end": 373.42, "word": " بقوله", "probability": 0.79833984375}, {"start": 373.42, "end": 373.6, "word": " ال", "probability": 0.810546875}, {"start": 373.6, "end": 374.0, "word": " F", "probability": 0.96337890625}, {"start": 374.0, "end": 374.52, "word": " bar", "probability": 0.90087890625}], "temperature": 1.0}, {"id": 13, "seek": 40700, "start": 380.32, "end": 407.0, "text": "no linear factor او no factor of first degree طب اذا مافيش فيه factor of first degree فيه factor of fourth degree لأ لأنه بدنا نضرب ال first في ال fourth بطلع اكسوس خمسة", "tokens": [1771, 8213, 5952, 1975, 2407, 572, 5952, 295, 700, 4314, 23032, 3555, 1975, 15730, 19446, 41185, 8592, 8978, 3224, 5952, 295, 700, 4314, 8978, 3224, 5952, 295, 6409, 4314, 5296, 10721, 5296, 33456, 3224, 47525, 8315, 8717, 11242, 25513, 2423, 700, 8978, 2423, 6409, 4724, 9566, 1211, 3615, 1975, 4117, 3794, 41779, 16490, 2304, 3794, 3660], "avg_logprob": -0.33552632415503786, "compression_ratio": 1.5492957746478873, "no_speech_prob": 0.0, "words": [{"start": 380.31999999999994, "end": 381.35999999999996, "word": "no", "probability": 0.1116943359375}, {"start": 381.35999999999996, "end": 382.4, "word": " linear", "probability": 0.223388671875}, {"start": 382.4, "end": 383.12, "word": " factor", "probability": 0.849609375}, {"start": 383.12, "end": 383.58, "word": " او", "probability": 0.5963134765625}, {"start": 383.58, "end": 383.86, "word": " no", "probability": 0.6083984375}, {"start": 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فيه", "probability": 0.6549072265625}, {"start": 399.3, "end": 399.82, "word": " factor", "probability": 0.9140625}, {"start": 399.82, "end": 400.12, "word": " of", "probability": 0.97607421875}, {"start": 400.12, "end": 400.62, "word": " fourth", "probability": 0.87890625}, {"start": 400.62, "end": 401.14, "word": " degree", "probability": 0.990234375}, {"start": 401.14, "end": 401.84, "word": " لأ", "probability": 0.5792236328125}, {"start": 401.84, "end": 403.8, "word": " لأنه", "probability": 0.6736653645833334}, {"start": 403.8, "end": 404.08, "word": " بدنا", "probability": 0.6068115234375}, {"start": 404.08, "end": 404.46, "word": " نضرب", "probability": 0.9918619791666666}, {"start": 404.46, "end": 404.64, "word": " ال", "probability": 0.78173828125}, {"start": 404.64, "end": 404.96, "word": " first", "probability": 0.724609375}, {"start": 404.96, "end": 405.16, "word": " في", "probability": 0.70751953125}, {"start": 405.16, "end": 405.28, "word": " ال", "probability": 0.8203125}, {"start": 405.28, "end": 405.54, "word": " fourth", "probability": 0.9375}, {"start": 405.54, "end": 405.96, "word": " بطلع", "probability": 0.806396484375}, {"start": 405.96, "end": 406.32, "word": " اكسوس", "probability": 0.64727783203125}, {"start": 406.32, "end": 407.0, "word": " خمسة", "probability": 0.92041015625}], "temperature": 1.0}, {"id": 14, "seek": 43342, "start": 407.12, "end": 433.42, "text": "يبقى كمان مستبعد تبقى من ال degree رقم 4 يبقى هذا بيدهي يعطينا ان ال F با of X has no factor of degree 4 يبقى ايش ليلتنا؟ يا اتنين يا تلاتين", "tokens": [1829, 3555, 4587, 7578, 9122, 2304, 7649, 3714, 14851, 3555, 22488, 6055, 3555, 4587, 7578, 9154, 2423, 4314, 12602, 4587, 2304, 1017, 7251, 3555, 4587, 7578, 23758, 4724, 25708, 3224, 1829, 37495, 9566, 1829, 8315, 16472, 2423, 479, 4724, 995, 295, 1783, 575, 572, 5952, 295, 4314, 1017, 7251, 3555, 4587, 7578, 1975, 1829, 8592, 5296, 26895, 2655, 8315, 22807, 35186, 1975, 2655, 1863, 9957, 35186, 6055, 1211, 9307, 9957], "avg_logprob": -0.3230633702076657, "compression_ratio": 1.472972972972973, "no_speech_prob": 0.0, "words": [{"start": 407.12, "end": 407.54, "word": "يبقى", "probability": 0.9173583984375}, {"start": 407.54, "end": 408.06, "word": " كمان", "probability": 0.9326171875}, {"start": 408.06, "end": 408.94, "word": " مستبعد", "probability": 0.9171142578125}, {"start": 408.94, "end": 409.66, "word": " تبقى", "probability": 0.8505859375}, {"start": 409.66, "end": 410.02, "word": " من", "probability": 0.830078125}, {"start": 410.02, "end": 410.52, "word": " ال", "probability": 0.387939453125}, {"start": 410.52, "end": 411.38, "word": " degree", "probability": 0.96435546875}, {"start": 411.38, "end": 412.0, "word": " رقم", "probability": 0.94677734375}, {"start": 412.0, "end": 412.44, "word": " 4", "probability": 0.370849609375}, {"start": 412.44, "end": 413.58, "word": " يبقى", "probability": 0.946044921875}, {"start": 413.58, "end": 414.0, "word": " هذا", "probability": 0.9609375}, {"start": 414.0, "end": 414.54, "word": " بيدهي", "probability": 0.517181396484375}, {"start": 414.54, "end": 415.3, "word": " يعطينا", "probability": 0.939208984375}, {"start": 415.3, "end": 416.14, "word": " ان", "probability": 0.6572265625}, {"start": 416.14, "end": 416.52, "word": " ال", "probability": 0.84130859375}, {"start": 416.52, "end": 416.92, "word": " F", "probability": 0.697265625}, {"start": 416.92, "end": 417.72, "word": " با", "probability": 0.23736572265625}, {"start": 417.72, "end": 418.52, "word": " of", "probability": 0.91796875}, {"start": 418.52, "end": 419.06, "word": " X", "probability": 0.88330078125}, {"start": 419.06, "end": 420.08, "word": " has", "probability": 0.759765625}, {"start": 420.08, "end": 421.16, "word": " no", "probability": 0.90625}, {"start": 421.16, "end": 422.94, "word": " factor", "probability": 0.82470703125}, {"start": 422.94, "end": 424.66, "word": " of", "probability": 0.9619140625}, {"start": 424.66, "end": 426.48, "word": " degree", 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1236.91, "end": 1237.55, "word": " تقسم", "probability": 0.9920247395833334}, {"start": 1237.55, "end": 1237.85, "word": " ال", "probability": 0.80419921875}, {"start": 1237.85, "end": 1238.49, "word": " AN", "probability": 0.93359375}, {"start": 1238.49, "end": 1239.95, "word": " ولكن", "probability": 0.7205810546875}, {"start": 1239.95, "end": 1240.29, "word": " ال", "probability": 0.58349609375}, {"start": 1240.29, "end": 1240.71, "word": " P", "probability": 0.97314453125}, {"start": 1240.71, "end": 1241.55, "word": " تقسم", "probability": 0.9777018229166666}, {"start": 1241.55, "end": 1241.89, "word": " ال", "probability": 0.89013671875}, {"start": 1241.89, "end": 1242.53, "word": " AN", "probability": 0.9462890625}, {"start": 1242.53, "end": 1243.77, "word": "-1", "probability": 0.4410400390625}, {"start": 1243.77, "end": 1245.35, "word": " وP", "probability": 0.4654541015625}, {"start": 1245.35, "end": 1246.61, "word": " تقسم", "probability": 0.9772135416666666}, {"start": 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then ال P لا تقسم ال C نوت تقسموه و ال P بتقسم ال B نوت ايه يعني", "tokens": [36622, 541, 300, 1975, 5172, 2655, 43042, 14407, 16472, 2423, 430, 39894, 4587, 38251, 2423, 363, 8717, 35473, 550, 2423, 430, 20193, 6055, 4587, 38251, 2423, 383, 8717, 35473, 6055, 4587, 38251, 2407, 3224, 4032, 2423, 430, 39894, 4587, 38251, 2423, 363, 8717, 35473, 1975, 1829, 3224, 37495, 22653], "avg_logprob": -0.2978125113248825, "compression_ratio": 1.6470588235294117, "no_speech_prob": 0.0, "words": [{"start": 1691.6, "end": 1692.54, "word": "suppose", "probability": 0.757568359375}, {"start": 1692.54, "end": 1693.36, "word": " that", "probability": 0.5654296875}, {"start": 1693.36, "end": 1695.98, "word": " افترضوا", "probability": 0.92861328125}, {"start": 1695.98, "end": 1696.88, "word": " ان", "probability": 0.880859375}, {"start": 1696.88, "end": 1698.22, "word": " ال", "probability": 0.77099609375}, {"start": 1698.22, "end": 1698.68, "word": " P", "probability": 0.68359375}, {"start": 1698.68, 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"probability": 0.8321940104166666}, {"start": 2266.71, "end": 2267.43, "word": " BT", "probability": 0.34912109375}, {"start": 2267.43, "end": 2269.41, "word": "-1", "probability": 0.8896484375}, {"start": 2269.41, "end": 2270.49, "word": " C1", "probability": 0.783447265625}, {"start": 2270.49, "end": 2274.13, "word": " طبعا؟", "probability": 0.720361328125}, {"start": 2274.13, "end": 2275.29, "word": " طيب،", "probability": 0.850830078125}, {"start": 2275.29, "end": 2275.97, "word": " الآن", "probability": 0.72119140625}, {"start": 2275.97, "end": 2276.49, "word": " P", "probability": 0.50146484375}, {"start": 2276.49, "end": 2277.27, "word": " بتقسم", "probability": 0.9337565104166666}, {"start": 2277.27, "end": 2277.67, "word": " الـ", "probability": 0.523681640625}, {"start": 2277.67, "end": 2278.19, "word": " AT", "probability": 0.45751953125}, {"start": 2278.19, "end": 2279.73, "word": " وP", "probability": 0.5906982421875}, {"start": 2279.73, "end": 2280.51, "word": " بتقسم", "probability": 0.9822591145833334}, {"start": 2280.51, "end": 2281.23, "word": " هدول", "probability": 0.9142252604166666}, {"start": 2281.23, "end": 2282.65, "word": " إذا", "probability": 0.6142578125}, {"start": 2282.65, "end": 2283.13, "word": " الفيب", "probability": 0.6708170572916666}, {"start": 2283.13, "end": 2283.53, "word": " تقسم", "probability": 0.9241536458333334}, {"start": 2283.53, "end": 2284.05, "word": " الفرق", "probability": 0.9899088541666666}, {"start": 2284.05, "end": 2284.69, "word": " بينهما", "probability": 0.8826497395833334}, {"start": 2284.69, "end": 2285.01, "word": " ولا", "probability": 0.8984375}, {"start": 2285.01, "end": 2285.41, "word": " لا", "probability": 0.7939453125}], "temperature": 1.0}, {"id": 78, "seek": 231288, "start": 2286.32, "end": 2312.88, "text": "يبقى هنا ساعة ال P بتقسم ال AT minus B not CT B not CT زائد B1 CT minus ال 1 زائد زائد BT minus ال 1 C1 بالشكل اللي عندها", "tokens": [1829, 3555, 4587, 7578, 34105, 8608, 995, 27884, 2423, 430, 39894, 4587, 38251, 2423, 8872, 3175, 363, 406, 19529, 363, 406, 19529, 30767, 16373, 3215, 363, 16, 19529, 3175, 2423, 502, 30767, 16373, 3215, 30767, 16373, 3215, 31144, 3175, 2423, 502, 383, 16, 20666, 8592, 28820, 13672, 1829, 43242, 11296], "avg_logprob": -0.3007046440068413, "compression_ratio": 1.3983739837398375, "no_speech_prob": 0.0, "words": [{"start": 2286.32, "end": 2287.34, "word": "يبقى", "probability": 0.8468017578125}, {"start": 2287.34, "end": 2287.84, "word": " هنا", "probability": 0.96484375}, {"start": 2287.84, "end": 2288.98, "word": " ساعة", "probability": 0.6381429036458334}, {"start": 2288.98, "end": 2289.52, "word": " ال", "probability": 0.67578125}, {"start": 2289.52, "end": 2290.08, "word": " P", "probability": 0.60205078125}, {"start": 2290.08, "end": 2291.76, "word": " بتقسم", "probability": 0.7086588541666666}, {"start": 2291.76, "end": 2292.58, "word": " ال", "probability": 0.92138671875}, {"start": 2292.58, "end": 2293.54, "word": " AT", "probability": 0.40771484375}, {"start": 2293.54, "end": 2295.22, "word": " minus", "probability": 0.2078857421875}, {"start": 2295.22, "end": 2296.4, "word": " B", "probability": 0.55810546875}, {"start": 2296.4, "end": 2297.06, "word": " not", "probability": 0.336181640625}, {"start": 2297.06, "end": 2298.36, "word": " CT", "probability": 0.955078125}, {"start": 2298.36, "end": 2299.5, "word": " B", "probability": 0.376220703125}, {"start": 2299.5, "end": 2299.98, "word": " not", "probability": 0.9169921875}, {"start": 2299.98, "end": 2300.76, "word": " CT", "probability": 0.9853515625}, {"start": 2300.76, "end": 2301.88, "word": " زائد", "probability": 0.7662760416666666}, {"start": 2301.88, "end": 2302.66, "word": " B1", "probability": 0.805419921875}, {"start": 2302.66, "end": 2303.78, "word": " CT", "probability": 0.92431640625}, {"start": 2303.78, "end": 2304.48, "word": " minus", "probability": 0.892578125}, {"start": 2304.48, "end": 2304.84, "word": " ال", "probability": 0.7890625}, {"start": 2304.84, "end": 2305.12, "word": " 1", "probability": 0.39111328125}, {"start": 2305.12, "end": 2306.96, "word": " زائد", "probability": 0.9593098958333334}, {"start": 2306.96, "end": 2307.8, "word": " زائد", "probability": 0.8712565104166666}, {"start": 2307.8, "end": 2308.58, "word": " BT", "probability": 0.68701171875}, {"start": 2308.58, "end": 2309.7, "word": " minus", "probability": 0.97998046875}, {"start": 2309.7, "end": 2310.04, "word": " ال", "probability": 0.97509765625}, {"start": 2310.04, "end": 2310.42, "word": " 1", "probability": 0.7880859375}, {"start": 2310.42, "end": 2311.62, "word": " C1", "probability": 0.876708984375}, {"start": 2311.62, "end": 2312.24, "word": " بالشكل", "probability": 0.96044921875}, {"start": 2312.24, "end": 2312.44, "word": " اللي", "probability": 0.898193359375}, {"start": 2312.44, "end": 2312.88, "word": " عندها", "probability": 0.734619140625}], "temperature": 1.0}, {"id": 79, "seek": 234339, "start": 2314.03, "end": 2343.39, "text": "إذاً ال P بتقسم و لل AT هي فوق بدي أشيلها و أحط القيم تبعتها يبقى BTC0 زائد BT-1C1 زائد زائد B1CT زائد CT-1 زائد B0CT", "tokens": [28814, 15730, 14111, 2423, 430, 39894, 4587, 38251, 4032, 24976, 8872, 39896, 6156, 30543, 4724, 16254, 5551, 8592, 26895, 11296, 4032, 5551, 5016, 9566, 25062, 32640, 6055, 3555, 34268, 11296, 7251, 3555, 4587, 7578, 363, 18238, 15, 30767, 16373, 3215, 31144, 12, 16, 34, 16, 30767, 16373, 3215, 30767, 16373, 3215, 363, 16, 10259, 30767, 16373, 3215, 19529, 12, 16, 30767, 16373, 3215, 363, 15, 10259], "avg_logprob": -0.3283582187410611, "compression_ratio": 1.4375, "no_speech_prob": 0.0, "words": [{"start": 2314.03, "end": 2314.63, "word": "إذاً", "probability": 0.5823567708333334}, {"start": 2314.63, "end": 2314.93, "word": " ال", "probability": 0.751953125}, {"start": 2314.93, "end": 2315.27, "word": " P", "probability": 0.5625}, {"start": 2315.27, "end": 2316.37, "word": " بتقسم", "probability": 0.7001953125}, {"start": 2316.37, "end": 2317.01, "word": " و", "probability": 0.7470703125}, {"start": 2317.01, "end": 2317.39, "word": " لل", "probability": 0.1414794921875}, {"start": 2317.39, "end": 2318.07, "word": " AT", "probability": 0.447998046875}, {"start": 2318.07, "end": 2318.41, "word": " هي", "probability": 0.88916015625}, {"start": 2318.41, "end": 2319.23, "word": " فوق", "probability": 0.893310546875}, {"start": 2319.23, "end": 2320.21, "word": " بدي", "probability": 0.2725830078125}, {"start": 2320.21, "end": 2320.71, "word": " أشيلها", "probability": 0.72930908203125}, {"start": 2320.71, "end": 2320.83, "word": " و", "probability": 0.80029296875}, {"start": 2320.83, "end": 2321.23, "word": " أحط", "probability": 0.8543294270833334}, {"start": 2321.23, "end": 2321.75, "word": " القيم", "probability": 0.6734619140625}, {"start": 2321.75, "end": 2322.73, "word": " تبعتها", "probability": 0.776611328125}, {"start": 2322.73, "end": 2323.75, "word": " يبقى", "probability": 0.909912109375}, {"start": 2323.75, "end": 2326.37, "word": " BTC0", "probability": 0.431640625}, {"start": 2326.37, "end": 2327.59, "word": " زائد", "probability": 0.593963623046875}, {"start": 2327.59, "end": 2328.51, "word": " BT", "probability": 0.658203125}, {"start": 2328.51, "end": 2330.71, "word": "-1C1", "probability": 0.725372314453125}, {"start": 2330.71, "end": 2331.91, "word": " زائد", "probability": 0.8859049479166666}, {"start": 2331.91, "end": 2332.83, "word": " زائد", "probability": 0.8955078125}, {"start": 2332.83, "end": 2335.45, "word": " B1CT", "probability": 0.880859375}, {"start": 2335.45, "end": 2336.97, "word": " زائد", "probability": 0.8790690104166666}, {"start": 2336.97, "end": 2338.31, "word": " CT", "probability": 0.9404296875}, {"start": 2338.31, "end": 2339.43, "word": "-1", "probability": 0.87451171875}, {"start": 2339.43, "end": 2340.65, "word": " زائد", "probability": 0.9444986979166666}, {"start": 2340.65, "end": 2343.39, "word": " B0CT", "probability": 0.8338216145833334}], "temperature": 1.0}, {"id": 80, "seek": 237238, "start": 2344.26, "end": 2372.38, "text": "ناقص إذا انت خلّي على كل واحدة من هدول يبقى ناقص B non CT ناقص B one CT minus ال one ناقص ناقص B T minus ال one C one طب أطلع هذه موجبة وهذه سالمة مع السلامة", "tokens": [1863, 995, 4587, 9381, 11933, 15730, 16472, 2655, 16490, 1211, 11703, 1829, 15844, 28242, 36764, 24401, 3660, 9154, 8032, 3215, 12610, 7251, 3555, 4587, 7578, 8717, 995, 4587, 9381, 363, 2107, 19529, 8717, 995, 4587, 9381, 363, 472, 19529, 3175, 2423, 472, 8717, 995, 4587, 9381, 8717, 995, 4587, 9381, 363, 314, 3175, 2423, 472, 383, 472, 23032, 3555, 5551, 9566, 1211, 3615, 29538, 3714, 29245, 49401, 37037, 24192, 8608, 45340, 3660, 20449, 21136, 37440, 3660], "avg_logprob": -0.2749594109398978, "compression_ratio": 1.5677419354838709, "no_speech_prob": 0.0, "words": [{"start": 2344.26, "end": 2345.06, "word": "ناقص", "probability": 0.73956298828125}, {"start": 2345.06, "end": 2345.32, "word": " إذا", "probability": 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0.64306640625}, {"start": 2352.22, "end": 2353.72, "word": " ناقص", "probability": 0.9625244140625}, {"start": 2353.72, "end": 2354.2, "word": " B", "probability": 0.953125}, {"start": 2354.2, "end": 2354.86, "word": " one", "probability": 0.4453125}, {"start": 2354.86, "end": 2356.06, "word": " CT", "probability": 0.94287109375}, {"start": 2356.06, "end": 2357.42, "word": " minus", "probability": 0.69482421875}, {"start": 2357.42, "end": 2357.9, "word": " ال", "probability": 0.7265625}, {"start": 2357.9, "end": 2358.24, "word": " one", "probability": 0.85302734375}, {"start": 2358.24, "end": 2359.48, "word": " ناقص", "probability": 0.98828125}, {"start": 2359.48, "end": 2360.46, "word": " ناقص", "probability": 0.9456787109375}, {"start": 2360.46, "end": 2361.42, "word": " B", "probability": 0.6298828125}, {"start": 2361.42, "end": 2362.14, "word": " T", "probability": 0.74072265625}, {"start": 2362.14, "end": 2362.86, "word": " minus", "probability": 0.9853515625}, {"start": 2362.86, "end": 2363.22, "word": " ال", "probability": 0.85107421875}, {"start": 2363.22, "end": 2363.74, "word": " one", "probability": 0.94921875}, {"start": 2363.74, "end": 2364.3, "word": " C", "probability": 0.9501953125}, {"start": 2364.3, "end": 2365.24, "word": " one", "probability": 0.9580078125}, {"start": 2365.24, "end": 2367.6, "word": " طب", "probability": 0.913330078125}, {"start": 2367.6, "end": 2368.2, "word": " أطلع", "probability": 0.7313232421875}, {"start": 2368.2, "end": 2369.04, "word": " هذه", "probability": 0.6064453125}, {"start": 2369.04, "end": 2369.54, "word": " موجبة", "probability": 0.756591796875}, {"start": 2369.54, "end": 2369.92, "word": " وهذه", "probability": 0.8515625}, {"start": 2369.92, "end": 2371.34, "word": " سالمة", "probability": 0.64892578125}, {"start": 2371.34, "end": 2371.6, "word": " مع", "probability": 0.89013671875}, {"start": 2371.6, "end": 2372.38, "word": " السلامة", "probability": 0.96435546875}], "temperature": 1.0}, {"id": 81, "seek": 240281, "start": 2373.05, "end": 2402.81, "text": "و هذه موجبة و هذه سالبة غير ما نصوف عليها و نظل ماشيين هذه موجبة و هذه سالبة إذا لن يلقى إلا من إلا ترم الأول يبقى بصيرها إن في تقسم ال BTC نقطة يبقى فيه تقسم و أخد منها صح؟ يبقى هذا معناه إن فيه", "tokens": [2407, 29538, 3714, 29245, 49401, 4032, 29538, 8608, 6027, 49401, 32771, 13546, 19446, 8717, 9381, 38688, 25894, 11296, 4032, 8717, 19913, 1211, 3714, 33599, 1829, 9957, 29538, 3714, 29245, 49401, 4032, 29538, 8608, 6027, 49401, 11933, 15730, 5296, 1863, 7251, 1211, 4587, 7578, 11933, 15040, 9154, 11933, 15040, 6055, 2288, 2304, 16247, 12610, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 11296, 36145, 8978, 6055, 4587, 38251, 2423, 363, 18238, 8717, 47432, 3660, 7251, 3555, 4587, 7578, 8978, 3224, 6055, 4587, 38251, 4032, 5551, 9778, 3215, 9154, 11296, 20328, 5016, 22807, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 36145, 8978, 3224], "avg_logprob": -0.26378676908857684, "compression_ratio": 1.9213483146067416, "no_speech_prob": 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السي نوت يبقى ال بي هتقسم ال بي تي لإن هذا بده يعطينا ان ال بي بتقسم ال بي تي because السبب لإن ال بي", "tokens": [3555, 2655, 4587, 38251, 2423, 4724, 1829, 6055, 1829, 420, 2423, 4724, 1829, 39894, 4587, 38251, 21136, 1829, 8717, 35473, 6156, 39319, 8315, 11331, 41193, 9957, 16472, 2423, 4724, 1829, 3714, 27842, 45367, 6055, 4587, 38251, 21136, 1829, 8717, 35473, 7251, 3555, 4587, 7578, 2423, 4724, 1829, 8032, 2655, 4587, 38251, 2423, 4724, 1829, 6055, 1829, 5296, 28814, 1863, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 2423, 4724, 1829, 39894, 4587, 38251, 2423, 4724, 1829, 6055, 1829, 570, 21136, 3555, 3555, 5296, 28814, 1863, 2423, 4724, 1829], "avg_logprob": -0.2940659978416529, "compression_ratio": 2.145985401459854, "no_speech_prob": 0.0, "words": [{"start": 2402.95, "end": 2403.89, "word": "بتقسم", "probability": 0.70989990234375}, {"start": 2403.89, "end": 2404.27, "word": " ال", "probability": 0.92333984375}, {"start": 2404.27, "end": 2404.69, "word": " بي", 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خمسة A وB وC وD الرقم C هيحله قدامك عندهم بس هناك محطش واحد حطه Ux زائد C", "tokens": [49628, 3555, 5551, 8592, 13546, 30731, 19446, 7251, 4117, 2655, 3555, 2423, 28820, 10943, 13672, 1829, 9122, 2655, 3555, 47395, 34105, 31439, 11331, 1211, 8608, 33604, 6027, 16490, 2304, 3794, 3660, 43242, 4117, 8978, 33251, 2655, 16758, 12602, 4587, 2304, 383, 16490, 2304, 3794, 3660, 316, 4032, 33, 4032, 34, 4032, 35, 34892, 4587, 2304, 383, 39896, 5016, 1211, 3224, 12174, 3215, 10943, 4117, 43242, 16095, 4724, 3794, 34105, 4117, 3714, 5016, 9566, 8592, 36764, 24401, 11331, 9566, 3224, 624, 87, 30767, 16373, 3215, 383], "avg_logprob": -0.1590661366665086, "compression_ratio": 1.5688622754491017, "no_speech_prob": 0.0, "words": [{"start": 3402.45, "end": 3403.05, "word": "بحب", "probability": 0.56884765625}, {"start": 3403.05, "end": 3403.97, "word": " أشير", "probability": 0.9134114583333334}, {"start": 3403.97, "end": 3404.37, "word": " إلى", "probability": 0.87109375}, {"start": 3404.37, "end": 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"word": " الكتاب", "probability": 0.9759114583333334}, {"start": 3411.73, "end": 3412.39, "word": " رقم", "probability": 0.9812825520833334}, {"start": 3412.39, "end": 3412.91, "word": " C", "probability": 0.80615234375}, {"start": 3412.91, "end": 3414.67, "word": " خمسة", "probability": 0.9346923828125}, {"start": 3414.67, "end": 3415.05, "word": " A", "probability": 0.736328125}, {"start": 3415.05, "end": 3415.67, "word": " وB", "probability": 0.759521484375}, {"start": 3415.67, "end": 3416.33, "word": " وC", "probability": 0.879638671875}, {"start": 3416.33, "end": 3416.81, "word": " وD", "probability": 0.957763671875}, {"start": 3416.81, "end": 3417.81, "word": " الرقم", "probability": 0.8971354166666666}, {"start": 3417.81, "end": 3418.13, "word": " C", "probability": 0.9658203125}, {"start": 3418.13, "end": 3418.79, "word": " هيحله", "probability": 0.8382568359375}, {"start": 3418.79, "end": 3419.29, "word": " قدامك", "probability": 0.9749755859375}, {"start": 3419.29, "end": 3420.09, "word": " عندهم", "probability": 0.7373046875}, {"start": 3420.09, "end": 3420.59, "word": " بس", "probability": 0.84716796875}, {"start": 3420.59, "end": 3421.11, "word": " هناك", "probability": 0.87451171875}, {"start": 3421.11, "end": 3421.89, "word": " محطش", "probability": 0.842529296875}, {"start": 3421.89, "end": 3422.63, "word": " واحد", "probability": 0.985107421875}, {"start": 3422.63, "end": 3424.33, "word": " حطه", "probability": 0.69189453125}, {"start": 3424.33, "end": 3424.95, "word": " Ux", "probability": 0.3212890625}, {"start": 3424.95, "end": 3426.03, "word": " زائد", "probability": 0.9222005208333334}, {"start": 3426.03, "end": 3426.37, "word": " C", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 116, "seek": 345600, "start": 3427.06, "end": 3456.0, "text": "يبقى مكان الـC احنا حاطينه واحد الحل هيو قدامك علّه احتباط سواء خمسة C هو هو لم يتغير بال contradiction نمرأيه بال contradiction نمرأيه بال contradiction نمرأي الـC بال contradiction كذلك كلهم التلاتة بال contradiction ونفس التكتيك اللي تبقى هو نفسه إلى هنا انتهت هذه المحاضرة ونكمل ان شاء الله", "tokens": [1829, 3555, 4587, 7578, 3714, 41361, 2423, 39184, 34, 1975, 5016, 8315, 11331, 41193, 9957, 3224, 36764, 24401, 21542, 1211, 39896, 2407, 12174, 3215, 10943, 4117, 11203, 11703, 3224, 1975, 33753, 3555, 41193, 8608, 2407, 16606, 16490, 2304, 3794, 3660, 383, 31439, 31439, 32767, 7251, 2655, 17082, 13546, 20666, 34937, 8717, 29973, 10721, 1829, 3224, 20666, 34937, 8717, 29973, 10721, 1829, 3224, 20666, 34937, 8717, 29973, 10721, 1829, 2423, 39184, 34, 20666, 34937, 9122, 8848, 23275, 28242, 16095, 16712, 1211, 9307, 3660, 20666, 34937, 4032, 1863, 36178, 16712, 4117, 31371, 4117, 13672, 1829, 6055, 3555, 4587, 7578, 31439, 8717, 36178, 3224, 30731, 34105, 16472, 47395, 2655, 29538, 9673, 5016, 46958, 25720, 4032, 1863, 24793, 1211, 16472, 13412, 16606, 21984], "avg_logprob": -0.21250000211099784, "compression_ratio": 1.9957627118644068, "no_speech_prob": 0.0, "words": [{"start": 3427.06, "end": 3427.38, "word": "يبقى", "probability": 0.6607666015625}, {"start": 3427.38, "end": 3427.74, "word": " مكان", "probability": 0.910888671875}, {"start": 3427.74, "end": 3428.0, "word": " الـC", "probability": 0.6259765625}, {"start": 3428.0, "end": 3428.22, "word": " احنا", "probability": 0.7874348958333334}, {"start": 3428.22, "end": 3428.76, "word": " حاطينه", "probability": 0.7174072265625}, {"start": 3428.76, "end": 3429.04, "word": " واحد", "probability": 0.992431640625}, {"start": 3429.04, "end": 3429.86, "word": " الحل", "probability": 0.775146484375}, {"start": 3429.86, "end": 3430.16, "word": " هيو", "probability": 0.681396484375}, {"start": 3430.16, "end": 3430.66, "word": " قدامك", "probability": 0.8392333984375}, {"start": 3430.66, "end": 3430.92, "word": " علّه", "probability": 0.4752604166666667}, {"start": 3430.92, "end": 3431.36, "word": " احتباط", "probability": 0.664306640625}, {"start": 3431.36, "end": 3431.72, "word": " سواء", "probability": 0.7571614583333334}, {"start": 3431.72, "end": 3432.32, "word": " خمسة", "probability": 0.8258056640625}, {"start": 3432.32, "end": 3432.56, "word": " C", "probability": 0.63671875}, {"start": 3432.56, "end": 3433.24, "word": " هو", "probability": 0.9140625}, {"start": 3433.24, "end": 3433.82, "word": " هو", "probability": 0.94677734375}, {"start": 3433.82, "end": 3434.54, "word": " لم", "probability": 0.9033203125}, {"start": 3434.54, "end": 3435.46, "word": " يتغير", "probability": 0.9951171875}, {"start": 3435.46, "end": 3436.04, "word": " بال", "probability": 0.95166015625}, {"start": 3436.04, "end": 3436.94, "word": " contradiction", "probability": 0.5771484375}, {"start": 3436.94, "end": 3438.44, "word": " نمرأيه", "probability": 0.643359375}, {"start": 3438.44, "end": 3438.6, "word": " بال", "probability": 0.96923828125}, {"start": 3438.6, "end": 3439.26, "word": " contradiction", "probability": 0.75048828125}, {"start": 3439.26, "end": 3439.96, "word": " نمرأيه", "probability": 0.8044921875}, {"start": 3439.96, "end": 3440.12, "word": " بال", "probability": 0.90673828125}, {"start": 3440.12, "end": 3440.84, "word": " contradiction", "probability": 0.9228515625}, {"start": 3440.84, "end": 3441.68, "word": " نمرأي", "probability": 0.892578125}, {"start": 3441.68, "end": 3441.88, "word": " الـC", "probability": 0.9033203125}, {"start": 3441.88, "end": 3442.2, "word": " بال", "probability": 0.94287109375}, {"start": 3442.2, "end": 3443.02, "word": " contradiction", "probability": 0.6708984375}, {"start": 3443.02, "end": 3443.8, "word": " كذلك", "probability": 0.9454752604166666}, {"start": 3443.8, "end": 3444.66, "word": " كلهم", "probability": 0.95703125}, {"start": 3444.66, "end": 3445.32, "word": " التلاتة", "probability": 0.9486083984375}, {"start": 3445.32, "end": 3445.52, "word": " بال", "probability": 0.974609375}, {"start": 3445.52, "end": 3446.28, "word": " contradiction", "probability": 0.7861328125}, {"start": 3446.28, "end": 3447.46, "word": " ونفس", "probability": 0.8805338541666666}, {"start": 3447.46, "end": 3448.52, "word": " التكتيك", "probability": 0.7611083984375}, {"start": 3448.52, "end": 3449.1, "word": " اللي", "probability": 0.919921875}, {"start": 3449.1, "end": 3449.7, "word": " تبقى", "probability": 0.8984375}, {"start": 3449.7, "end": 3450.12, "word": " هو", "probability": 0.97607421875}, {"start": 3450.12, "end": 3450.7, "word": " نفسه", "probability": 0.9947916666666666}, {"start": 3450.7, "end": 3451.54, "word": " إلى", "probability": 0.76953125}, {"start": 3451.54, "end": 3451.9, "word": " هنا", "probability": 0.98193359375}, {"start": 3451.9, "end": 3452.48, "word": " انتهت", "probability": 0.9142252604166666}, {"start": 3452.48, "end": 3452.8, "word": " هذه", "probability": 0.98828125}, {"start": 3452.8, "end": 3453.68, "word": " المحاضرة", "probability": 0.9837646484375}, {"start": 3453.68, "end": 3454.86, "word": " ونكمل", "probability": 0.9765625}, {"start": 3454.86, "end": 3455.22, "word": " ان", "probability": 0.71240234375}, {"start": 3455.22, "end": 3455.66, "word": " شاء", "probability": 0.98193359375}, {"start": 3455.66, "end": 3456.0, "word": " الله", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 117, "seek": 345902, "start": 3456.66, "end": 3459.02, "text": "المحاضرة القادمة", "tokens": [45340, 5016, 46958, 25720, 25062, 18513, 46007], "avg_logprob": -0.044403077103197575, "compression_ratio": 0.8611111111111112, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3456.66, "end": 3457.78, "word": "المحاضرة", "probability": 0.9398193359375}, {"start": 3457.78, "end": 3459.02, "word": " القادمة", "probability": 0.9944661458333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3459.099875, "duration_after_vad": 3258.1206249999864}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e0061cb39a7baebce02df48859a9590d0e054547
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qdIYyS1flw_raw.srt
@@ -0,0 +1,1820 @@
+1
+00:00:20,860 --> 00:00:26,560
+بسم الله الرحمن الرحيم احنا المرة اللي فاتت لم
+
+2
+00:00:26,560 --> 00:00:32,840
+نصور المحاضرة الماضية وذلك بسبب سوء الأحوال
+
+3
+00:00:32,840 --> 00:00:39,500
+الأرضية من قطع كهربا أو غيره فانعتدر للطلب الذين
+
+4
+00:00:39,500 --> 00:00:46,600
+يشاهدوننا على مستوى العالم وانتم منهم فتم يطأ
+
+5
+00:00:46,600 --> 00:00:51,220
+المحاضرة بدون تصويراليوم احنا بنكمل على المحاضرة،
+
+6
+00:00:51,220 --> 00:00:56,800
+المحاضرة لم نعطيها إلا نظرية واحدة وهي ال RDOS
+
+7
+00:00:56,800 --> 00:01:01,160
+Quality Test، تمام؟ وما بدني أظهر ليهم الذاكرين
+
+8
+00:01:01,160 --> 00:01:06,980
+هولا لأ، لإن بتعطي كمان إدارة عالية، تمام؟ ال ..
+
+9
+00:01:06,980 --> 00:01:12,200
+حد من ذاكره ما هو نقص النظرية؟ برهناه هنا اللي
+
+10
+00:01:12,200 --> 00:01:20,150
+واحنا ايوة؟أنا بقى أحكي بلدي مش مشكلة إذا
+
+11
+00:01:20,150 --> 00:01:34,570
+كان النفس
+
+12
+00:01:34,570 --> 00:01:41,150
+كالثالث أخذ القلعوم F of X موجودة في Z of X يعني
+
+13
+00:01:41,150 --> 00:01:47,760
+المعاملات كلهاأعداد صحيحة تمام روحنا أخدنا فيه
+
+14
+00:01:47,760 --> 00:01:56,760
+prime وشوفنا إيش هل ال F bar irreducible في ZP ولا
+
+15
+00:01:56,760 --> 00:02:03,380
+لأ إذا كانت F bar irreducible في ZP وفي نفس الوقت
+
+16
+00:02:03,380 --> 00:02:07,440
+كان ال degree لل F هي نفس ال degree لل F bar
+
+17
+00:02:07,440 --> 00:02:13,380
+نستنتجإن ال F of X الأصلية is irreducible على مين
+
+18
+00:02:13,380 --> 00:02:18,080
+على ست of rational numbers اللي هي مين اللي هي D
+
+19
+00:02:18,080 --> 00:02:23,840
+cubed هذا كان نص النظرية لما نعطي مثال كمان على
+
+20
+00:02:23,840 --> 00:02:30,920
+نفس النظرية هذه كتارة يبقى example three example
+
+21
+00:02:30,920 --> 00:02:37,160
+three show
+
+22
+00:02:37,160 --> 00:02:49,870
+thatshow that بينونا ان ال F of X التي تساعد X5
+
+23
+00:02:49,870 --> 00:02:58,810
+زيدي 2X زيدي الأربعة is irreducible
+
+24
+00:02:58,810 --> 00:03:05,590
+irreducible over اللي هو ال Q
+
+25
+00:03:20,810 --> 00:03:25,730
+الان لما نطلع على المعاملات بتاعة البرانوميل كلها
+
+26
+00:03:25,730 --> 00:03:32,590
+أعداد صحيحة إذا هذه موجودة وين؟ في Z of X يبقى ال
+
+27
+00:03:32,590 --> 00:03:43,910
+F of X موجودة في Z of X حيث نقطلوني بنروح أخد عدد
+
+28
+00:03:43,910 --> 00:03:54,480
+Prime وشوف ال F bar في ZPيبقى let في مثلا تساوي
+
+29
+00:03:54,480 --> 00:04:03,020
+تلاتة then بدي ال f bar ال f bar of x بدي أحسبها
+
+30
+00:04:03,020 --> 00:04:10,500
+في z تلاتة يبقى x plus خمسة كما هي 2x كما هي
+
+31
+00:04:10,500 --> 00:04:15,600
+الأربعة في z تلاتة عبارة عن إيش؟ عن واحد هذه
+
+32
+00:04:15,600 --> 00:04:23,070
+موجودة في zبelongs to z تلاتة of x يبقى دي belongs
+
+33
+00:04:23,070 --> 00:04:32,710
+في z تلاتة of x تمام الان بدي اشوف هل هذه بقدر
+
+34
+00:04:32,710 --> 00:04:39,750
+احللها الى عوامل والله بقدرش وين في z بيه تعالوا
+
+35
+00:04:39,750 --> 00:04:48,540
+نشوف نشوف ال F bar of zeroلنشتغل ولا بلات احنا في
+
+36
+00:04:48,540 --> 00:04:53,180
+Z تلاتة بدنا نشتغل ال Z تلاتة فيها تلاتة ناصر Zero
+
+37
+00:04:53,180 --> 00:04:59,220
+واحد و اتنين بتاع لو أخدت ال F bar of Zero يبقى ال
+
+38
+00:04:59,220 --> 00:05:06,960
+Zero Zero بضل قداش واحد بدنا ال F bar of واحد واحد
+
+39
+00:05:06,960 --> 00:05:12,660
+واحد اتنين و اتنين اربعة في Z تلاتة بواحد صحيح
+
+40
+00:05:12,660 --> 00:05:18,510
+بدنا ال F bar of اتنينإثنين و أصفر فليه بإتنين و
+
+41
+00:05:18,510 --> 00:05:23,630
+تلاتين شيل منهم تلاتين اللي هو مضاعفات التلاتة
+
+42
+00:05:23,630 --> 00:05:29,610
+بيبقى لنا جداش اتنين اتنين في اتنين باربع و اتنين
+
+43
+00:05:29,610 --> 00:05:33,870
+ستة مضاعفات التلاتة شيلهم بيبقى لنا جداش بقى
+
+44
+00:05:33,870 --> 00:05:39,450
+الواحد بقعد الكلام بدي أساوي واحد معناه هذا الكلام
+
+45
+00:05:39,450 --> 00:05:51,440
+ان ال F bar has no zerosنزد تلاتة كويس؟ No zeros
+
+46
+00:05:51,440 --> 00:05:56,740
+يعني في factor of linear degree أو of degree one
+
+47
+00:05:56,740 --> 00:06:02,720
+مش إمكانية لأنه لو كان هناك zero بقول X ناقص هذا
+
+48
+00:06:02,720 --> 00:06:07,920
+الرقم هو أحد ال factors لهذه ال polynomial يبقى ال
+
+49
+00:06:07,920 --> 00:06:14,000
+F bar has no zeros in Z تلاتة يبقى باجي بقوله ال F
+
+50
+00:06:14,000 --> 00:06:14,520
+bar
+
+51
+00:06:20,320 --> 00:06:27,600
+no linear factor او no factor
+
+52
+00:06:27,600 --> 00:06:34,960
+of first degree طب
+
+53
+00:06:34,960 --> 00:06:40,120
+اذا مافيش فيه factor of first degree فيه factor of
+
+54
+00:06:40,120 --> 00:06:45,280
+fourth degree لأ لأنه بدنا نضرب ال first في ال
+
+55
+00:06:45,280 --> 00:06:50,520
+fourth بطلع اكسوس خمسةيبقى كمان مستبعد تبقى من ال
+
+56
+00:06:50,520 --> 00:06:59,060
+degree رقم 4 يبقى هذا بيدهي يعطينا ان ال F با of X
+
+57
+00:06:59,060 --> 00:07:12,040
+has no factor of degree 4 يبقى ايش ليلتنا؟ يا
+
+58
+00:07:12,040 --> 00:07:18,180
+اتنين يا تلاتينبدي افترض ان في عندي factor of
+
+59
+00:07:18,180 --> 00:07:25,600
+second degree وش هو الشي اللي بده يصير يبقى هنا ال
+
+60
+00:07:25,600 --> 00:07:36,920
+F bar of X may have ربما يكون فيها factor of
+
+61
+00:07:36,920 --> 00:07:42,160
+second degree
+
+62
+00:07:43,810 --> 00:07:53,350
+من الدرجة الثانية in the form مثلًا X تربية زي AX
+
+63
+00:07:53,350 --> 00:08:04,150
+زي B هك صح ولا أقول AX تربية زي B X زي C؟ معامل
+
+64
+00:08:04,150 --> 00:08:09,190
+واحد يبقى .. انسى الموضوع هنا بتكون المعامل واحد
+
+65
+00:08:09,190 --> 00:08:15,150
+يبقى X تربية زي AX زي B السؤال هوفي زد ثلاث كم
+
+66
+00:08:15,150 --> 00:08:25,510
+احتمال بيجيبلي يعني؟ نين، ثلاثة، خمسة، ستة، كداش؟
+
+67
+00:08:25,510 --> 00:08:30,390
+تسعة احتمالات. بدنا نشوف ما هي الاحتمالات التسعة.
+
+68
+00:08:31,250 --> 00:08:39,190
+يبقى هنا sum for this factor
+
+69
+00:08:46,180 --> 00:08:52,040
+nine nine possibilities
+
+70
+00:08:52,040 --> 00:08:59,320
+نشوف
+
+71
+00:08:59,320 --> 00:09:06,320
+منهم التسعة دول احتمال هذا يكون TX تربيع بس الشريف
+
+72
+00:09:06,320 --> 00:09:16,180
+واحتمال يكون X تربيع زائد Xو احتمال يكون x تربيع
+
+73
+00:09:16,180 --> 00:09:26,940
+زائد 2x واحتمال يكون x تربيع زائد 2 واحتمال يكون x
+
+74
+00:09:26,940 --> 00:09:36,040
+تربيع زائد 2x زائد 1 1 2 3 4 5 واحتمال يكون x
+
+75
+00:09:36,040 --> 00:09:45,180
+تربيع زائد x زائد 1 واحتمال يكونX تربيع زائد واحد
+
+76
+00:09:45,180 --> 00:09:53,820
+واحتمال يكون X تربيع زائد X زائد اتنين والاحتمال
+
+77
+00:09:53,820 --> 00:09:59,600
+الاخير X تربيع زائد اتنين X زائد اتنين شوفيلي اذا
+
+78
+00:09:59,600 --> 00:10:03,520
+بتلاقي احتمال عاشر قوليلي يا عزيزي معاكي من هنا
+
+79
+00:10:03,520 --> 00:10:09,140
+لنهاية الفصل مش اليوم راحتك احنا بشغل في Z3 ه
+
+80
+00:10:09,490 --> 00:10:12,490
+معاملة الـ Zero، واحد واثنين، مانتعداش اتنين
+
+81
+00:10:12,490 --> 00:10:17,370
+ومابنزلش على الـ Zero. تمام؟ طيب، هاي كل احتمالات
+
+82
+00:10:17,370 --> 00:10:22,910
+الممكنة. طب تمسك كل واحد فيهم. احنا ايش قولنا هناك
+
+83
+00:10:22,910 --> 00:10:28,630
+و هناك؟ الـ F bar has no factor of first degree.
+
+84
+00:10:29,430 --> 00:10:34,250
+يعني لا يمكن يكون عندي معامل من الدرجة الأولى
+
+85
+00:10:34,250 --> 00:10:41,350
+نهائيًا. طب تعالى شوف هذا إيش بتسويه.هذه x في x،
+
+86
+00:10:41,350 --> 00:10:46,670
+هل ليس حصل ضرب معاملين من الدرجة الأولى؟ طيب، هذا
+
+87
+00:10:46,670 --> 00:10:52,950
+احتمال يكون x في x زائد واحد، حصل ضرب عاملين من
+
+88
+00:10:52,950 --> 00:10:59,270
+الدرجة الأولى، هذا بدي يعطينا x في x زائد اتنين،
+
+89
+00:10:59,270 --> 00:11:04,210
+حصل ضرب عاملين من الدرجة الأولى، هذا بدي يعطينا
+
+90
+00:11:05,590 --> 00:11:12,650
+يتحلل و الله لا يتحلل فعالي نشوف X زائد واحد X
+
+91
+00:11:12,650 --> 00:11:21,310
+زائد اتنين معقول؟ X في X ب X تربية زائد X و زائد
+
+92
+00:11:21,310 --> 00:11:26,610
+اتنين X زائد تلاتة X زد ثلاثة Zero فتبقى واحد في
+
+93
+00:11:26,610 --> 00:11:34,230
+اتنين باتنين هاي هذا عادي جدا X زائد واحد X زائد
+
+94
+00:11:34,230 --> 00:11:41,410
+واحدهذا ما بدري قداشى أبصر قداشى حاصر ضرب فو سيم
+
+95
+00:11:41,410 --> 00:11:49,950
+يبقى هنا X وهنا X ايش رايك نقول زائد اتنين وهنا
+
+96
+00:11:49,950 --> 00:11:56,130
+زائد اتنين بمشي الحال كحال الجو هي X تربية زائد
+
+97
+00:11:56,130 --> 00:12:02,090
+اتنين X زائد اتنين X زائد اربعة اكشلي تلاتة بضل
+
+98
+00:12:02,090 --> 00:12:07,410
+زائد X هي اتنين في اتنينأربعة شيلتلات اه و نصلي ال
+
+99
+00:12:07,410 --> 00:12:13,490
+100 المين طب كل واحد من هدول بده يساوي Zero و احنا
+
+100
+00:12:13,490 --> 00:12:20,290
+قلنا هنا مفيش Zero's الأفبار مالهاش Zero's صح ولا
+
+101
+00:12:20,290 --> 00:12:26,110
+لا؟ بمعنى كل احتمال من هذه الاحتمال هذه لا موجودة
+
+102
+00:12:26,110 --> 00:12:30,990
+لاو لأن من فوق قلنا مالهاش Zero's طب هذه بتساوي
+
+103
+00:12:30,990 --> 00:12:37,550
+Zero اه بتساوي Zeroهذه بتساوي zero at x يساوي zero
+
+104
+00:12:37,550 --> 00:12:44,330
+هذه بتساوي zero at x يساوي zero و ال x يساوي اتنين
+
+105
+00:12:44,330 --> 00:12:52,130
+حط x ب اتنين واحد تلاتة يبقى هاي zero راحة طب نمسك
+
+106
+00:12:52,130 --> 00:12:59,430
+هذه كده تساوي zero عند x يساوي zero او ال x يساوي
+
+107
+00:12:59,430 --> 00:13:04,860
+واحدحط واحد بصيرها تلاتة زيرو وحط زيرو بصير زيرو
+
+108
+00:13:04,860 --> 00:13:12,280
+هنا هذه بدها تساوي زيرو ال X يساوي اتنين وال X
+
+109
+00:13:12,280 --> 00:13:17,460
+يساوي واحد اتنين بصير زيرو واحد بصير الجثة ده زيرو
+
+110
+00:13:17,460 --> 00:13:24,400
+هذا الكلام بده يساوي زيرو ال X يساوي اتنين فقط
+
+111
+00:13:24,400 --> 00:13:30,110
+لإنه حط اتنين وواحد تلاتة اتنين وواحد تلاتةهذه
+
+112
+00:13:30,110 --> 00:13:38,150
+كمان بدها تساوي zero at x يساوي واحد تمام؟ يبقى
+
+113
+00:13:38,150 --> 00:13:44,870
+هذا الكلام كله ايه مسكي؟ هذا كله possible ولا
+
+114
+00:13:44,870 --> 00:13:52,690
+impossible؟ impossible ليش؟ يعني لا يمكن ان تكون
+
+115
+00:13:52,690 --> 00:13:55,990
+المعادلة من الدرجة التانية او ال factor اللي من
+
+116
+00:13:55,990 --> 00:14:01,450
+الدرجة التانيةيكون على أي صيغة من هذه الصيغة الستة
+
+117
+00:14:01,450 --> 00:14:05,550
+لإنه كل واحدة من الصيغة الستة بتجيب له zero واحنا
+
+118
+00:14:05,550 --> 00:14:13,150
+قولنا مافيش zeros في Z3 تمام؟ يبقى هذا الكلام كله
+
+119
+00:14:13,150 --> 00:14:19,410
+impossible on
+
+120
+00:14:19,410 --> 00:14:21,070
+Z3
+
+121
+00:14:22,810 --> 00:14:28,810
+يعنيش؟ يعني ال F bar has no zeros هذا الكلام مش
+
+122
+00:14:28,810 --> 00:14:32,590
+ممكن يحصل، إيش يعني مش ممكن يحصل؟ يعني لا يمكن
+
+123
+00:14:32,590 --> 00:14:36,790
+للمعادلة من الضرورية التانية أن تكون على أي شكل من
+
+124
+00:14:36,790 --> 00:14:40,910
+الأشكال الستة لأنه أي شكل من الأشكال الستة بدي
+
+125
+00:14:40,910 --> 00:14:45,990
+يزيني zeros وهذا يناقض الشغل اللي حسبناها حساب
+
+126
+00:14:45,990 --> 00:14:51,190
+بدينا، مالجيناش ولا zeros لل F bar على مين؟ على Z3
+
+127
+00:14:51,590 --> 00:14:57,750
+يبقى هذا كله غير ممكن، شو ضايل عندنا؟ تلاتة، طب
+
+128
+00:14:57,750 --> 00:15:03,390
+بتاجنا التلاتة هدول، بدي أعمللهم division أو long
+
+129
+00:15:03,390 --> 00:15:08,670
+division، قسمة مطولة، بدي أجسم هذه على هذا، وهذه
+
+130
+00:15:08,670 --> 00:15:13,630
+على التانية، وهذه على التالتة، هل تتم القسمة بدون
+
+131
+00:15:13,630 --> 00:15:18,130
+باقي، والله بيكون فيه باقي، في التلات حالات فيه
+
+132
+00:15:18,130 --> 00:15:23,090
+باقي، أنا والله جسمتها بيدي،كنت بدى أجرب أتأكد
+
+133
+00:15:23,090 --> 00:15:28,770
+هالكلام صح ولا مش صح؟ لجيته كله فيه باقي، مدى فيه
+
+134
+00:15:28,770 --> 00:15:35,690
+باقي يبقى ولا factor من الدرجة الثانية ومن ثم من
+
+135
+00:15:35,690 --> 00:15:39,970
+الدرجة التالتة بيكون أحد عوامل للإفبار يبقى
+
+136
+00:15:39,970 --> 00:15:48,210
+الإفبار is a radius على 63، مظبوط؟ يبقى هنا بقى
+
+137
+00:15:49,960 --> 00:16:02,420
+long by long division بالقسمة
+
+138
+00:16:02,420 --> 00:16:13,040
+المطولة any one of ال X تربية زي 1 او ال X تربية
+
+139
+00:16:13,040 --> 00:16:24,050
+زي X او 2 او ال X تربية زي 2x زائد اتنين is a
+
+140
+00:16:24,050 --> 00:16:41,290
+factor of any of هؤلاء is not a factor of
+
+141
+00:16:41,290 --> 00:16:52,200
+f of x يسوى x أص خمسة زائد اتنين xزائد واحد معناته
+
+142
+00:16:52,200 --> 00:17:00,420
+ايش Irreducible كل التسعة استبعداهم يبقى هنا ف ال
+
+143
+00:17:00,420 --> 00:17:10,780
+F bar of X is Irreducible over
+
+144
+00:17:10,780 --> 00:17:23,680
+33 and وزيادة على ذلكال degree لل F هي نفس ال
+
+145
+00:17:23,680 --> 00:17:32,580
+degree لل F bar اللي تساوي خمسة تمام؟ لما اتحققت
+
+146
+00:17:32,580 --> 00:17:36,680
+شروط النظرية نظرية
+
+147
+00:17:36,680 --> 00:17:40,920
+الكتبناها المرة اللي فاتت و رهنناها مدام تحققت
+
+148
+00:17:40,920 --> 00:17:45,660
+شروط النظرية يعني معناته ال F of X الأصلي is
+
+149
+00:17:45,660 --> 00:17:54,120
+irreducibleعلى الـ Q بروحيله و بقوله Y D above
+
+150
+00:17:54,120 --> 00:18:05,580
+theorem بالنظرية أعلى ال F of X اللي تساوي X أُس
+
+151
+00:18:05,580 --> 00:18:16,940
+خمسة زي اتنين X زائد أربعة is irreducible of Rلكن
+
+152
+00:18:16,940 --> 00:18:25,080
+هو هو المفروض يروحلك في أسلة في التمريين بشكل هذا
+
+153
+00:18:25,080 --> 00:18:28,820
+يمكن تلاقي درجة الرابعة، يمكن خمسة، يمكن درجة
+
+154
+00:18:28,820 --> 00:18:34,060
+تالتة، برضه زيك، بتاخدليك P prime، اتنين، تلاتة،
+
+155
+00:18:34,060 --> 00:18:38,420
+خمسة، سبعة، حسب طبيعة المثلة، و تشوف هل إلها zeros
+
+156
+00:18:38,420 --> 00:18:43,520
+ولا لا، ماطلعش zeros، بحط الاحتمالات الممكنة و
+
+157
+00:18:43,520 --> 00:18:48,660
+بشتغلها، عنسينا نقول شغلها يا بناتيبقى by division
+
+158
+00:18:48,660 --> 00:18:54,680
+algorithm هذه كلها is not a factor of ذلك ضايل
+
+159
+00:18:54,680 --> 00:18:58,840
+علينا ايش؟ ضايل علينا ان احنا خدنا من الدرجة
+
+160
+00:18:58,840 --> 00:19:03,840
+الثانية برضه there is no factor of third degree
+
+161
+00:19:03,840 --> 00:19:08,600
+لإن التانية هي بتكملي التالتة حصل الدرجة بيعطينا
+
+162
+00:19:08,600 --> 00:19:17,010
+105 هذه لسينا تقول يا بنات بدنا نحو هىبدنا نحطها
+
+163
+00:19:17,010 --> 00:19:36,790
+هنا وهي also وكذلك there is no factor of degree 3
+
+164
+00:19:36,790 --> 00:19:40,670
+نيجي
+
+165
+00:19:40,670 --> 00:19:43,050
+للنظرية اللي عندنا فعلا
+
+166
+00:20:06,080 --> 00:20:15,140
+موجودة أين؟ في Z of X if there is a prime K F
+
+167
+00:20:15,140 --> 00:20:23,160
+there is a prime P
+
+168
+00:20:28,910 --> 00:20:40,290
+بحيث ان ال P لا تقسم ال AN P لا تقسم ال AN ولكن ال
+
+169
+00:20:40,290 --> 00:20:55,470
+P تقسم ال AN-1 وP تقسم ال AN وP تقسم ال ANالـP
+
+170
+00:20:55,470 --> 00:21:04,150
+تربية لا تقسم الـA نوت الـP تربية لا تقسم الـA
+
+171
+00:21:04,150 --> 00:21:15,510
+نوت، ثم الـF of X ثم الـF of X is irreducible
+
+172
+00:21:15,510 --> 00:21:20,550
+over الـQ
+
+173
+00:21:35,260 --> 00:21:41,920
+إذا احنا الآن بهذه النظرية جيبنا شغلة ثانية للحكم
+
+174
+00:21:41,920 --> 00:21:46,880
+على ال polynomial بأنها irreducible المرة اللي
+
+175
+00:21:46,880 --> 00:21:52,680
+فاتت حطينا الشروط و من خلالها أثبتنا ان ال F of X
+
+176
+00:21:52,680 --> 00:21:58,660
+is irreducible فكان عندي بدي ال F of X موجودة في Z
+
+177
+00:21:58,660 --> 00:22:05,890
+of X بدي أدور على prime P تماموالاقى ان ال F bar
+
+178
+00:22:05,890 --> 00:22:12,030
+of X هه is irreducible على Z بيه وضرية ال F كانت
+
+179
+00:22:12,030 --> 00:22:16,430
+ضرية ال F bar ان حدث ذلك تبقى ال F of X تبقى
+
+180
+00:22:16,430 --> 00:22:20,750
+irreducible على Q الآن جيبنا طريقة تانية طريقة
+
+181
+00:22:20,750 --> 00:22:26,650
+تانية تتلخص في النظرية التالية ال F of X هي موجودة
+
+182
+00:22:26,650 --> 00:22:31,930
+في Z of X نفس المعطيات اللى موجودة في النظرية
+
+183
+00:22:31,930 --> 00:22:38,700
+السادسةقال إذا قدرت ألاقي prime P مش for any if
+
+184
+00:22:38,700 --> 00:22:45,200
+various إذا قدرنا نوجد a prime P بحيث ال PS لا
+
+185
+00:22:45,200 --> 00:22:53,200
+يقسم المعامل تبع XM لكنه يقسم جميع المعاملات
+
+186
+00:22:53,200 --> 00:22:59,820
+الأخرى لل Polynomial وموجعه لا يقسم العامل الأخر
+
+187
+00:22:59,820 --> 00:23:05,390
+اللي هو كل من تبع ال Polynomialإن حدث ذلك يبقى ال
+
+188
+00:23:05,390 --> 00:23:10,390
+F of X تبقى irreducible كذلك على مين؟ على ال IQ
+
+189
+00:23:10,390 --> 00:23:16,950
+.ماشي برهنة المرة اللي فاتت؟ التناقض صح ولا لا؟ و
+
+190
+00:23:16,950 --> 00:23:21,530
+الشبتر هذا غالب البرهين كلها بال contradiction. و
+
+191
+00:23:21,530 --> 00:23:26,370
+هذه كمان بينان برهنها بال contradiction بالتلاعب.
+
+192
+00:23:26,770 --> 00:23:29,270
+يبقى ال proof التالي ما هو المطلوب
+
+193
+00:23:33,990 --> 00:23:38,290
+إن ال F of X is irreducible عليكم، بتروح أفترضها
+
+194
+00:23:38,290 --> 00:23:47,870
+reducible يا جمالي بيقول ال F of X موجودة في Z of
+
+195
+00:23:47,870 --> 00:23:59,570
+X and ال F of X is reducible over
+
+196
+00:23:59,570 --> 00:24:06,360
+ال Qطب انا انا خدنا اللغية في هذا الشام طب ال
+
+197
+00:24:06,360 --> 00:24:10,640
+reducibility على ال Q بصحبها على مين؟ على ال Z
+
+198
+00:24:10,640 --> 00:24:19,900
+يبقى هنا بقول هذا بده يعطينا ان ال F of X is
+
+199
+00:24:19,900 --> 00:24:32,540
+reducible over Z هذا من وين ال previous theorem
+
+200
+00:24:33,320 --> 00:24:40,640
+هذه نظرية سابعة تجمعنا هذا الكلام ان ال F of X
+
+201
+00:24:40,640 --> 00:24:48,140
+بقدر اكتبها على الشكل G of X في 100 ال H of X طب
+
+202
+00:24:48,140 --> 00:24:57,540
+ال G و ال H وين موجودة؟ ال Z of X وين حيث ال G of
+
+203
+00:24:57,540 --> 00:25:05,800
+X و ال H of Xموجودة في Z of X مش حاجات دايكو بس
+
+204
+00:25:05,800 --> 00:25:12,780
+هذول بدهم يكونوا of lower degree than مين لأن ال F
+
+205
+00:25:12,780 --> 00:25:24,490
+يبقى and ال degree لل G و ال degree لمين لل Hأكبر
+
+206
+00:25:24,490 --> 00:25:30,130
+من او تساوي الواحد وأقل من ال degree تبع تلفر هي
+
+207
+00:25:30,130 --> 00:25:36,930
+كده؟ N أعلى أس عندى موجود N يبقى هذه ال polynomial
+
+208
+00:25:36,930 --> 00:25:44,270
+من الضغط النولية تمام طبعى كويس يبقى أنا صار عندى
+
+209
+00:25:44,270 --> 00:25:50,270
+F of X هي حاصل ضرب two polynomialsخلّيني أضع لكل
+
+210
+00:25:50,270 --> 00:25:55,130
+واحدة منهم شكل ونشوف إيش اللي بده يصير معانا يبقى
+
+211
+00:25:55,130 --> 00:26:03,130
+لو جيت قلت هنا لأ ال G of X بده يساوي ال PR X أُس
+
+212
+00:26:03,130 --> 00:26:11,270
+R PR minus ال one X أُس R minus ال one زائد P one
+
+213
+00:26:11,270 --> 00:26:22,060
+X زائد ال P نوع and ال H of Xcs x to the power s
+
+214
+00:26:22,060 --> 00:26:30,040
+cs minus ال 1 x to the power s minus ال 1 زائد
+
+215
+00:26:30,040 --> 00:26:39,140
+زائد اللي هو c1x زائد c0 فاحنا
+
+216
+00:26:39,140 --> 00:26:46,480
+عندنا f of x يساوي حاصل ضربهماإذا الحد فيكم بيقدر
+
+217
+00:26:46,480 --> 00:26:52,440
+يعرفلي قداش حاصل الضرب أخر تيرم في حاصل الضرب إيش
+
+218
+00:26:52,440 --> 00:26:57,860
+بيكون؟ P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+219
+00:26:57,860 --> 00:27:02,620
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+220
+00:27:02,620 --> 00:27:03,240
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+221
+00:27:03,240 --> 00:27:03,240
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+222
+00:27:03,240 --> 00:27:03,240
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+223
+00:27:03,240 --> 00:27:09,780
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P
+
+224
+00:27:14,000 --> 00:27:19,900
+5 خواش في صمم الموضوع ال P بتقسم ايه ال P بتقسم ال
+
+225
+00:27:19,900 --> 00:27:24,520
+A نوت تبقى ال P هتقسم ال B نوت C نوت صحيح ولا لأ
+
+226
+00:27:24,520 --> 00:27:35,200
+ال P بتقسم ال A نوت ال A نوت هو B نوت C نوت هذا
+
+227
+00:27:35,200 --> 00:27:43,470
+imply ان ال P بتقسم ال B نوت C نوتيبقى ال P يابدها
+
+228
+00:27:43,470 --> 00:27:50,230
+تقسم الأول يابدها تقسم الثاني يبقى هذا بدي أعطيكوا
+
+229
+00:27:50,230 --> 00:27:57,790
+ان P يابدها تقسم ال P نوت او ال P يابدها تقسم ال C
+
+230
+00:27:57,790 --> 00:28:06,470
+نوت إذا لو أخدناها تقسم أحدهما لن تقسم الآخر
+
+231
+00:28:06,470 --> 00:28:18,680
+مظبوط؟ أيوة يبقى هناsuppose that افترضوا ان ال P
+
+232
+00:28:18,680 --> 00:28:31,620
+بتقسم ال B نوت then ال P لا تقسم ال C نوت تقسموه و
+
+233
+00:28:31,620 --> 00:28:38,140
+ال P بتقسم ال B نوت ايه
+
+234
+00:28:38,140 --> 00:28:48,230
+يعنيصارت ال P تقسم ال P نوت ولا تقسم ال C نوت لا
+
+235
+00:28:48,230 --> 00:28:55,090
+ممكن اضيف شغلة مما يعزز ان ال P لا تقسم ال C نوت
+
+236
+00:28:55,090 --> 00:29:01,130
+ان ال P تربية لا تقسم ال A نوت ال P تربية لا تقسم
+
+237
+00:29:01,130 --> 00:29:06,370
+ال A نوت يعني لابدها تقسم ال P نوت ولا تقسم ال C
+
+238
+00:29:06,370 --> 00:29:12,120
+نوتلكن لما كان ال P بتقسم ال B نوت بصير الاحتمال
+
+239
+00:29:12,120 --> 00:29:19,640
+الاقوى ان P تربيع لا تقسم ال C نوت او ال P لا تقسم
+
+240
+00:29:19,640 --> 00:29:25,660
+ال C نوت مش مشكلة مش مشكلة كتير طبعا اذا ال P لا
+
+241
+00:29:25,660 --> 00:29:30,900
+تقسم ال B نوت شو رايك احنا روحنا جيبنا اخر تير في
+
+242
+00:29:30,900 --> 00:29:36,640
+حاصل الضرب السؤال هو شو رايك في اول تير من حاصل
+
+243
+00:29:36,640 --> 00:29:48,370
+الضربإيش بيكون؟ A N بده يساوي مين؟ P R C S صحيح؟
+
+244
+00:29:48,370 --> 00:30:00,170
+يبقى هنا ورصة وكذلك ال A N بده يساوي P R في C S
+
+245
+00:30:00,170 --> 00:30:07,480
+طيب إيش مواطعيننا؟إن ال P لا تقسم ال AN إذا لن
+
+246
+00:30:07,480 --> 00:30:14,840
+تقسم هذه لأن لن تقسم حاصل الضرب هذا يبقى since بما
+
+247
+00:30:14,840 --> 00:30:27,880
+أن ال P لا تقسم ال AN we have إن ال P لا تقسم ال
+
+248
+00:30:27,880 --> 00:30:30,400
+PR في ال CS
+
+249
+00:30:35,140 --> 00:30:41,460
+مافيش تفسيرك لهذه الأجازة لا تقسم الأول ولا تقسم
+
+250
+00:30:41,460 --> 00:30:49,780
+التاني طيب هذا بده يعطينا ان ال P لا تقسم ال PR
+
+251
+00:30:49,780 --> 00:31:02,020
+and ال P لا تقسم ال CS اخو خديلي هذا ال
+
+252
+00:31:02,020 --> 00:31:11,350
+P لا تقسم ال PRطبعا إذا ال P ممكن تقسم اللي بعده
+
+253
+00:31:11,350 --> 00:31:16,350
+تبقى للكلام اللي احنا جايلينه هنا صحيح ولا لأ إذا
+
+254
+00:31:16,350 --> 00:31:22,230
+ال P ممكن تقسم اللي هو الكل القيم اللي بعده يعني
+
+255
+00:31:22,230 --> 00:31:26,410
+PR minus ال one PR minus ال two لغاية P one و
+
+256
+00:31:26,410 --> 00:31:33,250
+لغاية P none صحيح ولا لأ طيب ال PR هذا الرقم
+
+257
+00:31:35,280 --> 00:31:43,060
+مظبوط؟ رقم الرقم هذا يمكن اه يمكن بدينا نعد من
+
+258
+00:31:43,060 --> 00:31:49,100
+عنده ويمكن قبل ويمكن بعده لإنه حاصر الضرر تبع هذا
+
+259
+00:31:49,100 --> 00:31:57,200
+ال G و ال S هل عدد العلاصر التانوس اللي هنا جد عدد
+
+260
+00:31:57,200 --> 00:32:03,110
+علاصر التانوس اللي هنا؟ ماحدش جال هيكواللي لو كان
+
+261
+00:32:03,110 --> 00:32:06,630
+اكيد كان بدل ما قولنا R و S خلينا أقولها R و
+
+262
+00:32:06,630 --> 00:32:11,030
+خلاصنا أو أقولها S و خلاصنا يبقى يمكن المعادلة
+
+263
+00:32:11,030 --> 00:32:15,570
+الأولى أو ال polynomial يكون فيها عشرة عناصر
+
+264
+00:32:15,570 --> 00:32:20,390
+مجموعة التاني يكون فيها ستة صحيح ولا لأ؟ يبقى
+
+265
+00:32:20,390 --> 00:32:28,570
+بجاني أخد رقم بحيث من عنده يبدأ العدل اللي هو تكون
+
+266
+00:32:28,570 --> 00:32:36,280
+ال PR لا تساوي Zeroيبقى بالدالي أقول له let T be
+
+267
+00:32:36,280 --> 00:32:43,100
+the smallest positive
+
+268
+00:32:43,100 --> 00:32:47,500
+integer
+
+269
+00:32:47,500 --> 00:32:50,520
+such
+
+270
+00:32:50,520 --> 00:32:55,840
+that بحيث
+
+271
+00:32:55,840 --> 00:33:06,180
+أن ال P لا تقسمفي ال B T في
+
+272
+00:33:06,180 --> 00:33:11,900
+ال R أنا مش عارف ان هي 8 بقول تخوض T هو أصغر رقم
+
+273
+00:33:11,900 --> 00:33:20,040
+من عنده ال P لا تقسم مين في ال B T تمام يبقى بتقسم
+
+274
+00:33:20,040 --> 00:33:28,260
+مين اللي بقعده صحيح ولا لأ يبقى هذه ممتازة يبقى ال
+
+275
+00:33:28,260 --> 00:33:35,070
+P بدها تقسم اللي بعدهاطيب ال VET هذا مش بده يقابله
+
+276
+00:33:35,070 --> 00:33:42,090
+واحد اسمه CT واتنين بده يقابلهم في حاصر الضرب واحد
+
+277
+00:33:42,090 --> 00:33:48,490
+اسمه ET لأن ال ET نتجت من حاصر الضرب هذا، صحيح ولا
+
+278
+00:33:48,490 --> 00:33:52,450
+لأ؟ طيب الان خليني أعرف مين هي ET هذا
+
+279
+00:34:11,960 --> 00:34:20,340
+قبل ما رأيت خضرسة هو T هادي أكبر من N ولا أصغر؟
+
+280
+00:34:20,340 --> 00:34:27,040
+ممكن تسويها؟ لأ يبقى هو أصغر من N صحيح ولا لأ؟ طيب
+
+281
+00:34:27,040 --> 00:34:33,900
+الآن consider وديلي
+
+282
+00:34:33,900 --> 00:34:43,370
+AT مين هي AT؟ وحاصل ضاربمعاملات من جيه ومعاملة من
+
+283
+00:34:43,370 --> 00:34:48,750
+اتش وبنجمعهم بيعطيني هذا المعامل اللي هو مين لو
+
+284
+00:34:48,750 --> 00:34:56,150
+روحتي قولتلك بي تي سي نوت زائد بي تي ماينوس الوان
+
+285
+00:34:56,150 --> 00:35:04,530
+سي وان زائد زائد ال بي وان سي تي ماينوس الوان زائد
+
+286
+00:35:04,530 --> 00:35:12,490
+ال بي نوت سي تيطبعا أخدنا أول مبدئ ال polynomial
+
+287
+00:35:12,490 --> 00:35:18,090
+حاصل ضرب two polynomials وكيف بنجيب المعامل تبع كل
+
+288
+00:35:18,090 --> 00:35:24,010
+x os n x os n minus one x os n minus two يبقى هذا
+
+289
+00:35:24,010 --> 00:35:29,090
+الشكل ال 80 طيب
+
+290
+00:35:29,090 --> 00:35:40,480
+الآن نجي لغاية السؤال هو هلالـP تقسم الـAT تقسم
+
+291
+00:35:40,480 --> 00:35:43,360
+الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ
+
+292
+00:35:43,360 --> 00:35:44,980
+تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم
+
+293
+00:35:44,980 --> 00:35:45,780
+الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ
+
+294
+00:35:45,780 --> 00:35:48,640
+تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم
+
+295
+00:35:48,640 --> 00:35:49,180
+الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ
+
+296
+00:35:49,180 --> 00:35:50,460
+تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم
+
+297
+00:35:50,460 --> 00:35:59,440
+الـAT لأ تقسم الـAT لأ تقسم الـAT لأ تقسم الـAT لأ
+
+298
+00:35:59,440 --> 00:36:03,400
+تقسم الـAT لأ تقسم الـAT ل
+
+299
+00:36:08,130 --> 00:36:18,950
+الـP بتقسم من الـAT السبب لأن T أقل من N لكن لو
+
+300
+00:36:18,950 --> 00:36:25,070
+كانت تسوى N، هنسفش جسمها بالمرة، هي مايكونش جسمه
+
+301
+00:36:25,070 --> 00:36:30,170
+نصيف زي ما بيقولوا، يبقى هنا هتجسمهم كلهم، مافيش
+
+302
+00:36:30,170 --> 00:36:37,590
+فائزة، يبقى P بتقسم من الـAT السبب لأن T أقل من N
+
+303
+00:36:38,000 --> 00:36:46,180
+تمام؟ خيب كويس الان قلنا هنا ال P لا تقسم ال P
+
+304
+00:36:46,180 --> 00:36:56,980
+تقسمين اللي بعده يبقى هنا also وكذلك ال P لا تقسم
+
+305
+00:36:56,980 --> 00:37:04,760
+ال P تي but ال P تقسم او divides
+
+306
+00:37:08,970 --> 00:37:16,410
+قول بي تي ماينوس ال one و بي تي ماينوس ال two و بي
+
+307
+00:37:16,410 --> 00:37:25,150
+one و بي نوت هذا بده يعطيلي ان ال P divide بدها
+
+308
+00:37:25,150 --> 00:37:33,470
+تقسم ايه بدها تقسم مثلا ال بي نوت CT
+
+309
+00:37:37,550 --> 00:37:54,130
+الـ V1 CT-1 زائد انظل للآخر انظل BT-1 C1 طبعا؟
+
+310
+00:37:54,130 --> 00:38:03,130
+طيب، الآن P بتقسم الـ AT وP بتقسم هدول إذا الفيب
+
+311
+00:38:03,130 --> 00:38:11,760
+تقسم الفرق بينهما ولا لايبقى هنا ساعة ال P بتقسم
+
+312
+00:38:11,760 --> 00:38:24,840
+ال AT minus B not CT B not CT زائد B1 CT minus ال
+
+313
+00:38:24,840 --> 00:38:34,630
+1 زائد زائد BT minus ال 1 C1 بالشكل اللي عندهاإذاً
+
+314
+00:38:34,630 --> 00:38:41,750
+ال P بتقسم و لل AT هي فوق بدي أشيلها و أحط القيم
+
+315
+00:38:41,750 --> 00:38:56,970
+تبعتها يبقى BTC0 زائد BT-1C1 زائد زائد B1CT زائد
+
+316
+00:38:56,970 --> 00:39:03,390
+CT-1 زائد B0CT
+
+317
+00:39:04,260 --> 00:39:09,940
+ناقص إذا انت خلّي على كل واحدة من هدول يبقى ناقص B
+
+318
+00:39:09,940 --> 00:39:22,140
+non CT ناقص B one CT minus ال one ناقص ناقص B T
+
+319
+00:39:22,140 --> 00:39:31,600
+minus ال one C one طب أطلع هذه موجبة وهذه سالمة مع
+
+320
+00:39:31,600 --> 00:39:38,410
+السلامةو هذه موجبة و هذه سالبة غير ما نصوف عليها و
+
+321
+00:39:38,410 --> 00:39:44,150
+نظل ماشيين هذه موجبة و هذه سالبة إذا لن يلقى إلا
+
+322
+00:39:44,150 --> 00:39:52,990
+من إلا ترم الأول يبقى بصيرها إن في تقسم ال BTC
+
+323
+00:39:52,990 --> 00:40:01,670
+نقطة يبقى فيه تقسم و أخد منها صح؟ يبقى هذا معناه
+
+324
+00:40:01,670 --> 00:40:11,250
+إن فيهبتقسم ال بي تي or ال بي بتقسم السي نوت فاحنا
+
+325
+00:40:11,250 --> 00:40:15,830
+حاطين ان ال بي ممنوع تقسم السي نوت يبقى ال بي
+
+326
+00:40:15,830 --> 00:40:24,970
+هتقسم ال بي تي لإن هذا بده يعطينا ان ال بي بتقسم
+
+327
+00:40:24,970 --> 00:40:34,720
+ال بي تي because السبب لإن ال بيلأ تقسم الـC not
+
+328
+00:40:34,720 --> 00:40:44,260
+طب استنى شوية طلعيلي هذه وطلعيلي لهذه هنا تقسم
+
+329
+00:40:44,260 --> 00:40:49,220
+الـB T وهنا بيبقى تقسم ال contradiction ولا لأ
+
+330
+00:40:49,220 --> 00:40:56,700
+يبقى this is a contradict that
+
+331
+00:41:01,710 --> 00:41:08,790
+هذا يناقض ان ال P لا تقسم ال B T طب ايش جاب
+
+332
+00:41:08,790 --> 00:41:14,970
+التناقض؟ جاب التناقض الفرض اللى فرضنا هذا صح هذا
+
+333
+00:41:14,970 --> 00:41:22,110
+يبقى الفرض اللى فرضنا غلط وعكسه هو الصح يبقى بس
+
+334
+00:41:22,110 --> 00:41:29,150
+وهكذا ال F of X is irreducible
+
+335
+00:41:30,680 --> 00:41:40,440
+over the cube هو المظهر نعطيك مثال توضيحي مباشر
+
+336
+00:41:40,440 --> 00:41:47,200
+مثال على
+
+337
+00:41:47,200 --> 00:41:57,140
+كيفية استخدام هذه النظرية مثلًا بيقول شهداد
+
+338
+00:41:57,140 --> 00:42:00,040
+الكوروناوية شهداد
+
+339
+00:42:01,390 --> 00:42:12,230
+that the polynomial which
+
+340
+00:42:12,230 --> 00:42:24,710
+is f of x to the seventh ثلاثة اكس وخمسة زائد
+
+341
+00:42:24,710 --> 00:42:26,830
+خمستاشر
+
+342
+00:42:32,460 --> 00:42:44,240
+عشرين X تكريم زائد عشرة X زائد عشرين اللي موجودة
+
+343
+00:42:44,240 --> 00:42:53,820
+في Z of X معناه هذه is irreducible
+
+344
+00:42:53,820 --> 00:42:58,460
+irreducible
+
+345
+00:42:58,460 --> 00:43:08,650
+of Rالكيموز. قال لي ولكن قال لي بييل لي ان كثيرة
+
+346
+00:43:08,650 --> 00:43:14,090
+الحدود اللي على الشكل هذا المعاملات كلهم انتجة زي
+
+347
+00:43:14,090 --> 00:43:19,250
+ما موجودة في Z of X is irreducible عالميا على
+
+348
+00:43:19,250 --> 00:43:25,010
+الكيموز. إذن بدنا نروح نختار ال prime number. نطلع
+
+349
+00:43:25,010 --> 00:43:31,200
+من ال prime number المناسب.أطلعيلي هنا في ال 15
+
+350
+00:43:31,200 --> 00:43:35,940
+ولا 20 ولا 10 ولا 20 مين ال prime number اللي
+
+351
+00:43:35,940 --> 00:43:42,220
+بيقسمهم كلهم خمسة بيقسم التلاتة 100% يفجأة بدي
+
+352
+00:43:42,220 --> 00:43:54,120
+أقوله هنا take the prime number بيتساوي
+
+353
+00:43:54,120 --> 00:44:03,220
+خمسة الآن الخمسةلا تقسم التلاتة يعني الخمسة لا
+
+354
+00:44:03,220 --> 00:44:11,500
+تقسم الان لكن الخمسة بتقسم اللي هو الخمستاشر
+
+355
+00:44:11,500 --> 00:44:20,460
+والخمسة بتقسم ناقص عشرين والخمسة بتقسم العشر
+
+356
+00:44:20,460 --> 00:44:29,030
+والخمسة بتقسم العشرين and الخمسة تربية مين هي
+
+357
+00:44:29,030 --> 00:44:36,510
+المناسبة؟ لا، ساقس من العشرين. اوش البرنامج
+
+358
+00:44:36,510 --> 00:44:42,150
+الموجودة في Zip Code X واتحققت شروط النظرية كلها.
+
+359
+00:44:42,490 --> 00:44:48,750
+يبقى بالنظرية ترد يوسف وخلصنا، دون شروط. يبقى هنا
+
+360
+00:44:48,750 --> 00:44:54,490
+بروح اقوله I The Above The.
+
+361
+00:44:57,450 --> 00:45:04,450
+by the above theorem ال F of X اللي عندها .. اللي
+
+362
+00:45:04,450 --> 00:45:13,270
+هي تلاتة X أُس خمسة زائد خمستاشر X أُس أربعة ناقص
+
+363
+00:45:13,270 --> 00:45:25,730
+عشرة X زائد عشرين is irreducible over
+
+364
+00:45:27,160 --> 00:45:32,000
+لكيوك أظن هذه نظرية سهل التعامل معاها مش زي اللي
+
+365
+00:45:32,000 --> 00:45:37,620
+قبلها برهانة صحيح أصعب من اللي قبلها لكن الشغل
+
+366
+00:45:37,620 --> 00:45:43,380
+ابقى بسيط لدى الان في نتيجة على هذه النظرية
+
+367
+00:45:43,380 --> 00:45:46,200
+النتيجة كانت تانية
+
+368
+00:45:57,850 --> 00:46:06,530
+طبعاً اكتشافها راحت يقولون الـ EIS, ENST,
+
+369
+00:46:08,090 --> 00:46:21,030
+EIN criteria هذا
+
+370
+00:46:21,030 --> 00:46:25,770
+توفى هو سنة 1850
+
+371
+00:46:26,500 --> 00:46:31,860
+واتكشفها سنة الف تمانية وتبانية واربعين قبل ميمون
+
+372
+00:46:31,860 --> 00:46:38,600
+بسنتين وكان هناك مدرس وبعدين طلعوا الشغل هذه الى
+
+373
+00:46:38,600 --> 00:46:46,060
+الوجود وهي موجودة في غالب كتب الجدد. تقول ما يكوّر
+
+374
+00:46:46,060 --> 00:46:54,000
+أي crime فيه. يبقى هذا أي crime مش شغل محدد.
+
+375
+00:46:57,840 --> 00:47:07,100
+is cyclotomic cyclotomic
+
+376
+00:47:07,100 --> 00:47:15,680
+polynomial في
+
+377
+00:47:15,680 --> 00:47:23,580
+اليابان اللي هي Phi P of X Phi P of X في X to the
+
+378
+00:47:23,580 --> 00:47:30,580
+power P ناقص واحدعلى x ناقص واحد يتساوي x بي ناقص
+
+379
+00:47:30,580 --> 00:47:38,740
+واحد x بي ناقص اتنين انضال زائد x زائد واحد is
+
+380
+00:47:38,740 --> 00:47:41,900
+irreducible
+
+381
+00:47:41,900 --> 00:47:53,300
+is irreducible over a q irreducible على مين على a
+
+382
+00:47:53,300 --> 00:47:53,500
+q
+
+383
+00:48:30,090 --> 00:48:37,310
+خلّى بقى كده بيقوللي اثبت ان هذه البراناية بدى على
+
+384
+00:48:37,310 --> 00:48:42,530
+الشكل هذا irreducible على مين؟ على ال F يقولوا
+
+385
+00:48:42,530 --> 00:48:52,050
+تعالى شوف بدي اخد F of X يبقى هنا let F of X
+
+386
+00:48:52,050 --> 00:48:59,950
+بيساوي Phi P of X plus 1هذه بده تجيبها من وين بده
+
+387
+00:48:59,950 --> 00:49:05,890
+تجيبها من هنا إذا نحشيل كل X وحط مكانها X plus one
+
+388
+00:49:05,890 --> 00:49:12,290
+يبقى هذه بيصير X plus one to the power of P ناقص
+
+389
+00:49:12,290 --> 00:49:19,150
+واحد X زائد واحد ناقص واحد يبقى الشيلة شيلنا كل X
+
+390
+00:49:19,150 --> 00:49:26,450
+وحطينا مكانها X زائد واحد هذه يا بناة هي لغوية ذات
+
+391
+00:49:26,450 --> 00:49:37,410
+الحدينبدي افكر لو فكتها يبقى X و P زي توفيق P من
+
+392
+00:49:37,410 --> 00:49:46,510
+الأشياء المخوذة اتنين يبقاش بصير زي P فبين في X و
+
+393
+00:49:46,510 --> 00:49:53,570
+P ناقص واحد اللي بعده P في P ناقص واحد على مضروب
+
+394
+00:49:53,570 --> 00:49:58,640
+الثاني اتنين في واحد اللي بعدهزائد P في P ناقص
+
+395
+00:49:58,640 --> 00:50:03,180
+واحد في P ناقص اتنين على مضغوب التلاتة زائد الى
+
+396
+00:50:03,180 --> 00:50:08,980
+اخرين ما علينا بيهمنيش كتير بيهمني اظل ماشي لغاية
+
+397
+00:50:08,980 --> 00:50:16,680
+مين لغاية P في X زائد واحد وعنده ناقص واحد زايد و4
+
+398
+00:50:16,680 --> 00:50:25,870
+وهذه كلها مقسمة على مين على Xالان زائد واحد و ناقص
+
+399
+00:50:25,870 --> 00:50:33,090
+واحد مالها مع السلامة يبقى هذه بدها تساوي X أس P
+
+400
+00:50:33,090 --> 00:50:42,070
+ناقص الواحد زائد P X أس P ناقص اتنين زائد زائد P
+
+401
+00:50:42,070 --> 00:50:51,330
+هذا كله مين؟ Phi P of X زائد واحد لو بدها تساوي
+
+402
+00:50:51,330 --> 00:51:00,730
+المين؟الـ F of X يبقى هاي كثيرة حدود و الـ Prime
+
+403
+00:51:00,730 --> 00:51:07,190
+هو P مضي أخد الـ Prime هو P فهذا الـ Prime P من
+
+404
+00:51:07,190 --> 00:51:14,970
+مكان يكون كدهش المعامل هنا الـ P تقسم الواحد لأ كل
+
+405
+00:51:14,970 --> 00:51:21,500
+حد من هذه الحدود يحتوي على P P في P ناقص واحدP في
+
+406
+00:51:21,500 --> 00:51:26,540
+P نقص واحد في P نقص اتنين لغاية اخر حد اللي هو P
+
+407
+00:51:26,540 --> 00:51:33,760
+وكل واحد منهم يقبل القسمة على P ما عدا مين؟ ما عدا
+
+408
+00:51:33,760 --> 00:51:42,800
+الاول اتنين العناصر كلهم هدول موجودة في Z of
+
+409
+00:51:42,800 --> 00:51:52,360
+X هدى ال polynomial موجودة في Z of Xإن كل المعاملة
+
+410
+00:51:52,360 --> 00:51:58,960
+أرقام صحية Integers تمام؟ طيب إذا المعلومة الأولى
+
+411
+00:51:58,960 --> 00:52:06,380
+اتحققت، المعلومة الثانية ال P ليه تقسم ال A N اللي
+
+412
+00:52:06,380 --> 00:52:18,140
+هي بواحد؟ الآن ال P تقسم ال A N تقسم ال A ال minus
+
+413
+00:52:18,140 --> 00:52:24,630
+ال one اللي هي Pبتقسم نفسها تمام؟ وذا وضلنا ماشي
+
+414
+00:52:24,630 --> 00:52:39,190
+ال P بتقسم ال A ناضله P and ال P ترفيع لا تقسم ال
+
+415
+00:52:39,190 --> 00:52:45,370
+A ناضله بساوي ال P في ترفيع بتقسم ال P بدون باقية
+
+416
+00:52:45,370 --> 00:52:51,890
+أبعادها إذا انت حققت مين؟الشروط النظرية مدام تحققت
+
+417
+00:52:51,890 --> 00:52:56,970
+شروط النظرية يبقى ال F of X لأنها irreducible
+
+418
+00:52:56,970 --> 00:53:05,090
+عالميا عالميا يبقى هذا بالتوافق فينا F of X اللي
+
+419
+00:53:05,090 --> 00:53:16,190
+هي بدها تساوي 5P of X زي واحد is irreducible over
+
+420
+00:53:18,580 --> 00:53:27,840
+Lithium وهذا المطلوب؟ لأ مش انا هذه 5PX زي 1 احنا
+
+421
+00:53:27,840 --> 00:53:33,980
+بدنا 5P of X صح ولا لأ؟ واحنا في هذا ال chapter
+
+422
+00:53:33,980 --> 00:53:39,240
+كلنا الحمد لله ماشيين الفراهين بالتناقض اذا انا
+
+423
+00:53:39,240 --> 00:53:46,740
+بروح اختار ان هذه Reducible وشوف وين بتوصل الدنيا
+
+424
+00:53:47,120 --> 00:53:52,780
+مظبوط، إذا وصلت لتناقض، مقناته عكسه هو الصحيح،
+
+425
+00:53:52,780 --> 00:53:59,260
+مظبوط؟ طيب، الان وصلنا إلى ماتي، تحققت كل شروط
+
+426
+00:53:59,260 --> 00:54:04,520
+فضرية، ال graph of x بفعي P of x هو irreducible
+
+427
+00:54:04,520 --> 00:54:10,760
+على K، مش هذا اللي بدي أثبته، أنا بدي أثبت أن فعي
+
+428
+00:54:10,760 --> 00:54:15,760
+P of x هي ال irreducible على K، اللي بدي أفترض
+
+429
+00:54:15,760 --> 00:54:25,730
+العكس،هروح اقول هنا I assume افترض انه Phi P of X
+
+430
+00:54:25,730 --> 00:54:41,530
+is irreducible over ال Q then شو اللي بده يصير Phi
+
+431
+00:54:41,530 --> 00:54:51,670
+P of X بده يساوي ال G of Xالـ H of X والـ
+
+432
+00:54:51,670 --> 00:55:00,450
+degree أو الـ G of X والـ H of X موجودة في الـ Q
+
+433
+00:55:00,450 --> 00:55:11,790
+of X والـ degree للـ G للـ G والـ degree للـ H أقل
+
+434
+00:55:11,790 --> 00:55:26,090
+من مين؟ أقل من ال degreeلـ Phi P of X أقل
+
+435
+00:55:26,090 --> 00:55:35,010
+من Phi P of X مافيش
+
+436
+00:55:35,010 --> 00:55:39,010
+رأيك؟ لو شيلت الـ X و حطيت بدالها X زائد واحد،
+
+437
+00:55:39,010 --> 00:55:45,110
+بتغير؟ هذي اللينية لو هذي اللينيةيبقى هذا بدي يقيل
+
+438
+00:55:45,110 --> 00:55:51,910
+فاي P of X زائد واحد بدي يسوي ال GX زائد واحد بال
+
+439
+00:55:51,910 --> 00:55:59,710
+HX زائد واحد يبقى هذا معناته ان فاي P of X زائد
+
+440
+00:55:59,710 --> 00:56:06,070
+واحد is reducible صحيح ولا لا؟ اذا احنا ايش قلنا
+
+441
+00:56:06,070 --> 00:56:16,190
+هنا؟ is reducible، مصر تناقض؟ تناقضيبقى هنا this
+
+442
+00:56:16,190 --> 00:56:19,890
+is contradiction
+
+443
+00:56:19,890 --> 00:56:26,750
+اللي فرضنا .. اللي فرضنا هو الغلط اللي جاب ال
+
+444
+00:56:26,750 --> 00:56:31,830
+contradiction ان الفرض هذه irreducible يبقى sir
+
+445
+00:56:31,830 --> 00:56:44,370
+phi P of X is irreducible over liquidبحب أشير إلى
+
+446
+00:56:44,370 --> 00:56:50,950
+ما يكتب الكلام اللي كتبته هنا هو حل سؤال خمسة عندك
+
+447
+00:56:50,950 --> 00:56:58,790
+في الكتاب رقم C خمسة A وB وC وD الرقم C هيحله
+
+448
+00:56:58,790 --> 00:57:07,380
+قدامك عندهم بس هناك محطش واحد حطه Ux زائد Cيبقى
+
+449
+00:57:07,380 --> 00:57:10,920
+مكان الـC احنا حاطينه واحد الحل هيو قدامك علّه
+
+450
+00:57:10,920 --> 00:57:16,040
+احتباط سواء خمسة C هو هو لم يتغير بال
+
+451
+00:57:16,040 --> 00:57:20,120
+contradiction نمرأيه بال contradiction نمرأيه بال
+
+452
+00:57:20,120 --> 00:57:23,800
+contradiction نمرأي الـC بال contradiction كذلك
+
+453
+00:57:23,800 --> 00:57:29,100
+كلهم التلاتة بال contradiction ونفس التكتيك اللي
+
+454
+00:57:29,100 --> 00:57:35,220
+تبقى هو نفسه إلى هنا انتهت هذه المحاضرة ونكمل ان
+
+455
+00:57:35,220 --> 00:57:39,020
+شاء اللهالمحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U.srt
new file mode 100644
index 0000000000000000000000000000000000000000..55a8bf53c228631e7d4eee0fb2a9a06886eaff2d
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U.srt
@@ -0,0 +1,1366 @@
+1
+00:00:21,060 --> 00:00:25,280
+بسم الله الرحمن الرحيم، نكمل ما ابتدأناه في
+
+2
+00:00:25,280 --> 00:00:30,860
+المحاضرة الماضية، وهو chapter a ring homomorphism
+
+3
+00:00:30,860 --> 00:00:35,600
+آخر حاجة كان معنا المرة اللي فاتت مثال، والآن نأتي
+
+4
+00:00:35,600 --> 00:00:42,180
+إلى نظرية جديدة، النظرية بتقول ما معنى little r ب
+
+5
+00:00:42,180 --> 00:00:44,420
+ring with unit one
+
+6
+00:00:48,500 --> 00:00:54,500
+هذه mapping، عرفنا function من الـ Z إلى R، طبعا الـ
+
+7
+00:00:54,500 --> 00:01:00,020
+Z دي هي مجموعة الأعداد الصحيحة، إلى ring R given by
+
+8
+00:01:00,020 --> 00:01:05,800
+Φ(N) = N × 1، بدنا نثبت أن هذه عبارة عن
+
+9
+00:01:05,800 --> 00:01:11,880
+ring homomorphism، مشان هيك الـ ring homomorphism في
+
+10
+00:01:11,880 --> 00:01:17,160
+عندي two conditions، بدنا نحققهم، الـ condition هو
+
+11
+00:01:17,160 --> 00:01:21,000
+اللي بيقول لو كان two elements x و y موجودات في الـ
+
+12
+00:01:21,000 --> 00:01:25,620
+ring، و في لما أثرت على هذا المجموع يبقى بيساوي Φ
+
+13
+00:01:25,620 --> 00:01:32,460
+(x) + Φ(y)، ولو Φ أثرت على الضرب x × y،
+
+14
+00:01:32,460 --> 00:01:37,800
+الناتج بيكون Φ(x) × Φ(y)، يبقى بنروح نطبق
+
+15
+00:01:37,800 --> 00:01:43,420
+هذا الكلام على الـ ring اللي قدامنا هذا، يبقى بدي
+
+16
+00:01:43,420 --> 00:01:49,980
+أبدأ الآن، بدي أقول: افترض عندي M و N عددين صحيحين
+
+17
+00:01:49,980 --> 00:01:58,380
+موجودة في Z، then بدي أخد تأثير الـ Φ على M +
+
+18
+00:01:58,380 --> 00:02:05,600
+N حسب التعريف اللي عندنا، يبقى هذا الكلام M +
+
+19
+00:02:05,600 --> 00:02:14,350
+N مضروب في الـ one، هذا بيساوي، بيساوي إيه؟ بده
+
+20
+00:02:14,350 --> 00:02:20,610
+بيساوي الـ M + N، هدول integers، يبقى عبارة بقدر
+
+21
+00:02:20,610 --> 00:02:26,830
+أحطهم 1 + 1 + 1، M + N من المرات
+
+22
+00:02:26,830 --> 00:02:35,030
+يبقى هذا الكلام 1 + 1 + 1 + 1،
+
+23
+00:02:35,030 --> 00:02:46,180
+كم مرة هدول؟ M + N times، يبقى M + N من المرات
+
+24
+00:02:46,180 --> 00:02:52,280
+يعني عدد هدول اللي عندنا، كل واحد فيهم لما نجمعهم
+
+25
+00:02:52,280 --> 00:02:59,800
+يكون عددهم M + N، طيب تمام، ممكن أجسمهم إلى جسمين،
+
+26
+00:02:59,800 --> 00:03:05,640
+القسم الأول 1 + 1 + ... + 1، هدول
+
+27
+00:03:05,640 --> 00:03:13,340
+بناخد M times، + برضه 1 + 1 + ... + 1،
+
+28
+00:03:13,340 --> 00:03:23,180
+و هدول N times، يبقى بناء عليه هذا الدرس هو M
+
+29
+00:03:23,180 --> 00:03:31,240
+في one + هدول عددهم N، يبقى N في one، حسب الـ
+
+30
+00:03:31,240 --> 00:03:38,460
+definition، يبقى الأول Φ(M)، والتاني Φ(N)
+
+31
+00:03:39,000 --> 00:03:44,440
+بناء عليه، أخدنا Φ(M + N)، جينا للنتيجة
+
+32
+00:03:44,440 --> 00:03:50,360
+تساوي Φ(M) + Φ(N)، وبالتالي حققنا الـ
+
+33
+00:03:50,360 --> 00:03:55,080
+condition الأول من الـ two conditions تبعات الـ ring
+
+34
+00:03:55,080 --> 00:04:00,460
+homomorphism، بقول إن بدنا نروح للـ condition الثاني،
+
+35
+00:04:00,460 --> 00:04:08,360
+بدنا ناخد Φ(M × N)، حسب الـ definition، يبقى M
+
+36
+00:04:08,750 --> 00:04:17,370
+× N × 1، طيب هذا الواحد هو الـ unity، يبقى لو
+
+37
+00:04:17,370 --> 00:04:22,550
+ضربت الـ element هذا كله في كمان unity، بيغير حاجة؟
+
+38
+00:04:22,550 --> 00:04:29,190
+لأ، يبقى هذا الكلام M × N × الـ unity × كمان الـ
+
+39
+00:04:29,190 --> 00:04:38,130
+unity، بيغيرش شيء، طيب الآن هذا بده يساوي الـ M × الـ
+
+40
+00:04:38,130 --> 00:04:47,210
+one مضروب × كذلك N × one، الأولى هذه اللي عبارة عن
+
+41
+00:04:47,210 --> 00:04:55,990
+مين؟ صورة الـ M، والتاني هذه صورة الـ N، يبقى بناء عليه
+
+42
+00:04:55,990 --> 00:05:02,370
+Φ(M) × N، طلع عندي Φ(M) × Φ(N)، يبقى
+
+43
+00:05:02,370 --> 00:05:15,830
+Thus، وهكذا Φ is a ring homomorphism، الآن
+
+44
+00:05:15,830 --> 00:05:24,110
+على هذه النظرية فيه ثلاث نتائج، نبدأ بالنتيجة
+
+45
+00:05:24,110 --> 00:05:30,330
+الأولى، على هذه النظرية، يبقى الـ first corollary بتقول
+
+46
+00:05:30,330 --> 00:05:35,330
+ما يأتي، corollary، corollary one
+
+47
+00:05:38,760 --> 00:05:46,640
+بيقول: if الـ R is a ring with unity، if الـ R is a
+
+48
+00:05:46,640 --> 00:05:56,140
+ring with unity، ring with unity، and the
+
+49
+00:05:56,140 --> 00:06:07,560
+characteristic of R، and the characteristic of R is
+
+50
+00:06:09,390 --> 00:06:19,530
+and greater than zero، then الـ R
+
+51
+00:06:19,530 --> 00:06:31,810
+contains a subring، contains a subring، contains
+
+52
+00:06:31,810 --> 00:06:38,490
+a subring isomorphic to
+
+53
+00:06:40,260 --> 00:06:53,440
+Z، and if the characteristic
+
+54
+00:06:53,440 --> 00:07:01,320
+of R is zero، then
+
+55
+00:07:01,320 --> 00:07:08,480
+R contains something، then R contains
+
+56
+00:07:23,490 --> 00:07:27,970
+isomorphic to Z
+
+57
+00:07:46,830 --> 00:07:50,870
+يبقى النظرية هذه اللي بين إيدينا عبارة عن نقطتين،
+
+58
+00:07:50,870 --> 00:07:57,610
+وليست نقطة واحدة، النقطة الأولى بتقول إيه؟ النقطة
+
+59
+00:07:57,610 --> 00:08:01,910
+المشتركة، بيقول: if you have an R ring with unity، إذا
+
+60
+00:08:01,910 --> 00:08:07,670
+كان الـ characteristic لـ R هو N، يبقى الـ R فيها sub
+
+61
+00:08:07,670 --> 00:08:12,870
+ring isomorphic لـ Z<sub>N</sub>، وإذا كان، نقطة ثانية، إذا كان
+
+62
+00:08:12,870 --> 00:08:17,490
+الـ characteristic للـ ring R هو zero، يبقى الـ ring
+
+63
+00:08:17,490 --> 00:08:23,170
+هذه تحتوي على sub ring isomorphic لـ set of integers
+
+64
+00:08:23,170 --> 00:08:28,870
+اللي هو Z أو اللي هي Z، نروح نثبت صحة هذه الـ
+
+65
+00:08:28,870 --> 00:08:34,330
+corollary، وهذه الـ corollary أساسية للـ corollaries
+
+66
+00:08:34,330 --> 00:08:38,330
+اللي بيجوا اللي بيجوا بعديها، طيب خليني أقول لكم
+
+67
+00:08:38,330 --> 00:08:43,230
+هنا الآن ما حددش شكل الـ unity، يبقى أنا بدي أفرض
+
+68
+00:08:43,230 --> 00:08:49,120
+أن الـ unity اللي هو عبارة عن مين؟ الواحد الصحيح، يبقى
+
+69
+00:08:49,120 --> 00:09:03,880
+let the one be the unity of the ring R، مافيش
+
+70
+00:09:03,880 --> 00:09:09,020
+بيقول هنا: قال لي إذا الـ characteristic يساوي N،
+
+71
+00:09:09,020 --> 00:09:16,220
+يبقى الـ R contains a subring isomorphic لـ Z<sub>N</sub>، يبقى
+
+72
+00:09:16,220 --> 00:09:24,200
+أنا بدي أخلّق subring، بروح أقول له: let الـ S كلّ
+
+73
+00:09:24,200 --> 00:09:31,260
+العناصر k مضروبة في 1، بحيث الـ k هذا عدد أخدته
+
+74
+00:09:31,260 --> 00:09:37,400
+من مين؟ أخدته من Z، يبقى
+
+75
+00:09:41,040 --> 00:09:48,440
+افترضت إني عندي S، الـ S هذه هي حاصل ضرب عدد من Z،
+
+76
+00:09:48,440 --> 00:09:54,800
+مضروب في مين؟ في الواحد الصحيح، أنا بدّي أُثبت الآن أن الـ
+
+77
+00:09:54,800 --> 00:10:06,760
+S is a subring، يبقى then الـ S is a subring، شو
+
+78
+00:10:06,760 --> 00:10:14,480
+السبب؟ because، النقطة الأولى، الـ S هذه is non-empty،
+
+79
+00:10:14,480 --> 00:10:25,740
+الـ S is non-empty، على الأقل فيها عنصر هو العنصر
+
+80
+00:10:25,740 --> 00:10:35,560
+الصفر، because الـ zero بيساوي zero × 1،
+
+81
+00:10:35,560 --> 00:10:43,150
+وهذا موجود هنا، موجود في S، يبقى non-empty، نقطة ثانية،
+
+82
+00:10:43,150 --> 00:10:52,330
+بدي أفرض إني عندي عنصرين موجودات في S، يبقى let
+
+83
+00:10:52,330 --> 00:11:02,150
+x و y موجودات في S، then شكل الـ x بيساوي
+
+84
+00:11:02,150 --> 00:11:06,170
+مثلا k × 1، and
+
+85
+00:11:20,220 --> 00:11:27,980
+يبقى k × 1 − m × 1، حسب الـ
+
+86
+00:11:27,980 --> 00:11:35,880
+distributive law، يبقى k − m × 1، الفرق ما
+
+87
+00:11:35,880 --> 00:11:41,480
+بين two integers هو integer مظبوط، مضروب في 1،
+
+88
+00:11:41,480 --> 00:11:48,820
+يبقى صار شكله موجود في S، يبقى هذا بده يعطينا إن الـ
+
+89
+00:11:48,820 --> 00:11:56,360
+x − y موجودة في S، الآن مشان أثبتها subring، الـ condition الثالث، بدي اروح اخذ حاصل
+
+90
+00:11:56,360 --> 00:12:02,480
+ضرب عنصرين من نفس الـ S، بدي يكون موجود في S، إذا لو
+
+91
+00:12:02,480 --> 00:12:08,840
+رحت أخدت الـ x × y، الـ x × y عبارة عن مين؟ اللي هو
+
+92
+00:12:08,840 --> 00:12:15,300
+k × 1 مضروب في الـ m × 1، لإن الـ x أخدته k
+
+93
+00:12:15,300 --> 00:12:23,160
+× 1، والـ y هو m × 1، يبقى هذا الكلام بقدر أقوله
+
+94
+00:12:23,160 --> 00:12:29,940
+على شكل k × m × 1، لأن الـ one × one بيساوي one
+
+95
+00:12:29,940 --> 00:12:36,710
+itself، لأن هو الـ unity، طيب هذا الصيغة k × m مش
+
+96
+00:12:36,710 --> 00:12:44,150
+هيجي عنصر موجود في Z، يكون مضروب في 1، يبقى
+
+97
+00:12:44,150 --> 00:12:49,210
+بناء عليه هذا يعطي لي إن الـ x × y موجود في S، و
+
+98
+00:12:49,210 --> 00:12:57,250
+هكذا الـ S is a subring of R، طب حتى الآن
+
+99
+00:12:57,250 --> 00:13:10,960
+أنا بس خلّقت subring، بس إيش بيقول هنا هو؟ الـ
+
+100
+00:13:10,960 --> 00:13:17,360
+characteristic، فهو لو كان يساوي N، يبقى R contains
+
+101
+00:13:17,360 --> 00:13:23,660
+a subring، هي جبتها، و هي مرفقة لمين؟ لـ Z<sub>N</sub>، يبقى أنا
+
+102
+00:13:23,660 --> 00:13:31,800
+بدي أجيب homomorphism من الـ subring هذه إلى، معرفش
+
+103
+00:13:31,800 --> 00:13:38,600
+مين؟ تطلع هي زات لمين؟ لـ Z<sub>N</sub>، تمام؟ بتكون عندك
+
+104
+00:13:38,600 --> 00:13:43,880
+isomorphism، بقوله بسيطة خالص، يبقى بروح بقوله
+
+105
+00:13:43,880 --> 00:13:48,780
+define a mapping or function
+
+106
+00:14:00,360 --> 00:14:13,020
+من Z إلى ... والله من S إلى Z<sub>N</sub>، من S إلى Z<sub>N</sub>، عفواً، من Z
+
+107
+00:14:13,020 --> 00:14:19,220
+إلى S، هذه، والله هذه بتفرقش عنها، بس مشان نلتزم بنصّ
+
+108
+00:14:19,220 --> 00:14:27,210
+النظرية، النظرية اللي من Z إلى R، يبقى من Z إلى S، هو
+
+109
+00:14:27,210 --> 00:14:38,070
+والله من Z onto S، تمام؟ إيه؟ تمام؟ by Φ
+
+110
+00:14:38,070 --> 00:14:47,570
+of ... بدي آخد element من وين؟ من Z، Φ(m) مثلاً،
+
+111
+00:14:47,570 --> 00:14:52,930
+بيساوي الـ element اللي هنا، شكله m × 1، طب احنا
+
+112
+00:14:52,930 --> 00:14:58,400
+ما وصلناش،  ما وصلناش لسه
+
+113
+00:14:58,400 --> 00:15:02,480
+للـ isomorphism لسة، احنا عرفنا function لأ، بس
+
+114
+00:15:02,480 --> 00:15:06,080
+احنا جبنا الـ subring، جبنا الـ subring صحيح، لكن من
+
+115
+00:15:06,080 --> 00:15:11,560
+الـ subring لـ Z<sub>N</sub>، سوينا حاجة؟ لأ ولا حاجة، ما سويناش
+
+116
+00:15:11,560 --> 00:15:16,500
+شيء، مشينا عنها؟ ما مشيناش، رايحين لها دكتور يزيد
+
+117
+00:15:16,500 --> 00:15:20,760
+from us، يزيد from us، بس اصبر شوية، بنت أنا ما وصلناش
+
+118
+00:15:20,760 --> 00:15:25,760
+لـ Z<sub>N</sub>، أنا أوصلك لـ Z<sub>N</sub> بسهولة، مش سهل إنك تجي تقلبها
+
+119
+00:15:25,760 --> 00:15:32,210
+ساعتها، لأ بس اصبر شوية، فاحنا بنقول: عرفنا Φ من Z
+
+120
+00:15:32,210 --> 00:15:40,190
+إلى subring هذه، بمين؟ بـ Φ(M) = M × 1، 100 في
+
+121
+00:15:40,190 --> 00:15:45,090
+الواحد، طيب هذه مش هو نص النظرية؟ يبقى هذه
+
+122
+00:15:45,090 --> 00:15:53,690
+homomorphism، يبقى then ... then Φ is a
+
+123
+00:15:53,690 --> 00:16:00,540
+homomorphism، هذا الكلام جبته من أين؟ from the
+
+124
+00:16:00,540 --> 00:16:08,200
+أعضاء الـ Theorem، يبقى
+
+125
+00:16:08,200 --> 00:16:14,500
+صار عندنا homomorphism، مظبوط؟
+
+126
+00:16:14,500 --> 00:16:19,160
+يبقى فيها عندنا نظرية اسمها الـ Isomorphism Theorem،
+
+127
+00:16:19,160 --> 00:16:29,350
+سمعنا فيها، سمعنا فيها؟ طيب، يبقى by the first
+
+128
+00:16:29,350 --> 00:16:34,230
+isomorphism
+
+129
+00:16:34,230 --> 00:16:39,070
+theorem،
+
+130
+00:16:39,070 --> 00:16:42,690
+الـ
+
+131
+00:16:42,690 --> 00:16:55,760
+Z modulo kernel للـ Φ isomorphic لـ Φ(Z)، مين
+
+132
+00:16:55,760 --> 00:17:02,740
+الـ Φ(Z)؟ اللي هي S، لإنه onto، يبقى هذه
+
+133
+00:17:02,740 --> 00:17:08,860
+بالـ Z، بتساوي S، طيب فيه معلومة حتى لسة ما
+
+134
+00:17:08,860 --> 00:17:15,600
+نستخدمها، إيش اللي بنستخدمها؟ الـ characteristic، يبقى
+
+135
+00:17:15,600 --> 00:17:24,240
+هنا if الـ characteristic للـ R
+
+136
+00:17:24,590 --> 00:17:33,170
+is n، وهو أكبر من الـ zero، then الـ kernel للـ Φ
+
+137
+00:17:33,170 --> 00:17:40,750
+هو الـ principal ideal generated by n، هذا بده إثبات،
+
+138
+00:17:40,750 --> 00:17:47,390
+يبقى بدنا نعمل له إثبات في البيت، كأننا بدأنا أخدنا
+
+139
+00:17:47,390 --> 00:17:50,790
+element في الـ kernel، نثبت إنه في الـ principal
+
+140
+00:17:50,790 --> 00:17:55,220
+ideal generated by n، والعملية العكسية طبعاً سويناها،
+
+141
+00:17:55,220 --> 00:18:00,060
+قبل هيك أثبتنا أكتر من مرة كلام زي هيك، يبقى بدنا
+
+142
+00:18:00,060 --> 00:18:05,220
+نحاول نثبت لي هذا الكلام، مدام الـ kernel هو الـ
+
+143
+00:18:05,220 --> 00:18:09,320
+principal ideal generated by N، إذا بقدر أستخدم الـ
+
+144
+00:18:09,320 --> 00:18:17,060
+kernel بالـ principal ideal generated by N، الـ
+
+145
+00:18:17,060 --> 00:18:26,570
+S isomorphic لـ Z modulo kernel، الآن، اللي هو بده
+
+146
+00:18:26,570 --> 00:18:31,850
+يساوي Z modulo principal ideal generated
+
+147
+00:18:31,850 --> 00:18:42,410
+by N، طيب سؤال، مين هي الـ ring هذه؟ الـ Z<sub>N</sub> صح ولا
+
+148
+00:18:42,410 --> 00:18:49,730
+لأ؟ يبقى هذه بتساوي مين؟ بتساوي Z<sub>N</sub>، بناءً عليه صار
+
+149
+00:18:49,730 --> 00:18:57,090
+الـ subring S isomorphic لمين؟ إلى Z<sub>N</sub>، وهو المطلوب
+
+150
+00:18:57,090 --> 00:19:01,770
+يبقى استعجلنا، استعجلنا عليه، توّ هاد احنا
+
+151
+00:19:01,770 --> 00:19:06,690
+أثبتنا بكل سهولة باستخدام الـ first isomorphism
+
+152
+00:19:06,690 --> 00:19:13,850
+theorem، حد فيكم عنده سؤال؟ قول لي ليش أخدنا الـ Φ
+
+153
+00:19:13,850 --> 00:19:20,020
+من Z إلى Z<sub>N</sub>؟ عشان نخلي S هي Φ(Z)، لأن
+
+154
+00:19:20,020 --> 00:19:26,080
+الـ first isomorphism بتقول: لو كان Φ من مين؟ من
+
+155
+00:19:26,080 --> 00:19:32,860
+function أو من R إلى S، فبدي آخد الـ element الـ ...
+
+156
+00:19:32,860 --> 00:19:38,620
+الـ isomorphism، Φ(R)، صورة الـ R كلها في الـ ring في
+
+157
+00:19:38,620 --> 00:19:44,360
+الـ ring الثانية اللي هي S، هنا في الـ Z بتساوي S،
+
+158
+00:19:44,360 --> 00:19:51,320
+طيب، بدنا نروح الآن لـ corollary رقم 2، بتاخد نصّ
+
+159
+00:19:51,320 --> 00:19:57,920
+النظرية مشان نطبق عليها الـ corollary
+
+160
+00:19:57,920 --> 00:20:13,500
+هذه؟
+
+161
+00:20:13,500 --> 00:20:20,590
+كيف اجت؟ ممتاز، الحين خذ أي رقم يعجبك؟ قداش
+
+162
+00:20:20,590 --> 00:20:26,690
+متكيّف؟ عشرة، عشرة، ممتاز جداً، زد فيها كم رقم؟ عشرة
+
+163
+00:20:26,690 --> 00:20:32,570
+عشرة، ولا مليون، كل رقم يجب أن يكون مضاعف لعشرة،
+
+164
+00:20:32,570 --> 00:20:36,770
+يبقى زي 1، 2 لغاية 9، زائد الـ
+
+165
+00:20:36,770 --> 00:20:39,630
+principal ideal generated by 10، لمن وصلنا
+
+166
+00:20:39,630 --> 00:20:42,970
+للعشرة هو صفر صفر، يعني الـ principal ideal
+
+167
+00:20:42,970 --> 00:20:46,110
+generated by 10، الـ 11 اعتبرها 1،
+
+168
+00:20:46,110 --> 00:20:51,730
+الـ 12 اعتبرها 2، وهكذا، يبقى بيبقى عندنا Z<sub>10</sub>، وهو
+
+169
+00:20:51,730 --> 00:21:03,130
+المطلوب، تمام، طيب نجي للـ corollary رقم 2، يبقى
+
+170
+00:21:03,130 --> 00:21:07,630
+corollary 2،
+
+171
+00:21:07,630 --> 00:21:15,950
+بيقول: for any positive integer M، for any positive
+
+172
+00:21:18,860 --> 00:21:
+
+223
+00:27:53,100 --> 00:28:02,300
+هذا هو عبارة عن ماذا؟ عن Z، ثم سيبيلي هذا الآن
+
+224
+00:28:02,300 --> 00:28:11,080
+اللي بحتاجه يقول if the characteristic is zero then
+
+225
+00:28:11,080 --> 00:28:14,240
+ال
+
+226
+00:28:14,240 --> 00:28:20,540
+S is isomorphic to the principal ideal Z module
+
+227
+00:28:20,540 --> 00:28:27,460
+generated by zero. قياسا عليها بالضبط تماما. طيب هذه
+
+228
+00:28:27,460 --> 00:28:34,420
+مين بتعطينا بالضبط Z itself لأن zero يقبل أي رقم
+
+229
+00:28:34,420 --> 00:28:40,480
+بدي يطلع نفس الرقم، يبقى هذا بدي يعطينا Z إذا هنا
+
+230
+00:28:40,480 --> 00:28:48,080
+is isomorphic to Z وهو المفترض. طيب
+
+231
+00:28:48,080 --> 00:28:53,350
+نرجع الآن لكورلري رقم ثلاثة. كتبناها؟ لا، لسه ما بدأنا
+
+232
+00:28:53,350 --> 00:29:02,030
+نكتبها. يبقى الكورلري رقم ثلاثة
+
+233
+00:29:02,030 --> 00:29:11,930
+بتقول
+
+234
+00:29:11,930 --> 00:29:22,470
+ما يعنيه if F is a field of
+
+235
+00:29:24,750 --> 00:29:30,350
+characteristic P then F contains a subfield
+
+236
+00:29:30,350 --> 00:29:41,330
+then F contains a subfield. contains a sub
+
+237
+00:29:41,330 --> 00:29:44,810
+field isomorphic to
+
+238
+00:29:54,350 --> 00:30:09,870
+the field F has characteristic zero then F
+
+239
+00:30:09,870 --> 00:30:20,290
+contains... then F contains a subfield...
+
+240
+00:30:20,290 --> 00:30:30,900
+contains a subfield isomorphic to zero. isomorphic
+
+241
+00:30:30,900 --> 00:30:36,580
+to isomorphic
+
+242
+00:30:36,580 --> 00:30:43,220
+to the rational numbers
+
+243
+00:30:43,220 --> 00:30:46,380
+اللي
+
+244
+00:30:46,380 --> 00:30:50,640
+هو الـQ (rational numbers)
+
+245
+00:31:05,450 --> 00:31:12,470
+السؤال هو: هل الـ field هو ring؟
+
+246
+00:31:12,470 --> 00:31:18,390
+مش حلّو الله، ring كمان، a commutative ring with
+
+247
+00:31:18,390 --> 00:31:24,670
+unity وكل عنصر غير صفري له معكوس، مظبوط؟ هذا الـ
+
+248
+00:31:24,670 --> 00:31:30,190
+field. يبقى بقول لو كان الـ F a field، يعني الـ ring
+
+249
+00:31:30,190 --> 00:31:35,950
+of characteristic P، يبقى الـ F  فيه subfield
+
+250
+00:31:35,950 --> 00:31:45,990
+isomorphic to Z<sub>P</sub>. بأجي بقول لك الـ
+
+251
+00:31:45,990 --> 00:31:54,910
+F، الـ F دي، الـ field دي
+
+252
+00:31:54,910 --> 00:32:06,500
+الـ field of characteristic P by the... قاعدة الـ
+
+253
+00:32:06,500 --> 00:32:17,440
+corollary when... corollary when there is... there
+
+254
+00:32:17,440 --> 00:32:24,660
+is a subfield. subfield
+
+255
+00:32:24,660 --> 00:32:27,400
+isomorphic
+
+256
+00:32:31,720 --> 00:32:37,440
+isomorphic to Z<sub>p</sub>
+
+257
+00:32:37,440 --> 00:32:42,480
+طيب
+
+258
+00:32:42,480 --> 00:32:55,460
+كيف الـ F is a field of characteristic
+
+259
+00:32:55,460 --> 00:33:00,420
+zero then there is
+
+260
+00:33:11,630 --> 00:33:22,830
+a subfield isomorphic to Q. هذا تطبيق لنص من نص
+
+261
+00:33:22,830 --> 00:33:27,990
+النظرية، بس هذا الكلام هيكون صعب. الأخير هذا مش داخل
+
+262
+00:33:27,990 --> 00:33:32,970
+مخنا الآن. أو تمام، هنخليه يدخل مخك وإن شاء الله
+
+263
+00:33:32,970 --> 00:33:41,440
+تعلّم. طيب، ليش؟ ليش هذا subfield isomorphic
+
+264
+00:33:41,440 --> 00:33:47,480
+to Q؟ مش لحقيقة النظرية هذه وإذا لكورلري
+
+265
+00:33:47,480 --> 00:33:52,620
+واحد، آه، مسحناها لكورلري، بتقول isomorphic to Z،
+
+266
+00:33:52,620 --> 00:33:58,120
+مظبوط؟ هذه  to Q، مش لـ Z، كله بسيط. تعالى
+
+267
+00:33:58,120 --> 00:34:05,570
+نشوف. إذا احنا بدنا نأخذ الـ S هذا subfield من مين؟
+
+268
+00:34:05,570 --> 00:34:14,430
+من اللي هو الـ R. نفترض نرجع نقول له: لأ، الـ S اللي هي
+
+269
+00:34:14,430 --> 00:34:21,590
+بده يساوي مين؟ بده يساوي the set of all elements A
+
+270
+00:34:21,590 --> 00:34:31,200
+على B such that A و B موجودة في Z والـ B
+
+271
+00:34:31,200 --> 00:34:38,100
+لا تساوي صفر، كويس؟
+
+272
+00:34:38,100 --> 00:34:45,300
+يبقى أخدت S تساوي هذه، then الـ
+
+273
+00:34:45,300 --> 00:34:54,920
+S هذه بتثبتها إنها إيه؟ إنها subfield. subfield. طيب كويس
+
+274
+00:34:55,300 --> 00:35:00,220
+يبقى لو أخدت S على الشكل اللي عندها هذا A على B
+
+275
+00:35:00,220 --> 00:35:08,400
+بحيث A و B موجودة في Z، يبقى
+
+276
+00:35:08,400 --> 00:35:13,780
+هذه subring. بقدر كل اللي بقدر أقوله حتى الآن sub
+
+277
+00:35:13,780 --> 00:35:21,340
+ring. then S is a subring.
+
+278
+00:35:23,890 --> 00:35:31,510
+طيب بدي آخذ جزء منها وهذا الجزء بدي أثبت أنه sub
+
+279
+00:35:31,510 --> 00:35:39,990
+field. إذا لو جيت وقلت: فرضا عندي set T
+
+280
+00:35:39,990 --> 00:35:49,350
+الـ set T على شكل AB<sup>-1</sup>  بحيث A و
+
+281
+00:35:49,350 --> 00:36:02,460
+B موجودة في S  و B لا تساوي صفر. want to show that
+
+282
+00:36:02,460 --> 00:36:12,000
+T is a subfield. عشان نقدر نطبق الجزء الثاني
+
+283
+00:36:12,000 --> 00:36:16,460
+من النظرية اللي بنقول عليها. لأن أنا ما بقدر أقول إن
+
+284
+00:36:16,460 --> 00:36:18,340
+أنا مش سهلة، فجأة جماعة.
+
+285
+00:36:27,960 --> 00:36:32,460
+عشان أثبت أن هذا الـ subset، خلّيني أرجع للشرط
+
+286
+00:36:32,460 --> 00:36:39,060
+الثاني. ماذا تعرف عن subset؟ أنا لو أخدت عنصرين في
+
+287
+00:36:39,060 --> 00:36:45,020
+هذه الـ set ولقيت الفرق فيما بينهم موجود فيها، ولو
+
+288
+00:36:45,020 --> 00:36:49,340
+أخذت العنصر الأول في معكوس الثاني وضربتهم بيكون في
+
+289
+00:36:49,340 --> 00:36:53,560
+نفس الـ set، إن حدث ذلك بقول هذا الـ subfield حسب ما
+
+290
+00:36:53,560 --> 00:36:58,260
+أعرف. عندكم في أحد الأسئلة، أدري قد إيش رقم السؤال
+
+291
+00:36:58,260 --> 00:37:03,120
+في قد إيش؟ خمسة وعشرين، كويس. بالنسبة لي الـ subfield
+
+292
+00:37:03,120 --> 00:37:09,300
+طب لاحظ، ما قالش non-empty، ما قالش non لأن الـ field
+
+293
+00:37:09,300 --> 00:37:13,600
+دائما يكون commutative و unity، أقل حاجة في الـ
+
+294
+00:37:13,600 --> 00:37:19,240
+unity. صح؟ يكون في ring يبقى كمان الـ zero موجود. تمام
+
+295
+00:37:19,920 --> 00:37:24,800
+طيب الآن أنا أدّعي أن هذا subfield، لذلك بأخذ
+
+296
+00:37:24,800 --> 00:37:32,140
+عنصرين في T، يبقى بأجي أقول: افترض أن الـ X و الـ Y
+
+297
+00:37:32,140 --> 00:37:39,160
+موجودة في T، then الـ X يا بنات بدي يكون على شكل AB<sup>-1</sup>
+
+298
+00:37:39,160 --> 00:37:49,000
+والـ Y بدي يكون على شكل CD<sup>-1</sup>، تمام؟
+
+299
+00:37:49,350 --> 00:37:57,030
+يبقى بأجي آخذ الـ X ناقص الـ Y. يبقى AB<sup>-1</sup>
+
+300
+00:37:57,030 --> 00:38:04,090
+ناقص CD<sup>-1</sup>. هل هذه على الشكل هذا؟ لا والله
+
+301
+00:38:04,090 --> 00:38:10,030
+ما هي على الشكل هذا أبدا. فماذا نفعل في هذه الحالة؟ قلت
+
+302
+00:38:10,030 --> 00:38:14,590
+بسيطة، بدي أخليها على الشكل، وماحدش يقدر يمسك عليه.
+
+303
+00:38:15,490 --> 00:38:22,230
+بقول: هذا يا بنات لو جيت ضربت AB<sup>-1</sup> في D D<sup>-1</sup>
+
+304
+00:38:22,230 --> 00:38:27,850
+يعني كأنه أنا ضربت في إيش؟ الـ unity اللي هو
+
+305
+00:38:27,850 --> 00:38:35,570
+الواحد ناقص CD<sup>-1</sup>. السؤال هو: ليش أخذت DD<sup>-1</sup>؟ مش أخذت BB<sup>-1</sup>؟ مش أخذت CC<sup>-1</sup>
+
+306
+00:38:35,570 --> 00:38:39,290
+مثلا؟ الإجابة بسيطة جدا، أنا عندي D<sup>-1</sup>
+
+307
+00:38:39,290 --> 00:38:43,880
+حبيت أضع هنا الـ D<sup>-1</sup> مشان أستخدم
+
+308
+00:38:43,880 --> 00:38:49,420
+distributive law وأقول شغلة على شغلة مشان أحطه
+
+309
+00:38:49,420 --> 00:38:53,660
+على شكل عنصر موجود وين؟ في T. إذا أنا حسبت الـ
+
+310
+00:38:53,660 --> 00:38:57,820
+distributive law، هذا بدي يعطيني AB<sup>-1</sup>D -
+
+311
+00:38:57,820 --> 00:39:04,800
+C في D<sup>-1</sup>D<sup>-1</sup>.  D<sup>-1</sup> خليتها برا
+
+312
+00:39:04,800 --> 00:39:11,770
+ضرب الباقي الآن. هذا عنصر وهذا عنصر ثاني على الشكل
+
+313
+00:39:11,770 --> 00:39:19,150
+اللي عندنا هذا، وده عنصر في معكوس الثاني، يبقى
+
+314
+00:39:19,150 --> 00:39:24,710
+صار هذا موجود في T. بدأت، الـ X - Y، بدأت، الـ X - Y من البداية
+
+315
+00:39:24,710 --> 00:39:35,490
+X - Y = AD<sup>-1</sup>. AB<sup>-1</sup> هنا CB<sup>-1</sup>
+
+316
+00:39:35,490 --> 00:39:43,780
+. هنا CB<sup>-1</sup>
+
+317
+00:39:43,780 --> 00:39:47,860
+هذا AB<sup>-1</sup>. أنا عمال أقول A يعني بمفهوم صحيح
+
+318
+00:39:47,860 --> 00:39:52,400
+يبقى A بالشكل اللي عندنا ده، وهذا AB<sup>-1</sup> وهذه
+
+319
+00:39:52,400 --> 00:40:00,580
+AB<sup>-1</sup>. مظبوط، معكم حاجة تمام. يبقى صارت على
+
+320
+00:40:00,580 --> 00:40:06,890
+شكل عنصر موجود في T. بداية، آخذ الـ X - Y، يبقى
+
+321
+00:40:06,890 --> 00:40:13,850
+يساوي الـ X بـ AB<sup>-1</sup> والـ Y بـ CD<sup>-1</sup>، لكل
+
+322
+00:40:13,850 --> 00:40:23,470
+<sup>-1</sup>. طيب هذا الكلام يساوي AB<sup>-1</sup>. هذا بده
+
+323
+00:40:23,470 --> 00:40:32,730
+يعطيني C<sup>-1</sup>D.  إيه؟
+
+324
+00:40:32,730 --> 00:40:41,970
+B<sup>-1</sup>  زي ما هي. CD<sup>-1</sup>. E<sup>-1</sup>  كل C
+
+325
+00:40:47,070 --> 00:40:54,130
+<sup>-1</sup> D<sup>-1</sup>.<sup>-1</sup> اللي هو D. صح؟ أيوة، طب
+
+326
+00:40:54,130 --> 00:41:00,540
+ليش قلبتهم؟ لأن احنا أخذنا في الـ group إن الـ AB<sup>-1</sup>
+
+327
+00:41:00,540 --> 00:41:04,800
+لكل <sup>-1</sup> يساوي B<sup>-1</sup>A<sup>-1</sup>. هذا هو الصحيح
+
+328
+00:41:04,800 --> 00:41:12,800
+لأن هذا في الـ commutative. نظرًا لـ commutative، خلت
+
+329
+00:41:12,800 --> 00:41:17,400
+كل واحد في مكانه وحطيت اللي هو الـ <sup>-1</sup> تبعه. هذا
+
+330
+00:41:17,400 --> 00:41:23,250
+يمنعني. بقدر أكتب A دي، ما فيش فيها <sup>-1</sup>، وهذا بقدر
+
+331
+00:41:23,250 --> 00:41:29,710
+أكتب، و BC لكل <sup>-1</sup> لأن الكمبيوتر مش BC
+
+332
+00:41:29,710 --> 00:41:34,150
+كلها BC، حتى لو حطيتها BC بتفرقش. إنما يبقى صار
+
+333
+00:41:34,150 --> 00:41:39,110
+element في معكوس الثاني موجود في T ولا لا، يبقى
+
+334
+00:41:39,110 --> 00:41:44,370
+هذا belongs to T. subfield.
+
+335
+00:41:51,540 --> 00:41:57,200
+إيه صار فيه؟ طيب
+
+336
+00:41:57,200 --> 00:42:02,960
+حتى الآن احنا وين والنتيجة وين؟ أنا بقول: صار فيه
+
+337
+00:42:02,960 --> 00:42:12,060
+الـ isomorphic to Q. إذا أنا بدي أروح أعرف define الـ
+
+338
+00:42:12,060 --> 00:42:20,320
+mapping من T إلى Q
+
+339
+00:42:23,580 --> 00:42:32,920
+by  Φ(element AB<sup>-1</sup>) بديها
+
+340
+00:42:32,920 --> 00:42:39,600
+element في Q. الـ Q (rational numbers)، يبقى A على B
+
+341
+00:42:39,600 --> 00:42:46,300
+وB مالها؟ لا تساوي صفر. يبقى فعلا هذه في Q و
+
+342
+00:42:46,300 --> 00:42:52,590
+فعلا هذه في Q. إذا أثبتت أن الـ Φ هي one
+
+343
+00:42:52,590 --> 00:42:59,130
+to one وأنتم بيكون خلصنا الـ isomorphism. مظبوط؟
+
+344
+00:42:59,130 --> 00:43:07,530
+إذا بدي أقول: Φ is a homomorphism. نقطة الأولى
+
+345
+00:43:07,530 --> 00:43:16,530
+إذا بدي آخذ الـ X بدها تساوي AB<sup>-1</sup>
+
+346
+00:43:16,530 --> 00:43:23,620
+وY بدها تساوي CD<sup>-1</sup>، اللي موجودة وين؟ اللي
+
+347
+00:43:23,620 --> 00:43:28,500
+موجودة في T. بدي
+
+348
+00:43:28,500 --> 00:43:37,760
+آخذ Φ(X + Y)، يبقى Φ(X)  لها AB<sup>-1</sup>
+
+349
+00:43:37,760 --> 00:43:48,220
++ CD<sup>-1</sup>. هذا شكله موجود في T هيك؟
+
+350
+00:43:48,220 --> 00:43:56,930
+ما بقدرش. مش صحيح. نضبطهم. يمكن نضبطها، بقول: بسيطة
+
+351
+00:43:56,930 --> 00:44:05,650
+إيش رأيكم؟ هذه أكتبها Φ(AB<sup>-1</sup>) مضروبة في D
+
+352
+00:44:05,650 --> 00:44:15,030
+D<sup>-1</sup> يعني الـ unity + الثانية CD<sup>-1</sup>
+
+353
+00:44:15,030 --> 00:44:19,870
+بدي أضربها في الـ BB<sup>-1</sup> اللي هو الـ unity كذلك
+
+354
+00:44:19,870 --> 00:44:31,680
+تمام؟ يبقى هذا الكلام يثبت... يثبت Φ، عندك هنا الـ
+
+355
+00:44:31,680 --> 00:44:39,920
+A دي مالها دعوة، مظبوط، في الـ B<sup>-1</sup> دي <sup>-1</sup>
+
+356
+00:44:39,920 --> 00:44:44,340
+خليت اللي مش فيهم <sup>-1</sup> مع بعض، واللي فيهم الـ
+
+357
+00:44:44,340 --> 00:44:52,710
+<sup>-1</sup> مع بعض. وهنا +  AD + BC. فاهمين؟ في الـ B<sup>-1</sup>
+
+358
+00:44:52,710 --> 00:45:00,790
+D<sup>-1</sup>. صار الـ element هذا هو الـ element
+
+359
+00:45:00,790 --> 00:45:08,110
+هذا، صح؟ بقدر أستخدم الـ distributive law. يبقى Φ
+
+360
+00:45:08,110 --> 00:45:19,250
+(AD + BC) كله في الـ BD<sup>-1</sup>. صار هذا
+
+361
+00:45:19,250 --> 00:45:26,570
+element في معكوسه الثاني، يبقى موجود في T ولا لا؟ إذا
+
+362
+00:45:26,570 --> 00:45:35,410
+هذا لما يؤثر عليه الفعل بيساوي AD + BC مقسوما
+
+363
+00:45:35,410 --> 00:45:40,710
+على BD. كنت من اكتشفتوا ليه ولا لا؟ هل اللي عملتوه هل
+
+364
+00:45:40,710 --> 00:45:46,230
+بينفع نعملوا في الخطوة اللي فاتت؟ X - Y. X - Y
+
+365
+00:45:46,230 --> 00:45:51,640
+ما ضبطتش ليه؟ لو مثلا عملناها زيه، بس اسمها
+
+366
+00:45:51,640 --> 00:45:55,620
+ما عنديش مشكلة، ما عنديش مشكلة، هذا أطول من هذا
+
+367
+00:45:55,620 --> 00:46:00,720
+شوية، لكن نفس الفكرة، نفس الفكرة. يبقى هذا الكلام
+
+368
+00:46:00,720 --> 00:46:05,480
+يساوي، بتوزع البسط على المقام، بتروح الـ D مع D،
+
+369
+00:46:05,480 --> 00:46:10,640
+بتطلع A على B. هذه بتروح الـ B مع الـ B، بتطلع
+
+370
+00:46:10,640 --> 00:46:22,180
+C على D. هذه مين؟ هذه Φ(AB<sup>-1</sup>) + Φ(CD<sup>-1</sup>). يعني Φ(X) + Φ(Y). هذا لسه نص
+
+371
+00:46:22,180 --> 00:46:30,540
+homomorphism.
+
+372
+00:46:30,540 --> 00:46:31,840
+الـ homomorphism.
+
+374
+00:46:50,600 --> 00:47:01,880
+يبقى أنا Φ(XY) = Φ(AD<sup>-1</sup> في CD<sup>-1</sup>)
+
+375
+00:47:01,880 --> 00:47:12,600
+يعني بقدر أقول: هذا Φ(AC في BD) الكل
+
+376
+00:47:12,600 --> 00:47:16,040
+<sup>-1</sup>. تمام؟
+
+377
+00:47:19,960 --> 00:47:27,100
+فبنعملش خطوة واحدة. يعني بقول: هذا AC B<sup>-1</sup>
+
+378
+00:47:27,100 --> 00:47:40,760
+D<sup>-1</sup> اللي بقدر أكتب فيه AC / BD. الكل <sup>-1</sup>. هذا
+
+379
+00:47:40,760 --> 00:47:49,080
+الكلام ينسب حسب الـ definition. يعني هذا AC على BD
+
+380
+00:47:49,790 --> 00:47:59,690
+يعني مين؟ يعني A على B في C على D.  A على B ليه؟ Φ
+
+381
+00:47:59,690 --> 00:48:09,030
+(AD<sup>-1</sup>) وهذه Φ(CD<sup>-1</sup>). يعني Φ
+
+382
+00:48:09,030 --> 00:48:17,710
+X في مين؟ في Φ(Y). يبقى يعني هذا كلام Φ
+
+383
+00:48:17,710 --> 00:48:27,320
+homomorphism. يبقى هنا Φ is a homomorphism. بنأتي
+
+384
+00:48:27,320 --> 00:48:34,360
+للأعلى لـ Φ is one to one. يبقى
+
+385
+00:48:34,360 --> 00:48:41,720
+بدي آخذ صورتين، Φ(AB<sup>-1</sup>) بدي أساوي Φ
+
+386
+00:48:41,720 --> 00:48:50,250
+(CD<sup>-1</sup>). يبقى then صورة هذه اللي هي مين؟ A على
+
+387
+00:48:50,250 --> 00:48:57,530
+B، وصورة هذا مين؟ C على D. إذا هذا الكلام بدي يعطيني
+
+388
+00:48:57,530 --> 00:49:06,690
+AD بدي يساوي CD. طيب، إيش رأيك لو جيت بقول لك: هذا الـ
+
+389
+00:49:06,690 --> 00:49:16,590
+AD في الـ B<sup>-1</sup>D<sup>-1</sup> بدي يساوي الـ BC الـ B<sup>-1</sup>
+
+390
+00:49:16,590 --> 00:49:23,590
+D<sup>-1</sup>. يعني ضربت في نفس مين؟ في
+
+391
+00:49:23,590 --> 00:49:31,290
+نفس الرقم. طب هذا إيش بده يعطينا؟ هذا بده يعطينا الـ
+
+392
+00:49:31,290 --> 00:49:38,690
+AB<sup>-1</sup> الـ AB<sup>-1</sup> في الـ DD<sup>-1</sup>، وهذا
+
+393
+00:49:38,690 --> 00:49:46,980
+بده يعطينا الـ BD<sup>
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4309340466b3e8e8f6e58e67eadf143ca8ba9b26
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_postprocess.srt
@@ -0,0 +1,1608 @@
+1
+00:00:21,060 --> 00:00:25,280
+بسم الله الرحمن الرحيم نكمل ما ابتدأناه في
+
+2
+00:00:25,280 --> 00:00:30,860
+المحاضرة الماضية وهو chapter a ring homomorphism
+
+3
+00:00:30,860 --> 00:00:35,600
+آخر حاجة كان معاك المرة اللي فتت مثال والآن نأتي
+
+4
+00:00:35,600 --> 00:00:42,180
+إلى نظرية جديدة النظرية بتقول ما يعني little r ب
+
+5
+00:00:42,180 --> 00:00:44,420
+ring with unit one
+
+6
+00:00:48,500 --> 00:00:54,500
+ذن دي mapping عرفنا function من ال Z إلى R طبعا ال
+
+7
+00:00:54,500 --> 00:01:00,020
+Z دي هي مجموعة الأعداد الصحيحة إلى ring R given by
+
+8
+00:01:00,020 --> 00:01:05,800
+Phi of N يساوي N في 1 بدنا نثبت أن هذه عبارة عن
+
+9
+00:01:05,800 --> 00:01:11,880
+ring homomorphism مشان هيك ال ring homomorphism في
+
+10
+00:01:11,880 --> 00:01:17,160
+عندي two conditions بدنا انحققهمالـ condition هو
+
+11
+00:01:17,160 --> 00:01:21,000
+اللي بيقول لو كان two elements x و y موجودات في ال
+
+12
+00:01:21,000 --> 00:01:25,620
+ring و في لما اتأثر على هذا المجموع يبقى بيسوي في
+
+13
+00:01:25,620 --> 00:01:32,460
+of x زائد في of y و لو في أثرت على الضرب x في y
+
+14
+00:01:32,460 --> 00:01:37,800
+الناتج بيكون في of x في في of y يبقى بنروح نطبق
+
+15
+00:01:37,800 --> 00:01:43,420
+هذا الكلام على ال ring اللي قدامنا هذايبقى بدي
+
+16
+00:01:43,420 --> 00:01:49,980
+أبدأ الآن بدي أقول له افترض عندي M و N أعداب صحيحة
+
+17
+00:01:49,980 --> 00:01:58,380
+موجودة في Z then بدي أخد تأثير ال Phi على M زائد
+
+18
+00:01:58,380 --> 00:02:05,600
+ال N حسب التعريف اللي عندنا يبقى هذا الكلام M زائد
+
+19
+00:02:05,600 --> 00:02:14,350
+N مضغوف من ال one هذا بده يساويبتساوي ايه؟ بده
+
+20
+00:02:14,350 --> 00:02:20,610
+بيساوي ال M زائد N هدول integers يبقى عبارة بقدر
+
+21
+00:02:20,610 --> 00:02:26,830
+احطهم واحد زائد واحد زائد واحد M زائد N من المرات
+
+22
+00:02:26,830 --> 00:02:35,030
+يبقى هذا الكلام واحد زائد واحد زائد واحد زائد واحد
+
+23
+00:02:35,030 --> 00:02:46,180
+كم مرة هدول؟ M زائد N timeيبقى M زائد N من المرات
+
+24
+00:02:46,180 --> 00:02:52,280
+يعني عدد هدول اللي عندنا كل واحد فيهم لما نجمعهم
+
+25
+00:02:52,280 --> 00:02:59,800
+يكون عددهم M زائد M طيب تمام ممكن أجسمهم إلى جسمين
+
+26
+00:02:59,800 --> 00:03:05,640
+القسم الأول واحد زائد واحد زائد زائد واحد هدول
+
+27
+00:03:05,640 --> 00:03:13,340
+بتاخدهم M times زائدبرضه واحد زائد واحد زائد زائد
+
+28
+00:03:13,340 --> 00:03:23,180
+واحد وهدول in times يبقى بناء عليه هذا بالدرساه M
+
+29
+00:03:23,180 --> 00:03:31,240
+في one زائد هدول عددهم in يبقى in في one حسب ال
+
+30
+00:03:31,240 --> 00:03:38,460
+definition يبقى الأول Phi of M والتاني Phi of M
+
+31
+00:03:39,000 --> 00:03:44,440
+بناء عليه أخدنا Phi of M زائد N لجينا النتيجة
+
+32
+00:03:44,440 --> 00:03:50,360
+تساوي Phi of M زائد Phi of M وبالتالي حققتنا ال
+
+33
+00:03:50,360 --> 00:03:55,080
+condition الأول من ال two conditions تبعات ال ring
+
+34
+00:03:55,080 --> 00:04:00,460
+همورفيزي بقوله أن بدنا نروح لل condition التاني
+
+35
+00:04:00,460 --> 00:04:08,360
+بدنا ناخده Phi of M في M حسب ال definition يبقى M
+
+36
+00:04:08,750 --> 00:04:17,370
+في N في واحد طيب هذا الواحد هو ال unity يبقى لو
+
+37
+00:04:17,370 --> 00:04:22,550
+ضربت ال element هذا كله في كمان unity بيغير حاجة؟
+
+38
+00:04:22,550 --> 00:04:29,190
+لأ يبقى هذا الكلام M N في ال unity في كمان ال
+
+39
+00:04:29,190 --> 00:04:38,130
+unity بيغيرش شيء طيب الآن هذا بده يساوي ال Mفي ال
+
+40
+00:04:38,130 --> 00:04:47,210
+one مضروب كذلك N في one الأولى هذه اللى عبارة عن
+
+41
+00:04:47,210 --> 00:04:55,990
+مين صورة ال M والتانى هذى صورة ال N يبقى بناء عليه
+
+42
+00:04:55,990 --> 00:05:02,370
+Phi of M في N طلع عندي Phi of M في Phi of N يبقى
+
+43
+00:05:02,370 --> 00:05:15,830
+Thus وهكذا Phi isEarring Homomorphism الآن
+
+44
+00:05:15,830 --> 00:05:24,110
+على هذه النظرية فيه ثلاث نتائج نبدأ بالنتيجة
+
+45
+00:05:24,110 --> 00:05:30,330
+الأولى على هذه النظرية يبقى ال first crawler بتقول
+
+46
+00:05:30,330 --> 00:05:35,330
+ما ياتي crawler crawler one
+
+47
+00:05:38,760 --> 00:05:46,640
+بيقول if ال R is a ring with unity if ال R is a
+
+48
+00:05:46,640 --> 00:05:56,140
+ring with unity ring with unity and the
+
+49
+00:05:56,140 --> 00:06:07,560
+characteristic of R and the characteristic of R is
+
+50
+00:06:09,390 --> 00:06:19,530
+and greater than zero then الـR
+
+51
+00:06:19,530 --> 00:06:31,810
+contains a subring contains a subring contains
+
+52
+00:06:31,810 --> 00:06:38,490
+a subring isomorphic to
+
+53
+00:06:40,260 --> 00:06:53,440
+زد ان if the characteristic
+
+54
+00:06:53,440 --> 00:07:01,320
+of R is zero then
+
+55
+00:07:01,320 --> 00:07:08,480
+R contains is something then R contains
+
+56
+00:07:23,490 --> 00:07:27,970
+isomorphic to z
+
+57
+00:07:46,830 --> 00:07:50,870
+يبقى النظرية هذه اللي بين أدينا عبارة عن نقطتين
+
+58
+00:07:50,870 --> 00:07:57,610
+وليست نقطة واحدة النقطة الأولى بتقول ماذي؟ النقطة
+
+59
+00:07:57,610 --> 00:08:01,910
+المشتركة بيقول you put an R ring with unity إذا
+
+60
+00:08:01,910 --> 00:08:07,670
+كان ال characteristic ل R هو N يبقى ال R فيها sub
+
+61
+00:08:07,670 --> 00:08:12,870
+ring isomorphic ل ZN وإذا كان نقطة ثانية إذا كان
+
+62
+00:08:12,870 --> 00:08:17,490
+ال characteristic لل ring R هو Zeroيبقى ال ring
+
+63
+00:08:17,490 --> 00:08:23,170
+هذه تحتوي على sub ring isomorphic لست of integers
+
+64
+00:08:23,170 --> 00:08:28,870
+اللي هو Z أو اللي هي Z نروح نثبت صحة هذه ال
+
+65
+00:08:28,870 --> 00:08:34,330
+crawlery وهذه ال crawlery أساسية لمين ال crawlers
+
+66
+00:08:34,330 --> 00:08:38,330
+اللي بيجوا مين اللي بيجوا بعديها طيب خلي أقولكوا
+
+67
+00:08:38,330 --> 00:08:43,230
+هنا الآن ماحددتش الشكل ال unity يبقى أنا بدي أفرض
+
+68
+00:08:43,230 --> 00:08:49,120
+أن ال unityاللي هو عبارة عن مين؟ الواحدة صحيح يبقى
+
+69
+00:08:49,120 --> 00:09:03,880
+let ال one be the unity of the ring R مافيش
+
+70
+00:09:03,880 --> 00:09:09,020
+بقول هنا قال لي إذا ال characteristic يساوي ان
+
+71
+00:09:09,020 --> 00:09:16,220
+يبقى ال R contains a sub ringIsomorphic ل ZN يبقى
+
+72
+00:09:16,220 --> 00:09:24,200
+انا بدي اخلق soft drink بروح اقول له لات ال S كل
+
+73
+00:09:24,200 --> 00:09:31,260
+العناص K المضروبة في واحد بحيث ال K هذا عدد اخدته
+
+74
+00:09:31,260 --> 00:09:37,400
+من مين اخدته من Z يبقى
+
+75
+00:09:41,040 --> 00:09:48,440
+افترضت انه عندى 6S الـ S هذه هي حاصل ضرب عدد من Z
+
+76
+00:09:48,440 --> 00:09:54,800
+مضروب في مين في الواحد الصحيح انا ابدعي الان ان ال
+
+77
+00:09:54,800 --> 00:10:06,760
+S is a sub ring يبقى then ال S is a sub ring شو
+
+78
+00:10:06,760 --> 00:10:14,480
+السبب؟ becauseالنقطة الأولى ال S هذه is non-empty
+
+79
+00:10:14,480 --> 00:10:25,740
+ال S is non-empty على الأقل فيها عنصر هو العنصر
+
+80
+00:10:25,740 --> 00:10:35,560
+الصفرين because ال zero بده يساوي zero في واحد
+
+81
+00:10:35,560 --> 00:10:43,150
+وهذا موجود هناموجود في اسم يبقى none in نقطة ثانية
+
+82
+00:10:43,150 --> 00:10:52,330
+بدى افترض انه عندى عنصرين موجودات في اسم يبقى let
+
+83
+00:10:52,330 --> 00:11:02,150
+x و ال y موجودات في اسم then شكل ال x بدى يسوي
+
+84
+00:11:02,150 --> 00:11:06,170
+مثلا k في ال one and
+
+85
+00:11:20,220 --> 00:11:27,980
+يبقى K في الـ 1 minus M في الـ 1 حسب الـ
+
+86
+00:11:27,980 --> 00:11:35,880
+distributive law يبقى K minus M في الـ 1الفرق ما
+
+87
+00:11:35,880 --> 00:11:41,480
+بين two integers هو integer مظبوط مضروب فيه ان
+
+88
+00:11:41,480 --> 00:11:48,820
+يبقى صار شكله موجود في S يبقى هذا بده يعطينا ان ال
+
+89
+00:11:48,820 --> 00:11:56,360
+X ناقص ال Y موجودة في S الآن مشان أثبتها ال
+
+90
+00:11:56,360 --> 00:12:02,480
+subring ال conditioning تالت بدي اروح اخو اخد حاصل
+
+91
+00:12:02,480 --> 00:12:08,840
+ضرب عنصرينمن نفس ال S بدي أكون موجود في S إذا لو
+
+92
+00:12:08,840 --> 00:12:15,300
+رحت أخدت ال X في Y ال X في Y عبارة عن مين اللي هو
+
+93
+00:12:15,300 --> 00:12:23,160
+K في واحد مضرب في ال M في واحد لإن ال X أخدته ال K
+
+94
+00:12:23,160 --> 00:12:29,940
+في 1 و ال Y ال M في 1 يبقى هذا الكلام بقدر أقوله
+
+95
+00:12:29,940 --> 00:12:36,710
+على شكل K M في 1لأن ال one في ال one بال one
+
+96
+00:12:36,710 --> 00:12:44,150
+itself لأن هو ال unity طيب هذا الصيغة ال K في M مش
+
+97
+00:12:44,150 --> 00:12:49,210
+هجرع ال element موجود في Z يكون مضروف في one يبقى
+
+98
+00:12:49,210 --> 00:12:57,250
+بناء عليه هذا يعطي لي ان ال X في Y موجود في S و
+
+99
+00:12:57,250 --> 00:13:10,960
+هكذا ال S is a sub ringof subring of R طب حتى الآن
+
+100
+00:13:10,960 --> 00:13:17,360
+أنا بس خلقت subring بس إيش بيقول هنا هو ال
+
+101
+00:13:17,360 --> 00:13:23,660
+characteristic فهو لو كان يساوي LN يبقى R contains
+
+102
+00:13:23,660 --> 00:13:31,800
+لsubring هيه جبتها عايزة و مرفقة لمين ل ZNيبقى انا
+
+103
+00:13:31,800 --> 00:13:38,600
+بدي اجيب homomorphism من ال sub ring هذه الى بعرفش
+
+104
+00:13:38,600 --> 00:13:43,880
+مين تطلع هو جالي لمين لزد ان تمام؟ بتكون عندك
+
+105
+00:13:43,880 --> 00:13:48,780
+isomorphism بقوله بسيطة خالص يبقى بروح بقوله
+
+106
+00:13:48,780 --> 00:13:55,520
+define if a mapping او function
+
+107
+00:14:00,360 --> 00:14:13,020
+الـ Z إلى .. والله من S إلى Z من S إلى Z عفوا من Z
+
+108
+00:14:13,020 --> 00:14:19,220
+إلى S هذي والله هذي بتفرقش عنها بس مشان نلتزم بنص
+
+109
+00:14:19,220 --> 00:14:27,210
+النظرية النظرية اللي من Z إلى A يبقى من Z إلى Sهو
+
+110
+00:14:27,210 --> 00:14:38,070
+الله من z on to s تمام؟ ايه؟ تمام؟ by five
+
+111
+00:14:38,070 --> 00:14:47,570
+of .. بده اخد element من وين؟ من z five of m مثلا
+
+112
+00:14:47,570 --> 00:14:52,930
+يسوى ال element اللي هنا شكله m في one طب احنا
+
+113
+00:14:52,930 --> 00:14:58,400
+ماعملاش ان الصبر يجعل زوجنا مصابر كيف؟ماوصلناش لسه
+
+114
+00:14:58,400 --> 00:15:02,480
+لل isomorphism الساعة ان اعرفنا function لأ بس
+
+115
+00:15:02,480 --> 00:15:06,080
+احنا جبنا ال sub ring جبنا ال sub ring صحيح لكن من
+
+116
+00:15:06,080 --> 00:15:11,560
+ال sub ring ل ZN سوينا حاجة؟ لأ ولا حاجة ماسويناش
+
+117
+00:15:11,560 --> 00:15:16,500
+اشي لش مشينا عنها؟ مامشيناش رايحيني لها دكتور يزيد
+
+118
+00:15:16,500 --> 00:15:20,760
+from us يزيد from us بس وصبر شوية بنت انا ماوصلناش
+
+119
+00:15:20,760 --> 00:15:25,760
+ل ZN انا هوصلك ل ZN بسهولة مش سهل انك تجي اقلبه
+
+120
+00:15:25,760 --> 00:15:32,210
+ساعتنالأ بس هو صبر شويه، فاحنا بقول عرفنا Phi من Z
+
+121
+00:15:32,210 --> 00:15:40,190
+الى Subring هذي بمين ب Phi of M يسوى M في 100 في
+
+122
+00:15:40,190 --> 00:15:45,090
+الواحد طيب هذي مش هو نص النظرية؟ يبقى هذي
+
+123
+00:15:45,090 --> 00:15:53,690
+homomorphism يبقى then .. then Phi is a
+
+124
+00:15:53,690 --> 00:16:00,540
+homomorphismهذا الكلام جيبته من أين؟ from the
+
+125
+00:16:00,540 --> 00:16:08,200
+أعضاء الـ Theorem يبقى
+
+126
+00:16:08,200 --> 00:16:14,500
+صار عندهم Homomorphism، مظبوط؟
+
+127
+00:16:14,500 --> 00:16:19,160
+يبقى فيها عندنا درية اسمها الـ Isomorphism Theorem
+
+128
+00:16:19,160 --> 00:16:29,350
+سمعنا فيها سمعنا فيها؟ طيبيبقى by the first
+
+129
+00:16:29,350 --> 00:16:34,230
+isomorphism
+
+130
+00:16:34,230 --> 00:16:39,070
+theorem
+
+131
+00:16:39,070 --> 00:16:42,690
+الـ
+
+132
+00:16:42,690 --> 00:16:55,760
+Z موديون الكيرن للـ 5 ايزو مورفك لل 5 of Zمين
+
+133
+00:16:55,760 --> 00:17:02,740
+الـPhi of Z؟ اللي هي S لإنه جالي Onto يبقى هذه
+
+134
+00:17:02,740 --> 00:17:08,860
+بالـE بدأت ساوى S طيب في معلومة حتى لأنا لم
+
+135
+00:17:08,860 --> 00:17:15,600
+نستخدمها إيش اللي بستخدمها؟ ال characteristic يبقى
+
+136
+00:17:15,600 --> 00:17:24,240
+هنا F ال characteristic للـR
+
+137
+00:17:24,590 --> 00:17:33,170
+is n هو أكبر مني الـ zero then الـ kernel ال alpha
+
+138
+00:17:33,170 --> 00:17:40,750
+هو ال principle ideal generated by n هذا بده قرار
+
+139
+00:17:40,750 --> 00:17:47,390
+يبقى بدنا ياكي تعمليله شك في البيت كأن بدأ أخد
+
+140
+00:17:47,390 --> 00:17:50,790
+element في ال kernel أثبت أنه في ال principle
+
+141
+00:17:50,790 --> 00:17:55,220
+ideal generated by nوالعملية العكسية طبعا سوينالك
+
+142
+00:17:55,220 --> 00:18:00,060
+قبل هيك أثبتنا أكتر من مرة كلام زي هيك يبقى بدنا
+
+143
+00:18:00,060 --> 00:18:05,220
+يحكي تثبتلي هذا الكلام مدام ال kernel هو ال
+
+144
+00:18:05,220 --> 00:18:09,320
+principle id generated by M إذا بقدر استخدم ال
+
+145
+00:18:09,320 --> 00:18:17,060
+kernel بال principle id generated by M ال
+
+146
+00:18:17,060 --> 00:18:26,570
+S أيزو موافق لل Zتبع الكيرن الانفاي اللي هو بده
+
+147
+00:18:26,570 --> 00:18:31,850
+يساوي Z مو موديولي ريفرنسيبال ايديو الـ generated
+
+148
+00:18:31,850 --> 00:18:42,410
+by N طيب سؤال مين هي ال رنج هذي؟ الاشة ZN صح ولا
+
+149
+00:18:42,410 --> 00:18:49,730
+لأ؟ يبقى هذي تساوي مين؟ تساوي ZN بناء ان عليه صار
+
+150
+00:18:49,730 --> 00:18:57,090
+ال sub ring SIsomorphic لمين الى Z إن و هو المطلوب
+
+151
+00:18:57,090 --> 00:19:01,770
+يبقى الاستعجلتوا له استعجلتوا عليه تو هاد احنا
+
+152
+00:19:01,770 --> 00:19:06,690
+أثبتنا بكل سهولة باستخدام ال first isomorphism
+
+153
+00:19:06,690 --> 00:19:13,850
+theorem حد فيكم تسأل أي سؤال قولي ليش أخدنا ال Phi
+
+154
+00:19:13,850 --> 00:19:20,020
+إن هقمتوا ال Z لأسفل؟ عشان نخلي اسم هي Phi of Zلأن
+
+155
+00:19:20,020 --> 00:19:26,080
+ال first isomorphism تقول لو كان Phi من مين؟ من
+
+156
+00:19:26,080 --> 00:19:32,860
+function او من R إلى S فبدي اخد ال element ال ..
+
+157
+00:19:32,860 --> 00:19:38,620
+ال isomorphism Phi of R صورة ال R كلها في main في
+
+158
+00:19:38,620 --> 00:19:44,360
+ال ring التانية اللي هي S هنا في اي تساوي الآخر؟
+
+159
+00:19:44,360 --> 00:19:51,320
+طيب بدنا نروح الآن ل crawl rear عقام 2بتخلي نص
+
+160
+00:19:51,320 --> 00:19:57,920
+النظرية مشان نطبق عليها الكرونة
+
+161
+00:19:57,920 --> 00:20:13,500
+هذي؟
+
+162
+00:20:13,500 --> 00:20:20,590
+كيف اجت؟ ممتاز، الحين خدي انه رقم ايه عاجبك؟قداش
+
+163
+00:20:20,590 --> 00:20:26,690
+متكيّب؟ عشرة عشرة ممتاز جدا زد فيها كام رقم؟ عشرة
+
+164
+00:20:26,690 --> 00:20:32,570
+عشرة ولا ملا مزايا كل رقم يجب أن يعمل مضيه له عشرة
+
+165
+00:20:32,570 --> 00:20:36,770
+يبقى زي الواحد اتنين لغاية تسعة سببات زائد ال
+
+166
+00:20:36,770 --> 00:20:39,630
+principle of identity generated by him لمن صلى
+
+167
+00:20:39,630 --> 00:20:42,970
+العشرة هو نوع صفر صفر يعني ال principle of
+
+168
+00:20:42,970 --> 00:20:46,110
+identity generated by him الاحداشر اعتبر واحد
+
+169
+00:20:46,110 --> 00:20:51,730
+اتناشر اعتبر اتنين وهكذايبقى بيبقى عند ZL و هو
+
+170
+00:20:51,730 --> 00:21:03,130
+المخطوط تمام طيب نجي للكرولري رقم اتنين يبقى
+
+171
+00:21:03,130 --> 00:21:07,630
+كرولري اتنين
+
+172
+00:21:07,630 --> 00:21:15,950
+بيقول for any positive integer M for any positive
+
+173
+00:21:18,860 --> 00:21:25,360
+انتجة M لمعرفة
+
+174
+00:21:25,360 --> 00:21:35,820
+لمعرفة
+
+175
+00:21:35,820 --> 00:21:53,030
+Phi من Z إلى ZM given byبعد ذلك فاي او X بس هو X
+
+176
+00:21:53,030 --> 00:22:00,190
+موديولو M X موديولو M is a ring homomorphism
+
+177
+00:22:17,510 --> 00:22:26,490
+خدّي بالك يبجي احنا بنعرف function refine a
+
+178
+00:22:26,490 --> 00:22:42,410
+mapping لو في من z الى zm باي طلعيني كويسي في of x
+
+179
+00:22:42,410 --> 00:22:52,650
+يسوى x modulo mالـ X هذا موجود في Z و لا في ZM؟ في
+
+180
+00:22:52,650 --> 00:22:58,870
+Z يعني انتجار صح؟ يبقى الـ X عجبار عن انتجار إذا
+
+181
+00:22:58,870 --> 00:23:11,050
+بقدر أقول هذا X في واحد M ZM الـ X modulo M جد ما
+
+182
+00:23:11,050 --> 00:23:16,050
+يكون هذا الرقم هو عبارة عن X في واحدوهذا موجود في
+
+183
+00:23:16,050 --> 00:23:21,990
+ZM مظبوط هك؟ صح؟ طيب يبقى ال function صلة بالشكل
+
+184
+00:23:21,990 --> 00:23:28,990
+هذا بنص النظرية ايه عندي؟ Phi من Z ل R Phi of N
+
+185
+00:23:28,990 --> 00:23:33,290
+يساوي ال N في واحد يبقى Ring همومورفزيوم ولا لا؟
+
+186
+00:23:33,290 --> 00:23:45,790
+يبقى هنا Phi Z above theorem النظرية تعالىfive is
+
+187
+00:23:45,790 --> 00:23:54,530
+a ring homomorphism وهو المطلوب خلاصنا طيب بدي
+
+188
+00:23:54,530 --> 00:24:00,850
+أمثلك إياها عدديًا كيف هي اختاري لك إما الرقم اللي
+
+189
+00:24:00,850 --> 00:24:08,760
+يعجبك كم بدك إياها؟ تلت عشرين كم؟ تلت عشرينفخلّيه
+
+190
+00:24:08,760 --> 00:24:11,940
+بس رقم صغير ماديش أقول زد تلاتة و عشرين و بدك تفت
+
+191
+00:24:11,940 --> 00:24:15,740
+مش اكتر يعني بل إن ما ينطبق عليه ينطبق على زد
+
+192
+00:24:15,740 --> 00:24:18,960
+اتنين ينطبق على زد خمسة ينطبق على زد سبعة ينطبق
+
+193
+00:24:18,960 --> 00:24:25,420
+على زد اطلاقية تمام؟ يبقى باجي بقول ه for example
+
+194
+00:24:25,420 --> 00:24:29,740
+إن
+
+195
+00:24:29,740 --> 00:24:39,240
+مثلا زد سبعة على سبيل المثال بدي أجي أخدالان الرقم
+
+196
+00:24:39,240 --> 00:24:52,180
+مثلا احداش موجود في الوزن صح؟ طيب هذا بدي يعطينا
+
+197
+00:24:52,180 --> 00:25:01,340
+في اض احداش طبقا لهذا الكلام بدي ساوى احداشر في
+
+198
+00:25:01,340 --> 00:25:07,730
+oneطبعا يعني واحد زائد واحد زائد واحد احداشر مرة
+
+199
+00:25:07,730 --> 00:25:13,750
+بيبقى هذا الكلام بالدرسة واحد زائد واحد زائد واحد
+
+200
+00:25:13,750 --> 00:25:23,930
+زائد زائد واحد احداشر times او احداشر صمندق مجموعة
+
+201
+00:25:23,930 --> 00:25:32,530
+جامعة طبعا السبعة فيهم و بقداسي سبعة ب zeroيعني
+
+202
+00:25:32,530 --> 00:25:40,030
+هذا الكلام بده يساوي واحد زائد واحد زائد واحد سبعة
+
+203
+00:25:40,030 --> 00:25:48,690
+times زائد واحد زائد واحد زائد واحد زائد واحد
+
+204
+00:25:48,690 --> 00:25:55,070
+السبعة times يبقى كم في زيت سبعة؟ Zero يبقى هذا
+
+205
+00:25:55,070 --> 00:26:01,850
+بده يعطينا Zero زائد أربعة ويساوي أربعةموجودة في Z
+
+206
+00:26:01,850 --> 00:26:08,830
+.. موجودة في Z7 ولا لا؟ يبقى belongs to Z7 يبقى
+
+207
+00:26:08,830 --> 00:26:15,150
+ملائكة عليه أي رقم موجود في Z بدي يكون له مناظر
+
+208
+00:26:15,150 --> 00:26:21,470
+موجود وين؟ موجود في Z7 و هكذا، هاي المقصود فيها
+
+209
+00:26:21,470 --> 00:26:27,890
+طيب، هذه quaterly بسيطة و مباشرة وإن شئتم فقولوا
+
+210
+00:26:27,890 --> 00:26:31,700
+trivialأستاذ بفضل الله بفضل الله بفضل الله بفضل
+
+211
+00:26:31,700 --> 00:26:34,240
+الله بفضل الله بفضل الله بفضل الله بفضل الله بفضل
+
+212
+00:26:34,240 --> 00:26:37,240
+الله بفضل الله بفضل الله بفضل الله بفضل الله بفضل
+
+213
+00:26:37,240 --> 00:26:48,220
+الله بفضل الله بفضل
+
+214
+00:26:48,220 --> 00:26:56,160
+الله بفضل
+
+215
+00:26:56,160 --> 00:27:03,460
+اللهمابرحناش الجزء؟ ماعشان حالي طيب نى دلان سقط
+
+216
+00:27:03,460 --> 00:27:08,140
+سهوان هذا و احنا كله بنقعد الخطأ و خيره الخطأين
+
+217
+00:27:08,140 --> 00:27:14,880
+ابتوابون أبنتهم طيب الجزء الثانى بيقول لي if ال
+
+218
+00:27:14,880 --> 00:27:25,090
+characteristic لل R is zero يبقى thenالأعلى كنت
+
+219
+00:27:25,090 --> 00:27:32,370
+أرسله bring isomorphic لمين لزد يبقى فيه عند S
+
+220
+00:27:32,370 --> 00:27:41,070
+isomorphic لمين لزد طيب احنا أخدنا إذا كان الجزء
+
+221
+00:27:41,070 --> 00:27:47,110
+الأول أثبتناه أثبتنا إن ال S isomorphic لزد
+
+222
+00:27:47,110 --> 00:27:53,100
+موديوله ل principle ideal generated by Nاللي قولنا
+
+223
+00:27:53,100 --> 00:28:02,300
+هذا هو عبارة عن ماذا؟ عن ZN ثم سيبيلي هذا الان
+
+224
+00:28:02,300 --> 00:28:11,080
+اللي بحتاجه يقول if ال characteristic is zero then
+
+225
+00:28:11,080 --> 00:28:14,240
+ال
+
+226
+00:28:14,240 --> 00:28:20,540
+S isomorphic لل Z module ال principle ideal
+
+227
+00:28:20,540 --> 00:28:27,460
+generated by zeroقياسا عليها بالضبط تماما طيب هذه
+
+228
+00:28:27,460 --> 00:28:34,420
+مين بتعطينا بالضبط زد itself لإن zero تفيل أي رقم
+
+229
+00:28:34,420 --> 00:28:40,480
+بدي يطلع نفس الرقم يبقى هذا بدي يعطينا زد إذا هنا
+
+230
+00:28:40,480 --> 00:28:48,080
+east isomorphic لزد و هو المفترض طيب
+
+231
+00:28:48,080 --> 00:28:53,350
+نرجع الأن لكرولري رقم تلاتة كتبناها لا لسهبدنا
+
+232
+00:28:53,350 --> 00:29:02,030
+نكتبها يبقى الكرول لرقم ثلاثة
+
+233
+00:29:02,030 --> 00:29:11,930
+بتقول
+
+234
+00:29:11,930 --> 00:29:22,470
+ما يعني if ال F is a field if F is a field of
+
+235
+00:29:24,750 --> 00:29:30,350
+characteristic P then ال F contains a sub field
+
+236
+00:29:30,350 --> 00:29:41,330
+then ال F contains a sub field contains a sub
+
+237
+00:29:41,330 --> 00:29:44,810
+field isomorphic to
+
+238
+00:29:54,350 --> 00:30:09,870
+F الـ F has a field of characteristic zero then F
+
+239
+00:30:09,870 --> 00:30:20,290
+contains .. then ال F contains a sub field ..
+
+240
+00:30:20,290 --> 00:30:30,900
+contains a sub fieldisomorphic صفر isomorphic
+
+241
+00:30:30,900 --> 00:30:36,580
+to isomorphic
+
+242
+00:30:36,580 --> 00:30:43,220
+to the rational numbers
+
+243
+00:30:43,220 --> 00:30:46,380
+اللي
+
+244
+00:30:46,380 --> 00:30:50,640
+هو الـQ rational numbers الـQ
+
+245
+00:31:05,450 --> 00:31:12,470
+السؤال هو ال field هو ring؟
+
+246
+00:31:12,470 --> 00:31:18,390
+مش حيال الله ring كمان، competitive ring with
+
+247
+00:31:18,390 --> 00:31:24,670
+unity وكل عنصر غير صفري له معكوث، مظبوط؟ هذا ال
+
+248
+00:31:24,670 --> 00:31:30,190
+field، يبقى بقول لو كان ال F a field يعني ال ring
+
+249
+00:31:30,190 --> 00:31:35,950
+of characteristic Pيبقى الـ F الـ P الـ sub field
+
+250
+00:31:35,950 --> 00:31:45,990
+عايزه موفق لمين لـ ZP باجي بقولك الـ
+
+251
+00:31:45,990 --> 00:31:54,910
+F الـ F دي ال field دي
+
+252
+00:31:54,910 --> 00:32:06,500
+ال field of characteristic P bythe .. قاعدة الـ
+
+253
+00:32:06,500 --> 00:32:17,440
+crullery when .. crullery when there is .. there
+
+254
+00:32:17,440 --> 00:32:24,660
+is a subfield subfield
+
+255
+00:32:24,660 --> 00:32:27,400
+isomorphic
+
+256
+00:32:31,720 --> 00:32:37,440
+isomorphic to zp
+
+257
+00:32:37,440 --> 00:32:42,480
+طيب
+
+258
+00:32:42,480 --> 00:32:55,460
+كيف ال F is a field of characteristic
+
+259
+00:32:55,460 --> 00:33:00,420
+zero then there is
+
+260
+00:33:11,630 --> 00:33:22,830
+Isofield isomorphic to leukemia هذا طبق لنص من نص
+
+261
+00:33:22,830 --> 00:33:27,990
+النظرية بس هذا الكلام هيكو صعب الأخير هذا مش داخل
+
+262
+00:33:27,990 --> 00:33:32,970
+مخنا أين او تمام هنخليه يدخل مخك وان شاء الله
+
+263
+00:33:32,970 --> 00:33:41,440
+تعالىطيب، ليش؟ ليش هذا درجة الصحيفة Isomorphic
+
+264
+00:33:41,440 --> 00:33:47,480
+تجلل ال EQ؟ مش لحقيقة المنظرية هذه وإذا لكرولري
+
+265
+00:33:47,480 --> 00:33:52,620
+واحد أه مسحناها لكرولري، بتقول Isomorphic تزد،
+
+266
+00:33:52,620 --> 00:33:58,120
+مظبوط؟ هذه تجلل ال EQ، مش لزد، كله بسيطة، تعالى
+
+267
+00:33:58,120 --> 00:34:05,570
+نشوف، إذااحنا بدنا ناخد ال S هذا sub field من مين؟
+
+268
+00:34:05,570 --> 00:34:14,430
+من اللي هو ال R نفجر نرجع نقول له لأ ال S اللي هي
+
+269
+00:34:14,430 --> 00:34:21,590
+بده يساوي مين؟ بده يساوي the set of all elements A
+
+270
+00:34:21,590 --> 00:34:31,200
+عالبي such that ال A هو ال Bموجودة في الـ Z والـ B
+
+271
+00:34:31,200 --> 00:34:38,100
+لا تساوي Z كويس؟
+
+272
+00:34:38,100 --> 00:34:45,300
+يبقى أخدت S تساوي هذه، then الـ
+
+273
+00:34:45,300 --> 00:34:54,920
+S هذه بتثبتها إنها إيه؟ إنها صبفيل صابفيل طيب كويس
+
+274
+00:34:55,300 --> 00:35:00,220
+يبقى لو أخدت S على الشكل اللي عندها هذا A على B
+
+275
+00:35:00,220 --> 00:35:08,400
+بحيث ال A و ال B موجودة في Z يبقى
+
+276
+00:35:08,400 --> 00:35:13,780
+هذه sub ring بقدرة كل اللي بقدر أقوله حتى الآن sub
+
+277
+00:35:13,780 --> 00:35:21,340
+ring then ال S is a sub ring
+
+278
+00:35:23,890 --> 00:35:31,510
+طيب بدي أخد جزء منها وهذا الجزء بدي أثبت أنه sub
+
+279
+00:35:31,510 --> 00:35:39,990
+field إذا لو جيتك و ذكرت فرضيلي في عندي set T ال
+
+280
+00:35:39,990 --> 00:35:49,350
+set T على شكل AB inverse AB inverse بحيث ال A و ال
+
+281
+00:35:49,350 --> 00:36:02,460
+B موجودة في Swill be لاتساوي 0. want to show ال
+
+282
+00:36:02,460 --> 00:36:12,000
+team as a sub field. عشان نقدر نطبق الجزء الثاني
+
+283
+00:36:12,000 --> 00:36:16,460
+من النظرية اللي بنقول عليه. لإن انا بارك أقول إن
+
+284
+00:36:16,460 --> 00:36:18,340
+أنا مش سهل فدج جماعة.
+
+285
+00:36:27,960 --> 00:36:32,460
+عشان أثبت أن هذا الـ Subject خلّيني أرجع للشرطة
+
+286
+00:36:32,460 --> 00:36:39,060
+للثانوية، ماذا تعرف Subject؟ أنا لو أخدت عنصرين في
+
+287
+00:36:39,060 --> 00:36:45,020
+هذه الستة و لقيت الفرق فيما بينهم موجود فيها و لو
+
+288
+00:36:45,020 --> 00:36:49,340
+أخدت العنصر الأول في معكس الثاني و ضربتهم بيكون في
+
+289
+00:36:49,340 --> 00:36:53,560
+نفس الستةإن حدث ذلك بقول هذا ال sub field حسب ما
+
+290
+00:36:53,560 --> 00:36:58,260
+أعرف عندكم في أحد الأسئلة لأدري قداشر رقم السؤال
+
+291
+00:36:58,260 --> 00:37:03,120
+في قداشر؟ خمسة وعشرين، كويس بالنسبالي ال sub field
+
+292
+00:37:03,120 --> 00:37:09,300
+طب لاحظي ماقليش non-empty ماقليش non لأن ال field
+
+293
+00:37:09,300 --> 00:37:13,600
+دائما ال communicative و ال unity أقل حاجة في ال
+
+294
+00:37:13,600 --> 00:37:19,240
+unity صح يكون في ring يبقى كمان ال zero موجود تمام
+
+295
+00:37:19,920 --> 00:37:24,800
+طيب الان انا ادعي ان هذا sub field لذلك بدأ اخد
+
+296
+00:37:24,800 --> 00:37:32,140
+عنصرين في T يبقى بدأجي اقول افترض ان ال X و ال Y
+
+297
+00:37:32,140 --> 00:37:39,160
+موجودة في T then ال X يا بنات بدي يكون على شكل AB
+
+298
+00:37:39,160 --> 00:37:49,000
+inverse و ال Y بدي يكون على شكل CD inverse تمام؟
+
+299
+00:37:49,350 --> 00:37:57,030
+يبقى بتاعي أخد ال X ناقص ال Y. يبقى ال X B inverse
+
+300
+00:37:57,030 --> 00:38:04,090
+ناقص C D inverse. هل هذه على الشكل هذا؟ لا والله
+
+301
+00:38:04,090 --> 00:38:10,030
+ما هي على الشكل هذا أبدا. فما هيش الحالة؟ قلت
+
+302
+00:38:10,030 --> 00:38:14,590
+بسيطة، بدي أخليها على الشكل وماحدش يقدر يمسك عليه.
+
+303
+00:38:15,490 --> 00:38:22,230
+بقول هاد يا بنات لو جيت Gold X B inverse في D D
+
+304
+00:38:22,230 --> 00:38:27,850
+inverse يعني كأنه انا ضارب في ايش ال unity اللي هو
+
+305
+00:38:27,850 --> 00:38:35,570
+الواحد ناقص C D inverse السؤال هو ليش أخد D D
+
+306
+00:38:35,570 --> 00:38:39,290
+inverse مش ماخدتش B B inverse مش ماخدتش C C
+
+307
+00:38:39,290 --> 00:38:43,880
+inverse مثلاالإجابة بسيطة جدا أنا عندي D inverse
+
+308
+00:38:43,880 --> 00:38:49,420
+حبيت أخلك هنا ال answer D inverse مشان استخدم
+
+309
+00:38:49,420 --> 00:38:53,660
+distributive law و أقوله شرفني على الشجر مشان أحطه
+
+310
+00:38:53,660 --> 00:38:57,820
+على شكل answer موجود وين في T إذا انا حاسب ال
+
+311
+00:38:57,820 --> 00:39:04,800
+distributive law هذا بدي يعطيني X B inverse D ناقص
+
+312
+00:39:04,800 --> 00:39:11,770
+ال C في D inverseD inverse D inverse خلّيتها برا
+
+313
+00:39:11,770 --> 00:39:19,150
+ضال الباقية الآن هذا عنصر وهذا عنصر تاني على الشكل
+
+314
+00:39:19,150 --> 00:39:24,710
+اللي عندنا هذا و لا ده عنصر في معكوس الثاني يبقى
+
+315
+00:39:24,710 --> 00:39:35,490
+صار هذا موجود في تي بدا ال XA بدا ال XA من البداية
+
+316
+00:39:35,490 --> 00:39:43,780
+X نقص Y بيسوي AP inverseA B Inverse هنا C B
+
+317
+00:39:43,780 --> 00:39:47,860
+Inverse اه
+
+318
+00:39:47,860 --> 00:39:52,400
+هذه A B Inverse انا عمال بقول A يعني بمطبخ صحيح
+
+319
+00:39:52,400 --> 00:40:00,580
+يبقى A بالشكل اللي عندنا ده وهذا A B Inverse وهذه
+
+320
+00:40:00,580 --> 00:40:06,890
+A B Inverse مظبوط معاكوا حاجة تماميبقى صارت على
+
+321
+00:40:06,890 --> 00:40:13,850
+شكل عنصر موجود في T بداية ياخد ال X Y inverse يبقى
+
+322
+00:40:13,850 --> 00:40:23,470
+يساوي ال X ب A B inverse وال Y بC D inverse لكل
+
+323
+00:40:23,470 --> 00:40:32,730
+inverse طيب هذا الكلام يساوي A B inverseهذا بده
+
+324
+00:40:32,730 --> 00:40:41,970
+يعطيني C inverse D ايه
+
+325
+00:40:41,970 --> 00:40:47,070
+B inverse زي مانيه C D inverse E inverse كل C
+
+326
+00:40:47,070 --> 00:40:54,130
+inverse D inverse Inverse اللي هو D صح؟ ايوة طب
+
+327
+00:40:54,130 --> 00:41:00,540
+ليش مجلبتهم؟لأنه احنا أخدنا في ال group ان ال A بي
+
+328
+00:41:00,540 --> 00:41:04,800
+لكل inverse يسوي B inverse A inverse هذا هو الصحيح
+
+329
+00:41:04,800 --> 00:41:12,800
+لأن هذا في ال commutative نظرا ال commutative خلت
+
+330
+00:41:12,800 --> 00:41:17,400
+كل واحد في مكان و حطيت اللي هو ال inverse تبعه هذا
+
+331
+00:41:17,400 --> 00:41:23,250
+يمنعك بقدر اكتب ايه دي مافيش فيه inverseوهذا بقدر
+
+332
+00:41:23,250 --> 00:41:29,710
+اكتب و بي سي لكل inverse لأن الكمبيوتر مش سي بي
+
+333
+00:41:29,710 --> 00:41:34,150
+كله بي سي حتى لو حطيتها سي بي بتفرقش انما يبقى صار
+
+334
+00:41:34,150 --> 00:41:39,110
+element في معاكوس الثاني موجود في T ولا لا يبقى
+
+335
+00:41:39,110 --> 00:41:44,370
+هذا belongs to T sub field
+
+336
+00:41:51,540 --> 00:41:57,200
+إيه صار فيه طيب
+
+337
+00:41:57,200 --> 00:42:02,960
+حتى الأن احنا وين والاسبابت وين انا بقول صار فيه
+
+338
+00:42:02,960 --> 00:42:12,060
+ال isomorphic لل Q إذا أنا بدي أروح أعرف define ال
+
+339
+00:42:12,060 --> 00:42:20,320
+mapping في من T إلى ال EQ
+
+340
+00:42:23,580 --> 00:42:32,920
+by phi of T العنصر A B inverse A B inverse بديها
+
+341
+00:42:32,920 --> 00:42:39,600
+element في ال Q ال Q rational numbers يبقى A على B
+
+342
+00:42:39,600 --> 00:42:46,300
+و ال B مالها لاتساوي Zero يبقى فعلا هذه في ال Q و
+
+343
+00:42:46,300 --> 00:42:52,590
+فعلا هذه في 2 إذا أثبتت أن ال Phi همومارفزيومone
+
+344
+00:42:52,590 --> 00:42:59,130
+to one وانتوا بيكون خلصنا ال isomorphism مظبوط؟
+
+345
+00:42:59,130 --> 00:43:07,530
+إذا بدالي أقوله Phi is a homomorphism نقطة الأولى
+
+346
+00:43:07,530 --> 00:43:16,530
+إذا بدالي أخد الفائلات ال X بدها تساوي AB inverse
+
+347
+00:43:16,530 --> 00:43:23,620
+وال Y بدها تساوي CD inverseاللي موجودة وين؟ اللي
+
+348
+00:43:23,620 --> 00:43:28,500
+موجودة في T بدي
+
+349
+00:43:28,500 --> 00:43:37,760
+أخد Phi of X زائد Y يبقى Phi of ال X له A B
+
+350
+00:43:37,760 --> 00:43:48,220
+inverse زائد C D inverse هذا شكله موجود في T هيك؟
+
+351
+00:43:48,220 --> 00:43:56,930
+مقدرش مش صحيحتظبطهم يمكن تظبط معاك بقوله بسيطة
+
+352
+00:43:56,930 --> 00:44:05,650
+اشرايكوا هذه اكتبها Phi of A B inverse مضروبة في D
+
+353
+00:44:05,650 --> 00:44:15,030
+D inverse يعني ال unity زائد التانية C D inverse
+
+354
+00:44:15,030 --> 00:44:19,870
+بدي اضربها في ال B B inverse اللي هو ال unity كذلك
+
+355
+00:44:19,870 --> 00:44:31,680
+تمام؟يبقى هذا الكلام يثابر يثابر في of عندك هنا ال
+
+356
+00:44:31,680 --> 00:44:39,920
+a دي مالوش دعوة مظبوط في ال b inverse دي inverse
+
+357
+00:44:39,920 --> 00:44:44,340
+خليت اللي مش فيهم inverse مع بعض و اللي فيهم ال
+
+358
+00:44:44,340 --> 00:44:52,710
+inverse مع بعض وهنا زائد border bcفاهمين في ال B
+
+359
+00:44:52,710 --> 00:45:00,790
+inverse D inverse صار ال element هذا هو ال element
+
+360
+00:45:00,790 --> 00:45:08,110
+هذا صح بقدر استخدم ال distributive law يبقى Phi of
+
+361
+00:45:08,110 --> 00:45:19,250
+ال A D زائد ال B C كله في ال B D inverse صار هذا
+
+362
+00:45:19,250 --> 00:45:26,570
+elementفي معكوسي الثاني يبقى موجود في T ولا لا إذا
+
+363
+00:45:26,570 --> 00:45:35,410
+هذا لما يؤثر عليها الفعل بدل سوى AD زائد BC مقسوما
+
+364
+00:45:35,410 --> 00:45:40,710
+على BD كنت من اكتساف ليه ولا لا؟ هل اللي عملتوا هل
+
+365
+00:45:40,710 --> 00:45:46,230
+بينفع أعملوا في الخطوة اللي فار؟ X نقص Y X نقص Y
+
+366
+00:45:46,230 --> 00:45:51,640
+ما نزمتش ليه؟لو لسه مثلًا عملناها زيه، بس اسمه
+
+367
+00:45:51,640 --> 00:45:55,620
+ماعديش مشكلة، ماعديش مشكلة، هذا القطوع أتجل من هذا
+
+368
+00:45:55,620 --> 00:46:00,720
+شوية، لكن نفس الفكرة، نفس الفكرة، يبقى هذا الكلام
+
+369
+00:46:00,720 --> 00:46:05,480
+يسام، بتوزع البسط على المقام، بتروح ال D مع D،
+
+370
+00:46:05,480 --> 00:46:10,640
+بتطلع جدًا A على B، هذي بتروح ال B مع ال B، بتطلع
+
+371
+00:46:10,640 --> 00:46:22,180
+C على D، هذي مين؟ هذي PhiRAB Inverse زائد Phi of C
+
+372
+00:46:22,180 --> 00:46:30,540
+D Inverse يعني Phi of X زائد Phi of R هذا لسه نص
+
+373
+00:46:30,540 --> 00:46:31,840
+ال homomorphism
+
+374
+00:46:50,600 --> 00:47:01,880
+يبقى انا Phi of XY سواء Phi of AD inverse في CD
+
+375
+00:47:01,880 --> 00:47:12,600
+inverse يعني بقدر اقول هذا Phi of AC في BD الكل
+
+376
+00:47:12,600 --> 00:47:16,040
+inverse تمام؟
+
+377
+00:47:19,960 --> 00:47:27,100
+فطمة ينبلش فطمة واحدة يعني بيقول هذا AC B inverse
+
+378
+00:47:27,100 --> 00:47:40,760
+D inverse اللي بقدر اكتب في ا AC B D كل انفرز هذا
+
+379
+00:47:40,760 --> 00:47:49,080
+الكلام ينسب حسب ال definition يعني هذا AC على BD
+
+380
+00:47:49,790 --> 00:47:59,690
+يعني مين؟ يعني A على B في C على D A على B ليه؟ Phi
+
+381
+00:47:59,690 --> 00:48:09,030
+of A D Inverse وهذه Phi of C D Inverse يعني Phi of
+
+382
+00:48:09,030 --> 00:48:17,710
+X في مين؟ في Phi of Y يبقى يعني هذا كلام Phi
+
+383
+00:48:17,710 --> 00:48:27,320
+homomorphismيبقى هنا سا فاي is a homomorphism بنا
+
+384
+00:48:27,320 --> 00:48:34,360
+نجي الأعلى لفاي is one to one يبقى
+
+385
+00:48:34,360 --> 00:48:41,720
+بدي أاخد صورتين فاي of a, b inverse بدي أسوأ فاي
+
+386
+00:48:41,720 --> 00:48:50,250
+of c, d inverse يبقى then صورة هذه اللي همينA على
+
+387
+00:48:50,250 --> 00:48:57,530
+B وصورة هذا مين C على D إذا هذا الكلام بدي أعطيك
+
+388
+00:48:57,530 --> 00:49:06,690
+AD بدي سوى مين DC طيب إيش رأيك لو جيت بقولك هذا ال
+
+389
+00:49:06,690 --> 00:49:16,590
+AD في ال B inverse D inverse بدي سوى ال BCالـ B
+
+390
+00:49:16,590 --> 00:49:23,590
+inverse D inverse يعني ضربت اتنين في نفس مين في
+
+391
+00:49:23,590 --> 00:49:31,290
+نفس الرقم طب هذا ايش بده يعطينا هذا بده يعطينا ال
+
+392
+00:49:31,290 --> 00:49:38,690
+A B inverse ال A B inverse في ال D D inverse وهذا
+
+393
+00:49:38,690 --> 00:49:46,980
+بده يعطينا ال B D inverseفى C D Inverse هذا بقدرش
+
+394
+00:49:46,980 --> 00:49:53,400
+يا بنات هذا بقدرش يبقى هذا بدي يعطيك ان ال A B
+
+395
+00:49:53,400 --> 00:50:02,160
+Inverse بدي يساوي C فى D Inverse تمام طيب بدأت
+
+396
+00:50:02,160 --> 00:50:07,120
+بفاي A B Inverse بيساوي فاي فى C D Inverse ووصلت
+
+397
+00:50:07,120 --> 00:50:15,840
+لهذا يبقى فاي is one twentyأخر حاجة في القنبلة يجب
+
+398
+00:50:15,840 --> 00:50:23,740
+أن أقول خذ ال X موجودة في ال Q يجب أن أرى إنها أصل
+
+399
+00:50:23,740 --> 00:50:32,040
+في T أو لا لأ يجب أن أقول X موجودة في A على B والـ
+
+400
+00:50:32,040 --> 00:50:39,360
+B لا تساوي 0 هذا يجب أن أقول لك أن Xبساوي a على b
+
+401
+00:50:39,360 --> 00:50:45,600
+اللي هو main فاي of a بينبرت لذلك فاي is on top
+
+402
+00:50:45,600 --> 00:50:51,780
+يبقى داصر فاي is an isomorphism
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..09e0043e8c26244febb243ac4239fda701422627
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4442, "start": 21.06, "end": 44.42, "text": "بسم الله الرحمن الرحيم نكمل ما ابتدأناه في المحاضرة الماضية وهو chapter a ring homomorphism آخر حاجة كان معاك المرة اللي فتت مثال والآن نأتي إلى نظرية جديدة النظرية بتقول ما يعني little r ب ring with unit one", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 24793, 1211, 19446, 48127, 2655, 3215, 10721, 8315, 3224, 8978, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 37037, 2407, 7187, 257, 4875, 3655, 32702, 1434, 19753, 34740, 11331, 26108, 3660, 25961, 20449, 995, 4117, 9673, 25720, 13672, 1829, 6156, 2655, 2655, 50113, 6027, 4032, 6027, 148, 48506, 8717, 10721, 31371, 30731, 8717, 19913, 2288, 10632, 10874, 16254, 41891, 28239, 19913, 2288, 10632, 39894, 39648, 19446, 37495, 22653, 707, 367, 4724, 4875, 365, 4985, 472], "avg_logprob": -0.22977941877701702, "compression_ratio": 1.5885167464114833, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 21.06, "end": 21.38, 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338.76, "end": 367.56, "text": "بيقول if ال R is a ring with unity if ال R is a ring with unity ring with unity and the characteristic of R and the characteristic of R is", "tokens": [3555, 1829, 39648, 498, 2423, 497, 307, 257, 4875, 365, 18205, 498, 2423, 497, 307, 257, 4875, 365, 18205, 4875, 365, 18205, 293, 264, 16282, 295, 497, 293, 264, 16282, 295, 497, 307], "avg_logprob": -0.18497243085328272, "compression_ratio": 1.75, "no_speech_prob": 0.0, "words": [{"start": 338.76, "end": 339.16, "word": "بيقول", "probability": 0.62109375}, {"start": 339.16, "end": 339.34, "word": " if", "probability": 0.67724609375}, {"start": 339.34, "end": 339.56, "word": " ال", "probability": 0.7880859375}, {"start": 339.56, "end": 339.72, "word": " R", "probability": 0.26611328125}, {"start": 339.72, "end": 340.06, "word": " is", "probability": 0.93212890625}, {"start": 340.06, "end": 340.54, "word": " a", "probability": 0.9443359375}, {"start": 340.54, "end": 340.88, "word": " ring", "probability": 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0.58349609375}], "temperature": 1.0}, {"id": 16, "seek": 49613, "start": 466.83, "end": 496.13, "text": "يبقى النظرية هذه اللي بين أدينا عبارة عن نقطتين وليست نقطة واحدة النقطة الأولى بتقول ماذي؟ النقطة المشتركة بيقول you put an R ring with unity إذا كان ال characteristic ل R هو N يبقى ال R فيها sub ring isomorphic ل ZN وإذا كان نقطة ثانية إذا كان ال characteristic لل ring R هو Zero", "tokens": [1829, 3555, 4587, 7578, 28239, 19913, 2288, 10632, 29538, 13672, 1829, 49374, 5551, 16254, 8315, 6225, 3555, 9640, 3660, 18871, 8717, 47432, 2655, 9957, 4032, 20292, 14851, 8717, 47432, 3660, 36764, 24401, 3660, 28239, 47432, 3660, 16247, 12610, 7578, 39894, 39648, 3714, 45636, 1829, 22807, 28239, 47432, 3660, 9673, 8592, 2655, 31747, 3660, 4724, 1829, 39648, 291, 829, 364, 497, 4875, 365, 18205, 11933, 15730, 25961, 2423, 2517, 468, 299, 5296, 497, 31439, 426, 7251, 3555, 4587, 7578, 2423, 497, 8978, 11296, 1422, 4875, 307, 32702, 299, 5296, 1176, 45, 4032, 28814, 15730, 25961, 8717, 47432, 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هذه ال crawlery وهذه ال crawlery أساسية لمين ال crawlers اللي بيجوا مين اللي بيجوا بعديها طيب خلي أقولكوا هنا الآن ماحددتش الشكل ال unity يبقى أنا بدي أفرض أن ال unity", "tokens": [1829, 3555, 4587, 7578, 2423, 4875, 29538, 6055, 33753, 45865, 15844, 1422, 4875, 307, 32702, 299, 5296, 14851, 295, 41674, 13672, 1829, 31439, 1176, 34051, 13672, 1829, 39896, 1176, 8717, 32887, 5016, 8717, 12984, 3555, 2655, 20328, 5016, 3660, 29538, 2423, 24767, 2109, 37037, 24192, 2423, 24767, 2109, 5551, 3794, 32277, 10632, 32767, 9957, 2423, 24767, 433, 13672, 1829, 4724, 1829, 7435, 14407, 3714, 9957, 13672, 1829, 4724, 1829, 7435, 14407, 45030, 16254, 11296, 23032, 1829, 3555, 16490, 20292, 5551, 39648, 4117, 14407, 34105, 6024, 48506, 19446, 24401, 3215, 2655, 8592, 25124, 28820, 2423, 18205, 7251, 3555, 4587, 7578, 41850, 4724, 16254, 5551, 5172, 43042, 14739, 2423, 18205], "avg_logprob": -0.25602064001450847, "compression_ratio": 1.7468354430379747, "no_speech_prob": 0.0, "words": [{"start": 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553.48, "end": 577.4, "text": "Isomorphic ل ZN يبقى انا بدي اخلق soft drink بروح اقول له لات ال S كل العناص K المضروبة في واحد بحيث ال K هذا عدد اخدته من مين اخدته من Z يبقى", "tokens": [40, 539, 76, 18191, 299, 5296, 1176, 45, 7251, 3555, 4587, 7578, 1975, 8315, 4724, 16254, 1975, 9778, 1211, 4587, 2787, 2822, 4724, 32887, 5016, 1975, 39648, 46740, 5296, 9307, 2423, 318, 28242, 18863, 1863, 33546, 591, 9673, 11242, 32887, 49401, 8978, 36764, 24401, 4724, 5016, 1829, 12984, 2423, 591, 23758, 6225, 3215, 3215, 1975, 9778, 3215, 47395, 9154, 3714, 9957, 1975, 9778, 3215, 47395, 9154, 1176, 7251, 3555, 4587, 7578], "avg_logprob": -0.3925781105127599, "compression_ratio": 1.4012345679012346, "no_speech_prob": 0.0, "words": [{"start": 553.48, "end": 554.62, "word": "Isomorphic", "probability": 0.67470703125}, {"start": 554.62, "end": 554.86, "word": " ل", "probability": 0.15283203125}, {"start": 554.86, "end": 555.46, "word": " ZN", "probability": 0.3902587890625}, {"start": 555.46, "end": 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"probability": 0.93994140625}, {"start": 564.2, "end": 565.18, "word": " العناص", "probability": 0.880859375}, {"start": 565.18, "end": 565.9, "word": " K", "probability": 0.294921875}, {"start": 565.9, "end": 567.34, "word": " المضروبة", "probability": 0.9241943359375}, {"start": 567.34, "end": 567.58, "word": " في", "probability": 0.837890625}, {"start": 567.58, "end": 568.22, "word": " واحد", "probability": 0.96142578125}, {"start": 568.22, "end": 569.2, "word": " بحيث", "probability": 0.938232421875}, {"start": 569.2, "end": 569.5, "word": " ال", "probability": 0.67431640625}, {"start": 569.5, "end": 569.72, "word": " K", "probability": 0.869140625}, {"start": 569.72, "end": 570.12, "word": " هذا", "probability": 0.325439453125}, {"start": 570.12, "end": 570.62, "word": " عدد", "probability": 0.9659830729166666}, {"start": 570.62, "end": 571.26, "word": " اخدته", "probability": 0.79595947265625}, {"start": 571.26, "end": 571.5, "word": " من", "probability": 0.9853515625}, {"start": 571.5, "end": 571.88, "word": " مين", "probability": 0.73046875}, {"start": 571.88, "end": 573.2, "word": " اخدته", "probability": 0.8543701171875}, {"start": 573.2, "end": 575.98, "word": " من", "probability": 0.9541015625}, {"start": 575.98, "end": 576.32, "word": " Z", "probability": 0.751953125}, {"start": 576.32, "end": 577.4, "word": " يبقى", "probability": 0.8187255859375}], "temperature": 1.0}, {"id": 20, "seek": 60808, "start": 581.04, "end": 608.08, "text": "افترضت انه عندى 6S الـ S هذه هي حاصل ضرب عدد من Z مضروب في مين في الواحد الصحيح انا ابدعي الان ان ال S is a sub ring يبقى then ال S is a sub ring شو السبب؟ because", "tokens": [31845, 2655, 43042, 2655, 16472, 3224, 43242, 7578, 1386, 50, 2423, 39184, 318, 29538, 39896, 11331, 33546, 1211, 48812, 25513, 6225, 3215, 3215, 9154, 1176, 3714, 11242, 32887, 3555, 8978, 3714, 9957, 8978, 2423, 14407, 24401, 31767, 5016, 1829, 5016, 1975, 8315, 48127, 3215, 3615, 1829, 2423, 7649, 16472, 2423, 318, 307, 257, 1422, 4875, 7251, 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"probability": 0.7828776041666666}, {"start": 642.55, "end": 643.15, "word": " ثانية", "probability": 0.9637044270833334}, {"start": 643.15, "end": 645.45, "word": " بدى", "probability": 0.5538330078125}, {"start": 645.45, "end": 646.07, "word": " افترض", "probability": 0.9100341796875}, {"start": 646.07, "end": 646.81, "word": " انه", "probability": 0.6644287109375}, {"start": 646.81, "end": 647.27, "word": " عندى", "probability": 0.718505859375}, {"start": 647.27, "end": 648.47, "word": " عنصرين", "probability": 0.9295654296875}, {"start": 648.47, "end": 649.67, "word": " موجودات", "probability": 0.957275390625}, {"start": 649.67, "end": 649.91, "word": " في", "probability": 0.908203125}, {"start": 649.91, "end": 650.37, "word": " اسم", "probability": 0.993896484375}, {"start": 650.37, "end": 651.67, "word": " يبقى", "probability": 0.9659423828125}, {"start": 651.67, "end": 652.33, "word": " let", "probability": 0.81787109375}, {"start": 652.33, "end": 653.97, "word": " x", 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"word": "يبقى", "probability": 0.614898681640625}, {"start": 681.58, "end": 681.72, "word": " K", "probability": 0.11737060546875}, {"start": 681.72, "end": 682.48, "word": " في", "probability": 0.52685546875}, {"start": 682.48, "end": 682.82, "word": " الـ", "probability": 0.6300048828125}, {"start": 682.82, "end": 683.08, "word": " 1", "probability": 0.362548828125}, {"start": 683.08, "end": 684.16, "word": " minus", "probability": 0.07537841796875}, {"start": 684.16, "end": 685.06, "word": " M", "probability": 0.919921875}, {"start": 685.06, "end": 685.62, "word": " في", "probability": 0.93408203125}, {"start": 685.62, "end": 685.94, "word": " الـ", "probability": 0.919189453125}, {"start": 685.94, "end": 686.24, "word": " 1", "probability": 0.7109375}, {"start": 686.24, "end": 687.78, "word": " حسب", "probability": 0.59967041015625}, {"start": 687.78, "end": 687.98, "word": " الـ", "probability": 0.701171875}, {"start": 687.98, "end": 688.96, "word": " distributive", "probability": 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"probability": 0.8331705729166666}], "temperature": 1.0}, {"id": 31, "seek": 92628, "start": 897.28, "end": 926.28, "text": "ماوصلناش لسه لل isomorphism الساعة ان اعرفنا function لأ بس احنا جبنا ال sub ring جبنا ال sub ring صحيح لكن من ال sub ring ل ZN سوينا حاجة؟ لأ ولا حاجة ماسويناش اشي لش مشينا عنها؟ مامشيناش رايحيني لها دكتور يزيد from us يزيد from us بس وصبر شوية بنت انا ماوصلناش ل ZN انا هوصلك ل ZN بسهولة مش سهل انك تجي اقلبه ساعتنا", "tokens": [15042, 2407, 36520, 1863, 33599, 5296, 3794, 3224, 24976, 307, 32702, 1434, 21136, 995, 27884, 16472, 1975, 3615, 28480, 8315, 2445, 5296, 10721, 4724, 3794, 1975, 5016, 8315, 10874, 3555, 8315, 2423, 1422, 4875, 10874, 3555, 8315, 2423, 1422, 4875, 20328, 5016, 1829, 5016, 44381, 9154, 2423, 1422, 4875, 5296, 1176, 45, 8608, 2407, 9957, 995, 11331, 26108, 3660, 22807, 5296, 10721, 49429, 11331, 26108, 3660, 19446, 3794, 2407, 9957, 33599, 1975, 8592, 1829, 5296, 8592, 3714, 8592, 1829, 8315, 18871, 11296, 22807, 19446, 2304, 8592, 1829, 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"end": 900.0, "word": " ان", "probability": 0.24951171875}, {"start": 900.0, "end": 900.46, "word": " اعرفنا", "probability": 0.90185546875}, {"start": 900.46, "end": 901.08, "word": " function", "probability": 0.64111328125}, {"start": 901.08, "end": 902.26, "word": " لأ", "probability": 0.59417724609375}, {"start": 902.26, "end": 902.48, "word": " بس", "probability": 0.9775390625}, {"start": 902.48, "end": 902.72, "word": " احنا", "probability": 0.9345703125}, {"start": 902.72, "end": 903.06, "word": " جبنا", "probability": 0.8956705729166666}, {"start": 903.06, "end": 903.2, "word": " ال", "probability": 0.80322265625}, {"start": 903.2, "end": 903.38, "word": " sub", "probability": 0.1517333984375}, {"start": 903.38, "end": 903.68, "word": " ring", "probability": 0.55224609375}, {"start": 903.68, "end": 904.46, "word": " جبنا", "probability": 0.9072265625}, {"start": 904.46, "end": 904.58, "word": " ال", "probability": 0.483154296875}, {"start": 904.58, "end": 904.76, "word": " 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"end": 916.56, "word": " from", "probability": 0.13525390625}, {"start": 916.56, "end": 916.96, "word": " us", "probability": 0.34765625}, {"start": 916.96, "end": 917.8, "word": " يزيد", "probability": 0.83642578125}, {"start": 917.8, "end": 918.0, "word": " from", "probability": 0.904296875}, {"start": 918.0, "end": 918.38, "word": " us", "probability": 0.93505859375}, {"start": 918.38, "end": 918.9, "word": " بس", "probability": 0.866943359375}, {"start": 918.9, "end": 919.26, "word": " وصبر", "probability": 0.703857421875}, {"start": 919.26, "end": 919.7, "word": " شوية", "probability": 0.8922526041666666}, {"start": 919.7, "end": 920.0, "word": " بنت", "probability": 0.439453125}, {"start": 920.0, "end": 920.14, "word": " انا", "probability": 0.703369140625}, {"start": 920.14, "end": 920.76, "word": " ماوصلناش", "probability": 0.937109375}, {"start": 920.76, "end": 920.92, "word": " ل", "probability": 0.97998046875}, {"start": 920.92, "end": 921.34, "word": " ZN", "probability": 0.822265625}, {"start": 921.34, "end": 921.52, "word": " انا", "probability": 0.860107421875}, {"start": 921.52, "end": 922.02, "word": " هوصلك", "probability": 0.660888671875}, {"start": 922.02, "end": 922.2, "word": " ل", "probability": 0.9853515625}, {"start": 922.2, "end": 922.74, "word": " ZN", "probability": 0.91015625}, {"start": 922.74, "end": 923.94, "word": " بسهولة", "probability": 0.99375}, {"start": 923.94, "end": 924.18, "word": " مش", "probability": 0.9873046875}, {"start": 924.18, "end": 924.6, "word": " سهل", "probability": 0.9641927083333334}, {"start": 924.6, "end": 924.88, "word": " انك", "probability": 0.84619140625}, {"start": 924.88, "end": 925.12, "word": " تجي", "probability": 0.8675130208333334}, {"start": 925.12, "end": 925.76, "word": " اقلبه", "probability": 0.64910888671875}, {"start": 925.76, "end": 926.28, "word": " ساعتنا", "probability": 0.8428955078125}], "temperature": 1.0}, {"id": 32, "seek": 95537, "start": 926.49, "end": 955.37, "text": "لأ بس هو صبر شويه، فاحنا بقول عرفنا Phi من Z الى Subring هذي بمين ب Phi of M يسوى M في 100 في الواحد طيب هذي مش هو نص النظرية؟ يبقى هذي homomorphism يبقى then .. then Phi is a homomorphism", "tokens": [1211, 10721, 4724, 3794, 31439, 20328, 26890, 13412, 45865, 3224, 12399, 6156, 39319, 8315, 4724, 39648, 6225, 28480, 8315, 41435, 9154, 1176, 2423, 7578, 8511, 2937, 8032, 8848, 1829, 4724, 2304, 9957, 4724, 41435, 295, 376, 7251, 3794, 2407, 7578, 376, 8978, 2319, 8978, 2423, 14407, 24401, 23032, 1829, 3555, 8032, 8848, 1829, 37893, 31439, 8717, 9381, 28239, 19913, 2288, 10632, 22807, 7251, 3555, 4587, 7578, 8032, 8848, 1829, 3655, 32702, 1434, 7251, 3555, 4587, 7578, 550, 4386, 550, 41435, 307, 257, 3655, 32702, 1434], "avg_logprob": -0.338662777875745, "compression_ratio": 1.4421052631578948, "no_speech_prob": 0.0, "words": [{"start": 926.49, "end": 926.89, "word": "لأ", "probability": 0.760498046875}, {"start": 926.89, "end": 927.11, "word": " بس", "probability": 0.6873779296875}, {"start": 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"probability": 0.7151692708333334}, {"start": 942.23, "end": 942.43, "word": " مش", "probability": 0.9833984375}, {"start": 942.43, "end": 942.61, "word": " هو", "probability": 0.98291015625}, {"start": 942.61, "end": 942.89, "word": " نص", "probability": 0.990478515625}, {"start": 942.89, "end": 944.47, "word": " النظرية؟", "probability": 0.87763671875}, {"start": 944.47, "end": 944.81, "word": " يبقى", "probability": 0.97998046875}, {"start": 944.81, "end": 945.09, "word": " هذي", "probability": 0.5619303385416666}, {"start": 945.09, "end": 946.15, "word": " homomorphism", "probability": 0.83740234375}, {"start": 946.15, "end": 947.65, "word": " يبقى", "probability": 0.90771484375}, {"start": 947.65, "end": 948.17, "word": " then", "probability": 0.6162109375}, {"start": 948.17, "end": 948.85, "word": " ..", "probability": 0.2496337890625}, {"start": 948.85, "end": 951.23, "word": " then", "probability": 0.6142578125}, {"start": 951.23, "end": 952.07, "word": " Phi", "probability": 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22807, 23032, 1829, 3555], "avg_logprob": -0.26186709690697585, "compression_ratio": 1.5146198830409356, "no_speech_prob": 0.0, "words": [{"start": 955.82, "end": 956.22, "word": "هذا", "probability": 0.943359375}, {"start": 956.22, "end": 956.74, "word": " الكلام", "probability": 0.97265625}, {"start": 956.74, "end": 957.2, "word": " جيبته", "probability": 0.85369873046875}, {"start": 957.2, "end": 957.36, "word": " من", "probability": 0.9794921875}, {"start": 957.36, "end": 958.06, "word": " أين؟", "probability": 0.6702473958333334}, {"start": 958.06, "end": 958.8, "word": " from", "probability": 0.68408203125}, {"start": 958.8, "end": 960.54, "word": " the", "probability": 0.346923828125}, {"start": 960.54, "end": 962.0, "word": " أعضاء", "probability": 0.64569091796875}, {"start": 962.0, "end": 962.72, "word": " الـ", "probability": 0.6158447265625}, {"start": 962.72, "end": 964.16, "word": " Theorem", "probability": 0.5816650390625}, {"start": 964.16, "end": 968.2, "word": " يبقى", "probability": 0.9227294921875}, {"start": 968.2, "end": 968.6, "word": " صار", "probability": 0.74609375}, {"start": 968.6, "end": 969.08, "word": " عندهم", "probability": 0.7861328125}, {"start": 969.08, "end": 970.6, "word": " Homomorphism،", "probability": 0.70526123046875}, {"start": 970.6, "end": 974.5, "word": " مظبوط؟", "probability": 0.9152018229166666}, {"start": 974.5, "end": 975.08, "word": " يبقى", "probability": 0.9454345703125}, {"start": 975.08, "end": 975.34, "word": " فيها", "probability": 0.8681640625}, {"start": 975.34, "end": 975.68, "word": " عندنا", "probability": 0.95458984375}, {"start": 975.68, "end": 976.1, "word": " درية", "probability": 0.4115804036458333}, {"start": 976.1, "end": 976.7, "word": " اسمها", "probability": 0.94580078125}, {"start": 976.7, "end": 976.84, "word": " الـ", "probability": 0.705078125}, {"start": 976.84, "end": 978.22, "word": " Isomorphism", "probability": 0.8084309895833334}, {"start": 978.22, "end": 979.16, "word": " Theorem", "probability": 0.6484375}, {"start": 979.16, "end": 980.56, "word": " سمعنا", "probability": 0.9605712890625}, {"start": 980.56, "end": 980.94, "word": " فيها", "probability": 0.992431640625}, {"start": 980.94, "end": 982.46, "word": " سمعنا", "probability": 0.83074951171875}, {"start": 982.46, "end": 983.5, "word": " فيها؟", "probability": 0.8883463541666666}, {"start": 983.5, "end": 984.22, "word": " طيب", "probability": 0.9259440104166666}], "temperature": 1.0}, {"id": 34, "seek": 101369, "start": 984.37, "end": 1013.69, "text": "يبقى by the first isomorphism theorem الـ Z موديون الكيرن للـ 5 ايزو مورفك لل 5 of Z", "tokens": [1829, 3555, 4587, 7578, 538, 264, 700, 307, 32702, 1434, 20904, 2423, 39184, 1176, 3714, 2407, 16254, 11536, 33251, 13546, 1863, 24976, 39184, 1025, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 24976, 1025, 295, 1176], "avg_logprob": -0.3857685810810811, "compression_ratio": 1.1470588235294117, "no_speech_prob": 0.0, "words": [{"start": 984.37, "end": 985.29, "word": "يبقى", "probability": 0.927978515625}, {"start": 985.29, "end": 985.85, "word": " by", "probability": 0.462646484375}, {"start": 985.85, "end": 987.43, "word": " the", "probability": 0.7509765625}, {"start": 987.43, "end": 989.35, "word": " first", "probability": 0.88330078125}, {"start": 989.35, "end": 994.23, "word": " isomorphism", "probability": 0.9519856770833334}, {"start": 994.23, "end": 999.07, "word": " theorem", "probability": 0.8857421875}, {"start": 999.07, "end": 1002.69, "word": " الـ", "probability": 0.4520263671875}, {"start": 1002.69, "end": 1002.93, "word": " Z", "probability": 0.43359375}, {"start": 1002.93, "end": 1004.81, "word": " موديون", "probability": 0.656494140625}, {"start": 1004.81, "end": 1006.13, "word": " الكيرن", "probability": 0.6984049479166666}, {"start": 1006.13, "end": 1006.63, "word": " للـ", "probability": 0.5435791015625}, {"start": 1006.63, "end": 1007.23, "word": " 5", "probability": 0.371337890625}, {"start": 1007.23, 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"text": "موجودة في الـ Z والـ B لا تساوي Z كويس؟ يبقى أخدت S تساوي هذه، then الـ S هذه بتثبتها إنها إيه؟ إنها صبفيل صابفيل طيب كويس", "tokens": [2304, 29245, 23328, 3660, 8978, 2423, 39184, 1176, 16070, 39184, 363, 20193, 6055, 3794, 995, 45865, 1176, 9122, 45865, 3794, 22807, 7251, 3555, 4587, 7578, 5551, 9778, 3215, 2655, 318, 6055, 3794, 995, 45865, 29538, 12399, 550, 2423, 39184, 318, 29538, 39894, 12984, 3555, 2655, 11296, 36145, 11296, 11933, 1829, 3224, 22807, 36145, 11296, 20328, 3555, 5172, 26895, 20328, 16758, 5172, 26895, 23032, 1829, 3555, 9122, 45865, 3794], "avg_logprob": -0.2787590631540271, "compression_ratio": 1.5255474452554745, "no_speech_prob": 0.0, "words": [{"start": 2067.14, "end": 2068.44, "word": "موجودة", "probability": 0.949462890625}, {"start": 2068.44, "end": 2068.8, "word": " في", "probability": 0.98388671875}, {"start": 2068.8, "end": 2069.54, "word": " الـ", "probability": 0.6552734375}, {"start": 2069.54, "end": 2069.92, "word": " Z", "probability": 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"end": 2121.34, "text": "يبقى لو أخدت S على الشكل اللي عندها هذا A على B بحيث ال A و ال B موجودة في Z يبقى هذه sub ring بقدرة كل اللي بقدر أقوله حتى الآن sub ring then ال S is a sub ring", "tokens": [1829, 3555, 4587, 7578, 45164, 5551, 9778, 3215, 2655, 318, 15844, 25124, 28820, 13672, 1829, 43242, 11296, 23758, 316, 15844, 363, 4724, 5016, 1829, 12984, 2423, 316, 4032, 2423, 363, 3714, 29245, 23328, 3660, 8978, 1176, 7251, 3555, 4587, 7578, 29538, 1422, 4875, 4724, 28543, 25720, 28242, 13672, 1829, 4724, 28543, 2288, 5551, 39648, 3224, 11331, 49975, 6024, 48506, 1422, 4875, 550, 2423, 318, 307, 257, 1422, 4875], "avg_logprob": -0.21942934782608695, "compression_ratio": 1.54375, "no_speech_prob": 0.0, "words": [{"start": 2095.3, "end": 2095.66, "word": "يبقى", "probability": 0.66522216796875}, {"start": 2095.66, "end": 2095.86, "word": " لو", "probability": 0.6044921875}, {"start": 2095.86, "end": 2096.42, "word": " أخدت", "probability": 0.9373779296875}, {"start": 2096.42, "end": 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2150.93, "word": " موجودة", "probability": 0.97998046875}, {"start": 2150.93, "end": 2151.19, "word": " في", "probability": 0.94921875}, {"start": 2151.19, "end": 2151.51, "word": " S", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 74, "seek": 217834, "start": 2151.8, "end": 2178.34, "text": "will be لاتساوي 0. want to show ال team as a sub field. عشان نقدر نطبق الجزء الثاني من النظرية اللي بنقول عليه. لإن انا بارك أقول إن أنا مش سهل فدج جماعة.", "tokens": [86, 388, 75, 312, 5296, 9307, 3794, 995, 45865, 1958, 13, 528, 281, 855, 2423, 1469, 382, 257, 1422, 2519, 13, 6225, 8592, 7649, 8717, 28543, 2288, 8717, 9566, 3555, 4587, 25724, 11622, 38207, 6024, 104, 7649, 1829, 9154, 28239, 19913, 2288, 10632, 13672, 1829, 44945, 39648, 47356, 13, 5296, 28814, 1863, 1975, 8315, 4724, 9640, 4117, 5551, 39648, 36145, 41850, 37893, 8608, 3224, 1211, 6156, 3215, 7435, 10874, 15042, 27884, 13], "avg_logprob": -0.4163099380388652, "compression_ratio": 1.3872832369942196, 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" أثبتت", "probability": 0.86083984375}, {"start": 2569.36, "end": 2570.22, "word": " أن", "probability": 0.60498046875}, {"start": 2570.22, "end": 2570.42, "word": " ال", "probability": 0.611328125}, {"start": 2570.42, "end": 2570.64, "word": " Phi", "probability": 0.70263671875}, {"start": 2570.64, "end": 2571.72, "word": " همومارفزيوم", "probability": 0.6713104248046875}], "temperature": 1.0}, {"id": 89, "seek": 260135, "start": 2572.07, "end": 2601.35, "text": "one to one وانتوا بيكون خلصنا ال isomorphism مظبوط؟ إذا بدالي أقوله Phi is a homomorphism نقطة الأولى إذا بدالي أخد الفائلات ال X بدها تساوي AB inverse وال Y بدها تساوي CD inverse", "tokens": [546, 281, 472, 4032, 7649, 2655, 14407, 4724, 1829, 30544, 16490, 1211, 9381, 8315, 2423, 307, 32702, 1434, 3714, 19913, 3555, 2407, 9566, 22807, 11933, 15730, 47525, 6027, 1829, 5551, 39648, 3224, 41435, 307, 257, 3655, 32702, 1434, 8717, 47432, 3660, 16247, 12610, 7578, 11933, 15730, 47525, 6027, 1829, 5551, 9778, 3215, 27188, 16373, 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CD", "probability": 0.91064453125}, {"start": 2600.27, "end": 2601.35, "word": " inverse", "probability": 0.83447265625}], "temperature": 1.0}, {"id": 90, "seek": 263126, "start": 2601.74, "end": 2631.26, "text": "اللي موجودة وين؟ اللي موجودة في T بدي أخد Phi of X زائد Y يبقى Phi of ال X له A B inverse زائد C D inverse هذا شكله موجود في T هيك؟ مقدرش مش صحيح", "tokens": [6027, 20292, 3714, 29245, 23328, 3660, 4032, 9957, 22807, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 314, 4724, 16254, 5551, 9778, 3215, 41435, 295, 1783, 30767, 16373, 3215, 398, 7251, 3555, 4587, 7578, 41435, 295, 2423, 1783, 46740, 316, 363, 17340, 30767, 16373, 3215, 383, 413, 17340, 23758, 13412, 28820, 3224, 3714, 29245, 23328, 8978, 314, 39896, 4117, 22807, 3714, 28543, 2288, 8592, 37893, 20328, 5016, 1829, 5016], "avg_logprob": -0.2463768115942029, "compression_ratio": 1.4701986754966887, "no_speech_prob": 0.0, "words": [{"start": 2601.74, "end": 2602.2, "word": "اللي", "probability": 0.814208984375}, {"start": 2602.2, "end": 2602.82, "word": " موجودة", "probability": 0.986572265625}, {"start": 2602.82, "end": 2603.34, "word": " وين؟", "probability": 0.515380859375}, {"start": 2603.34, "end": 2603.62, "word": " اللي", "probability": 0.9443359375}, {"start": 2603.62, "end": 2604.3, "word": " موجودة", "probability": 0.98681640625}, {"start": 2604.3, "end": 2604.56, "word": " في", "probability": 0.95849609375}, {"start": 2604.56, "end": 2605.0, "word": " T", "probability": 0.53564453125}, {"start": 2605.0, "end": 2608.5, "word": " بدي", "probability": 0.288543701171875}, {"start": 2608.5, "end": 2609.0, "word": " أخد", "probability": 0.81689453125}, {"start": 2609.0, "end": 2609.8, "word": " Phi", "probability": 0.2283935546875}, {"start": 2609.8, "end": 2610.28, "word": " of", "probability": 0.8603515625}, {"start": 2610.28, "end": 2610.96, "word": " X", "probability": 0.87744140625}, {"start": 2610.96, "end": 2611.8, "word": " زائد", "probability": 0.8487955729166666}, {"start": 2611.8, "end": 2612.34, "word": " Y", "probability": 0.84375}, {"start": 2612.34, "end": 2613.44, "word": " يبقى", "probability": 0.9398193359375}, {"start": 2613.44, "end": 2614.04, "word": " Phi", "probability": 0.9560546875}, {"start": 2614.04, "end": 2614.66, "word": " of", "probability": 0.89990234375}, {"start": 2614.66, "end": 2615.48, "word": " ال", "probability": 0.3759765625}, {"start": 2615.48, "end": 2615.94, "word": " X", "probability": 0.69970703125}, {"start": 2615.94, "end": 2616.34, "word": " له", "probability": 0.767578125}, {"start": 2616.34, "end": 2617.08, "word": " A", "probability": 0.7724609375}, {"start": 2617.08, "end": 2617.76, "word": " B", "probability": 0.82421875}, {"start": 2617.76, "end": 2618.64, "word": " inverse", "probability": 0.615234375}, {"start": 2618.64, "end": 2619.86, "word": " زائد", "probability": 0.9420572916666666}, {"start": 2619.86, "end": 2620.62, "word": " C", "probability": 0.89306640625}, {"start": 2620.62, "end": 2621.66, "word": " D", "probability": 0.9794921875}, {"start": 2621.66, "end": 2622.38, "word": " inverse", "probability": 0.94091796875}, {"start": 2622.38, "end": 2624.42, "word": " هذا", "probability": 0.58984375}, {"start": 2624.42, "end": 2625.68, "word": " شكله", "probability": 0.8836263020833334}, {"start": 2625.68, "end": 2626.32, "word": " موجود", "probability": 0.9861653645833334}, {"start": 2626.32, "end": 2626.58, "word": " في", "probability": 0.98779296875}, {"start": 2626.58, "end": 2626.92, "word": " T", "probability": 0.943359375}, {"start": 2626.92, "end": 2628.22, "word": " هيك؟", "probability": 0.7150065104166666}, {"start": 2628.22, "end": 2630.06, "word": " مقدرش", "probability": 0.8114013671875}, {"start": 2630.06, "end": 2630.7, "word": " مش", "probability": 0.54443359375}, {"start": 2630.7, "end": 2631.26, "word": " صحيح", "probability": 0.976806640625}], "temperature": 1.0}, {"id": 91, "seek": 266151, "start": 2632.03, "end": 2661.51, "text": "تظبطهم يمكن تظبط معاك بقوله بسيطة اشرايكوا هذه اكتبها Phi of A B inverse مضروبة في D D inverse يعني ال unity زائد التانية C D inverse بدي اضربها في ال B B inverse اللي هو ال unity كذلك تمام؟", "tokens": [2655, 19913, 3555, 9566, 16095, 7251, 43020, 6055, 19913, 3555, 9566, 20449, 995, 4117, 4724, 39648, 3224, 4724, 3794, 1829, 9566, 3660, 1975, 8592, 23557, 1829, 4117, 14407, 29538, 1975, 4117, 2655, 3555, 11296, 41435, 295, 316, 363, 17340, 3714, 11242, 32887, 49401, 8978, 413, 413, 17340, 37495, 22653, 2423, 18205, 30767, 16373, 3215, 16712, 7649, 10632, 383, 413, 17340, 4724, 16254, 1975, 11242, 25513, 11296, 8978, 2423, 363, 363, 17340, 13672, 1829, 31439, 2423, 18205, 9122, 8848, 23275, 46811, 10943, 22807], "avg_logprob": -0.2964984982846731, "compression_ratio": 1.5508021390374331, "no_speech_prob": 0.0, "words": [{"start": 2632.03, "end": 2633.25, "word": "تظبطهم", "probability": 0.47470703125}, {"start": 2633.25, "end": 2633.87, "word": " يمكن", "probability": 0.7802734375}, {"start": 2633.87, "end": 2634.45, 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"word": " مضروبة", "probability": 0.7344970703125}, {"start": 2644.67, "end": 2645.03, "word": " في", "probability": 0.92431640625}, {"start": 2645.03, "end": 2645.65, "word": " D", "probability": 0.642578125}, {"start": 2645.65, "end": 2646.07, "word": " D", "probability": 0.93798828125}, {"start": 2646.07, "end": 2646.95, "word": " inverse", "probability": 0.7607421875}, {"start": 2646.95, "end": 2647.77, "word": " يعني", "probability": 0.89794921875}, {"start": 2647.77, "end": 2647.93, "word": " ال", "probability": 0.97705078125}, {"start": 2647.93, "end": 2648.43, "word": " unity", "probability": 0.888671875}, {"start": 2648.43, "end": 2650.99, "word": " زائد", "probability": 0.5902099609375}, {"start": 2650.99, "end": 2652.43, "word": " التانية", "probability": 0.9505208333333334}, {"start": 2652.43, "end": 2653.17, "word": " C", "probability": 0.7978515625}, {"start": 2653.17, "end": 2654.21, "word": " D", "probability": 0.93798828125}, {"start": 2654.21, "end": 2655.03, "word": " inverse", "probability": 0.8115234375}, {"start": 2655.03, "end": 2655.81, "word": " بدي", "probability": 0.69091796875}, {"start": 2655.81, "end": 2656.45, "word": " اضربها", "probability": 0.9346923828125}, {"start": 2656.45, "end": 2656.65, "word": " في", "probability": 0.9345703125}, {"start": 2656.65, "end": 2656.81, "word": " ال", "probability": 0.64990234375}, {"start": 2656.81, "end": 2657.01, "word": " B", "probability": 0.470947265625}, {"start": 2657.01, "end": 2657.23, "word": " B", "probability": 0.95751953125}, {"start": 2657.23, "end": 2657.89, "word": " inverse", "probability": 0.861328125}, {"start": 2657.89, "end": 2658.47, "word": " اللي", "probability": 0.782958984375}, {"start": 2658.47, "end": 2658.63, "word": " هو", "probability": 0.9892578125}, {"start": 2658.63, "end": 2658.75, "word": " ال", "probability": 0.99462890625}, {"start": 2658.75, "end": 2659.09, "word": " unity", "probability": 0.97998046875}, {"start": 2659.09, "end": 2659.87, "word": " كذلك", "probability": 0.9500325520833334}, {"start": 2659.87, "end": 2661.51, "word": " تمام؟", "probability": 0.8439127604166666}], "temperature": 1.0}, {"id": 92, "seek": 269062, "start": 2661.84, "end": 2690.62, "text": "يبقى هذا الكلام يثابر يثابر في of عندك هنا ال a دي مالوش دعوة مظبوط في ال b inverse دي inverse خليت اللي مش فيهم inverse مع بعض و اللي فيهم ال inverse مع بعض وهنا زائد border bc", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 7251, 12984, 16758, 2288, 7251, 12984, 16758, 2288, 8978, 295, 43242, 4117, 34105, 2423, 257, 11778, 1829, 3714, 6027, 2407, 8592, 11778, 3615, 2407, 3660, 3714, 19913, 3555, 2407, 9566, 8978, 2423, 272, 17340, 11778, 1829, 17340, 16490, 20292, 2655, 13672, 1829, 37893, 8978, 16095, 17340, 20449, 45030, 11242, 4032, 13672, 1829, 8978, 16095, 2423, 17340, 20449, 45030, 11242, 37037, 8315, 30767, 16373, 3215, 7838, 272, 66], "avg_logprob": -0.2855674412689711, "compression_ratio": 1.725, "no_speech_prob": 0.0, "words": [{"start": 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"word": " مالوش", "probability": 0.8677978515625}, {"start": 2673.66, "end": 2674.28, "word": " دعوة", "probability": 0.96435546875}, {"start": 2674.28, "end": 2675.54, "word": " مظبوط", "probability": 0.88388671875}, {"start": 2675.54, "end": 2676.3, "word": " في", "probability": 0.55615234375}, {"start": 2676.3, "end": 2676.64, "word": " ال", "probability": 0.94775390625}, {"start": 2676.64, "end": 2677.16, "word": " b", "probability": 0.70947265625}, {"start": 2677.16, "end": 2678.3, "word": " inverse", "probability": 0.71533203125}, {"start": 2678.3, "end": 2679.22, "word": " دي", "probability": 0.6558837890625}, {"start": 2679.22, "end": 2679.92, "word": " inverse", "probability": 0.875}, {"start": 2679.92, "end": 2681.68, "word": " خليت", "probability": 0.73095703125}, {"start": 2681.68, "end": 2681.9, "word": " اللي", "probability": 0.94287109375}, {"start": 2681.9, "end": 2682.16, "word": " مش", "probability": 0.256591796875}, {"start": 2682.16, "end": 2682.46, "word": " فيهم", 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0.6737060546875}, {"start": 3036.06, "end": 3036.42, "word": " أن", "probability": 0.4326171875}, {"start": 3036.42, "end": 3036.96, "word": " X", "probability": 0.947265625}], "temperature": 1.0}, {"id": 105, "seek": 305178, "start": 3037.3, "end": 3051.78, "text": "بساوي a على b اللي هو main فاي of a بينبرت لذلك فاي is on top يبقى داصر فاي is an isomorphism", "tokens": [3555, 3794, 995, 45865, 257, 15844, 272, 13672, 1829, 31439, 2135, 6156, 47302, 295, 257, 4724, 9957, 26890, 2655, 5296, 8848, 23275, 6156, 47302, 307, 322, 1192, 7251, 3555, 4587, 7578, 11778, 33546, 2288, 6156, 47302, 307, 364, 307, 32702, 1434], "avg_logprob": -0.5398065419424147, "compression_ratio": 1.1858407079646018, "no_speech_prob": 0.0, "words": [{"start": 3037.3, "end": 3038.0, "word": "بساوي", "probability": 0.56463623046875}, {"start": 3038.0, "end": 3038.36, "word": " a", "probability": 0.494384765625}, {"start": 3038.36, "end": 3038.84, "word": " على", "probability": 0.5390625}, {"start": 3038.84, "end": 3039.36, "word": " b", "probability": 0.87158203125}, {"start": 3039.36, "end": 3039.94, "word": " اللي", "probability": 0.853759765625}, {"start": 3039.94, "end": 3040.16, "word": " هو", "probability": 0.9853515625}, {"start": 3040.16, "end": 3040.6, "word": " main", "probability": 0.619140625}, {"start": 3040.6, "end": 3041.5, "word": " فاي", "probability": 0.36273193359375}, {"start": 3041.5, "end": 3041.92, "word": " of", "probability": 0.66357421875}, {"start": 3041.92, "end": 3042.42, "word": " a", "probability": 0.9443359375}, {"start": 3042.42, "end": 3043.44, "word": " بينبرت", "probability": 0.4210205078125}, {"start": 3043.44, "end": 3044.16, "word": " لذلك", "probability": 0.771240234375}, {"start": 3044.16, "end": 3044.6, "word": " فاي", "probability": 0.706787109375}, {"start": 3044.6, "end": 3044.88, "word": " is", "probability": 0.7607421875}, {"start": 3044.88, "end": 3045.26, "word": " on", "probability": 0.100830078125}, {"start": 3045.26, "end": 3045.6, "word": " top", "probability": 0.2354736328125}, {"start": 3045.6, "end": 3046.72, "word": " يبقى", "probability": 0.93994140625}, {"start": 3046.72, "end": 3047.28, "word": " داصر", "probability": 0.4097493489583333}, {"start": 3047.28, "end": 3048.3, "word": " فاي", "probability": 0.82763671875}, {"start": 3048.3, "end": 3049.08, "word": " is", "probability": 0.93359375}, {"start": 3049.08, "end": 3049.94, "word": " an", "probability": 0.4482421875}, {"start": 3049.94, "end": 3051.78, "word": " isomorphism", "probability": 0.9044596354166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3054.933375, "duration_after_vad": 2905.0074999999847}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4309340466b3e8e8f6e58e67eadf143ca8ba9b26
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5Eqt_t24V4U_raw.srt
@@ -0,0 +1,1608 @@
+1
+00:00:21,060 --> 00:00:25,280
+بسم الله الرحمن الرحيم نكمل ما ابتدأناه في
+
+2
+00:00:25,280 --> 00:00:30,860
+المحاضرة الماضية وهو chapter a ring homomorphism
+
+3
+00:00:30,860 --> 00:00:35,600
+آخر حاجة كان معاك المرة اللي فتت مثال والآن نأتي
+
+4
+00:00:35,600 --> 00:00:42,180
+إلى نظرية جديدة النظرية بتقول ما يعني little r ب
+
+5
+00:00:42,180 --> 00:00:44,420
+ring with unit one
+
+6
+00:00:48,500 --> 00:00:54,500
+ذن دي mapping عرفنا function من ال Z إلى R طبعا ال
+
+7
+00:00:54,500 --> 00:01:00,020
+Z دي هي مجموعة الأعداد الصحيحة إلى ring R given by
+
+8
+00:01:00,020 --> 00:01:05,800
+Phi of N يساوي N في 1 بدنا نثبت أن هذه عبارة عن
+
+9
+00:01:05,800 --> 00:01:11,880
+ring homomorphism مشان هيك ال ring homomorphism في
+
+10
+00:01:11,880 --> 00:01:17,160
+عندي two conditions بدنا انحققهمالـ condition هو
+
+11
+00:01:17,160 --> 00:01:21,000
+اللي بيقول لو كان two elements x و y موجودات في ال
+
+12
+00:01:21,000 --> 00:01:25,620
+ring و في لما اتأثر على هذا المجموع يبقى بيسوي في
+
+13
+00:01:25,620 --> 00:01:32,460
+of x زائد في of y و لو في أثرت على الضرب x في y
+
+14
+00:01:32,460 --> 00:01:37,800
+الناتج بيكون في of x في في of y يبقى بنروح نطبق
+
+15
+00:01:37,800 --> 00:01:43,420
+هذا الكلام على ال ring اللي قدامنا هذايبقى بدي
+
+16
+00:01:43,420 --> 00:01:49,980
+أبدأ الآن بدي أقول له افترض عندي M و N أعداب صحيحة
+
+17
+00:01:49,980 --> 00:01:58,380
+موجودة في Z then بدي أخد تأثير ال Phi على M زائد
+
+18
+00:01:58,380 --> 00:02:05,600
+ال N حسب التعريف اللي عندنا يبقى هذا الكلام M زائد
+
+19
+00:02:05,600 --> 00:02:14,350
+N مضغوف من ال one هذا بده يساويبتساوي ايه؟ بده
+
+20
+00:02:14,350 --> 00:02:20,610
+بيساوي ال M زائد N هدول integers يبقى عبارة بقدر
+
+21
+00:02:20,610 --> 00:02:26,830
+احطهم واحد زائد واحد زائد واحد M زائد N من المرات
+
+22
+00:02:26,830 --> 00:02:35,030
+يبقى هذا الكلام واحد زائد واحد زائد واحد زائد واحد
+
+23
+00:02:35,030 --> 00:02:46,180
+كم مرة هدول؟ M زائد N timeيبقى M زائد N من المرات
+
+24
+00:02:46,180 --> 00:02:52,280
+يعني عدد هدول اللي عندنا كل واحد فيهم لما نجمعهم
+
+25
+00:02:52,280 --> 00:02:59,800
+يكون عددهم M زائد M طيب تمام ممكن أجسمهم إلى جسمين
+
+26
+00:02:59,800 --> 00:03:05,640
+القسم الأول واحد زائد واحد زائد زائد واحد هدول
+
+27
+00:03:05,640 --> 00:03:13,340
+بتاخدهم M times زائدبرضه واحد زائد واحد زائد زائد
+
+28
+00:03:13,340 --> 00:03:23,180
+واحد وهدول in times يبقى بناء عليه هذا بالدرساه M
+
+29
+00:03:23,180 --> 00:03:31,240
+في one زائد هدول عددهم in يبقى in في one حسب ال
+
+30
+00:03:31,240 --> 00:03:38,460
+definition يبقى الأول Phi of M والتاني Phi of M
+
+31
+00:03:39,000 --> 00:03:44,440
+بناء عليه أخدنا Phi of M زائد N لجينا النتيجة
+
+32
+00:03:44,440 --> 00:03:50,360
+تساوي Phi of M زائد Phi of M وبالتالي حققتنا ال
+
+33
+00:03:50,360 --> 00:03:55,080
+condition الأول من ال two conditions تبعات ال ring
+
+34
+00:03:55,080 --> 00:04:00,460
+همورفيزي بقوله أن بدنا نروح لل condition التاني
+
+35
+00:04:00,460 --> 00:04:08,360
+بدنا ناخده Phi of M في M حسب ال definition يبقى M
+
+36
+00:04:08,750 --> 00:04:17,370
+في N في واحد طيب هذا الواحد هو ال unity يبقى لو
+
+37
+00:04:17,370 --> 00:04:22,550
+ضربت ال element هذا كله في كمان unity بيغير حاجة؟
+
+38
+00:04:22,550 --> 00:04:29,190
+لأ يبقى هذا الكلام M N في ال unity في كمان ال
+
+39
+00:04:29,190 --> 00:04:38,130
+unity بيغيرش شيء طيب الآن هذا بده يساوي ال Mفي ال
+
+40
+00:04:38,130 --> 00:04:47,210
+one مضروب كذلك N في one الأولى هذه اللى عبارة عن
+
+41
+00:04:47,210 --> 00:04:55,990
+مين صورة ال M والتانى هذى صورة ال N يبقى بناء عليه
+
+42
+00:04:55,990 --> 00:05:02,370
+Phi of M في N طلع عندي Phi of M في Phi of N يبقى
+
+43
+00:05:02,370 --> 00:05:15,830
+Thus وهكذا Phi isEarring Homomorphism الآن
+
+44
+00:05:15,830 --> 00:05:24,110
+على هذه النظرية فيه ثلاث نتائج نبدأ بالنتيجة
+
+45
+00:05:24,110 --> 00:05:30,330
+الأولى على هذه النظرية يبقى ال first crawler بتقول
+
+46
+00:05:30,330 --> 00:05:35,330
+ما ياتي crawler crawler one
+
+47
+00:05:38,760 --> 00:05:46,640
+بيقول if ال R is a ring with unity if ال R is a
+
+48
+00:05:46,640 --> 00:05:56,140
+ring with unity ring with unity and the
+
+49
+00:05:56,140 --> 00:06:07,560
+characteristic of R and the characteristic of R is
+
+50
+00:06:09,390 --> 00:06:19,530
+and greater than zero then الـR
+
+51
+00:06:19,530 --> 00:06:31,810
+contains a subring contains a subring contains
+
+52
+00:06:31,810 --> 00:06:38,490
+a subring isomorphic to
+
+53
+00:06:40,260 --> 00:06:53,440
+زد ان if the characteristic
+
+54
+00:06:53,440 --> 00:07:01,320
+of R is zero then
+
+55
+00:07:01,320 --> 00:07:08,480
+R contains is something then R contains
+
+56
+00:07:23,490 --> 00:07:27,970
+isomorphic to z
+
+57
+00:07:46,830 --> 00:07:50,870
+يبقى النظرية هذه اللي بين أدينا عبارة عن نقطتين
+
+58
+00:07:50,870 --> 00:07:57,610
+وليست نقطة واحدة النقطة الأولى بتقول ماذي؟ النقطة
+
+59
+00:07:57,610 --> 00:08:01,910
+المشتركة بيقول you put an R ring with unity إذا
+
+60
+00:08:01,910 --> 00:08:07,670
+كان ال characteristic ل R هو N يبقى ال R فيها sub
+
+61
+00:08:07,670 --> 00:08:12,870
+ring isomorphic ل ZN وإذا كان نقطة ثانية إذا كان
+
+62
+00:08:12,870 --> 00:08:17,490
+ال characteristic لل ring R هو Zeroيبقى ال ring
+
+63
+00:08:17,490 --> 00:08:23,170
+هذه تحتوي على sub ring isomorphic لست of integers
+
+64
+00:08:23,170 --> 00:08:28,870
+اللي هو Z أو اللي هي Z نروح نثبت صحة هذه ال
+
+65
+00:08:28,870 --> 00:08:34,330
+crawlery وهذه ال crawlery أساسية لمين ال crawlers
+
+66
+00:08:34,330 --> 00:08:38,330
+اللي بيجوا مين اللي بيجوا بعديها طيب خلي أقولكوا
+
+67
+00:08:38,330 --> 00:08:43,230
+هنا الآن ماحددتش الشكل ال unity يبقى أنا بدي أفرض
+
+68
+00:08:43,230 --> 00:08:49,120
+أن ال unityاللي هو عبارة عن مين؟ الواحدة صحيح يبقى
+
+69
+00:08:49,120 --> 00:09:03,880
+let ال one be the unity of the ring R مافيش
+
+70
+00:09:03,880 --> 00:09:09,020
+بقول هنا قال لي إذا ال characteristic يساوي ان
+
+71
+00:09:09,020 --> 00:09:16,220
+يبقى ال R contains a sub ringIsomorphic ل ZN يبقى
+
+72
+00:09:16,220 --> 00:09:24,200
+انا بدي اخلق soft drink بروح اقول له لات ال S كل
+
+73
+00:09:24,200 --> 00:09:31,260
+العناص K المضروبة في واحد بحيث ال K هذا عدد اخدته
+
+74
+00:09:31,260 --> 00:09:37,400
+من مين اخدته من Z يبقى
+
+75
+00:09:41,040 --> 00:09:48,440
+افترضت انه عندى 6S الـ S هذه هي حاصل ضرب عدد من Z
+
+76
+00:09:48,440 --> 00:09:54,800
+مضروب في مين في الواحد الصحيح انا ابدعي الان ان ال
+
+77
+00:09:54,800 --> 00:10:06,760
+S is a sub ring يبقى then ال S is a sub ring شو
+
+78
+00:10:06,760 --> 00:10:14,480
+السبب؟ becauseالنقطة الأولى ال S هذه is non-empty
+
+79
+00:10:14,480 --> 00:10:25,740
+ال S is non-empty على الأقل فيها عنصر هو العنصر
+
+80
+00:10:25,740 --> 00:10:35,560
+الصفرين because ال zero بده يساوي zero في واحد
+
+81
+00:10:35,560 --> 00:10:43,150
+وهذا موجود هناموجود في اسم يبقى none in نقطة ثانية
+
+82
+00:10:43,150 --> 00:10:52,330
+بدى افترض انه عندى عنصرين موجودات في اسم يبقى let
+
+83
+00:10:52,330 --> 00:11:02,150
+x و ال y موجودات في اسم then شكل ال x بدى يسوي
+
+84
+00:11:02,150 --> 00:11:06,170
+مثلا k في ال one and
+
+85
+00:11:20,220 --> 00:11:27,980
+يبقى K في الـ 1 minus M في الـ 1 حسب الـ
+
+86
+00:11:27,980 --> 00:11:35,880
+distributive law يبقى K minus M في الـ 1الفرق ما
+
+87
+00:11:35,880 --> 00:11:41,480
+بين two integers هو integer مظبوط مضروب فيه ان
+
+88
+00:11:41,480 --> 00:11:48,820
+يبقى صار شكله موجود في S يبقى هذا بده يعطينا ان ال
+
+89
+00:11:48,820 --> 00:11:56,360
+X ناقص ال Y موجودة في S الآن مشان أثبتها ال
+
+90
+00:11:56,360 --> 00:12:02,480
+subring ال conditioning تالت بدي اروح اخو اخد حاصل
+
+91
+00:12:02,480 --> 00:12:08,840
+ضرب عنصرينمن نفس ال S بدي أكون موجود في S إذا لو
+
+92
+00:12:08,840 --> 00:12:15,300
+رحت أخدت ال X في Y ال X في Y عبارة عن مين اللي هو
+
+93
+00:12:15,300 --> 00:12:23,160
+K في واحد مضرب في ال M في واحد لإن ال X أخدته ال K
+
+94
+00:12:23,160 --> 00:12:29,940
+في 1 و ال Y ال M في 1 يبقى هذا الكلام بقدر أقوله
+
+95
+00:12:29,940 --> 00:12:36,710
+على شكل K M في 1لأن ال one في ال one بال one
+
+96
+00:12:36,710 --> 00:12:44,150
+itself لأن هو ال unity طيب هذا الصيغة ال K في M مش
+
+97
+00:12:44,150 --> 00:12:49,210
+هجرع ال element موجود في Z يكون مضروف في one يبقى
+
+98
+00:12:49,210 --> 00:12:57,250
+بناء عليه هذا يعطي لي ان ال X في Y موجود في S و
+
+99
+00:12:57,250 --> 00:13:10,960
+هكذا ال S is a sub ringof subring of R طب حتى الآن
+
+100
+00:13:10,960 --> 00:13:17,360
+أنا بس خلقت subring بس إيش بيقول هنا هو ال
+
+101
+00:13:17,360 --> 00:13:23,660
+characteristic فهو لو كان يساوي LN يبقى R contains
+
+102
+00:13:23,660 --> 00:13:31,800
+لsubring هيه جبتها عايزة و مرفقة لمين ل ZNيبقى انا
+
+103
+00:13:31,800 --> 00:13:38,600
+بدي اجيب homomorphism من ال sub ring هذه الى بعرفش
+
+104
+00:13:38,600 --> 00:13:43,880
+مين تطلع هو جالي لمين لزد ان تمام؟ بتكون عندك
+
+105
+00:13:43,880 --> 00:13:48,780
+isomorphism بقوله بسيطة خالص يبقى بروح بقوله
+
+106
+00:13:48,780 --> 00:13:55,520
+define if a mapping او function
+
+107
+00:14:00,360 --> 00:14:13,020
+الـ Z إلى .. والله من S إلى Z من S إلى Z عفوا من Z
+
+108
+00:14:13,020 --> 00:14:19,220
+إلى S هذي والله هذي بتفرقش عنها بس مشان نلتزم بنص
+
+109
+00:14:19,220 --> 00:14:27,210
+النظرية النظرية اللي من Z إلى A يبقى من Z إلى Sهو
+
+110
+00:14:27,210 --> 00:14:38,070
+الله من z on to s تمام؟ ايه؟ تمام؟ by five
+
+111
+00:14:38,070 --> 00:14:47,570
+of .. بده اخد element من وين؟ من z five of m مثلا
+
+112
+00:14:47,570 --> 00:14:52,930
+يسوى ال element اللي هنا شكله m في one طب احنا
+
+113
+00:14:52,930 --> 00:14:58,400
+ماعملاش ان الصبر يجعل زوجنا مصابر كيف؟ماوصلناش لسه
+
+114
+00:14:58,400 --> 00:15:02,480
+لل isomorphism الساعة ان اعرفنا function لأ بس
+
+115
+00:15:02,480 --> 00:15:06,080
+احنا جبنا ال sub ring جبنا ال sub ring صحيح لكن من
+
+116
+00:15:06,080 --> 00:15:11,560
+ال sub ring ل ZN سوينا حاجة؟ لأ ولا حاجة ماسويناش
+
+117
+00:15:11,560 --> 00:15:16,500
+اشي لش مشينا عنها؟ مامشيناش رايحيني لها دكتور يزيد
+
+118
+00:15:16,500 --> 00:15:20,760
+from us يزيد from us بس وصبر شوية بنت انا ماوصلناش
+
+119
+00:15:20,760 --> 00:15:25,760
+ل ZN انا هوصلك ل ZN بسهولة مش سهل انك تجي اقلبه
+
+120
+00:15:25,760 --> 00:15:32,210
+ساعتنالأ بس هو صبر شويه، فاحنا بقول عرفنا Phi من Z
+
+121
+00:15:32,210 --> 00:15:40,190
+الى Subring هذي بمين ب Phi of M يسوى M في 100 في
+
+122
+00:15:40,190 --> 00:15:45,090
+الواحد طيب هذي مش هو نص النظرية؟ يبقى هذي
+
+123
+00:15:45,090 --> 00:15:53,690
+homomorphism يبقى then .. then Phi is a
+
+124
+00:15:53,690 --> 00:16:00,540
+homomorphismهذا الكلام جيبته من أين؟ from the
+
+125
+00:16:00,540 --> 00:16:08,200
+أعضاء الـ Theorem يبقى
+
+126
+00:16:08,200 --> 00:16:14,500
+صار عندهم Homomorphism، مظبوط؟
+
+127
+00:16:14,500 --> 00:16:19,160
+يبقى فيها عندنا درية اسمها الـ Isomorphism Theorem
+
+128
+00:16:19,160 --> 00:16:29,350
+سمعنا فيها سمعنا فيها؟ طيبيبقى by the first
+
+129
+00:16:29,350 --> 00:16:34,230
+isomorphism
+
+130
+00:16:34,230 --> 00:16:39,070
+theorem
+
+131
+00:16:39,070 --> 00:16:42,690
+الـ
+
+132
+00:16:42,690 --> 00:16:55,760
+Z موديون الكيرن للـ 5 ايزو مورفك لل 5 of Zمين
+
+133
+00:16:55,760 --> 00:17:02,740
+الـPhi of Z؟ اللي هي S لإنه جالي Onto يبقى هذه
+
+134
+00:17:02,740 --> 00:17:08,860
+بالـE بدأت ساوى S طيب في معلومة حتى لأنا لم
+
+135
+00:17:08,860 --> 00:17:15,600
+نستخدمها إيش اللي بستخدمها؟ ال characteristic يبقى
+
+136
+00:17:15,600 --> 00:17:24,240
+هنا F ال characteristic للـR
+
+137
+00:17:24,590 --> 00:17:33,170
+is n هو أكبر مني الـ zero then الـ kernel ال alpha
+
+138
+00:17:33,170 --> 00:17:40,750
+هو ال principle ideal generated by n هذا بده قرار
+
+139
+00:17:40,750 --> 00:17:47,390
+يبقى بدنا ياكي تعمليله شك في البيت كأن بدأ أخد
+
+140
+00:17:47,390 --> 00:17:50,790
+element في ال kernel أثبت أنه في ال principle
+
+141
+00:17:50,790 --> 00:17:55,220
+ideal generated by nوالعملية العكسية طبعا سوينالك
+
+142
+00:17:55,220 --> 00:18:00,060
+قبل هيك أثبتنا أكتر من مرة كلام زي هيك يبقى بدنا
+
+143
+00:18:00,060 --> 00:18:05,220
+يحكي تثبتلي هذا الكلام مدام ال kernel هو ال
+
+144
+00:18:05,220 --> 00:18:09,320
+principle id generated by M إذا بقدر استخدم ال
+
+145
+00:18:09,320 --> 00:18:17,060
+kernel بال principle id generated by M ال
+
+146
+00:18:17,060 --> 00:18:26,570
+S أيزو موافق لل Zتبع الكيرن الانفاي اللي هو بده
+
+147
+00:18:26,570 --> 00:18:31,850
+يساوي Z مو موديولي ريفرنسيبال ايديو الـ generated
+
+148
+00:18:31,850 --> 00:18:42,410
+by N طيب سؤال مين هي ال رنج هذي؟ الاشة ZN صح ولا
+
+149
+00:18:42,410 --> 00:18:49,730
+لأ؟ يبقى هذي تساوي مين؟ تساوي ZN بناء ان عليه صار
+
+150
+00:18:49,730 --> 00:18:57,090
+ال sub ring SIsomorphic لمين الى Z إن و هو المطلوب
+
+151
+00:18:57,090 --> 00:19:01,770
+يبقى الاستعجلتوا له استعجلتوا عليه تو هاد احنا
+
+152
+00:19:01,770 --> 00:19:06,690
+أثبتنا بكل سهولة باستخدام ال first isomorphism
+
+153
+00:19:06,690 --> 00:19:13,850
+theorem حد فيكم تسأل أي سؤال قولي ليش أخدنا ال Phi
+
+154
+00:19:13,850 --> 00:19:20,020
+إن هقمتوا ال Z لأسفل؟ عشان نخلي اسم هي Phi of Zلأن
+
+155
+00:19:20,020 --> 00:19:26,080
+ال first isomorphism تقول لو كان Phi من مين؟ من
+
+156
+00:19:26,080 --> 00:19:32,860
+function او من R إلى S فبدي اخد ال element ال ..
+
+157
+00:19:32,860 --> 00:19:38,620
+ال isomorphism Phi of R صورة ال R كلها في main في
+
+158
+00:19:38,620 --> 00:19:44,360
+ال ring التانية اللي هي S هنا في اي تساوي الآخر؟
+
+159
+00:19:44,360 --> 00:19:51,320
+طيب بدنا نروح الآن ل crawl rear عقام 2بتخلي نص
+
+160
+00:19:51,320 --> 00:19:57,920
+النظرية مشان نطبق عليها الكرونة
+
+161
+00:19:57,920 --> 00:20:13,500
+هذي؟
+
+162
+00:20:13,500 --> 00:20:20,590
+كيف اجت؟ ممتاز، الحين خدي انه رقم ايه عاجبك؟قداش
+
+163
+00:20:20,590 --> 00:20:26,690
+متكيّب؟ عشرة عشرة ممتاز جدا زد فيها كام رقم؟ عشرة
+
+164
+00:20:26,690 --> 00:20:32,570
+عشرة ولا ملا مزايا كل رقم يجب أن يعمل مضيه له عشرة
+
+165
+00:20:32,570 --> 00:20:36,770
+يبقى زي الواحد اتنين لغاية تسعة سببات زائد ال
+
+166
+00:20:36,770 --> 00:20:39,630
+principle of identity generated by him لمن صلى
+
+167
+00:20:39,630 --> 00:20:42,970
+العشرة هو نوع صفر صفر يعني ال principle of
+
+168
+00:20:42,970 --> 00:20:46,110
+identity generated by him الاحداشر اعتبر واحد
+
+169
+00:20:46,110 --> 00:20:51,730
+اتناشر اعتبر اتنين وهكذايبقى بيبقى عند ZL و هو
+
+170
+00:20:51,730 --> 00:21:03,130
+المخطوط تمام طيب نجي للكرولري رقم اتنين يبقى
+
+171
+00:21:03,130 --> 00:21:07,630
+كرولري اتنين
+
+172
+00:21:07,630 --> 00:21:15,950
+بيقول for any positive integer M for any positive
+
+173
+00:21:18,860 --> 00:21:25,360
+انتجة M لمعرفة
+
+174
+00:21:25,360 --> 00:21:35,820
+لمعرفة
+
+175
+00:21:35,820 --> 00:21:53,030
+Phi من Z إلى ZM given byبعد ذلك فاي او X بس هو X
+
+176
+00:21:53,030 --> 00:22:00,190
+موديولو M X موديولو M is a ring homomorphism
+
+177
+00:22:17,510 --> 00:22:26,490
+خدّي بالك يبجي احنا بنعرف function refine a
+
+178
+00:22:26,490 --> 00:22:42,410
+mapping لو في من z الى zm باي طلعيني كويسي في of x
+
+179
+00:22:42,410 --> 00:22:52,650
+يسوى x modulo mالـ X هذا موجود في Z و لا في ZM؟ في
+
+180
+00:22:52,650 --> 00:22:58,870
+Z يعني انتجار صح؟ يبقى الـ X عجبار عن انتجار إذا
+
+181
+00:22:58,870 --> 00:23:11,050
+بقدر أقول هذا X في واحد M ZM الـ X modulo M جد ما
+
+182
+00:23:11,050 --> 00:23:16,050
+يكون هذا الرقم هو عبارة عن X في واحدوهذا موجود في
+
+183
+00:23:16,050 --> 00:23:21,990
+ZM مظبوط هك؟ صح؟ طيب يبقى ال function صلة بالشكل
+
+184
+00:23:21,990 --> 00:23:28,990
+هذا بنص النظرية ايه عندي؟ Phi من Z ل R Phi of N
+
+185
+00:23:28,990 --> 00:23:33,290
+يساوي ال N في واحد يبقى Ring همومورفزيوم ولا لا؟
+
+186
+00:23:33,290 --> 00:23:45,790
+يبقى هنا Phi Z above theorem النظرية تعالىfive is
+
+187
+00:23:45,790 --> 00:23:54,530
+a ring homomorphism وهو المطلوب خلاصنا طيب بدي
+
+188
+00:23:54,530 --> 00:24:00,850
+أمثلك إياها عدديًا كيف هي اختاري لك إما الرقم اللي
+
+189
+00:24:00,850 --> 00:24:08,760
+يعجبك كم بدك إياها؟ تلت عشرين كم؟ تلت عشرينفخلّيه
+
+190
+00:24:08,760 --> 00:24:11,940
+بس رقم صغير ماديش أقول زد تلاتة و عشرين و بدك تفت
+
+191
+00:24:11,940 --> 00:24:15,740
+مش اكتر يعني بل إن ما ينطبق عليه ينطبق على زد
+
+192
+00:24:15,740 --> 00:24:18,960
+اتنين ينطبق على زد خمسة ينطبق على زد سبعة ينطبق
+
+193
+00:24:18,960 --> 00:24:25,420
+على زد اطلاقية تمام؟ يبقى باجي بقول ه for example
+
+194
+00:24:25,420 --> 00:24:29,740
+إن
+
+195
+00:24:29,740 --> 00:24:39,240
+مثلا زد سبعة على سبيل المثال بدي أجي أخدالان الرقم
+
+196
+00:24:39,240 --> 00:24:52,180
+مثلا احداش موجود في الوزن صح؟ طيب هذا بدي يعطينا
+
+197
+00:24:52,180 --> 00:25:01,340
+في اض احداش طبقا لهذا الكلام بدي ساوى احداشر في
+
+198
+00:25:01,340 --> 00:25:07,730
+oneطبعا يعني واحد زائد واحد زائد واحد احداشر مرة
+
+199
+00:25:07,730 --> 00:25:13,750
+بيبقى هذا الكلام بالدرسة واحد زائد واحد زائد واحد
+
+200
+00:25:13,750 --> 00:25:23,930
+زائد زائد واحد احداشر times او احداشر صمندق مجموعة
+
+201
+00:25:23,930 --> 00:25:32,530
+جامعة طبعا السبعة فيهم و بقداسي سبعة ب zeroيعني
+
+202
+00:25:32,530 --> 00:25:40,030
+هذا الكلام بده يساوي واحد زائد واحد زائد واحد سبعة
+
+203
+00:25:40,030 --> 00:25:48,690
+times زائد واحد زائد واحد زائد واحد زائد واحد
+
+204
+00:25:48,690 --> 00:25:55,070
+السبعة times يبقى كم في زيت سبعة؟ Zero يبقى هذا
+
+205
+00:25:55,070 --> 00:26:01,850
+بده يعطينا Zero زائد أربعة ويساوي أربعةموجودة في Z
+
+206
+00:26:01,850 --> 00:26:08,830
+.. موجودة في Z7 ولا لا؟ يبقى belongs to Z7 يبقى
+
+207
+00:26:08,830 --> 00:26:15,150
+ملائكة عليه أي رقم موجود في Z بدي يكون له مناظر
+
+208
+00:26:15,150 --> 00:26:21,470
+موجود وين؟ موجود في Z7 و هكذا، هاي المقصود فيها
+
+209
+00:26:21,470 --> 00:26:27,890
+طيب، هذه quaterly بسيطة و مباشرة وإن شئتم فقولوا
+
+210
+00:26:27,890 --> 00:26:31,700
+trivialأستاذ بفضل الله بفضل الله بفضل الله بفضل
+
+211
+00:26:31,700 --> 00:26:34,240
+الله بفضل الله بفضل الله بفضل الله بفضل الله بفضل
+
+212
+00:26:34,240 --> 00:26:37,240
+الله بفضل الله بفضل الله بفضل الله بفضل الله بفضل
+
+213
+00:26:37,240 --> 00:26:48,220
+الله بفضل الله بفضل
+
+214
+00:26:48,220 --> 00:26:56,160
+الله بفضل
+
+215
+00:26:56,160 --> 00:27:03,460
+اللهمابرحناش الجزء؟ ماعشان حالي طيب نى دلان سقط
+
+216
+00:27:03,460 --> 00:27:08,140
+سهوان هذا و احنا كله بنقعد الخطأ و خيره الخطأين
+
+217
+00:27:08,140 --> 00:27:14,880
+ابتوابون أبنتهم طيب الجزء الثانى بيقول لي if ال
+
+218
+00:27:14,880 --> 00:27:25,090
+characteristic لل R is zero يبقى thenالأعلى كنت
+
+219
+00:27:25,090 --> 00:27:32,370
+أرسله bring isomorphic لمين لزد يبقى فيه عند S
+
+220
+00:27:32,370 --> 00:27:41,070
+isomorphic لمين لزد طيب احنا أخدنا إذا كان الجزء
+
+221
+00:27:41,070 --> 00:27:47,110
+الأول أثبتناه أثبتنا إن ال S isomorphic لزد
+
+222
+00:27:47,110 --> 00:27:53,100
+موديوله ل principle ideal generated by Nاللي قولنا
+
+223
+00:27:53,100 --> 00:28:02,300
+هذا هو عبارة عن ماذا؟ عن ZN ثم سيبيلي هذا الان
+
+224
+00:28:02,300 --> 00:28:11,080
+اللي بحتاجه يقول if ال characteristic is zero then
+
+225
+00:28:11,080 --> 00:28:14,240
+ال
+
+226
+00:28:14,240 --> 00:28:20,540
+S isomorphic لل Z module ال principle ideal
+
+227
+00:28:20,540 --> 00:28:27,460
+generated by zeroقياسا عليها بالضبط تماما طيب هذه
+
+228
+00:28:27,460 --> 00:28:34,420
+مين بتعطينا بالضبط زد itself لإن zero تفيل أي رقم
+
+229
+00:28:34,420 --> 00:28:40,480
+بدي يطلع نفس الرقم يبقى هذا بدي يعطينا زد إذا هنا
+
+230
+00:28:40,480 --> 00:28:48,080
+east isomorphic لزد و هو المفترض طيب
+
+231
+00:28:48,080 --> 00:28:53,350
+نرجع الأن لكرولري رقم تلاتة كتبناها لا لسهبدنا
+
+232
+00:28:53,350 --> 00:29:02,030
+نكتبها يبقى الكرول لرقم ثلاثة
+
+233
+00:29:02,030 --> 00:29:11,930
+بتقول
+
+234
+00:29:11,930 --> 00:29:22,470
+ما يعني if ال F is a field if F is a field of
+
+235
+00:29:24,750 --> 00:29:30,350
+characteristic P then ال F contains a sub field
+
+236
+00:29:30,350 --> 00:29:41,330
+then ال F contains a sub field contains a sub
+
+237
+00:29:41,330 --> 00:29:44,810
+field isomorphic to
+
+238
+00:29:54,350 --> 00:30:09,870
+F الـ F has a field of characteristic zero then F
+
+239
+00:30:09,870 --> 00:30:20,290
+contains .. then ال F contains a sub field ..
+
+240
+00:30:20,290 --> 00:30:30,900
+contains a sub fieldisomorphic صفر isomorphic
+
+241
+00:30:30,900 --> 00:30:36,580
+to isomorphic
+
+242
+00:30:36,580 --> 00:30:43,220
+to the rational numbers
+
+243
+00:30:43,220 --> 00:30:46,380
+اللي
+
+244
+00:30:46,380 --> 00:30:50,640
+هو الـQ rational numbers الـQ
+
+245
+00:31:05,450 --> 00:31:12,470
+السؤال هو ال field هو ring؟
+
+246
+00:31:12,470 --> 00:31:18,390
+مش حيال الله ring كمان، competitive ring with
+
+247
+00:31:18,390 --> 00:31:24,670
+unity وكل عنصر غير صفري له معكوث، مظبوط؟ هذا ال
+
+248
+00:31:24,670 --> 00:31:30,190
+field، يبقى بقول لو كان ال F a field يعني ال ring
+
+249
+00:31:30,190 --> 00:31:35,950
+of characteristic Pيبقى الـ F الـ P الـ sub field
+
+250
+00:31:35,950 --> 00:31:45,990
+عايزه موفق لمين لـ ZP باجي بقولك الـ
+
+251
+00:31:45,990 --> 00:31:54,910
+F الـ F دي ال field دي
+
+252
+00:31:54,910 --> 00:32:06,500
+ال field of characteristic P bythe .. قاعدة الـ
+
+253
+00:32:06,500 --> 00:32:17,440
+crullery when .. crullery when there is .. there
+
+254
+00:32:17,440 --> 00:32:24,660
+is a subfield subfield
+
+255
+00:32:24,660 --> 00:32:27,400
+isomorphic
+
+256
+00:32:31,720 --> 00:32:37,440
+isomorphic to zp
+
+257
+00:32:37,440 --> 00:32:42,480
+طيب
+
+258
+00:32:42,480 --> 00:32:55,460
+كيف ال F is a field of characteristic
+
+259
+00:32:55,460 --> 00:33:00,420
+zero then there is
+
+260
+00:33:11,630 --> 00:33:22,830
+Isofield isomorphic to leukemia هذا طبق لنص من نص
+
+261
+00:33:22,830 --> 00:33:27,990
+النظرية بس هذا الكلام هيكو صعب الأخير هذا مش داخل
+
+262
+00:33:27,990 --> 00:33:32,970
+مخنا أين او تمام هنخليه يدخل مخك وان شاء الله
+
+263
+00:33:32,970 --> 00:33:41,440
+تعالىطيب، ليش؟ ليش هذا درجة الصحيفة Isomorphic
+
+264
+00:33:41,440 --> 00:33:47,480
+تجلل ال EQ؟ مش لحقيقة المنظرية هذه وإذا لكرولري
+
+265
+00:33:47,480 --> 00:33:52,620
+واحد أه مسحناها لكرولري، بتقول Isomorphic تزد،
+
+266
+00:33:52,620 --> 00:33:58,120
+مظبوط؟ هذه تجلل ال EQ، مش لزد، كله بسيطة، تعالى
+
+267
+00:33:58,120 --> 00:34:05,570
+نشوف، إذااحنا بدنا ناخد ال S هذا sub field من مين؟
+
+268
+00:34:05,570 --> 00:34:14,430
+من اللي هو ال R نفجر نرجع نقول له لأ ال S اللي هي
+
+269
+00:34:14,430 --> 00:34:21,590
+بده يساوي مين؟ بده يساوي the set of all elements A
+
+270
+00:34:21,590 --> 00:34:31,200
+عالبي such that ال A هو ال Bموجودة في الـ Z والـ B
+
+271
+00:34:31,200 --> 00:34:38,100
+لا تساوي Z كويس؟
+
+272
+00:34:38,100 --> 00:34:45,300
+يبقى أخدت S تساوي هذه، then الـ
+
+273
+00:34:45,300 --> 00:34:54,920
+S هذه بتثبتها إنها إيه؟ إنها صبفيل صابفيل طيب كويس
+
+274
+00:34:55,300 --> 00:35:00,220
+يبقى لو أخدت S على الشكل اللي عندها هذا A على B
+
+275
+00:35:00,220 --> 00:35:08,400
+بحيث ال A و ال B موجودة في Z يبقى
+
+276
+00:35:08,400 --> 00:35:13,780
+هذه sub ring بقدرة كل اللي بقدر أقوله حتى الآن sub
+
+277
+00:35:13,780 --> 00:35:21,340
+ring then ال S is a sub ring
+
+278
+00:35:23,890 --> 00:35:31,510
+طيب بدي أخد جزء منها وهذا الجزء بدي أثبت أنه sub
+
+279
+00:35:31,510 --> 00:35:39,990
+field إذا لو جيتك و ذكرت فرضيلي في عندي set T ال
+
+280
+00:35:39,990 --> 00:35:49,350
+set T على شكل AB inverse AB inverse بحيث ال A و ال
+
+281
+00:35:49,350 --> 00:36:02,460
+B موجودة في Swill be لاتساوي 0. want to show ال
+
+282
+00:36:02,460 --> 00:36:12,000
+team as a sub field. عشان نقدر نطبق الجزء الثاني
+
+283
+00:36:12,000 --> 00:36:16,460
+من النظرية اللي بنقول عليه. لإن انا بارك أقول إن
+
+284
+00:36:16,460 --> 00:36:18,340
+أنا مش سهل فدج جماعة.
+
+285
+00:36:27,960 --> 00:36:32,460
+عشان أثبت أن هذا الـ Subject خلّيني أرجع للشرطة
+
+286
+00:36:32,460 --> 00:36:39,060
+للثانوية، ماذا تعرف Subject؟ أنا لو أخدت عنصرين في
+
+287
+00:36:39,060 --> 00:36:45,020
+هذه الستة و لقيت الفرق فيما بينهم موجود فيها و لو
+
+288
+00:36:45,020 --> 00:36:49,340
+أخدت العنصر الأول في معكس الثاني و ضربتهم بيكون في
+
+289
+00:36:49,340 --> 00:36:53,560
+نفس الستةإن حدث ذلك بقول هذا ال sub field حسب ما
+
+290
+00:36:53,560 --> 00:36:58,260
+أعرف عندكم في أحد الأسئلة لأدري قداشر رقم السؤال
+
+291
+00:36:58,260 --> 00:37:03,120
+في قداشر؟ خمسة وعشرين، كويس بالنسبالي ال sub field
+
+292
+00:37:03,120 --> 00:37:09,300
+طب لاحظي ماقليش non-empty ماقليش non لأن ال field
+
+293
+00:37:09,300 --> 00:37:13,600
+دائما ال communicative و ال unity أقل حاجة في ال
+
+294
+00:37:13,600 --> 00:37:19,240
+unity صح يكون في ring يبقى كمان ال zero موجود تمام
+
+295
+00:37:19,920 --> 00:37:24,800
+طيب الان انا ادعي ان هذا sub field لذلك بدأ اخد
+
+296
+00:37:24,800 --> 00:37:32,140
+عنصرين في T يبقى بدأجي اقول افترض ان ال X و ال Y
+
+297
+00:37:32,140 --> 00:37:39,160
+موجودة في T then ال X يا بنات بدي يكون على شكل AB
+
+298
+00:37:39,160 --> 00:37:49,000
+inverse و ال Y بدي يكون على شكل CD inverse تمام؟
+
+299
+00:37:49,350 --> 00:37:57,030
+يبقى بتاعي أخد ال X ناقص ال Y. يبقى ال X B inverse
+
+300
+00:37:57,030 --> 00:38:04,090
+ناقص C D inverse. هل هذه على الشكل هذا؟ لا والله
+
+301
+00:38:04,090 --> 00:38:10,030
+ما هي على الشكل هذا أبدا. فما هيش الحالة؟ قلت
+
+302
+00:38:10,030 --> 00:38:14,590
+بسيطة، بدي أخليها على الشكل وماحدش يقدر يمسك عليه.
+
+303
+00:38:15,490 --> 00:38:22,230
+بقول هاد يا بنات لو جيت Gold X B inverse في D D
+
+304
+00:38:22,230 --> 00:38:27,850
+inverse يعني كأنه انا ضارب في ايش ال unity اللي هو
+
+305
+00:38:27,850 --> 00:38:35,570
+الواحد ناقص C D inverse السؤال هو ليش أخد D D
+
+306
+00:38:35,570 --> 00:38:39,290
+inverse مش ماخدتش B B inverse مش ماخدتش C C
+
+307
+00:38:39,290 --> 00:38:43,880
+inverse مثلاالإجابة بسيطة جدا أنا عندي D inverse
+
+308
+00:38:43,880 --> 00:38:49,420
+حبيت أخلك هنا ال answer D inverse مشان استخدم
+
+309
+00:38:49,420 --> 00:38:53,660
+distributive law و أقوله شرفني على الشجر مشان أحطه
+
+310
+00:38:53,660 --> 00:38:57,820
+على شكل answer موجود وين في T إذا انا حاسب ال
+
+311
+00:38:57,820 --> 00:39:04,800
+distributive law هذا بدي يعطيني X B inverse D ناقص
+
+312
+00:39:04,800 --> 00:39:11,770
+ال C في D inverseD inverse D inverse خلّيتها برا
+
+313
+00:39:11,770 --> 00:39:19,150
+ضال الباقية الآن هذا عنصر وهذا عنصر تاني على الشكل
+
+314
+00:39:19,150 --> 00:39:24,710
+اللي عندنا هذا و لا ده عنصر في معكوس الثاني يبقى
+
+315
+00:39:24,710 --> 00:39:35,490
+صار هذا موجود في تي بدا ال XA بدا ال XA من البداية
+
+316
+00:39:35,490 --> 00:39:43,780
+X نقص Y بيسوي AP inverseA B Inverse هنا C B
+
+317
+00:39:43,780 --> 00:39:47,860
+Inverse اه
+
+318
+00:39:47,860 --> 00:39:52,400
+هذه A B Inverse انا عمال بقول A يعني بمطبخ صحيح
+
+319
+00:39:52,400 --> 00:40:00,580
+يبقى A بالشكل اللي عندنا ده وهذا A B Inverse وهذه
+
+320
+00:40:00,580 --> 00:40:06,890
+A B Inverse مظبوط معاكوا حاجة تماميبقى صارت على
+
+321
+00:40:06,890 --> 00:40:13,850
+شكل عنصر موجود في T بداية ياخد ال X Y inverse يبقى
+
+322
+00:40:13,850 --> 00:40:23,470
+يساوي ال X ب A B inverse وال Y بC D inverse لكل
+
+323
+00:40:23,470 --> 00:40:32,730
+inverse طيب هذا الكلام يساوي A B inverseهذا بده
+
+324
+00:40:32,730 --> 00:40:41,970
+يعطيني C inverse D ايه
+
+325
+00:40:41,970 --> 00:40:47,070
+B inverse زي مانيه C D inverse E inverse كل C
+
+326
+00:40:47,070 --> 00:40:54,130
+inverse D inverse Inverse اللي هو D صح؟ ايوة طب
+
+327
+00:40:54,130 --> 00:41:00,540
+ليش مجلبتهم؟لأنه احنا أخدنا في ال group ان ال A بي
+
+328
+00:41:00,540 --> 00:41:04,800
+لكل inverse يسوي B inverse A inverse هذا هو الصحيح
+
+329
+00:41:04,800 --> 00:41:12,800
+لأن هذا في ال commutative نظرا ال commutative خلت
+
+330
+00:41:12,800 --> 00:41:17,400
+كل واحد في مكان و حطيت اللي هو ال inverse تبعه هذا
+
+331
+00:41:17,400 --> 00:41:23,250
+يمنعك بقدر اكتب ايه دي مافيش فيه inverseوهذا بقدر
+
+332
+00:41:23,250 --> 00:41:29,710
+اكتب و بي سي لكل inverse لأن الكمبيوتر مش سي بي
+
+333
+00:41:29,710 --> 00:41:34,150
+كله بي سي حتى لو حطيتها سي بي بتفرقش انما يبقى صار
+
+334
+00:41:34,150 --> 00:41:39,110
+element في معاكوس الثاني موجود في T ولا لا يبقى
+
+335
+00:41:39,110 --> 00:41:44,370
+هذا belongs to T sub field
+
+336
+00:41:51,540 --> 00:41:57,200
+إيه صار فيه طيب
+
+337
+00:41:57,200 --> 00:42:02,960
+حتى الأن احنا وين والاسبابت وين انا بقول صار فيه
+
+338
+00:42:02,960 --> 00:42:12,060
+ال isomorphic لل Q إذا أنا بدي أروح أعرف define ال
+
+339
+00:42:12,060 --> 00:42:20,320
+mapping في من T إلى ال EQ
+
+340
+00:42:23,580 --> 00:42:32,920
+by phi of T العنصر A B inverse A B inverse بديها
+
+341
+00:42:32,920 --> 00:42:39,600
+element في ال Q ال Q rational numbers يبقى A على B
+
+342
+00:42:39,600 --> 00:42:46,300
+و ال B مالها لاتساوي Zero يبقى فعلا هذه في ال Q و
+
+343
+00:42:46,300 --> 00:42:52,590
+فعلا هذه في 2 إذا أثبتت أن ال Phi همومارفزيومone
+
+344
+00:42:52,590 --> 00:42:59,130
+to one وانتوا بيكون خلصنا ال isomorphism مظبوط؟
+
+345
+00:42:59,130 --> 00:43:07,530
+إذا بدالي أقوله Phi is a homomorphism نقطة الأولى
+
+346
+00:43:07,530 --> 00:43:16,530
+إذا بدالي أخد الفائلات ال X بدها تساوي AB inverse
+
+347
+00:43:16,530 --> 00:43:23,620
+وال Y بدها تساوي CD inverseاللي موجودة وين؟ اللي
+
+348
+00:43:23,620 --> 00:43:28,500
+موجودة في T بدي
+
+349
+00:43:28,500 --> 00:43:37,760
+أخد Phi of X زائد Y يبقى Phi of ال X له A B
+
+350
+00:43:37,760 --> 00:43:48,220
+inverse زائد C D inverse هذا شكله موجود في T هيك؟
+
+351
+00:43:48,220 --> 00:43:56,930
+مقدرش مش صحيحتظبطهم يمكن تظبط معاك بقوله بسيطة
+
+352
+00:43:56,930 --> 00:44:05,650
+اشرايكوا هذه اكتبها Phi of A B inverse مضروبة في D
+
+353
+00:44:05,650 --> 00:44:15,030
+D inverse يعني ال unity زائد التانية C D inverse
+
+354
+00:44:15,030 --> 00:44:19,870
+بدي اضربها في ال B B inverse اللي هو ال unity كذلك
+
+355
+00:44:19,870 --> 00:44:31,680
+تمام؟يبقى هذا الكلام يثابر يثابر في of عندك هنا ال
+
+356
+00:44:31,680 --> 00:44:39,920
+a دي مالوش دعوة مظبوط في ال b inverse دي inverse
+
+357
+00:44:39,920 --> 00:44:44,340
+خليت اللي مش فيهم inverse مع بعض و اللي فيهم ال
+
+358
+00:44:44,340 --> 00:44:52,710
+inverse مع بعض وهنا زائد border bcفاهمين في ال B
+
+359
+00:44:52,710 --> 00:45:00,790
+inverse D inverse صار ال element هذا هو ال element
+
+360
+00:45:00,790 --> 00:45:08,110
+هذا صح بقدر استخدم ال distributive law يبقى Phi of
+
+361
+00:45:08,110 --> 00:45:19,250
+ال A D زائد ال B C كله في ال B D inverse صار هذا
+
+362
+00:45:19,250 --> 00:45:26,570
+elementفي معكوسي الثاني يبقى موجود في T ولا لا إذا
+
+363
+00:45:26,570 --> 00:45:35,410
+هذا لما يؤثر عليها الفعل بدل سوى AD زائد BC مقسوما
+
+364
+00:45:35,410 --> 00:45:40,710
+على BD كنت من اكتساف ليه ولا لا؟ هل اللي عملتوا هل
+
+365
+00:45:40,710 --> 00:45:46,230
+بينفع أعملوا في الخطوة اللي فار؟ X نقص Y X نقص Y
+
+366
+00:45:46,230 --> 00:45:51,640
+ما نزمتش ليه؟لو لسه مثلًا عملناها زيه، بس اسمه
+
+367
+00:45:51,640 --> 00:45:55,620
+ماعديش مشكلة، ماعديش مشكلة، هذا القطوع أتجل من هذا
+
+368
+00:45:55,620 --> 00:46:00,720
+شوية، لكن نفس الفكرة، نفس الفكرة، يبقى هذا الكلام
+
+369
+00:46:00,720 --> 00:46:05,480
+يسام، بتوزع البسط على المقام، بتروح ال D مع D،
+
+370
+00:46:05,480 --> 00:46:10,640
+بتطلع جدًا A على B، هذي بتروح ال B مع ال B، بتطلع
+
+371
+00:46:10,640 --> 00:46:22,180
+C على D، هذي مين؟ هذي PhiRAB Inverse زائد Phi of C
+
+372
+00:46:22,180 --> 00:46:30,540
+D Inverse يعني Phi of X زائد Phi of R هذا لسه نص
+
+373
+00:46:30,540 --> 00:46:31,840
+ال homomorphism
+
+374
+00:46:50,600 --> 00:47:01,880
+يبقى انا Phi of XY سواء Phi of AD inverse في CD
+
+375
+00:47:01,880 --> 00:47:12,600
+inverse يعني بقدر اقول هذا Phi of AC في BD الكل
+
+376
+00:47:12,600 --> 00:47:16,040
+inverse تمام؟
+
+377
+00:47:19,960 --> 00:47:27,100
+فطمة ينبلش فطمة واحدة يعني بيقول هذا AC B inverse
+
+378
+00:47:27,100 --> 00:47:40,760
+D inverse اللي بقدر اكتب في ا AC B D كل انفرز هذا
+
+379
+00:47:40,760 --> 00:47:49,080
+الكلام ينسب حسب ال definition يعني هذا AC على BD
+
+380
+00:47:49,790 --> 00:47:59,690
+يعني مين؟ يعني A على B في C على D A على B ليه؟ Phi
+
+381
+00:47:59,690 --> 00:48:09,030
+of A D Inverse وهذه Phi of C D Inverse يعني Phi of
+
+382
+00:48:09,030 --> 00:48:17,710
+X في مين؟ في Phi of Y يبقى يعني هذا كلام Phi
+
+383
+00:48:17,710 --> 00:48:27,320
+homomorphismيبقى هنا سا فاي is a homomorphism بنا
+
+384
+00:48:27,320 --> 00:48:34,360
+نجي الأعلى لفاي is one to one يبقى
+
+385
+00:48:34,360 --> 00:48:41,720
+بدي أاخد صورتين فاي of a, b inverse بدي أسوأ فاي
+
+386
+00:48:41,720 --> 00:48:50,250
+of c, d inverse يبقى then صورة هذه اللي همينA على
+
+387
+00:48:50,250 --> 00:48:57,530
+B وصورة هذا مين C على D إذا هذا الكلام بدي أعطيك
+
+388
+00:48:57,530 --> 00:49:06,690
+AD بدي سوى مين DC طيب إيش رأيك لو جيت بقولك هذا ال
+
+389
+00:49:06,690 --> 00:49:16,590
+AD في ال B inverse D inverse بدي سوى ال BCالـ B
+
+390
+00:49:16,590 --> 00:49:23,590
+inverse D inverse يعني ضربت اتنين في نفس مين في
+
+391
+00:49:23,590 --> 00:49:31,290
+نفس الرقم طب هذا ايش بده يعطينا هذا بده يعطينا ال
+
+392
+00:49:31,290 --> 00:49:38,690
+A B inverse ال A B inverse في ال D D inverse وهذا
+
+393
+00:49:38,690 --> 00:49:46,980
+بده يعطينا ال B D inverseفى C D Inverse هذا بقدرش
+
+394
+00:49:46,980 --> 00:49:53,400
+يا بنات هذا بقدرش يبقى هذا بدي يعطيك ان ال A B
+
+395
+00:49:53,400 --> 00:50:02,160
+Inverse بدي يساوي C فى D Inverse تمام طيب بدأت
+
+396
+00:50:02,160 --> 00:50:07,120
+بفاي A B Inverse بيساوي فاي فى C D Inverse ووصلت
+
+397
+00:50:07,120 --> 00:50:15,840
+لهذا يبقى فاي is one twentyأخر حاجة في القنبلة يجب
+
+398
+00:50:15,840 --> 00:50:23,740
+أن أقول خذ ال X موجودة في ال Q يجب أن أرى إنها أصل
+
+399
+00:50:23,740 --> 00:50:32,040
+في T أو لا لأ يجب أن أقول X موجودة في A على B والـ
+
+400
+00:50:32,040 --> 00:50:39,360
+B لا تساوي 0 هذا يجب أن أقول لك أن Xبساوي a على b
+
+401
+00:50:39,360 --> 00:50:45,600
+اللي هو main فاي of a بينبرت لذلك فاي is on top
+
+402
+00:50:45,600 --> 00:50:51,780
+يبقى داصر فاي is an isomorphism
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5WB6jBEi9nU_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5WB6jBEi9nU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d5b9f277c9b81a294f65fbffee47147cd8f1525a
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5WB6jBEi9nU_raw.srt
@@ -0,0 +1,1944 @@
+1
+00:00:20,690 --> 00:00:25,630
+بسم الله الرحمن الرحيم نواصل الآن اللي هو الشبطة
+
+2
+00:00:25,630 --> 00:00:31,710
+14 والمرة اللي فاتت أعطينا تعريف للـ ID واخدنا على
+
+3
+00:00:31,710 --> 00:00:37,970
+ذلك خمسة أمثلة وهذا هو المثال السادس المثال السادس
+
+4
+00:00:37,970 --> 00:00:41,910
+بيقول افترض ان R عبارة عن كمية ال ring with unity
+
+5
+00:00:41,910 --> 00:00:46,970
+واخدنا مجموعة من العناصر من ال ring R وليكن A1 و
+
+6
+00:00:46,970 --> 00:00:54,480
+A2 و ANكوّننا ست جديدة هذه السفرة مزالها بالرمز I
+
+7
+00:00:54,480 --> 00:01:01,840
+هي الست التي تولد بالعناصر A1 و A2 و AN شو شكل
+
+8
+00:01:01,840 --> 00:01:09,100
+العنصر فيها كل عنصر فيها شكله R1 A1 R2 A2 لغاية RN
+
+9
+00:01:09,100 --> 00:01:15,700
+AN يعني أخدت كل عنصر من عناصر الست A وضربته في
+
+10
+00:01:15,700 --> 00:01:20,820
+عنصر من عناصر R و جمالكل هذا بيعطينا عنصر واحد في
+
+11
+00:01:20,820 --> 00:01:26,720
+مين في الست اللي عندنا اللي هو I يبقى هذا عبارة عن
+
+12
+00:01:26,720 --> 00:01:32,360
+ideal بدنا نثبت صحة هذا الكلام هذا ال ideal اسمه
+
+13
+00:01:32,360 --> 00:01:38,280
+the ideal generated by A1 و A2 و لغاية AN يبقى هو
+
+14
+00:01:38,280 --> 00:01:47,040
+ال ideal اللي تكون من العناصر A1 و A2 لغاية AN
+
+15
+00:01:47,680 --> 00:01:54,000
+الاهم solution احنا مشان نثبت ان ال set هي عبارة
+
+16
+00:01:54,000 --> 00:02:01,100
+عن ideal بدنا نروح نثبت ثلاث نقاط من انتي لو أخدت
+
+17
+00:02:01,100 --> 00:02:05,560
+عنصرين من هذه ال set طرحتهم بد يكون الناتج موجود
+
+18
+00:02:05,560 --> 00:02:09,300
+في نفس ال set لو أخدت element من هذه ال set و
+
+19
+00:02:09,300 --> 00:02:14,200
+element من ارض ضربته في هذا العنصر من اليمين او من
+
+20
+00:02:14,200 --> 00:02:19,240
+الشمالبدي يكون في نفس ال set لان اذا حدث ذلك هذه
+
+21
+00:02:19,240 --> 00:02:24,840
+ال set بسميها ايش I دي طيب احنا الان نجي للنقطة
+
+22
+00:02:24,840 --> 00:02:31,320
+الاولى انا ادعي ان هذه ال set is non-empty يبقى
+
+23
+00:02:31,320 --> 00:02:41,790
+باجي بقول ال I is non-empty ليش؟بدنا عنصر واحد على
+
+24
+00:02:41,790 --> 00:02:49,610
+الأقل نثبته موجود فيها because a zero بقدر اكتب هو
+
+25
+00:02:49,610 --> 00:02:58,130
+r واحد zero r اتنين zero زائد r in zero و ال R I
+
+26
+00:02:58,130 --> 00:03:04,110
+موجودة في R مظبوط؟ كده اش بطلع Zero زائد Zero زائد
+
+27
+00:03:04,110 --> 00:03:09,660
+Zero زائد Zero كله a zero فقطيبقى الـ zero عنصر
+
+28
+00:03:09,660 --> 00:03:18,760
+هذا موجود في الـ set I لذلك الـ I is من M تمام؟
+
+29
+00:03:18,760 --> 00:03:24,620
+يبقى هنا نقول because، ما هو السبب؟ السبب خلوه
+
+30
+00:03:24,620 --> 00:03:31,800
+قدامنا، النقطة الثانية، سأخذ عنصرين في نفس الـ I
+
+31
+00:03:31,800 --> 00:03:41,230
+يبقى let X وY موجودة في Ithen بتعرف شكل ال X و ال
+
+32
+00:03:41,230 --> 00:03:47,230
+Y عبارة عن ايه يبقى ال X في هذه الحالة مقدر اقول
+
+33
+00:03:47,230 --> 00:03:59,610
+R1 A1 زائد R2 A2 زائد RN AN و ال RI موجودة في R
+
+34
+00:03:59,610 --> 00:04:05,330
+طيب و ال Y R1
+
+35
+00:04:05,330 --> 00:04:13,200
+هذي نفسهاأو الارض نفسها؟ لأ لأ ليس بالضرورة الارض
+
+36
+00:04:13,200 --> 00:04:16,600
+الثابتة
+
+37
+00:04:16,600 --> 00:04:23,160
+هي A1 وA2 وA3 لغاية AN يبقى الارض هذول متغيرات
+
+38
+00:04:23,160 --> 00:04:28,800
+ماعنهم مش خيوط اي عناصر من ال ring R يبقى لو روحت
+
+39
+00:04:28,800 --> 00:04:40,050
+قلت S1 A1 S2 A2 زائد SN ANوالـ S I موجودة في R
+
+40
+00:04:40,050 --> 00:04:47,090
+فبالمطلوب أثبت أن الفرق فيما بينهما موجود في الـ I
+
+41
+00:04:47,090 --> 00:04:54,670
+إذا بدي أخد ال X ناقص ال Y يبقى ال X ناقص ال Y بدي
+
+42
+00:04:54,670 --> 00:05:04,470
+أطرح كل عضم منهم يبقى R 1 ناقص S 1 في الـ A I زاد
+
+43
+00:05:04,470 --> 00:05:14,810
+R 2نقص S2 في الـ A2 زائد زائد ال R N نقص ال S N
+
+44
+00:05:14,810 --> 00:05:23,350
+كله في ال A M أليس هذا على شكل العمصر اللي فوق نعم
+
+45
+00:05:23,350 --> 00:05:33,150
+لإن ال R I نقص S I موجودة في R يبقى هذا موجود في I
+
+46
+00:05:33,150 --> 00:05:34,050
+because
+
+47
+00:05:36,490 --> 00:05:47,610
+الـ R I ناقص الـ S I موجود في الـ Ring A طيب، الآن
+
+48
+00:05:47,610 --> 00:05:53,770
+بدي أجد النقطة الثالثة بدي أخد عنصر من الـ Ring A
+
+49
+00:05:53,770 --> 00:05:59,330
+و أخد عنصر من الـ Seat I وأثبت إنه حاصل ضربه من
+
+50
+00:05:59,330 --> 00:06:06,930
+اليمين و من الشمالموجود في I إن حدث ذلك يبقى يقول
+
+51
+00:06:06,930 --> 00:06:12,910
+خلاص لو صرت ال I is M I D يبقى هنا باني بقوله
+
+52
+00:06:12,910 --> 00:06:21,670
+افترض ان R موجودة في R and ال X موجودة في ال I
+
+53
+00:06:21,670 --> 00:06:30,930
+then ال R موجودة في R and ال X بدأ تسوي R عن E عن
+
+54
+00:06:31,400 --> 00:06:42,800
+R2A2 بالزائد زائد RNAM والـRI موجودة في الـR وI
+
+55
+00:06:42,800 --> 00:06:50,160
+بتاخد من الواحد divided ال M يبقى لو جيت على ال RX
+
+56
+00:06:50,160 --> 00:06:59,280
+يساوي الـRP ده يشيل ال X ويحط النت اليميناللي هي
+
+57
+00:06:59,280 --> 00:07:11,280
+ال R 1 A 1 زائد ال R 2 A 2 زائد زائد ال R N A N
+
+58
+00:07:11,280 --> 00:07:18,320
+بقدر ادخل ال R حسب ال distributive law على كل عنصر
+
+59
+00:07:18,320 --> 00:07:26,440
+من هذه العناصر يعني لو دخلت تصير مين؟ R في R 1 A 1
+
+60
+00:07:26,440 --> 00:07:40,060
+زائد Rفي R2E2 زائد زائد RN فيها زائد R في RNAN
+
+61
+00:07:40,060 --> 00:07:47,920
+طيب هذا الكلام yourself بتستخدم الآن خاصية ال
+
+62
+00:07:47,920 --> 00:07:53,260
+associativity على ال ring R هدول كل واحد فيهم من
+
+63
+00:07:53,260 --> 00:07:59,570
+التلاتة هدول عمصر موجود وين؟الـ R ، هذول في الـ R
+
+64
+00:07:59,570 --> 00:08:03,510
+، هذول في الـ R خاصية ال associativity صحيحة على
+
+65
+00:08:03,510 --> 00:08:11,130
+الـ R يبقى بده يعطيني R R1 في الـ A1 R R2 في الـ
+
+66
+00:08:11,130 --> 00:08:22,300
+A2 هنا زائد زائد R RN في من الـ AMهذه الصيغة مش هي
+
+67
+00:08:22,300 --> 00:08:29,200
+الصيغة اللي عندنا هذه لإنه RR1 في R وRR2 في R وRRN
+
+68
+00:08:29,200 --> 00:08:36,600
+في R يبقى هذا الكلام كله موجود وين؟ موجود في I
+
+69
+00:08:36,600 --> 00:08:48,620
+since ليش؟ لأن ال RRI موجود في ال ring R itselfطيب
+
+70
+00:08:48,620 --> 00:08:53,420
+بناء عليه أثبتنا الخواص التلاتة يبقى بروح بقوله
+
+71
+00:08:53,420 --> 00:09:01,460
+راس ال I اللي هي بدها الانصر المتولد بال A1 و ال
+
+72
+00:09:01,460 --> 00:09:15,690
+A2 و ال AN هذا is an ideal of Rاذا بتلاحظوا يا
+
+73
+00:09:15,690 --> 00:09:21,530
+بنات هذا هو تعميم لل principle ideal generated by
+
+74
+00:09:21,530 --> 00:09:25,490
+A ال principle ideal generated by A يقول كل
+
+75
+00:09:25,490 --> 00:09:31,870
+العناصر AR أو RA لأن هذه commutative مش مشكلة
+
+76
+00:09:31,870 --> 00:09:38,850
+عندنا فيها يبقى كل العناصر RA بحيث ال R موجودة في
+
+77
+00:09:38,850 --> 00:09:43,570
+R احنا أثبتنا ال R X بتثير
+
+78
+00:09:51,200 --> 00:09:57,260
+XR موجودة في R بنفس الطريقة يبقى صارت ضرب من
+
+79
+00:09:57,260 --> 00:10:02,700
+اليمين و لا ضرب من الشمال يبقى صارت two sided ID
+
+80
+00:10:02,700 --> 00:10:11,480
+هذا هو المثال رقم ستة بقى نروح للمثال رقم ستة مثال
+
+81
+00:10:11,480 --> 00:10:21,650
+رقم سبعة ومص على ماية بيقول الاناللي هو Z of X مين
+
+82
+00:10:21,650 --> 00:10:30,390
+هي هذه مجموعة ال polynomials اللي العوامل تبعات ال
+
+83
+00:10:30,390 --> 00:10:37,050
+X كلهم ثوابت والثوابت هذه ماخدينها من مين ال set
+
+84
+00:10:37,050 --> 00:10:44,510
+of integers كلهم أعداد صحية يبقى B the ring of all
+
+85
+00:10:44,510 --> 00:10:54,140
+polynomialsthe pairing of all polynomials
+
+86
+00:10:54,140 --> 00:10:57,860
+polynomials
+
+87
+00:10:57,860 --> 00:11:05,600
+with integer coefficients
+
+88
+00:11:05,600 --> 00:11:11,080
+كله
+
+89
+00:11:11,080 --> 00:11:22,310
+بمعاملات ذات عداد صحيح بدي أخد سنةI ثابت من Z of X
+
+90
+00:11:22,310 --> 00:11:35,250
+Such that بحيث ان ال I كل العناصر F of X بحيث ان
+
+91
+00:11:35,250 --> 00:11:45,390
+ال F of X بدي ساوي ANXN AN minus one XN minus one
+
+92
+00:11:45,950 --> 00:11:56,710
+زائد a1x زائدي اتنين m و ال m موجودة في z و ال m
+
+93
+00:11:56,710 --> 00:12:08,990
+موجودة في z show that show that ميلي ان ال Iis an
+
+94
+00:12:08,990 --> 00:12:18,810
+ideal of R بيقول إن هذا ideal of الـR اللي يمين
+
+95
+00:12:18,810 --> 00:12:22,250
+اللي هي Z of X
+
+96
+00:12:36,860 --> 00:12:43,400
+نقرأ سؤال مرة تانية و بدي أتكلم كلام أو أوضح
+
+97
+00:12:43,400 --> 00:12:49,100
+الصيغة الرياضية تبعته السؤال بيقول خُلْد Z of X هي
+
+98
+00:12:49,100 --> 00:12:56,260
+ring اللي هي كثيرات الحدود بحيث المعاملات تبعت
+
+99
+00:12:56,260 --> 00:13:02,100
+كثيرات الحدود كلها أعداد صحيحة طبعا أخدناها قبل
+
+100
+00:13:02,100 --> 00:13:08,040
+ذلك و أثبتنا إن هذه رمجةماله هو ال integer
+
+101
+00:13:08,040 --> 00:13:14,280
+coefficients موجودة في z خدلي say subset من z of x
+
+102
+00:13:14,280 --> 00:13:21,660
+مين هي هذه ال set هي set I كل العناصر f of x such
+
+103
+00:13:21,660 --> 00:13:27,020
+that f of x تسوى ال polynomial هذه بس تطلعيلي هنا
+
+104
+00:13:27,020 --> 00:13:33,960
+كتبنا زائدين M إيش يعني قصده يقوليقول كل ال
+
+105
+00:13:33,960 --> 00:13:39,220
+polynomial اللي المقدار الثابت فيها هو عدد زوجي
+
+106
+00:13:39,220 --> 00:13:44,720
+طبعا احنا أخدناها كمثال قبلين المقدار الثابت صفر
+
+107
+00:13:44,720 --> 00:13:50,620
+مظبوط و أثبتنا أنها عادين هنا بقول اللي المقدار
+
+108
+00:13:50,620 --> 00:13:56,260
+الثابت هو عدد زوجي مش أي عدد و بدأت تروح تثبت أن
+
+109
+00:13:56,260 --> 00:14:03,350
+هذه عبارة عن إيش عبارة عن عادين و ده بسيطة جدايبقى
+
+110
+00:14:03,350 --> 00:14:07,530
+الثلاث خطوات يومان إمتي و ال first between two
+
+111
+00:14:07,530 --> 00:14:13,050
+أنصرين منها موجود فيها و حاصل ضرب أنصر من ال ring
+
+112
+00:14:13,050 --> 00:14:17,730
+أو أنصر من هذه السثة لو ضربناهم في بعض يمين أو
+
+113
+00:14:17,730 --> 00:14:24,590
+شمال موجود داخلها طبعا لو رجعنا بالذاكرة قليلا إلى
+
+114
+00:14:24,590 --> 00:14:31,930
+الوراق للمحاضرة الماضية أخر مثال مثال خمسةشبه قوي
+
+115
+00:14:31,930 --> 00:14:36,790
+وكبير جدا ما بين هذا المثال والمثال الأول لكن
+
+116
+00:14:36,790 --> 00:14:43,910
+بداية بدنا نثبت أن هذا .. أن هذه أو هذه الست ليست
+
+117
+00:14:43,910 --> 00:14:54,430
+فارغة non-empty تمام فبعدين بقوله الآن that set I
+
+118
+00:14:54,430 --> 00:15:02,070
+is non-empty أفضل صفر موجودزي مجهدنا نقدرنا نمتي
+
+119
+00:15:02,070 --> 00:15:09,610
+هتلي ولو عمصر واحد تاني because لو
+
+120
+00:15:09,610 --> 00:15:14,810
+أخدت F of Zero فانا كده كده ايش بده يساوي؟ Zero
+
+121
+00:15:14,810 --> 00:15:19,110
+Zero Zero Zero اتنين M يبقى اتنين M اتنين M عدد
+
+122
+00:15:19,110 --> 00:15:23,910
+زوجي و لا لا بولونوميل و الحد الثابت فيها عدد زوجي
+
+123
+00:15:23,910 --> 00:15:32,080
+اذا هذه موجودة وينفي I لأن هذا موجود في I مدى ما
+
+124
+00:15:32,080 --> 00:15:38,220
+موجود في I يبقى الـ I ما من ال empty الان ال
+
+125
+00:15:38,220 --> 00:15:44,360
+condition اتنين الان ال condition تلاتة are the
+
+126
+00:15:44,360 --> 00:15:52,100
+same نفس الشكل as example خمسة
+
+127
+00:15:53,010 --> 00:15:57,470
+لذلن مش هروح اضايق الوقت و اكرر فيه اترى ايه او
+
+128
+00:15:57,470 --> 00:16:04,330
+راجعي مثال خمسة بتكون واصلتي الى الإيجابة طيب نجيب
+
+129
+00:16:04,330 --> 00:16:08,770
+سؤال بس سؤال calculus المرة هذه اللي عارفينه
+
+130
+00:16:08,770 --> 00:16:12,950
+ومتذكرين ال calculus بتلاقوه ان شاء الله بصير طيب
+
+131
+00:16:12,950 --> 00:16:21,790
+مثال رقم تمانية تمانية بيقول ما ياتياللي بيقول
+
+132
+00:16:21,790 --> 00:16:31,470
+consider the ring consider the ring اللي هى R
+
+133
+00:16:31,470 --> 00:16:41,770
+تساوى R تساوى كل العناصر F of X such that such
+
+134
+00:16:41,770 --> 00:16:49,130
+that ال F of X is a real valued function is a real
+
+135
+00:16:49,710 --> 00:17:03,810
+value function among little s that capital S هي كل
+
+136
+00:17:03,810 --> 00:17:11,010
+العناصر g of x اللي موجودة في ال ring R such that
+
+137
+00:17:11,010 --> 00:17:19,500
+ال G is a differentiable functionدالة قابلة
+
+138
+00:17:19,500 --> 00:17:32,360
+للاشتقاء show that show that بيّل إن ال S is a sub
+
+139
+00:17:32,360 --> 00:17:42,720
+ring of R but not an ideal
+
+140
+00:18:19,270 --> 00:18:25,310
+السؤال مرة تانية يقول خذ يا رينج اه كل الدوال التي
+
+141
+00:18:25,310 --> 00:18:31,490
+لها قيمة لو اواطبها بأي عدد حقيقي الـ real valued
+
+142
+00:18:31,490 --> 00:18:35,750
+function يعني لو اواطب عدد حقيقي من الست في real
+
+143
+00:18:35,750 --> 00:18:40,290
+number بلاقي اللي لها قيمة عددية يعني الدوال
+
+144
+00:18:40,290 --> 00:18:47,600
+المعرفة تمام؟مين الـS؟ كل الـG of X الموجودة في
+
+145
+00:18:47,600 --> 00:18:53,820
+الـRing R تحيط الـG تكون قابلة للاشتقاء، وكل الدول
+
+146
+00:18:53,820 --> 00:18:57,460
+قابلة للاشتقاء؟ لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+147
+00:18:57,460 --> 00:18:58,820
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+148
+00:18:58,820 --> 00:18:59,160
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+149
+00:18:59,160 --> 00:19:01,340
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+150
+00:19:01,340 --> 00:19:09,820
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+151
+00:19:09,820 --> 00:19:11,460
+لأ،
+
+152
+00:19:12,980 --> 00:19:18,920
+لا الدالة معرفة ولا مشتقتها معرفة، بس هذه خارج
+
+153
+00:19:18,920 --> 00:19:23,860
+نطاق الـRing R منها. احنا بنتكلم على الدوال
+
+154
+00:19:23,860 --> 00:19:30,380
+المعرفة. طيب هي الدالة وقتاش بيكون مشتقتها does
+
+155
+00:19:30,380 --> 00:19:38,100
+not exist في كام مكان، في كام حالة، في كده شهدانة
+
+156
+00:19:38,100 --> 00:19:44,820
+شهيد في كل قلص ايه؟في كام حالة غير قابلة للاشتقاء؟
+
+157
+00:19:44,820 --> 00:19:47,960
+تقدرش؟
+
+158
+00:19:47,960 --> 00:19:53,020
+غير متصلة؟
+
+159
+00:19:53,020 --> 00:20:00,100
+طيب، وإذا غير متصلة، غير قابلة للاشتقاء، يبقى أربع
+
+160
+00:20:00,100 --> 00:20:04,980
+حالات. الحالة الأولى، لو رسمت الرسم بالبالي، لو
+
+161
+00:20:04,980 --> 00:20:12,390
+طلع عندي corner. لو كان الرسم فيها كصبع.لو كان
+
+162
+00:20:12,390 --> 00:20:18,430
+فيها Vertical Tangent لأن المشتقة عند ال Vertical
+
+163
+00:20:18,430 --> 00:20:23,230
+Tangent بيصير Infinity مش معرفة الأمر الرابع ما
+
+164
+00:20:23,230 --> 00:20:31,990
+قالته زميلتكم .. شو اسمها؟ مقداد؟
+
+165
+00:20:31,990 --> 00:20:37,590
+زقلان، زقلان، زقلان، زقلان، زقلان، زقلان، زقلان،
+
+166
+00:20:37,590 --> 00:20:37,690
+زقلان، زقلان، زقلان، زقلان، زقلان، زقلان، زقلان،
+
+167
+00:20:37,690 --> 00:20:37,750
+زقلان، زقلان، زقلان، زقلان، زقلان، زقلان، زقلان،
+
+168
+00:20:37,750 --> 00:20:37,750
+زقلان، زقلان، زقلان، زقلان، زقلان، زقلان، زقلان،
+
+169
+00:20:37,750 --> 00:20:41,840
+زقلان، زقلان، زقلان، زقلان، زقلان، زقلان،يبقى هي
+
+170
+00:20:41,840 --> 00:20:45,720
+الاربع حالات اللى الدالة بتكون عندها غير قابلة
+
+171
+00:20:45,720 --> 00:20:50,980
+للاشتغال مثال بسيط عكس مقالة زميلتكوا في لاتر لما
+
+172
+00:20:50,980 --> 00:20:55,140
+أعطتني الدالة واحد على X واحد على X مش معرفة وهنا
+
+173
+00:20:55,140 --> 00:21:00,280
+جالي real valued function يعني الدالة لها قيمة
+
+174
+00:21:00,280 --> 00:21:06,380
+حقيقية متعوق بيها تمام لو قلت F of X يسوي absolute
+
+175
+00:21:06,380 --> 00:21:12,690
+value ل X ناقص واحدالدالة معرفة عند X يساوي واحد و
+
+176
+00:21:12,690 --> 00:21:18,510
+هي القيمة صفر absolute value لل X ناقص واحدة عند
+
+177
+00:21:18,510 --> 00:21:23,590
+الواحد تاخد صفر الدالة دالة متواصلة و معرفة لكنها
+
+178
+00:21:23,590 --> 00:21:30,270
+غير قابلة للاشتراك عند X يساوي واحد لأنه يوجد عندي
+
+179
+00:21:30,270 --> 00:21:36,730
+corner شرحنا الكوادة في كل قلصين ولا لأ؟ اللهم
+
+180
+00:21:36,730 --> 00:21:42,750
+اجعله خيال يا رب نشيناطبعا؟ يبقى .. يبقى هذا مثال
+
+181
+00:21:42,750 --> 00:21:49,510
+بسيط على دالة معرفة والمشتقة منها غير موجودة يبقى
+
+182
+00:21:49,510 --> 00:21:54,770
+هذه مش من الدوالة بتبعتنا انا بدي اخد في اسم ايه
+
+183
+00:21:54,770 --> 00:22:00,450
+الدوالة اللي قابلة للاشتقاء؟ يبقى مثل اي نوع من
+
+184
+00:22:00,450 --> 00:22:05,370
+الأرواح الأربعة برا ايش؟ برا الاس اللي عندنا هذا
+
+185
+00:22:05,370 --> 00:22:11,170
+برا الاس هذا، لكن يكون موجود وين؟موجود في R يعني R
+
+186
+00:22:11,170 --> 00:22:16,210
+فيها دوال معرفة زي absolute value of X أو absolute
+
+187
+00:22:16,210 --> 00:22:20,250
+value of X ناقص واحد موجودة في ال ring اللي فوق
+
+188
+00:22:20,250 --> 00:22:24,610
+لكن مش موجودة في الست اللي عندها لإنها غير قابل
+
+189
+00:22:24,610 --> 00:22:29,610
+اشتقاق لكنها لها قيمة حقيقية عند أي نقطة موجودة
+
+190
+00:22:29,610 --> 00:22:34,230
+وين في ال domain طيب كده نرسى كل ال Geographic
+
+191
+00:22:34,230 --> 00:22:40,880
+بحيث G تبقى differentiable functionيعني دالة قابلة
+
+192
+00:22:40,880 --> 00:22:46,660
+للاشتقاء بيقول يبين لي إن ال S دي بتنفع تكون sub
+
+193
+00:22:46,660 --> 00:22:53,780
+brain لكنها ليست ideal بيقول له بسيط إذا على
+
+194
+00:22:53,780 --> 00:22:59,300
+الخواصة ثلاثة لل sub brain ونشوف ما هي الخاصية غير
+
+195
+00:22:59,300 --> 00:23:05,660
+المحققة بالنسبة لل ideal وبالتالي بيكون مالها ليست
+
+196
+00:23:05,660 --> 00:23:13,750
+ideal طيبنبدأ بالنقطة الأولى أنا أدعي أن ال S is
+
+197
+00:23:13,750 --> 00:23:17,710
+non-empty
+
+198
+00:23:17,710 --> 00:23:23,890
+S is non-empty بيبقى بنقدر نجيب ده اللي واحدة بس
+
+199
+00:23:23,890 --> 00:23:33,350
+تبقى موجودة في S بيكون في لبنها صحيح because if
+
+200
+00:23:33,350 --> 00:23:41,500
+ال F of X يسوى Aوالـ A هذا كونسطن مين ما يكون يكون
+
+201
+00:23:41,500 --> 00:23:47,080
+موجة بسالب صفر لو روحنا نشتاق الدالة هذه ايش
+
+202
+00:23:47,080 --> 00:23:53,620
+بتعطينا بناها؟ يبقى احنا سمناها G سمناها G بيخليها
+
+203
+00:23:53,620 --> 00:24:01,120
+G of X يبقى G of X يسوى مقال انه G prime of X يسوى
+
+204
+00:24:01,120 --> 00:24:06,520
+قدراش؟ Zero Zero real valued function قيمة تمام
+
+205
+00:24:06,810 --> 00:24:12,290
+معناته الدلق قابل الاشتقاق ولا لا؟ يفجأ هذا بجه
+
+206
+00:24:12,290 --> 00:24:20,390
+يقينا ان ال G is the differential function تمام
+
+207
+00:24:20,390 --> 00:24:26,070
+يفجأ اسمه ممكن لإنه قدرت تلاقي دلق بهذا الشكل، هذه
+
+208
+00:24:26,070 --> 00:24:32,230
+كام دلق؟ مالة نهاية من الدوال، يفجأ هذه تمثل مال
+
+209
+00:24:32,230 --> 00:24:36,610
+مش عجب دلق واحد، أقولك مالة نهاية من الدوال؟موجودة
+
+210
+00:24:36,610 --> 00:24:42,190
+وين؟ موجودة في الإسراء ليه أحدهم أو التي تجمعهم
+
+211
+00:24:42,190 --> 00:24:51,010
+تمام؟ إذا ندلها لنا إتنين بتاخد عنصرين موجودات في
+
+212
+00:24:51,010 --> 00:24:55,990
+الإسراء يبقى بدالي أقوله افترض عندي جي واحد وجي
+
+213
+00:24:55,990 --> 00:25:05,860
+اتنين موجودة في الإسراء ثانيالـ G1 prime of X and
+
+214
+00:25:05,860 --> 00:25:16,400
+الـ G2 prime of X exist إيش يعني؟ يعني G1 و G2
+
+215
+00:25:16,400 --> 00:25:27,430
+قابلة للاشتقاء هذا معناهإن الـ G1 and الـ G2 are
+
+216
+00:25:27,430 --> 00:25:34,770
+differentiable functions طيب بدنا نيجي ناخد الفرق
+
+217
+00:25:34,770 --> 00:25:41,470
+في ما بينهم الـ G1 نقص G2 قطر قطر قطر قطر قطر قطر
+
+218
+00:25:41,470 --> 00:25:42,830
+قطر قطر قطر قطر قطر قطر قطر قطر قطر قطر قطر قطر
+
+219
+00:25:42,830 --> 00:25:47,690
+قطر قطر قطر قطر قطر قطر قطر قطر
+
+220
+00:25:50,540 --> 00:25:55,700
+بقينا نقول مشتقة المجموع الجبري لدالتين يسوى
+
+221
+00:25:55,700 --> 00:26:01,800
+المجموع الجبري للمشتقتين، مظبوط؟ إذا هذا شغل
+
+222
+00:26:01,800 --> 00:26:07,940
+كالقلص، مش شغل جبر، يبقى هذا بيساوي G واحد prime
+
+223
+00:26:07,940 --> 00:26:16,040
+of X ناقص G إتنين prime of X، يبقى الفرق ما بين
+
+224
+00:26:16,040 --> 00:26:24,940
+الإتنين exist، تمام؟هذا معناه هذا موجود في S يبقى
+
+225
+00:26:24,940 --> 00:26:35,820
+هذا معناه ان ال G1 ماقص G2 is different يعني G1
+
+226
+00:26:35,820 --> 00:26:45,880
+ماقص G2 موجودة في S بدنا نروح للشرط التالت الشرط
+
+227
+00:26:45,880 --> 00:26:52,930
+التالت بدنا ناخدجي واحد جي اتنين الكل prime as a
+
+228
+00:26:52,930 --> 00:26:59,870
+function of X أظن هذا الكلام يسوى جي واحد A prime
+
+229
+00:26:59,870 --> 00:27:07,030
+في جي اتنين prime غلط غلط هذه مشتقة حاصل ضرب
+
+230
+00:27:07,030 --> 00:27:11,110
+ذالثيني بجدال الأولى في مشتقة الثانية زي دي
+
+231
+00:27:11,110 --> 00:27:18,640
+الثانية في مشتقة الأولىيبقى هذه الدالة الأولى في
+
+232
+00:27:18,640 --> 00:27:26,260
+مشتقة الدالة الثانية زائد مشتقة الدالة الأولى في
+
+233
+00:27:26,260 --> 00:27:32,620
+الدالة الثانية الحين جي واحد و جي اتنين أنا ماخدهم
+
+234
+00:27:32,620 --> 00:27:39,900
+وين؟ في الاس يعني كل واحدة فيهم قابلة للاشتقاء إذا
+
+235
+00:27:39,900 --> 00:27:46,490
+هذه قابلة للاشتقاءوهذه مشتقتها موجودة لأنها قابلة
+
+236
+00:27:46,490 --> 00:27:52,270
+للاشتقاق إذا حصل الضرب هذا كله ماله موجود قابل
+
+237
+00:27:52,270 --> 00:27:58,850
+الاشتقاق وهذا حصل الضرب برضه قابل الاشتقاق يبقى
+
+238
+00:27:58,850 --> 00:28:05,870
+هذه بدها تكون موجود في S هذا بدي يعطينا انه G1 G2
+
+239
+00:28:05,870 --> 00:28:11,500
+موجود في S بناء على هذا الكلامبصير ال S هي عبارة
+
+240
+00:28:11,500 --> 00:28:22,620
+عن sub ring يبقى هنا سؤال S is a sub ring of A
+
+241
+00:28:22,620 --> 00:28:25,700
+finally
+
+242
+00:28:25,700 --> 00:28:34,000
+أخيرا جالي اثبت اثبت ان ال S هذه مانفعش تكون ideal
+
+243
+00:28:34,000 --> 00:28:40,040
+ماهي اش ideal sub ring بين مشيالكلكن ايديل يبعد
+
+244
+00:28:40,040 --> 00:28:45,360
+الله شوف لك شغل غيرها الشغل. بيقول الان عشان أثبت
+
+245
+00:28:45,360 --> 00:28:50,860
+انها ايديل بدي اخد element من S و element من R
+
+246
+00:28:50,860 --> 00:28:57,580
+واضربهم في بعض واشوف هل هذا الكلام موجود في S ولا
+
+247
+00:28:57,580 --> 00:29:04,420
+غير موجود في S. إذا باجي بقوله خدلي G موجودة في S.
+
+248
+00:29:05,550 --> 00:29:15,090
+الـ F موجودة في A then الـ G is differentiable
+
+249
+00:29:15,090 --> 00:29:29,490
+function and الـ F is not necessary differentiable
+
+250
+00:29:30,890 --> 00:29:34,370
+لأن الـR تحتوي الـdifferentiable وغير
+
+251
+00:29:34,370 --> 00:29:38,250
+الـdifferentiable يبقى الـF اللي أخدتها ليس
+
+252
+00:29:38,250 --> 00:29:43,970
+بالضرورة تكون قابلة للاشتقاء. الآن لو جهزة بنات
+
+253
+00:29:43,970 --> 00:29:53,330
+أخدت الـHumane، أخدت الـGF prime السؤال هو هل هذا
+
+254
+00:29:53,330 --> 00:29:59,990
+يساوي؟ والله نشوف اليساوي في الأول. هل هذا يساوي؟
+
+255
+00:30:00,220 --> 00:30:09,600
+الـG في الـF prime زائد الـG prime في الـF؟
+
+256
+00:30:09,600 --> 00:30:14,300
+ليس بالضرورة، ليش؟ ان هذى الـdifferentiable هذى
+
+257
+00:30:14,300 --> 00:30:19,180
+ليس بالضرورة، لأ هذى الـdifferentiable هذى ليس
+
+258
+00:30:19,180 --> 00:30:24,300
+بالضرورة، يبقى هذا الكلام بيسويش هذا إلا في حالة
+
+259
+00:30:24,300 --> 00:30:32,180
+differentiable، يبقى هذه صارت مالهاdoes not belong
+
+260
+00:30:32,180 --> 00:30:46,800
+to S because ال F is not necessary differentiable
+
+261
+00:30:46,800 --> 00:30:56,200
+يبقى هنا سواء ال S is not I
+
+262
+00:31:00,400 --> 00:31:06,860
+احنا المحاضرة الماضية وما أخدناه اليوم كله أمثلة
+
+263
+00:31:06,860 --> 00:31:11,940
+على حكاية مين ال ideal وهل ال set اللي بناخدها أو
+
+264
+00:31:11,940 --> 00:31:16,080
+ال subset اللي بناخدها من هناك ممكن تكون ideal
+
+265
+00:31:16,080 --> 00:31:20,520
+وممكن ما تكونش ideal، إيش يطلع عندنا ideal وإيش
+
+266
+00:31:20,520 --> 00:31:25,280
+يطلع عندنا ما هوش ideal هذا هو النقطة الأولى من
+
+267
+00:31:25,280 --> 00:31:29,440
+هذا الشرطةالنقطة الثانية او العمود الفقري الثاني
+
+268
+00:31:29,440 --> 00:31:33,500
+من هذا الشفتر اللي هو ال factor ring او ال
+
+269
+00:31:33,500 --> 00:31:39,120
+quotient ring فنروح نعطيها التعريف وهو اللذي لن
+
+270
+00:31:39,120 --> 00:31:43,520
+يختلف عن تعريف ال factor group اللي درس في جبر
+
+271
+00:31:43,520 --> 00:31:51,340
+حديث واحد if an agent has a definition بقول
+
+272
+00:31:51,340 --> 00:32:00,970
+لك يا بي انا اديك بي ring اlet ال a be an ideal of
+
+273
+00:32:00,970 --> 00:32:14,730
+pairing up the set of cosets the set of cosets
+
+274
+00:32:14,730 --> 00:32:25,150
+اللي على الشكل a زائد ال a such thatالـ R موجودة
+
+275
+00:32:25,150 --> 00:32:36,250
+في R موجودة في R بتساوي R modulo A is called A
+
+276
+00:32:36,250 --> 00:32:45,390
+factor is called A factor أو quotient
+
+277
+00:32:53,330 --> 00:32:58,790
+كلمة Quosette هذه أول مرة نسمعها في جبر حديد اتنين
+
+278
+00:32:58,790 --> 00:33:04,490
+لكن ذهبنا منها واحنا في جبر حديد واحد اه بس كانها
+
+279
+00:33:04,490 --> 00:33:20,890
+ذات على ال groups وليس على ال rings الان
+
+280
+00:33:20,890 --> 00:33:28,690
+ما هي ال Quosetteهلأ عندى كان عندى group G جيت
+
+281
+00:33:28,690 --> 00:33:34,410
+أخدت منها sub group H من ال group الاصلية جيت على
+
+282
+00:33:34,410 --> 00:33:41,870
+عناصر G وخلت العنصر كل عنصر من G أثر عليها إما
+
+283
+00:33:41,870 --> 00:33:46,490
+بالضرب أو بالجمع أو العملية المعرفة على ال group
+
+284
+00:33:46,490 --> 00:33:53,380
+كان جمع ضرب طرح غيره إلى آخرهكل مرة سينتج مجموعة
+
+285
+00:33:53,380 --> 00:33:57,800
+من العناصر و أحيانا العناصر اللي بتتساوى اللي
+
+286
+00:33:57,800 --> 00:34:01,880
+بتتساوى برميها علي شجة يجب باخد بس واحد منهم
+
+287
+00:34:01,880 --> 00:34:05,920
+ماباخدش باقي اللي بيساووا يمكن هذه المجموعة بتكوين
+
+288
+00:34:05,920 --> 00:34:11,400
+لي cosets من ال group الأصلية ال cosets هدول
+
+289
+00:34:11,400 --> 00:34:18,220
+بيكونولي عناصر ال factor group G modulo H تمام
+
+290
+00:34:18,530 --> 00:34:23,530
+بجينا نقول جي مدن يدش علاصرها كذا وكذا كل عنصر من
+
+291
+00:34:23,530 --> 00:34:28,990
+علاصرها اللي هو بده يساوي مين بده يساوي كو ست وهذه
+
+292
+00:34:28,990 --> 00:34:35,010
+استخدمناها في إثبات النظرية المشهورة في جميع كتب
+
+293
+00:34:35,010 --> 00:34:41,950
+الجبر وهي نظرية Lagrange Lagrange theorem وهو إن
+
+294
+00:34:41,950 --> 00:34:48,320
+ال order لل subgroup يسم ال order لل groupما ده ان
+
+295
+00:34:48,320 --> 00:34:53,360
+في عندنا فكرة قديمة بدنا نجددها قال لي خدلي A
+
+296
+00:34:53,360 --> 00:34:58,660
+عبارة عن ال ID الفرنج R يبقى ال 6 of course it's
+
+297
+00:34:58,660 --> 00:35:04,680
+كل العناصر اللي على الصيرة R زائد A حيث R موجودة
+
+298
+00:35:04,680 --> 00:35:10,100
+في R و اللي بدأ تكون لي 6 جديدة اسمها R modulo A
+
+299
+00:35:10,100 --> 00:35:15,500
+كنت في ال group سميها G modulo H حيث ال H هي بال
+
+300
+00:35:15,500 --> 00:35:22,190
+sub groupيبقى هذه اسمها Factoring او Co-centering.
+
+301
+00:35:22,270 --> 00:35:27,430
+تمام؟ طيب الآن في نظرية على ال factor of growth
+
+302
+00:35:27,430 --> 00:35:34,190
+لنتعرف على هذه النظرية ونحاول ان نبرهينها. النظرية
+
+303
+00:35:34,190 --> 00:35:34,770
+بتقول
+
+304
+00:35:44,250 --> 00:35:51,510
+بتقول let ال a بيه a sub ring of R let ال a بيه a
+
+305
+00:35:51,510 --> 00:36:06,410
+sub ring of R the set of four sets the set of four
+
+306
+00:36:06,410 --> 00:36:13,980
+sets اللي هو امين ال set of four setsاللي هي كل
+
+307
+00:36:13,980 --> 00:36:23,080
+العناصر R زائد A بحيث R موجودة في R مالها is a
+
+308
+00:36:23,080 --> 00:36:33,860
+ring is a ring is a ring under the operations
+
+309
+00:36:33,860 --> 00:36:38,800
+under the operations
+
+310
+00:36:41,530 --> 00:36:49,750
+تحت العملياتين اللي هو ال S زائد ال A زائد ال T
+
+311
+00:36:49,750 --> 00:37:04,600
+زائد ال A بدي ساوي S زائد T زائد ال A and ال Sزائد
+
+312
+00:37:04,600 --> 00:37:16,300
+ال A مضروب في ال T زائد ال A يساوي ST زائد ال A if
+
+313
+00:37:16,300 --> 00:37:24,480
+and only if if and only if ال A is an ideal
+
+314
+00:37:42,700 --> 00:37:46,880
+مجينا نقول في حالة ال factor group مشان تبقى ال
+
+315
+00:37:46,880 --> 00:37:51,980
+group factor group لازم يكون ال g modulo h ال h is
+
+316
+00:37:51,980 --> 00:37:57,240
+a normal sub group تمام أول ما بديت في الجبر هنا
+
+317
+00:37:57,240 --> 00:38:04,300
+قلتلكوا ال id اللي عندنا في جبر حديث اتنين تعادل
+
+318
+00:38:04,300 --> 00:38:09,560
+normal sub group في حالة من ال groups وهذا قد نحن
+
+319
+00:38:09,560 --> 00:38:15,400
+وصلناإلى ما قلناه لكم في أول محاضرة جئتوا فيها
+
+320
+00:38:15,400 --> 00:38:21,760
+إليكم نظرية بتقول خد لل a-subring من R مش كل
+
+321
+00:38:21,760 --> 00:38:27,900
+subring بتكون ID فرض ال a-subring يبقى ال set of
+
+322
+00:38:27,900 --> 00:38:31,380
+cosets اللي بالشكل اللي يعني انها there is a ring
+
+323
+00:38:31,380 --> 00:38:38,400
+تحت العمليتين هدول الجمع وضع if and only if ال a
+
+324
+00:38:38,400 --> 00:38:44,610
+is an IDهذا الكلام صحيح لو كان الـA ID وليس
+
+325
+00:38:44,610 --> 00:38:50,330
+Subring ما هو كل ID هو عبارة عن Subring. يعني احنا
+
+326
+00:38:50,330 --> 00:38:54,650
+ما نقدر نحكم على الـSet انها ID الا اذا كانت
+
+327
+00:38:54,650 --> 00:39:00,690
+Subring في الأساس.شوف يا بناة يبقى كلمة If and
+
+328
+00:39:00,690 --> 00:39:06,630
+only if يعني ان البرهان سيصير في اتجاهين. يبقى
+
+329
+00:39:06,630 --> 00:39:11,610
+الان بدنا ناخد الاتجاه الأول.يبقى بداجي اقوله
+
+330
+00:39:11,610 --> 00:39:25,850
+assume that ان ال a is an id ايش بده اثبت ان ال R
+
+331
+00:39:25,850 --> 00:39:32,230
+مدينه a is a ring يبقى بده اروح اثبت ان كل ال
+
+332
+00:39:32,230 --> 00:39:36,970
+cosets هدول عبارة عن ال ring تحت من تحت العمليات
+
+333
+00:39:36,970 --> 00:39:44,720
+اللي اتنين هدوليجي هنا want to show want to show
+
+334
+00:39:44,720 --> 00:39:54,340
+that ان ال a modulo a is a ring طيب أنا مشان أثبت
+
+335
+00:39:54,340 --> 00:40:01,940
+six انها ring فبدي أعمل ستة خواص و لا ست خواص ست
+
+336
+00:40:01,940 --> 00:40:08,090
+خواص و ليس ستة خواصلأن العدد يخالف المعدود من
+
+337
+00:40:08,090 --> 00:40:12,990
+تلاتة لتسعة، إلا إذا سبق المعدود العدد جاز
+
+338
+00:40:12,990 --> 00:40:20,330
+الوجهان. نقول البنات الست وممكن نقول البنات الستة
+
+339
+00:40:20,330 --> 00:40:25,530
+عشقتين صح، لكن لما نقول ست بنات لازم التذكير
+
+340
+00:40:25,530 --> 00:40:31,810
+والتأليف يحدث هنا، فهذه قاعدة نحوية والقواعد نحو
+
+341
+00:40:31,810 --> 00:40:38,410
+مثل ما أن الرياضياتكذلك قواعد واحنا بنشتغل على هذه
+
+342
+00:40:38,410 --> 00:40:43,850
+القواعد طيب نفترضنا انه IID اللي بدنا نثبت ان ال R
+
+343
+00:40:43,850 --> 00:40:48,830
+modulo I is array يبقى الحطوة الأولى بده يثبت انها
+
+344
+00:40:48,830 --> 00:40:54,270
+Available تحت عملية الجمع و Associative تحت عملية
+
+345
+00:40:54,270 --> 00:40:59,030
+الجمع و Zero element تحت عملية الجمع وناقص element
+
+346
+00:40:59,030 --> 00:41:04,540
+تحت عملية الجمعبظل الطرف و الجمع ال associativity
+
+347
+00:41:04,540 --> 00:41:12,160
+و ال distributor مظبوط؟ طب خلينا نثبت أول خاصة طيب
+
+348
+00:41:12,160 --> 00:41:17,300
+الآن يا بنات لو جيت كرسي الافقار و عمليها عملية
+
+349
+00:41:17,300 --> 00:41:23,260
+الجمع abelian ولا لا abelian a group؟ جمع ا زي ات
+
+350
+00:41:23,260 --> 00:41:27,280
+بيه سوى بيه زي اديه عادي جدا مش الطرف عملية واحدة
+
+351
+00:41:27,280 --> 00:41:38,190
+بسيبقى هذا يعني is abelian a girl طيب هذا يعني ان
+
+352
+00:41:38,190 --> 00:41:44,350
+ال 6 ايه تحت عملية الجامعة abelian ولا لا يبقى هذا
+
+353
+00:41:44,350 --> 00:41:54,250
+يعني is abelian هذا يعني ان ال a هو ال plus is
+
+354
+00:41:54,250 --> 00:41:54,850
+normal
+
+355
+00:41:58,870 --> 00:42:06,790
+صح؟ نسيت مش بيجينا نقول normal subgroup ونحط ال
+
+356
+00:42:06,790 --> 00:42:15,690
+condition ان ال AR او ال AH بدي سوى HA ان حدد ذلك
+
+357
+00:42:15,690 --> 00:42:25,050
+او ال H1 بدي سوى H2A وكمان صيغة تالتة وكمان صيغة
+
+358
+00:42:25,050 --> 00:42:28,490
+رابعة من خلال الأسئلةلإثبات الـ Normal Subgroup.
+
+359
+00:42:28,570 --> 00:42:33,750
+لكن أخدنا القاعدة إن لو كانت الـR أبيليان، إذن
+
+360
+00:42:33,750 --> 00:42:39,650
+عملية الإبدال سهلة جدا وبالتالي كل Abelian group,
+
+361
+00:42:40,030 --> 00:42:46,390
+any subgroup منها is Normal. يجي هذا بدي يعطينا
+
+362
+00:42:46,390 --> 00:42:58,070
+Normal in R plus. ما ده Normal.يبقى سؤال الـR
+
+363
+00:42:58,070 --> 00:43:07,710
+مدينه إيه مع منية الجامعة exist؟
+
+364
+00:43:07,710 --> 00:43:14,190
+and abelian exist و abelian في نفسها exist and
+
+365
+00:43:14,190 --> 00:43:23,500
+abelian الـR abelian و الـA abelianو ال A صارت
+
+366
+00:43:23,500 --> 00:43:27,580
+normal subgroup و ال R modulo A exist و في نفس
+
+367
+00:43:27,580 --> 00:43:32,160
+الوقت abelian إذا هنا يتحقق ال condition الأول ولا
+
+368
+00:43:32,160 --> 00:43:38,340
+لا؟ من ال ring إذا ال condition الأول خلصنا منه،
+
+369
+00:43:38,340 --> 00:43:43,020
+أيه قولي؟ نحن
+
+370
+00:43:43,020 --> 00:43:47,900
+أخدنا عملية الجامعة بس فأتكلم عن R تحت عملية
+
+371
+00:43:47,900 --> 00:43:52,940
+الجامعة، أتكلمتش عن الضرب لسهكلم على الجمع، لكن لو
+
+372
+00:43:52,940 --> 00:43:57,480
+حطيت ضرب، فهو سيصبح ضرب أبيليا من الضرب وليس
+
+373
+00:43:57,480 --> 00:44:03,900
+بالجمع، ويطلع يتعمق تحفظك زائد، زائد، زائد، طبعا؟
+
+374
+00:44:03,900 --> 00:44:08,380
+انا بتكلم كإني داشتر في ال groups، لسه ما قلت
+
+375
+00:44:08,380 --> 00:44:14,340
+شريط، طبعا؟طيب people are exist and abelian تمام
+
+376
+00:44:14,340 --> 00:44:19,660
+طيب صارت هذه abelian group يبقى احنا حققنا ال
+
+377
+00:44:19,660 --> 00:44:24,280
+condition الأول من مين؟ من ال ringزينجي ل ال
+
+378
+00:44:24,280 --> 00:44:28,420
+condition التاني ال condition التاني قال ليه خاصية
+
+379
+00:44:28,420 --> 00:44:37,480
+ال associativity برضه صحيحة يبقى ال check ذات
+
+380
+00:44:37,910 --> 00:44:45,150
+اكتديلي ان the associative
+
+381
+00:44:45,150 --> 00:44:49,490
+law
+
+382
+00:44:49,490 --> 00:44:58,170
+قانون ال associativity ال associativity is hold
+
+383
+00:44:58,170 --> 00:45:03,310
+under addition
+
+384
+00:45:03,310 --> 00:45:05,570
+تحت عملية الجمع
+
+385
+00:45:10,160 --> 00:45:13,300
+يبقى air condition التاني بدنا نيجي الى ال zero
+
+386
+00:45:13,300 --> 00:45:26,840
+element ال a is the zero او ال a او ال zero زائد a
+
+387
+00:45:26,840 --> 00:45:38,440
+يسوى a is the zero element of R modulo a because
+
+388
+00:45:40,890 --> 00:45:48,250
+وبيثبت ان فعلا هذا هو zero علمي because if ال a
+
+389
+00:45:48,250 --> 00:45:58,230
+زائد ال a موجود في ال a modulo a then لو أخدت ال a
+
+390
+00:45:58,230 --> 00:46:06,750
+زائد ال a زائد ال zero زائد ال a حسب ال definition
+
+391
+00:46:06,750 --> 00:46:12,640
+اللي احنا خاطينه على الجامعة هذايبقى هذا الكلام
+
+392
+00:46:12,640 --> 00:46:19,780
+بالنسبة للـ R زائد الـ Zero زائد الـ A يعني الـ R
+
+393
+00:46:19,780 --> 00:46:26,500
+زائد الـ A لأن الـ R زائد الـ A جمعته مع الـ Zero
+
+394
+00:46:26,500 --> 00:46:32,520
+Element طلع نفس الـ R زائد الـ A ففعلا الـ A هو
+
+395
+00:46:32,520 --> 00:46:40,230
+الـ Zero Elementالآن بدي أجيب المعكوس الجمعي للـR
+
+396
+00:46:40,230 --> 00:46:45,690
+زائد A. يبقى بجب ان اقول ان هنا ذا additive
+
+397
+00:46:45,690 --> 00:46:57,790
+inverse of الـR زائد الـA is ناقص R زائد الـA.
+
+398
+00:46:58,290 --> 00:47:03,370
+Because الـR
+
+399
+00:47:03,370 --> 00:47:12,750
+زائد الـAزائد ناقص ال R زائد ال A بالدوسة حسب
+
+400
+00:47:12,750 --> 00:47:20,250
+تعريف الجمعي اللي تحت هنا يبقى R ناقص ال R زائد ال
+
+401
+00:47:20,250 --> 00:47:28,070
+A يبقى Zero زائد ال A يبقى ال Zero Element يبقى كم
+
+402
+00:47:28,070 --> 00:47:34,030
+خاصية حققنا يا بنات؟ تلاتة ولا اربعة؟ اربع خاصة
+
+403
+00:47:34,190 --> 00:47:39,190
+ظلنا بس تنتيل التنتيل هذول بالنسبة لعملية مين؟
+
+404
+00:47:39,190 --> 00:47:44,310
+الدرب والسادسة الدرب والجامعة ال distributed يبقى
+
+405
+00:47:44,310 --> 00:47:50,030
+خلينا نشوف خاصية ال associativity يبقى هنا the
+
+406
+00:47:50,030 --> 00:48:01,790
+operation on ال R modulo A is associative
+
+407
+00:48:10,850 --> 00:48:21,970
+يبقى associated for F ال S زائد ال A والT زائد ال
+
+408
+00:48:21,970 --> 00:48:32,010
+A والR زائد ال A موجودة في ال A modulo A ثاني
+
+409
+00:48:32,010 --> 00:48:38,010
+بالنسبة لخاصية ال associativity يبقى بدي أخد ال S
+
+410
+00:48:38,010 --> 00:48:46,280
+زائد ال Aمضروبة في الـT زائد الـA مضروبة في الـR
+
+411
+00:48:46,280 --> 00:48:53,640
+زائد الـA جسام يبقى بدي أضرب هدول في بعض هاي خاصية
+
+412
+00:48:53,640 --> 00:48:58,520
+الضرب عندنا هنا معرفة بهذا الشكل يبقى هذه بدي
+
+413
+00:48:58,520 --> 00:49:10,070
+أسلحلي ST زائد الـA في الـR زائد الـAالـR زائد
+
+414
+00:49:10,070 --> 00:49:20,130
+الـA.طيب هذا الكلام بده يساوي S T لـR زائد الـA
+
+415
+00:49:20,130 --> 00:49:28,070
+.الان السؤال هو الـS والـT والـR أين موجودة؟ الـR
+
+416
+00:49:28,070 --> 00:49:32,290
+itself والـR رنجي بخاصية ال associativity عليها
+
+417
+00:49:32,290 --> 00:49:41,010
+صحيحة. إذا هذا الكلام بده يساوي Sفى TR زائد ال A
+
+418
+00:49:41,010 --> 00:49:48,370
+بيدرجعها الى أصلها كحاصن ضارب يبقى هذه تانية S
+
+419
+00:49:48,370 --> 00:49:57,590
+زائد ال A مضروبة فى TR زائد ال A بيدرجعها الى
+
+420
+00:49:57,590 --> 00:50:04,610
+أصلها كمان مرة يبقى ال S زائد ال A مالكش دعوةوهذه
+
+421
+00:50:04,610 --> 00:50:09,350
+اللي جوا بده اعرضها كحاصل ضرب ل two elements يبقى
+
+422
+00:50:09,350 --> 00:50:18,910
+بقول T زائد ال A مضغوبة في S زائد R زائد ال P R
+
+423
+00:50:18,910 --> 00:50:27,210
+زائد ال T يبقى هاية فال R زائد ال A لوحدها ضالت مع
+
+424
+00:50:27,210 --> 00:50:31,330
+التانية هنا ال S زائد ال A لوحدها هذه خاصية ال
+
+425
+00:50:31,330 --> 00:50:39,240
+associativity تمام؟ضال علينا مين؟ ضال علينا مين؟
+
+426
+00:50:39,240 --> 00:50:44,500
+خاصية الرابع، خاصية الرابع هي مزيد ما بين الطرف
+
+427
+00:50:44,500 --> 00:50:53,220
+والجامع، مظبوط؟ يبقى هنا the distributer
+
+428
+00:51:05,510 --> 00:51:12,990
+and about كما هو أعلى يعني إيش يا بنات؟ بدي أخد
+
+429
+00:51:12,990 --> 00:51:17,710
+element و أخد مجموع two elements و أدخل هذه على
+
+430
+00:51:17,710 --> 00:51:23,150
+هذه و أشوف مظبوط الكلام هذا ولا لأ، خلصنا؟ لا
+
+431
+00:51:23,150 --> 00:51:30,010
+ماخلصلاش، ماخلصنا، أكيد ماخلصتش، أيوة احنا بنذكر
+
+432
+00:51:30,010 --> 00:51:35,120
+لما كنا في ال roadلما روحنا على ال potion tray
+
+433
+00:51:35,120 --> 00:51:41,400
+قلنا بدنا نثبت ان عملية الضرب هذه is well defined.
+
+434
+00:51:41,960 --> 00:51:45,920
+Well defined يعني مهرفة تعريفا صحيحا.
+
+435
+00:51:49,220 --> 00:51:55,480
+طيب finally the
+
+436
+00:51:55,480 --> 00:51:57,400
+operation
+
+437
+00:52:00,200 --> 00:52:12,620
+the operation on ال a modular a is will define ايش
+
+438
+00:52:12,620 --> 00:52:23,680
+يعني will define ذات اسم ادنا نوضحها if ال S زائد
+
+439
+00:52:23,680 --> 00:52:33,990
+ال A يساوي ال S prime زائد ال Aand الـ T زائد الـ
+
+440
+00:52:33,990 --> 00:52:41,790
+A يسوى T Prime زائد الـ A then اللي هو الـ S T
+
+441
+00:52:41,790 --> 00:52:48,370
+زائد الـ A يسوى الـ S Prime T Prime زائد الـ A
+
+442
+00:52:48,370 --> 00:52:52,850
+يعني احنا عندنا هدول الطرفين متساوين و هد طرفين
+
+443
+00:52:52,850 --> 00:52:59,290
+هدول متساوين هل حاصر ضرب هدول في بعضالحاصل ضرب
+
+444
+00:52:59,290 --> 00:53:03,990
+هدول في بعض ولا لأ هذا اللي احنا قدرتناه بتكون
+
+445
+00:53:03,990 --> 00:53:09,370
+والده final فعلا بتكون ال R modulo A is A ready
+
+446
+00:53:09,370 --> 00:53:16,690
+إذا بدأت أخد يا بنات ال S زائد ال A بدأ أضربها في
+
+447
+00:53:16,690 --> 00:53:23,530
+مين؟ في T زائد ال A وشوف وين بدأ توصيه هذا الكلام
+
+448
+00:53:23,530 --> 00:53:30,780
+بده ساويSB ذائد ال A هذا الكلام ساوي S زائد ال A
+
+449
+00:53:30,780 --> 00:53:35,940
+او بدي اخد ال اولى
+
+450
+00:53:35,940 --> 00:53:45,200
+S زائد ال A ساوي S prime زائد ال A ايش ممكن اكتب
+
+451
+00:53:45,200 --> 00:53:53,040
+هذه ممكن اكتب S ناقص S prime زائد ال A ساوي ال A
+
+452
+00:53:53,300 --> 00:53:59,960
+أضفنا سلب S prime لمين؟ للطرفين هذا ايش معناه؟ ان
+
+453
+00:53:59,960 --> 00:54:04,500
+ال elements زايد ايه يسوى ال A itself ايش معناه؟
+
+454
+00:54:04,500 --> 00:54:11,120
+ان هذا العمصر موجود في ايه؟ موجود في A هذا معناه
+
+455
+00:54:11,120 --> 00:54:18,580
+ان ال S ناقص S prime موجود في A هذا معناه ان ال S
+
+456
+00:54:18,580 --> 00:54:28,070
+ناقص S primeبتساوي ال a for some a اللي موجود في a
+
+457
+00:54:28,070 --> 00:54:40,150
+أو ال S بتساوي S prime زائد اللي هو من ال a أضف
+
+458
+00:54:40,150 --> 00:54:46,490
+نموذج S prime للطرفين بنفس الطريقة similarly
+
+459
+00:54:50,810 --> 00:54:58,250
+similarly ال T تساوي T prime زائد ال B و ال A و ال
+
+460
+00:54:58,250 --> 00:55:04,930
+B موجودة في ال A هاي يقولنا A موجود في A و كذلك ال
+
+461
+00:55:04,930 --> 00:55:11,630
+B موجود في B طب احنا إيش بدنا؟ بدنا ال S في T إذا
+
+462
+00:55:11,630 --> 00:55:17,910
+لو ضربت ال S في T يبقى ال S في T بساوي S prime
+
+463
+00:55:17,910 --> 00:55:25,710
+زائد ال Aفى T Prime زائد ال B نفكر قصة يبقى هذا
+
+464
+00:55:25,710 --> 00:55:33,930
+بدى يعطينا S Prime T Prime زائد A T Prime زائد S
+
+465
+00:55:33,930 --> 00:55:46,430
+Prime B زائد A بB طيب احنا بدنا S T زائد A بدنا ال
+
+466
+00:55:46,430 --> 00:55:52,750
+S T زائد A يسوى هذا زائد Aيبقى هذا الكلام يسوي S'
+
+467
+00:55:53,370 --> 00:56:04,810
+T' A T' S' B زائد A B زائد A إذا أحنا وصلنا لإنه
+
+468
+00:56:04,810 --> 00:56:11,830
+ST يسوي هذا العنصر إذا ST زي ال A عادل سيسوي هذا
+
+469
+00:56:11,830 --> 00:56:19,130
+العنصر زي A السؤال هو هذا موجود في أيامنا؟لأن A وB
+
+470
+00:56:19,130 --> 00:56:29,670
+موجودة في A وA وB موجودة في A وB موجودة
+
+471
+00:56:29,670 --> 00:56:33,250
+في A وS موجودة في R وA موجودة في A وS موجودة في R
+
+472
+00:56:33,250 --> 00:56:34,290
+وA موجودة في A وS موجودة في R وA موجودة في A وS
+
+473
+00:56:34,290 --> 00:56:37,530
+موجودة في R وA موجودة في A وS موجودة في A وS
+
+474
+00:56:37,530 --> 00:56:39,830
+موجودة في R وA موجودة في A وS موجودة في R وA
+
+475
+00:56:39,830 --> 00:56:46,990
+موجودة في A وS موجودة في A وS موجودة في A وS
+
+476
+00:56:46,990 --> 00:56:46,990
+موجودة في A وS موجودة في A وS موجودة في A وS
+
+477
+00:56:46,990 --> 00:56:46,990
+موجودة في A وS موجودة في A وS موجودة في A وS
+
+478
+00:56:46,990 --> 00:56:46,990
+موجودة في A وS موجدة في A وS موجدة في A وS موجدة
+
+479
+00:56:47,200 --> 00:56:54,700
+الـ A L M I D يبقى هذا مش بيعطينا أمنة بيعطينا ان
+
+480
+00:56:54,700 --> 00:57:00,840
+ال S T زائد ال A يسبق هذا مادام كله موجود فيها
+
+481
+00:57:00,840 --> 00:57:07,580
+يبقى هذا الجمع بدي يعطينا A يبقى S Prime T Prime
+
+482
+00:57:07,580 --> 00:57:15,160
+زائد A قبله هذا وهو المطلوب ليه بروح بقوله Thus
+
+483
+00:57:15,880 --> 00:57:26,900
+وهكذا بص اللي هو الار موديول a is a ring اللي هي
+
+484
+00:57:26,900 --> 00:57:34,060
+ال factoring طبعا؟ ضايق الاتجاه التاني الآن لو كان
+
+485
+00:57:34,060 --> 00:57:40,100
+لأ لو كانت هذه factoring يبقى ال a بتاعة ال person
+
+486
+00:57:40,100 --> 00:57:44,320
+ID للمرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3232bbc3f8d825e1696d0b08270add39fa04dd9e
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA.srt
@@ -0,0 +1,1402 @@
+1
+00:00:20,820 --> 00:00:25,440
+بسم الله الرحمن الرحيم، نكمل ما ابتدأنا به في المرة
+
+2
+00:00:25,440 --> 00:00:31,420
+الماضية، وهو حل أسئلة من أسئلة التمرين على chapter
+
+3
+00:00:31,420 --> 00:00:37,640
+17. وصلنا المرة اللي فاتت إلى chapter 10، إلى سؤال
+
+4
+00:00:37,640 --> 00:00:43,320
+10، وفي سؤال 10 مكون من عدة نقاط، تعرضنا للنقطة
+
+5
+00:00:43,320 --> 00:00:49,390
+الأولى والثالثة، وقلنا أن الاثنتين هدول زي بعض. كذلك
+
+6
+00:00:49,390 --> 00:00:54,410
+تعرضنا للثانية، والآن الرابعة، الثالثة الرابعة
+
+7
+00:00:54,410 --> 00:00:58,810
+اللي هي نمرة دي، والخامسة أخذنا مثل زيها، بقى لا
+
+8
+00:00:58,810 --> 00:01:03,810
+داعي نضيع وقت فيها، نيجي لمين؟ للخامسة اللي عندنا
+
+9
+00:01:03,810 --> 00:01:11,010
+بدي أروح الآن على اللي هو الـ field Z2، بس بدنا نروح
+
+10
+00:01:11,010 --> 00:01:16,520
+نجيب الـ F bar. السؤال هو: هل هذه irreducible، والباقي
+
+11
+00:01:16,520 --> 00:01:22,920
+irreducible عالميا على اللي هو reduced operational
+
+12
+00:01:22,920 --> 00:01:29,660
+number. يبقى بجي بقوله solution on
+
+13
+00:01:29,660 --> 00:01:39,440
+Z2. بدي يصير عندنا الـ F bar of X تساوي X⁵
+
+14
+00:01:39,440 --> 00:01:46,230
++ X² + 1.  أنه الخمسة 2 +
+
+15
+00:01:46,230 --> 00:01:50,250
+2 + 1.  2ات مع السلامة اللي لها في Z2
+
+16
+00:01:50,250 --> 00:01:55,090
+و ضلها 2 + 1 يبقى آلة الـ F bar of X  = X⁵
+
+17
+00:01:55,090 --> 00:02:01,210
++ X² + 1. الآن بدنا نشوف هل لها
+
+18
+00:02:01,210 --> 00:02:07,870
+هذه أصفار؟ والله مالهاش أصفار. الآن لو جيت حطيت Zero
+
+19
+00:02:07,870 --> 00:02:15,890
+واحد، يبقى Zero ليس صفرا من أصفارها. طيب الواحد
+
+20
+00:02:15,890 --> 00:02:22,790
+واحد، واحد، واحد، ثلاثة في Z2 = واحد. يبقى مالهاش أصفار.
+
+21
+00:02:22,790 --> 00:02:29,970
+يبقى الـ F of Zero يبقى يساوي واحد، والـ F of واحد
+
+22
+00:02:29,970 --> 00:02:37,830
+كذلك يبقى يساوي واحد. هذا بدي يعطينا أن F bar has
+
+23
+00:02:39,160 --> 00:02:49,720
+no zeros in Z2. يعني معناته الدرجة الأولى مستبعدة،
+
+24
+00:02:49,720 --> 00:02:56,480
+والدرجة الثالثة مستبعدة. يبقى هذا بده يعطينا if
+
+25
+00:02:56,480 --> 00:03:10,050
+F bar of x has no factor of degree one. تمام؟ يبقى
+
+26
+00:03:10,050 --> 00:03:16,350
+معناته هذه ما فيش عندي element أو factor منها الـ
+
+27
+00:03:16,350 --> 00:03:20,190
+degree اللي واحد، أو has no linear degree linear
+
+28
+00:03:20,190 --> 00:03:26,110
+factor. ما عنديش factor يكون خطيا، يبقى في المقابل
+
+29
+00:03:26,110 --> 00:03:30,110
+ما عنديش factor من الدرجة الرابعة، لأن الدرجة
+
+30
+00:03:30,110 --> 00:03:34,130
+الرابعة مع الدرجة الأولى بيعطينا الدرجة الخامسة.
+
+31
+00:03:34,130 --> 00:03:49,420
+and so ولذلك الـ F bar has no factor of degree four.
+
+32
+00:03:49,420 --> 00:03:53,400
+لا من الدرجة الأولى ولا من الدرجة الرابعة، يبقى
+
+33
+00:03:53,400 --> 00:03:59,180
+اللي ضايل عندنا الدرجة الثانية أو الدرجة الثالثة، لأن لو
+
+34
+00:03:59,180 --> 00:04:05,140
+افترضنا أن عندنا factor من الدرجة الثالثة، بدنا
+
+35
+00:04:05,140 --> 00:04:11,380
+نشوف شكله، ومين ممكن يجيبلي عناصر. تمام؟ يبقى مضطر
+
+36
+00:04:11,380 --> 00:04:21,920
+أقوله assume، افترض أن الـ F bar of X has a factor
+
+37
+00:04:21,920 --> 00:04:25,600
+of
+
+38
+00:04:25,600 --> 00:04:40,280
+degree 2، من الدرجة الثانية مثلا، that is هذا الـ
+
+39
+00:04:40,280 --> 00:04:49,180
+factor that is in the form، يبقى في الشكل التالي
+
+40
+00:04:49,180 --> 00:04:58,780
+اللي هو الـ X تربيع + X + V. بتشوف في كم
+
+41
+00:04:58,780 --> 00:05:07,100
+احتمال لهذه في Z2. يبقى بادي بقول we have four
+
+42
+00:05:07,100 --> 00:05:10,480
+possibilities.
+
+43
+00:05:10,480 --> 00:05:14,780
+يبقى
+
+44
+00:05:14,780 --> 00:05:20,360
+في عندي أربع احتمالات للدرجة الثانية. احتمال أن
+
+45
+00:05:20,360 --> 00:05:29,000
+يكون X تربيع فقط، واحتمال أن يكون X تربيع + X،
+
+46
+00:05:29,000 --> 00:05:38,810
+واحتمال أن يكون X تربيع + 1، واحتمال أن يكون X
+
+47
+00:05:38,810 --> 00:05:45,090
+تربيع + X + 1.  في الـ X، نجي للاحتمالات
+
+48
+00:05:45,090 --> 00:05:49,790
+الأولى. يبقى الاحتمال الأول، لو كان X تربيع، بقدر
+
+49
+00:05:49,790 --> 00:05:56,630
+أحلله X في X. تمام؟ ولو كان لي احتمالي الثاني، بقدر
+
+50
+00:05:56,630 --> 00:06:02,510
+أحلله X في X + 1. ولو كان لي احتمالي الثالث،
+
+51
+00:06:02,510 --> 00:06:11,780
+بقدر أحلله X + 1 في X + 1. طبعا اللي تاخد X
+
+52
+00:06:11,780 --> 00:06:18,020
+في X = X تربيع + X، و + X = 2X، واحنا
+
+53
+00:06:18,020 --> 00:06:23,300
+بنشتغل في Z2، يبقى بـ Zero مع السلامة، ما ضلش إلا واحد
+
+54
+00:06:23,300 --> 00:06:28,440
+في واحد. اليومين بواحد. التلات احتمالات دول حللهم
+
+55
+00:06:28,440 --> 00:06:34,400
+إلى حاصل ضرب عاملين من الدرجة الأولى. هل هذا ممكن؟
+
+56
+00:06:34,870 --> 00:06:41,050
+لا، لأن استبعدنا الدرجة الأولى فوق هيو. يبقى هذا كله
+
+57
+00:06:41,050 --> 00:06:50,270
+impossible. يبقى هذا impossible. كل احتمالات هذه غير
+
+58
+00:06:50,270 --> 00:06:57,370
+ممكنة. السبب because because
+
+59
+00:06:57,370 --> 00:07:15,840
+الـ F bar of X has no factor of first degree. بيظل
+
+60
+00:07:15,840 --> 00:07:21,480
+احتمال تاني اللي عندنا. الآن لو جسمنا الـ
+
+61
+00:07:21,480 --> 00:07:26,680
+polynomial الأصلية على الـ polynomial هذه، لا يمكن
+
+62
+00:07:26,680 --> 00:07:32,140
+يطلع هذا أحد العوامل، يعني لا يمكن يطلع الناتج بدون
+
+63
+00:07:32,140 --> 00:07:36,480
+باقي. لازم يطلع الناتج بمين؟ بباقي. يبقى لو راحت
+
+64
+00:07:36,480 --> 00:07:42,800
+جبت، ومسكت القلم، وقسمت الـ polynomial اللي عندنا على
+
+65
+00:07:42,800 --> 00:07:48,360
+هذه، هتلاقي لازم يبقى باقي، وأظن أن الباقي هو واحد.
+
+66
+00:07:48,360 --> 00:07:55,380
+صحيح، تمام؟ وبالتالي هذه لا تقسم من اللي فوق. يبقى
+
+67
+00:07:55,380 --> 00:08:00,840
+باجي بقوله هذه by long division
+
+68
+00:08:03,750 --> 00:08:16,050
+الـ X تربيع + X + 1 is not a factor of F
+
+69
+00:08:16,050 --> 00:08:23,930
+bar of X. معناته أن هو factor of second degree
+
+70
+00:08:23,930 --> 00:08:37,470
+تمام؟ يبقى هنا no factor of F bar of x of second
+
+71
+00:08:37,470 --> 00:08:43,130
+degree. مدام
+
+72
+00:08:43,130 --> 00:08:46,790
+مافيش من الدرجة الثانية، ممكن يكون من الدرجة
+
+73
+00:08:46,790 --> 00:08:51,810
+الثالثة. برضه لأ، لإنه حاصل ضربه، ويطلع لي 100 الدرجة
+
+74
+00:08:51,810 --> 00:08:59,250
+الخامسة. يبقى هذا يقينًا كذلك no factor of third
+
+75
+00:08:59,250 --> 00:09:00,090
+degree.
+
+76
+00:09:02,330 --> 00:09:09,630
+الـ degree. يبقى إيش تفسيرنا لهذا الكلام؟ أن الـ F bar
+
+77
+00:09:09,630 --> 00:09:15,890
+is irreducible على Z2. بس ضلت واحدة بشكل أن يكون
+
+78
+00:09:15,890 --> 00:09:21,770
+الـ degree لـ F هي degree لـ F bar. يبقى الآن بقى اللي
+
+79
+00:09:21,770 --> 00:09:30,570
+بقوله since الـ degree للـ F هي نفس الـ degree للـ F
+
+80
+00:09:30,570 --> 00:09:39,730
+bar، اللي هي تساوي خمسة. We have أن الـ F bar of X
+
+81
+00:09:39,730 --> 00:09:48,870
+اللي تساوي X⁵ + X² + 1 is
+
+82
+00:09:48,870 --> 00:10:00,250
+irreducible over Z2. هذا بدي يعطينا إيه؟ by a
+
+83
+00:10:00,250 --> 00:10:08,790
+previous theorem. by a previous theorem. بنظرية
+
+84
+00:10:08,790 --> 00:10:17,150
+السابقة. الـ F of X اللي هي تساوي X⁵ +
+
+85
+00:10:17,150 --> 00:10:26,050
+X² + 1 is irreducible over
+
+86
+00:10:28,200 --> 00:10:34,960
+الـ Q. على
+
+87
+00:10:34,960 --> 00:10:40,780
+هيك بيقول إن هنا سؤال عشرة. بدنا نروح لسؤال 11. سؤال
+
+88
+00:10:40,780 --> 00:10:47,220
+11 بيقول لي show that الـ X⁴ + 1 is reducible
+
+89
+00:10:47,220 --> 00:10:55,160
+على الـ Q، but reducible على مين؟ على R. سؤال 11
+
+90
+00:10:55,160 --> 00:11:05,160
+بيقول show that إن الـ X⁴ + 1 is
+
+91
+00:11:05,160 --> 00:11:18,400
+irreducible over Q، but reducible over R.
+
+92
+00:11:39,300 --> 00:11:46,800
+بيقول: يبين لي أن الـ X⁴ + 1 is irreducible
+
+93
+00:11:46,800 --> 00:11:55,580
+على الـ field Q، اللي هي الـ rational numbers، لكنه ليس
+
+94
+00:11:55,580 --> 00:12:02,480
+irreducible، يعني irreducible على مين؟ على R. نقوله
+
+95
+00:12:02,480 --> 00:12:06,700
+بسيطة. بدنا نرجع لأي نظرية من النظريات اللي
+
+96
+00:12:06,700 --> 00:12:12,030
+درسناها، أو أي سؤال سابق من المسائل اللي اتعرضنا
+
+97
+00:12:12,030 --> 00:12:19,050
+عليهم، ونحاول نحل المسألة. الآن، الآن لو جيت لي هذه
+
+98
+00:12:19,050 --> 00:12:27,350
+المثلة، ورحت سميت هذه F of X، يبقى الـ F of X بيساوي
+
+99
+00:12:27,350 --> 00:12:34,850
+X⁴ + 1. لو روحت يابا جيب F of (X
+
+100
+00:12:34,850 --> 00:12:37,750
++ 1) على سبيل المثال.
+
+101
+00:12:40,510 --> 00:12:47,390
+يبقى بدي أشيل كل X وأحط مكانها X + 1. يبقى
+
+102
+00:12:47,390 --> 00:12:55,010
+هذه بدي أساوي X + 1⁴ + 1. بدي أضغط
+
+103
+00:12:55,010 --> 00:12:59,650
+هذه، وأشوفها جدّيش. ابتدي طبعا X + 1 لكل
+
+104
+00:12:59,650 --> 00:13:06,230
+تربيع في X + 1 لكل تربيع. تمام؟ يبقى هذه
+
+105
+00:13:06,230 --> 00:13:12,110
+عبارة عن X² + 2X + 1 في X²
+
+106
+00:13:12,110 --> 00:13:18,270
++ 2X + 1. بتعطيني فك الجوش اللي عندنا.
+
+107
+00:13:18,270 --> 00:13:25,690
+هذا تمام؟ بقول لك كويس. يبقى هذه X⁴ +
+
+108
+00:13:25,690 --> 00:13:34,670
+2X³ + X² + 2X³ +
+
+109
+00:13:34,670 --> 00:13:43,830
+4X² + 2X، وهنا X² +
+
+110
+00:13:43,830 --> 00:13:52,230
+2X + 1. بيجي نجمع، بصير عندنا الـ F of (X
+
+111
+00:13:52,230 --> 00:13:59,550
++ 1) على الشكل التالي: X⁴ + 4X³
+
+112
+00:13:59,550 --> 00:14:10,250
++ 4X² + 6X² + 4
+
+113
+00:14:10,250 --> 00:14:16,030
+X + 2، عندنا + 1، وهنا عندنا 1، يبقى
+
+114
+00:14:16,030 --> 00:14:22,110
+هاي 2. يبقى هذا الشكل الـ polynomial. اندعى واضح
+
+115
+00:14:22,110 --> 00:14:29,350
+أن هذه الـ polynomial موجودة في Z[X].
+
+116
+00:14:30,260 --> 00:14:36,320
+تمام؟ كل هذه موجودة، معاملاتها أعداد صحيحة.
+
+117
+00:14:36,320 --> 00:14:41,960
+طيب، بتروح تدور على prime. مين أول prime قابلنا في
+
+118
+00:14:41,960 --> 00:14:47,560
+الدنيا؟ اتنين. اتنين بتجرب المعاملات هذه كلها،
+
+119
+00:14:47,560 --> 00:14:57,620
+معاملات. 4، 2، طبعا. يبقى بادي بيقوله نعم،
+
+120
+00:14:59,010 --> 00:15:05,650
+الاتنين لا يقسم الواحد. هو معامل X⁴. اتنين
+
+121
+00:15:05,650 --> 00:15:13,010
+بيقسم الأربعة، اتنين بيقسم الستة، اتنين بيقسم الأربعة،
+
+122
+00:15:13,010 --> 00:15:21,530
+اتنين بيقسم الاتنين، and اتنين تربيع يساوي أربعة، لا
+
+123
+00:15:21,530 --> 00:15:28,990
+يقسم اتنين. by a previous theorem. هذا الـ F of X
+
+124
+00:15:28,990 --> 00:15:37,530
++ 1 is irreducible على الـ Q. بنرجع بعد إيه
+
+125
+00:15:37,530 --> 00:15:50,030
+الـ previous theorem. بنظرية سابقة. الـ F of X +
+
+126
+00:15:50,030 --> 00:16:03,380
+واحد is irreducible over Q. Thank you. طيب،
+
+127
+00:16:03,380 --> 00:16:09,420
+المرة اللي فاتت بدأناكم بـ exercise رقم خمسة، وقلنا خمسة C
+
+128
+00:16:09,420 --> 00:16:15,000
+وروّحنا على C، وروحنا أثبتنا F of X + C. مين ما
+
+129
+00:16:15,000 --> 00:16:19,420
+تكون الـ C موجودة في الـ field. صحيح؟ تبقى أنا عندي هنا
+
+130
+00:16:19,420 --> 00:16:24,520
+C في كم؟ إيه؟ بواحد. إذا كانت هذه irreducible، فالـ
+
+131
+00:16:24,520 --> 00:16:34,680
+F of X is reducible. يبقى هنا by exercise
+
+132
+00:16:34,680 --> 00:16:46,540
+خمسة part C. الـ F of X اللي هي الأصلية is reducible
+
+133
+00:16:46,540 --> 00:16:51,280
+over the Q.
+
+134
+00:16:55,690 --> 00:17:01,050
+خلاص المطلب كله ولا بس نصه؟ نص المطلب ده، اللي أثبت
+
+135
+00:17:01,050 --> 00:17:05,790
+إن الـ polynomial هذه irreducible على الـ Q، لكنها
+
+136
+00:17:05,790 --> 00:17:15,610
+reducible على مين؟ على R. طيب. طيب لو جيت للـ X⁴
+
+137
+00:17:15,610 --> 00:17:21,970
++ 1، دي فرق بين المربعين؟ والله مجموع مربعين.
+
+138
+00:17:23,080 --> 00:17:29,100
+مجموع مربعين. يبقى حسب علمنا القديم، مالهاش تحليل،
+
+139
+00:17:29,100 --> 00:17:33,380
+مظبوط؟ ما فيش رأيك؟ زد 2 له تحليل؟ كيف؟ زد
+
+140
+00:17:33,380 --> 00:17:37,220
+2 له تحليل؟ احنا ما لمش زد 2، احنا مش على الـ
+
+141
+00:17:37,220 --> 00:17:41,600
+في زد 2، احنا الآن في Q، صحيح ولا لأ؟ يعني
+
+142
+00:17:41,600 --> 00:17:46,340
+احنا لم نتعرض لـ زد 2، لأن احنا ما جبناش F bar
+
+143
+00:17:46,340 --> 00:17:51,070
+على الإطلاق، تمام؟ في هذا السؤال، تمام؟ بدي أقول
+
+144
+00:17:51,070 --> 00:17:57,290
+لكن ممكن أنحللها، واحنا مش داريين كيف انحللها. يبقى
+
+145
+00:17:57,290 --> 00:18:07,170
+هاتي. بقدر أقول X² + √2 X +
+
+146
+00:18:07,170 --> 00:18:16,790
+1 في X² − √2 X + 1. معقول
+
+147
+00:18:16,790 --> 00:18:23,420
+معقول؟ X² في X² هي X⁴، و 1 في 1
+
+148
+00:18:23,420 --> 00:18:29,060
+هي 1. هذا موجب مع سالب لما نضربهما 1 هيطلع عكس
+
+149
+00:18:29,060 --> 00:18:34,100
+التاني. واحد بإشارة موجب وواحد بإشارة سالب. لكن هل
+
+150
+00:18:34,100 --> 00:18:40,300
+هذا موجود في Q يا بنات؟ لا، لأن الـ Q is irrational
+
+151
+00:18:40,300 --> 00:18:45,110
+مش rational. الـ Q ده set of rational numbers. يبقى هذا
+
+152
+00:18:45,110 --> 00:18:49,570
+مش موجود في الـ Q، لكن هو موجود وين؟ في R، لأن الـ R
+
+153
+00:18:49,570 --> 00:18:55,730
+تشمل الـ rational و الـ irrational numbers. طيب، الآن
+
+154
+00:18:55,730 --> 00:19:03,670
+باجي بقوله اللي هو الـ X² + √2 X
+
+155
+00:19:03,670 --> 00:19:10,290
++ 1، والـ X² − √2 X + 1،
+
+156
+00:19:10,290 --> 00:19:17,450
+does not belong to Q. مش موجودة في Q. السبب جذر
+
+157
+00:19:17,450 --> 00:19:22,790
+2 هو اللي جابها. مش موجودة في Q، مش موجودة بـ Q
+
+158
+00:19:22,790 --> 00:19:32,970
+but belonging to R. لكنها موجودة في R، مادة موجودة
+
+159
+00:19:32,970 --> 00:19:39,630
+في R. إذا حللنا الـ X⁴ + 1 على صورة حاصل ضرب
+
+160
+00:19:39,930 --> 00:19:43,870
+two polynomials، وهذه الـ polynomials موجودة في
+
+161
+00:19:43,870 --> 00:19:50,310
+R، ردوا سبل R. صحيح ولا لأ؟ يبقى باجي بقوله
+
+162
+00:19:50,310 --> 00:20:02,930
+this means that، هذا يعني أن الـ X⁴ + 1
+
+163
+00:20:02,930 --> 00:20:07,370
+is reducible.
+
+164
+00:20:17,920 --> 00:20:23,980
+في واحد أَشْطَر منا شوية، دارس الـ complex كويس، اخذ
+
+165
+00:20:23,980 --> 00:20:30,140
+مادة في الـ complex وناجح فيها بجدارة، راح يحلل X⁴
+
+166
+00:20:30,140 --> 00:20:35,770
++ 1 إلى أربعة عوامل complex، وأنتم عارفين
+
+167
+00:20:35,770 --> 00:20:41,810
+عمله. بيجي العنصر ومرافقه الـ conjugate التابع، تمام؟ يحلل
+
+168
+00:20:41,810 --> 00:20:46,050
+عنصر ومرافقه، عنصر ومرافقه، هي الأربعة حلول لما
+
+169
+00:20:46,050 --> 00:20:51,530
+نضرب العنصر مع مرافقه، صلى ريان البرهان، والعنصر
+
+170
+00:20:51,530 --> 00:20:56,090
+التالي مع مرافقه، صلى عهد. تمام؟ يبقى هو من الـ
+
+171
+00:20:56,090 --> 00:20:59,610
+complex، وصل لمين؟ للـ Real. يعني في الـ complex
+
+172
+00:20:59,610 --> 00:21:04,580
+reduction، ولبس أربعة عناصر. حولها لـ Real. لستوا
+
+223
+00:26:19,500 --> 00:26:26,640
+F of X يساوي X تربيع زي X زي أرفع. معناته فيها
+
+224
+00:26:26,640 --> 00:26:33,980
+factor من الدرجة الأولى؟ لأ، هذا بده يعطينا أن ال F
+
+225
+00:26:33,980 --> 00:26:44,820
+of X has no linear factor أو no factor of degree
+
+226
+00:26:46,770 --> 00:26:50,930
+معنديش ولا واحد من الدرجة الأولى. طب هي من الدرجة
+
+227
+00:26:50,930 --> 00:26:54,870
+الثانية. لو تتحدث عن الدرجة الأولى، فدرجة الأولى، طب
+
+228
+00:26:54,870 --> 00:26:59,230
+ولا واحد من الدرجة الأولى، يبقى لا يمكن تحليلها لأن
+
+229
+00:26:59,230 --> 00:27:05,350
+الدرجة الأولى irreducible، كذلك مالهاش تحليل الدرجة
+
+230
+00:27:05,350 --> 00:27:11,570
+الأولى. يبقى هذا بده يعطينا أن ال F of X is
+
+231
+00:27:11,570 --> 00:27:15,490
+irreducible over
+
+232
+00:27:17,840 --> 00:27:24,980
+زي أحد هذه
+
+233
+00:27:24,980 --> 00:27:31,660
+كان سؤال اثنين، سؤال أربعة عشر، ال F of X ما أعطيني
+
+234
+00:27:31,660 --> 00:27:36,280
+هذه، write of X as a product of reducible
+
+235
+00:27:36,280 --> 00:27:42,380
+polynomials. سؤال
+
+236
+00:27:42,380 --> 00:27:50,810
+أربعة عشر، أربعة عشر بيقول ال F of X اللي بدها
+
+237
+00:27:50,810 --> 00:28:02,910
+تساوي X تكعيب زائد X تربيع زائد X زائد واحد موجودة
+
+238
+00:28:02,910 --> 00:28:15,930
+في Z<sub>2</sub>[X]. طيب، write ال F of X، write ال F of X as
+
+239
+00:28:16,360 --> 00:28:26,020
+a product of irreducible polynomials. of irreducible
+
+240
+00:28:26,020 --> 00:28:34,660
+polynomials. أنزل
+
+241
+00:28:47,150 --> 00:28:56,810
+كم تحانَات اليوم؟ نرجع لسؤالنا مرة ثانية قريباً كده.
+
+242
+00:28:56,810 --> 00:29:01,130
+ما أعطيني polynomial، و ال polynomial موجودة في Z<sub>2</sub>
+
+243
+00:29:01,130 --> 00:29:06,250
+وقولوا اكتب لل F of X as a product of irreducible
+
+244
+00:29:06,250 --> 00:29:14,270
+polynomials على Z<sub>2</sub>. السؤال هو: هل هذا معناه أن ال F
+
+245
+00:29:14,270 --> 00:29:19,290
+of X هذه irreducible؟ وما .. إيه ال irreducible على
+
+246
+00:29:19,290 --> 00:29:24,090
+زتة؟ irreducible .. irreducible .. irreducible ..
+
+247
+00:29:24,090 --> 00:29:26,950
+irreducible .. irreducible .. irreducible ..
+
+248
+00:29:26,950 --> 00:29:27,550
+irreducible .. irreducible .. irreducible ..
+
+249
+00:29:27,550 --> 00:29:27,850
+irreducible .. irreducible .. irreducible ..
+
+250
+00:29:27,850 --> 00:29:28,890
+irreducible .. irreducible .. irreducible ..
+
+251
+00:29:28,890 --> 00:29:31,690
+irreducible .. irreducible .. irreducible ..
+
+252
+00:29:31,690 --> 00:29:32,570
+irreducible .. irreducible .. irreducible ..
+
+253
+00:29:32,570 --> 00:29:35,450
+irreducible .. irreducible .. irreducible ..
+
+254
+00:29:35,450 --> 00:29:37,810
+irreducible .. irreducible .. irreducible ..
+
+255
+00:29:37,810 --> 00:29:42,430
+irreducible .. irreducible .. irreducible ..
+
+256
+00:29:42,430 --> 00:29:45,430
+irreducible
+
+257
+00:29:45,690 --> 00:29:50,390
+لكن كل واحدة من الاتنين أو التلاتة هي الـ
+
+258
+00:29:50,390 --> 00:29:55,170
+reducible. إذا قدرت أعمل البرنامج عصر درجة two
+
+259
+00:29:55,170 --> 00:30:00,030
+factors أو three factors على الأكثر، لأننا من
+
+260
+00:30:00,030 --> 00:30:04,690
+الدرجة الثالثة، يبقى يا two factors يا three
+
+261
+00:30:04,690 --> 00:30:10,190
+factors. وكل واحد من الاتنين أو التلاتة بتكون الـ
+
+262
+00:30:10,190 --> 00:30:14,330
+reducible. يبقى كل factor irreducible، لكن الـ
+
+263
+00:30:14,330 --> 00:30:18,390
+polynomial الأصلي يبقى irreducible لإني قدرت
+
+264
+00:30:18,390 --> 00:30:22,830
+أحللها وأكتبها على صيغة حاصل ضرب. طيب ماشي، نيجي لده
+
+265
+00:30:22,830 --> 00:30:28,930
+قال: يكتبلي هذه على صيغة حاصل ضرب irreducible
+
+266
+00:30:28,930 --> 00:30:33,870
+polynomials. بقوله: ماشي، بجي لأول وقت، بقول F of zero
+
+267
+00:30:33,870 --> 00:30:39,700
+وواحد، حقه إيه؟ طيب، F of واحد، بزيه، و يبقى صار ال X
+
+268
+00:30:39,700 --> 00:30:46,560
+ناقص واحد is a factor. طبعاً هذا لو فكرت في حكاية
+
+269
+00:30:46,560 --> 00:30:51,620
+التعويض. في واحد شاطر في التحليل، قال إيه؟ قال: أنا
+
+270
+00:30:51,620 --> 00:30:55,780
+راح أدّي تحليل وخلص، و بجيب عامل من الدرجة الأولى
+
+271
+00:30:55,780 --> 00:30:59,060
+زي ما جيبت أنت عامل، هو هو نفس العامل بالضبط، ومثل
+
+272
+00:30:59,060 --> 00:31:05,320
+كده، قالي: هذا ال F of X you said بتاخد هدول مع بعض
+
+273
+00:31:05,320 --> 00:31:10,380
+وهدول مع بعض، كله ماشي، قال: بدّي أخد X تربيع من
+
+274
+00:31:10,380 --> 00:31:15,420
+الأولى والثانية، بدّي أخليها زي ما هي، قولّ له: تمام، قال:
+
+275
+00:31:15,420 --> 00:31:21,400
+من قانون التوزيع، هاي X تربيع برة، بظل X زائد واحد
+
+276
+00:31:21,400 --> 00:31:27,440
+زائد القوس اللي ضايل، X زائد واحد، قولّ له: تمام، قالّ لي:
+
+277
+00:31:27,440 --> 00:31:35,040
+علي التوزيع كمان مرة، يبقى كمان مرة، بصير X زائد واحد
+
+278
+00:31:35,040 --> 00:31:41,500
+هي، وخدناه برة، بظل مين؟ في X تربيع زائد واحد، قلنا
+
+279
+00:31:41,500 --> 00:31:46,760
+له: والله سيجعلها تكتب كده على حاصل two factors،
+
+280
+00:31:46,760 --> 00:31:52,280
+واحد منهم الـ irreducible، قلنا إنه من الدرجة الأولى،
+
+281
+00:31:52,280 --> 00:31:58,180
+والثانية مش خير بنشوف، لكن إحنا قلنا إن الواحد هو
+
+282
+00:31:58,180 --> 00:32:04,550
+صفر لهذه، الدليل X ناقص واحد هو أحد العوامل. أنت طالع
+
+283
+00:32:04,550 --> 00:32:10,730
+عندك هنا X ناقص واحد، غلط، الله، صح صح صح صح صح صح صح
+
+284
+00:32:10,730 --> 00:32:13,670
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+285
+00:32:13,670 --> 00:32:13,710
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+286
+00:32:13,710 --> 00:32:16,310
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+287
+00:32:16,310 --> 00:32:22,890
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+288
+00:32:22,890 --> 00:32:25,530
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+289
+00:32:25,530 --> 00:32:31,630
+صح صح صح صح صح صح صح صح صح صح صح
+
+290
+00:32:31,630 --> 00:32:38,530
+صح. هذه ال X زائد واحد اللي برة، وهذه بدّي أحللها، X
+
+291
+00:32:38,530 --> 00:32:43,870
+زائد واحد، X زائد واحد، هتيجي تقولي: هو مجموع
+
+292
+00:32:43,870 --> 00:32:49,470
+المربعين، بتحلل، لكنك بتشتغل وين؟ بتشتغل في الريال، و
+
+293
+00:32:49,470 --> 00:32:52,690
+الله، في Z<sub>2</sub>، تقولي: في Z<sub>2</sub>، بيقولها: لا،
+
+294
+00:32:52,690 --> 00:32:55,950
+يبقى الريال مالوش دَوا، هذه مجموع المربعين اللي
+
+295
+00:32:55,950 --> 00:32:59,710
+بلغتنا القديمة، مالهاش تتبعت الإعدادية، مالهاش
+
+296
+00:32:59,710 --> 00:33:03,780
+تحليل. هذا، لكن إحنا بنشتغل في Z<sub>2</sub>، إذا اختلف
+
+297
+00:33:03,780 --> 00:33:08,760
+الوضع، هدول لو ضربتهم في بعض بيعطوني هذه الإجابة.
+
+298
+00:33:08,760 --> 00:33:15,580
+نعم، X في X، X تربيع، هيئة زائد X، و زائد X، بزائد
+
+299
+00:33:15,580 --> 00:33:20,500
+اثنين X، في Z<sub>2</sub>، Zero، مع السلامة، راح تظل واحد
+
+300
+00:33:20,500 --> 00:33:25,440
+في واحد في واحد، هيئة، يبقى تحليلنا سليم مئة بالمئة.
+
+301
+00:33:25,440 --> 00:33:32,620
+يبقى هذا عبارة عن جذر الكل تكعيبي. يبقى الحل سبعها X
+
+302
+00:33:32,620 --> 00:33:38,520
+يساوي واحد، Of multiplicity ثلاث، طبعاً، طيب،
+
+303
+00:33:38,520 --> 00:33:42,300
+multiplicity ثلاث، والله مش ثلاث، كل واحد فيهم من
+
+304
+00:33:42,300 --> 00:33:50,160
+أي درجة، الدرجة الأولى irreducible. يبقى هنا، since
+
+305
+00:33:50,160 --> 00:33:57,340
+إما أن، أني Linear Polynomial،
+
+306
+00:34:12,430 --> 00:34:21,890
+F of X is a product of
+
+307
+00:34:21,890 --> 00:34:28,930
+irreducible polynomials.
+
+308
+00:34:45,460 --> 00:34:52,980
+لازم أجيب لكم polynomial زيكم، وتشوفوا ما يناسبها
+
+309
+00:34:52,980 --> 00:34:57,820
+من هالنظريات اللي فاتت، وتشوفوها irreducible،
+
+310
+00:34:57,820 --> 00:35:04,680
+والله irreducible، اه طبعاً لازم أجيب لكم حلول، وأحدد لكم،
+
+311
+00:35:04,680 --> 00:35:09,760
+أقول لكم شوفوها لي: هل هي reducible ولا irreducible
+
+312
+00:35:09,760 --> 00:35:14,500
+على ال field فلان، وأعطيكم field مين، يطلع ما أعرف،
+
+313
+00:35:14,500 --> 00:35:18,960
+رغم إني ما أعطيتش ولا سؤال بالامتحان حتى هذه اللحظة،
+
+314
+00:35:18,960 --> 00:35:23,560
+لكن أنا في تصوّري إني هجيب سؤال بالشكل اللي عندنا.
+
+315
+00:35:23,560 --> 00:35:30,960
+طيب هذا كان سؤال أربعة عشر، بدنا سؤال ثلاثة وعشرين.
+
+316
+00:35:31,180 --> 00:35:37,520
+سؤال 23، عارف والله يا بنت الحلقة ليش اللي بديها،
+
+317
+00:35:37,520 --> 00:35:48,440
+سؤال 23 بيقول: ما يكفي، find all zeros، find all
+
+318
+00:35:48,440 --> 00:35:57,280
+zeros and multiplicities and their multiplicities
+
+319
+00:35:57,280 --> 00:36:00,460
+and their
+
+320
+00:36:07,250 --> 00:36:13,490
+multiplicities، multiplicities of
+
+321
+00:36:13,490 --> 00:36:25,950
+ال F of X، قدر ساب اللي هو X أس خمسة زائد اللي هو
+
+322
+00:36:25,950 --> 00:36:33,590
+أربعة X أس أربعة، أربعة X<sup>4</sup> زائد أربعة X
+
+323
+00:36:33,590 --> 00:36:46,750
+تكعيب ناقص X تربيع ناقص أربعة X زائد واحد زائد
+
+324
+00:36:46,750 --> 00:36:54,410
+واحد over Z<sub>5</sub>، over
+
+325
+00:36:54,410 --> 00:36:57,750
+Z<sub>5</sub>
+
+326
+00:36:58,760 --> 00:37:04,880
+خمسة. نقرأ
+
+327
+00:37:04,880 --> 00:37:09,640
+السؤال ونشوف بما يوحي السؤال قبل أن نبدأ الحلول.
+
+328
+00:37:09,640 --> 00:37:16,160
+هذه كل ال zeros وال multiplicities تبعها من ال F
+
+329
+00:37:16,160 --> 00:37:22,080
+of X على Z<sub>5</sub>. السؤال هو: هل هذا يعني أن ال F of X
+
+330
+00:37:22,080 --> 00:37:27,240
+is reducible؟ والله إيه reducible؟ رجّالي هات لي
+
+331
+00:37:27,240 --> 00:37:31,520
+zeros، معناته في عوامل، وأول شيء بنبدأ بالدرجة
+
+332
+00:37:31,520 --> 00:37:36,400
+الأولى، يبقى أنا أبدأ أروح على Z<sub>5</sub>، أشوف في أصفار
+
+333
+00:37:36,400 --> 00:37:41,080
+لهذه ال polynomial أم لا؟ طبعاً F of Zero يساوي Zero،
+
+334
+00:37:41,080 --> 00:37:49,040
+يبقى Zero، حُطّ على شكلّ ني GF of واحد واحد، يعطينا هذا
+
+335
+00:37:49,040 --> 00:37:59,120
+و هذا خمسة و .. و هذا أربعة، وهنا ناقص واحد بثلاثة
+
+336
+00:37:59,120 --> 00:38:06,360
+أو ناقص أربعة، زي أربعة مع ثلاثة، يظل هنا ناقص واحد زي
+
+337
+00:38:06,360 --> 00:38:13,260
+واحد، يساوي زيرو. يبقى اللي بقوله ال F of واحد يساوي
+
+338
+00:38:13,260 --> 00:38:20,640
+زيرو. نيجي لل F of اثنين، اثنين، باثنين وثلاثين، في Z
+
+339
+00:38:20,640 --> 00:38:27,760
+<sub>5</sub> بيظل كده؟ اثنين. هذا ستة عشر، في Z<sub>5</sub> بيظل
+
+340
+00:38:27,760 --> 00:38:32,560
+واحد. في أربعة بأربعة، واثنين ستة، بيظل معانا واحد.
+
+341
+00:38:33,160 --> 00:38:37,020
+هذا ثمانية في أربعة باثنين وثلاثين، اثنين واحد
+
+342
+00:38:37,020 --> 00:38:45,520
+ثلاثة، ثلاثة، وهنا عندك ناقص أربعة، بيظل ناقص واحد،
+
+343
+00:38:45,520 --> 00:38:52,370
+ناقص واحد، و ما ب .. اه، كده إحنا قلنا؟ نظرنا في
+
+344
+00:38:52,370 --> 00:39:00,750
+كدهش؟ تاني مرة اثنين؟ اثنين، هذه اثنين وثلاثين، بيظل
+
+345
+00:39:00,750 --> 00:39:08,410
+اثنين تمام؟ وهذه ستة عشر، أربعة، أربعة وستين، أربعة و
+
+346
+00:39:08,410 --> 00:39:14,070
+ستين، بيظل خمسة، بيظل زائد أربعة واثنين، ستة، بيظل
+
+347
+00:39:14,070 --> 00:39:20,560
+واحد. يجي لهذه ثمانية في أربعة باثنين وثلاثين، ثلاثين
+
+348
+00:39:20,560 --> 00:39:21,960
+ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين
+
+349
+00:39:21,960 --> 00:39:22,980
+ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين
+
+350
+00:39:22,980 --> 00:39:28,960
+ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين
+
+351
+00:39:28,960 --> 00:39:29,240
+ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين
+
+352
+00:39:29,240 --> 00:39:32,960
+ثلاثين ثلاثين ثلاثين ثلاثين ثلاثين
+
+353
+00:39:32,960 --> 00:39:39,700
+ثلاثين ثلاثين ثلاثين
+
+354
+00:39:41,600 --> 00:39:46,640
+لأ، بدأت على زيرو، كيف هذا؟ مرة ثانية، مرة ثانية، مرة
+
+355
+00:39:46,640 --> 00:39:50,880
+ثانية، ثلاثة بتطلع زيرو، ثلاثة بتطلع زيرو، هذا بيطلع
+
+356
+00:39:50,880 --> 00:39:55,280
+اثنين، هذا بيطلع اثنين، هذا بيطلع اثني عشر، زيرو بيبقى
+
+357
+00:39:55,280 --> 00:39:59,200
+ناقص اثنين، وبعدين بيبقى اثنين، يبقى لا يمكن أن
+
+358
+00:39:59,200 --> 00:40:07,400
+تساوي زيرو. فبنشوف F of ثلاثة، F of ثلاثة معاكم
+
+359
+00:40:07,400 --> 00:40:13,300
+Calculator؟ بتدخل ثلاثة في ثلاثة، بتسعة، تسعة في تسعة
+
+360
+00:40:13,300 --> 00:40:17,880
+وواحد، وثمانين، وبيضل معايا واحد، بيضل مين؟ بيضل
+
+361
+00:40:17,880 --> 00:40:26,240
+واحد، اللي هو ثلاثة، ثلاثة في واحد بثلاثة، بيضل ثلاثة
+
+362
+00:40:26,240 --> 00:40:31,940
+من الأول، مظبوط؟ طيب، إذا لو روحنا على Z<sub>5</sub>
+
+363
+00:40:31,940 --> 00:40:37,600
+بنلاقي إن ال polynomial هذه، الأصفار تبعها فقط واحد
+
+364
+00:40:37,600 --> 00:40:46,880
+وثلاثة. يبقى هنا، أنا بدّي أضمن الواحد و ثلاثة
+
+365
+00:40:46,880 --> 00:41:01,380
+are the only zeros of ال F of X. So، ال X ناقص واحد
+
+366
+00:41:01,380 --> 00:41:16,120
+و ال X ناقص ثلاثة are factors of F of X. that is
+
+367
+00:41:16,120 --> 00:41:25,740
+F of X بده يساوي X ناقص واحد في X ناقص ثلاثة في
+
+368
+00:41:25,740 --> 00:41:30,770
+قُصر، قديش هنا عندنا معادلة من الدرجة الخامسة، هدول
+
+369
+00:41:30,770 --> 00:41:34,110
+من الدرجة الثانية، بتطلع معادلة من الدرجة
+
+370
+00:41:34,110 --> 00:41:38,690
+الثالثة. إذا بنروح نجسم، جسمة، مطولة، المعادلة اللي
+
+371
+00:41:38,690 --> 00:41:43,110
+عندنا على حاصل ضرب هدول، بروح في الهام الشيء،
+
+372
+00:41:43,110 --> 00:41:49,350
+بقوله: X زائد خمسة، زائد أربعة X زائد أربعة، زائد
+
+373
+00:41:49,350 --> 00:41:56,090
+أربعة X، تقريباً ناقص X، تقريباً ناقص أربعة X زائد
+
+374
+00:41:56,090 --> 00:42:02,010
+واحد، مقسّمة على حاصل ضرب هدولة منها. هي X تكعيب،
+
+375
+00:42:02,010 --> 00:42:10,730
+ناقص X، ناقص ثلاثة X، ناقص أربعة X زائد ثلاثة.
+
+376
+00:42:12,330 --> 00:42:22,430
+سمعون؟ هذه فيها X تكعيب، X أس خمسة ناقص أربعة X
+
+377
+00:42:22,430 --> 00:42:31,380
+أس أربعة، وهنا زائد ثلاثة X تكعيب، زائد بيصير ناقص،
+
+378
+00:42:31,380 --> 00:42:39,640
+وهذه زائد وهذه ناقص، لا يوجد هنا ثمانية X أس أربعة،
+
+379
+00:42:39,640 --> 00:42:49,740
+في Z<sub>5</sub>، Z<sub>5</sub>، ثلاثة X أس أربعة، هذه ناقص X
+
+380
+00:42:49,740 --> 00:42:56,220
+تكعيب، إن ثلاثة راجع أربعة، هذه بالموجب، وبعدها بالسالب،
+
+381
+00:42:56,220 --> 00:43:02,520
+وبضل ناقص X تربيع، أربعة، أربعة ناقص، مو زائد أربعة،
+
+382
+00:43:02,520 --> 00:43:08,720
+اه، زائد X تكعيب، زائد X تكعيب، ثلاثة، وبضل عندنا
+
+383
+00:43:08,720 --> 00:43:16,140
+ناقص X تربيع، ناقص أربعة X، زي ده نواصل القسم، يبقى
+
+384
+00:43:16,140 --> 00:43:24,370
+زائد ثلاثة X تربيع. بصير عندي ثلاثة X أس أربعة ناقص
+
+385
+00:43:24,370 --> 00:43:33,310
+اثني عشر X تكعيب، وهنا زائد تسعة X تربيع، زائد تسعة X
+
+386
+00:43:33,310 --> 00:43:38,790
+تربيع، زائد بصير ناقص، وهذه زائد وهذه ناقص، هذه مع
+
+387
+00:43:38,790 --> 00:43:45,310
+السلامة، بصير عندنا اثني عشر X تكعيب، و X تكعيب،
+
+388
+00:43:48,820 --> 00:43:55,660
+طبعاً، كان مرة ثانية، مرة ثانية، الآن ثلاثة X تربيع في
+
+389
+00:43:55,660 --> 00:44:02,240
+X تربيع، ثلاثة X أس الله، ثلاثة في أربعة، اثني عشر X
+
+390
+00:44:02,240 --> 00:44:09,800
+تكعيب، اثني عشر X تكعيب، بالسالب، بدنا نخليها موجبة، وهذه
+
+391
+00:44:09,800 --> 00:44:1
+
+445
+00:51:17,170 --> 00:51:27,590
+اتنين يبقى زائد X تربيع زائد اتنين X زائد اتنين
+
+446
+00:51:27,590 --> 00:51:35,530
+فقط  لغيره هذه زائد بيصير ناقص وهذه ناقص بيبقى ال X
+
+447
+00:51:35,530 --> 00:51:43,570
+X زائد اتنين يبقى زائد واحد  بـ X زائد اتنين صفر و
+
+448
+00:51:43,570 --> 00:51:51,430
+صفر إذا صارت المثل هذه X تربيع زائد X زائد واحد
+
+449
+00:51:51,430 --> 00:51:58,420
+هل الواحد بيخليها صفر؟ طبعاً لأ، التلاتة بيخليها
+
+450
+00:51:58,420 --> 00:52:05,400
+صفر؟ لأ، يبقى ولا واحد فيهم بأصفار تمام؟ يبقى هنا
+
+451
+00:52:05,400 --> 00:52:12,220
+صار the zeros are
+
+452
+00:52:12,220 --> 00:52:23,460
+one of one dct one تمام؟ and
+
+453
+00:52:34,120 --> 00:52:41,800
+طيب هنا انتهينا من هذا الـ section وبعد غد إن شاء
+
+454
+00:52:41,800 --> 00:52:47,420
+الله سنبدأ آخر section في المقرر
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ccb79738fca510c5c2d688cc7bc11dba0e945ce6
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4784, "start": 20.82, "end": 47.84, "text": "بسم الله الرحمن الرحيم نكمل ما ابتدأنا به في المرة الماضية وهو حل أسئلة من أسئلة التمرين على chapter 17 وصلنا المرة اللي فاتت إلى chapter 10 إلى سؤال 10 وفي سؤال 10 مكون من عدة نقاط تعرضنا للنقطة الأولى والثالثة وقلنا التنتين هدول زي بعض", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 24793, 1211, 19446, 48127, 2655, 3215, 10721, 8315, 39627, 8978, 9673, 25720, 9673, 46958, 10632, 37037, 2407, 11331, 1211, 5551, 3794, 19986, 37977, 9154, 5551, 3794, 19986, 37977, 16712, 29973, 9957, 15844, 7187, 3282, 4032, 36520, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 30731, 7187, 1266, 30731, 8608, 33604, 6027, 1266, 4032, 41185, 8608, 33604, 6027, 1266, 3714, 30544, 9154, 6225, 41891, 8717, 4587, 41193, 37279, 43042, 8315, 24976, 1863, 47432, 3660, 16247, 12610, 7578, 16070, 12984, 6027, 12984, 3660, 4032, 4587, 1211, 8315, 16712, 29399, 9957, 8032, 3215, 12610, 30767, 1829, 45030, 11242], "avg_logprob": -0.13421285546050882, "compression_ratio": 1.85, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 20.82, "end": 21.16, "word": "بسم", "probability": 0.882080078125}, {"start": 21.16, "end": 21.36, "word": " الله", "probability": 0.96533203125}, {"start": 21.36, "end": 21.78, "word": " الرحمن", "probability": 0.9612630208333334}, {"start": 21.78, "end": 22.3, "word": " الرحيم", "probability": 0.9939778645833334}, {"start": 22.3, "end": 23.74, "word": " نكمل", "probability": 0.9407552083333334}, {"start": 23.74, "end": 23.88, "word": " ما", "probability": 0.83642578125}, {"start": 23.88, "end": 24.5, "word": " ابتدأنا", "probability": 0.9453125}, {"start": 24.5, "end": 24.8, "word": " به", "probability": 0.76953125}, {"start": 24.8, "end": 25.0, "word": " في", "probability": 0.765625}, {"start": 25.0, "end": 25.44, "word": " المرة", "probability": 0.990966796875}, {"start": 25.44, "end": 26.54, "word": " الماضية", "probability": 0.9951171875}, {"start": 26.54, "end": 27.2, "word": " وهو", "probability": 0.7376708984375}, {"start": 27.2, "end": 27.82, "word": " حل", "probability": 0.976806640625}, {"start": 27.82, "end": 28.5, "word": " أسئلة", "probability": 0.9678955078125}, {"start": 28.5, "end": 28.7, "word": " من", "probability": 0.9443359375}, {"start": 28.7, "end": 29.22, "word": " أسئلة", "probability": 0.986083984375}, {"start": 29.22, "end": 29.96, "word": " التمرين", "probability": 0.9754231770833334}, {"start": 29.96, "end": 30.7, "word": " على", "probability": 0.85888671875}, {"start": 30.7, "end": 31.42, "word": " chapter", "probability": 0.5986328125}, {"start": 31.42, "end": 32.3, "word": " 17", "probability": 0.744140625}, {"start": 32.3, "end": 33.26, "word": " وصلنا", "probability": 0.9264322916666666}, {"start": 33.26, "end": 33.54, "word": " المرة", "probability": 0.959228515625}, {"start": 33.54, "end": 33.72, "word": " اللي", "probability": 0.731689453125}, {"start": 33.72, "end": 34.18, "word": " فاتت", 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"word": "Zeros", "probability": 0.334686279296875}, {"start": 160.38, "end": 161.58, "word": " in", "probability": 0.2119140625}, {"start": 161.58, "end": 162.74, "word": " the", "probability": 0.736328125}, {"start": 162.74, "end": 163.56, "word": " two", "probability": 0.5625}, {"start": 163.56, "end": 166.16, "word": " يعني", "probability": 0.869140625}, {"start": 166.16, "end": 166.62, "word": " معناته", "probability": 0.8287760416666666}, {"start": 166.62, "end": 167.24, "word": " الدرجة", "probability": 0.9078776041666666}, {"start": 167.24, "end": 168.32, "word": " الأولى", "probability": 0.97314453125}, {"start": 168.32, "end": 169.72, "word": " مستبعدة", "probability": 0.904296875}, {"start": 169.72, "end": 170.54, "word": " و", "probability": 0.56396484375}, {"start": 170.54, "end": 171.1, "word": " الدرجة", "probability": 0.96337890625}, {"start": 171.1, "end": 171.88, "word": " التالتة", "probability": 0.73260498046875}, {"start": 171.88, "end": 173.78, "word": " مستبعدة", 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{"start": 209.41, "end": 209.67, "word": " لإن", "probability": 0.72509765625}, {"start": 209.67, "end": 210.11, "word": " الدرجة", "probability": 0.9607747395833334}, {"start": 210.11, "end": 210.43, "word": " الرابعة", "probability": 0.9737955729166666}, {"start": 210.43, "end": 210.63, "word": " مع", "probability": 0.990234375}, {"start": 210.63, "end": 211.17, "word": " الدرجة", "probability": 0.9895833333333334}, {"start": 211.17, "end": 211.53, "word": " الأولى", "probability": 0.9376627604166666}, {"start": 211.53, "end": 212.19, "word": " بيعطينا", "probability": 0.853857421875}, {"start": 212.19, "end": 213.27, "word": " الدرجة", "probability": 0.98583984375}, {"start": 213.27, "end": 214.13, "word": " الخامسة", "probability": 0.8651123046875}, {"start": 214.13, "end": 214.65, "word": " and", "probability": 0.3134765625}, {"start": 214.65, "end": 215.39, "word": " so", "probability": 0.66845703125}, {"start": 215.39, "end": 217.41, "word": " ولذلك", "probability": 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{"start": 257.94, "end": 259.54, "word": " has", "probability": 0.81494140625}, {"start": 259.54, "end": 260.56, "word": " a", "probability": 0.97802734375}, {"start": 260.56, "end": 261.92, "word": " factor", "probability": 0.92431640625}, {"start": 261.92, "end": 265.6, "word": " of", "probability": 0.5634765625}, {"start": 265.6, "end": 267.36, "word": " degree", "probability": 0.947265625}, {"start": 267.36, "end": 269.58, "word": " 2", "probability": 0.55810546875}, {"start": 269.58, "end": 270.36, "word": " من", "probability": 0.87890625}, {"start": 270.36, "end": 271.06, "word": " الدرجة", "probability": 0.8575846354166666}, {"start": 271.06, "end": 271.58, "word": " الثانية", "probability": 0.9461669921875}, {"start": 271.58, "end": 272.3, "word": " مثلا", "probability": 0.95849609375}, {"start": 272.3, "end": 275.02, "word": " that", "probability": 0.69189453125}, {"start": 275.02, "end": 275.62, "word": " is", "probability": 0.96435546875}], "temperature": 1.0}, {"id": 10, "seek": 30544, "start": 277.1, "end": 305.44, "text": "I am هذا ال factor that is in the form يبقى في الشكل التالي اللي هو ال X ترمية زائد X زائد V بتشوف في أكم احتمال لهذه في Z2 يبقى بادي بقول we have", "tokens": [40, 669, 23758, 2423, 5952, 300, 307, 294, 264, 1254, 7251, 3555, 4587, 7578, 8978, 25124, 28820, 16712, 6027, 1829, 13672, 1829, 31439, 2423, 1783, 6055, 2288, 2304, 10632, 30767, 16373, 3215, 1783, 30767, 16373, 3215, 691, 39894, 8592, 38688, 8978, 5551, 24793, 1975, 33753, 2304, 6027, 46740, 24192, 8978, 1176, 17, 7251, 3555, 4587, 7578, 4724, 995, 16254, 4724, 39648, 321, 362], "avg_logprob": -0.3046875111758709, "compression_ratio": 1.39375, "no_speech_prob": 0.0, "words": [{"start": 277.1, "end": 277.54, "word": "I", "probability": 0.24658203125}, {"start": 277.54, "end": 278.08, "word": " am", "probability": 0.208984375}, {"start": 278.08, "end": 280.04, "word": " هذا", "probability": 0.7958984375}, {"start": 280.04, "end": 280.28, "word": " ال", "probability": 0.8291015625}, {"start": 280.28, "end": 280.8, "word": " factor", "probability": 0.6865234375}, {"start": 280.8, "end": 281.38, "word": " that", "probability": 0.291259765625}, {"start": 281.38, "end": 281.94, "word": " is", "probability": 0.833984375}, {"start": 281.94, "end": 284.5, "word": " in", "probability": 0.53515625}, {"start": 284.5, "end": 285.74, "word": " the", "probability": 0.5390625}, {"start": 285.74, "end": 286.52, "word": " form", "probability": 0.95703125}, {"start": 286.52, "end": 287.6, "word": " يبقى", "probability": 0.938720703125}, {"start": 287.6, "end": 287.76, "word": " في", "probability": 0.830078125}, {"start": 287.76, "end": 288.38, "word": " الشكل", "probability": 0.974609375}, {"start": 288.38, "end": 289.18, "word": " التالي", "probability": 0.9427083333333334}, {"start": 289.18, "end": 289.76, "word": " اللي", "probability": 0.6715087890625}, {"start": 289.76, "end": 289.96, "word": " هو", "probability": 0.955078125}, {"start": 289.96, "end": 290.16, "word": " ال", "probability": 0.2366943359375}, {"start": 290.16, "end": 290.4, "word": " X", "probability": 0.603515625}, {"start": 290.4, "end": 291.12, "word": " ترمية", "probability": 0.71417236328125}, {"start": 291.12, "end": 292.24, "word": " زائد", "probability": 0.7052408854166666}, {"start": 292.24, "end": 293.14, "word": " X", "probability": 0.30126953125}, {"start": 293.14, "end": 294.44, "word": " زائد", "probability": 0.9495442708333334}, {"start": 294.44, "end": 295.38, "word": " V", "probability": 0.89111328125}, {"start": 295.38, "end": 297.72, "word": " بتشوف", "probability": 0.8898111979166666}, {"start": 297.72, "end": 297.98, "word": " في", "probability": 0.83203125}, {"start": 297.98, "end": 298.78, "word": " أكم", "probability": 0.853515625}, {"start": 298.78, "end": 299.82, "word": " احتمال", "probability": 0.9798583984375}, {"start": 299.82, "end": 300.48, "word": " لهذه", "probability": 0.62255859375}, {"start": 300.48, "end": 300.86, "word": " في", "probability": 0.89306640625}, {"start": 300.86, "end": 301.7, "word": " Z2", "probability": 0.821533203125}, {"start": 301.7, "end": 303.06, "word": " يبقى", "probability": 0.9656982421875}, {"start": 303.06, "end": 303.52, "word": " بادي", "probability": 0.59912109375}, {"start": 303.52, "end": 304.14, "word": " بقول", "probability": 0.964599609375}, {"start": 304.14, "end": 304.48, "word": " we", "probability": 0.5419921875}, {"start": 304.48, "end": 305.44, "word": " have", "probability": 0.970703125}], "temperature": 1.0}, {"id": 11, "seek": 33510, "start": 306.62, "end": 335.1, "text": "4 possibilities يبقى في عندي أربع احتمالات للدرجة الثانية احتمال ان يكون x تربيع فقط واحتمال ان يكون x تربيع زائد x واحتمال ان يكون x تربيع زائد 1", "tokens": [19, 12178, 7251, 3555, 4587, 7578, 8978, 18871, 16254, 5551, 25513, 3615, 1975, 33753, 2304, 6027, 9307, 24976, 3215, 47341, 3660, 6024, 104, 7649, 10632, 1975, 33753, 2304, 6027, 16472, 7251, 30544, 2031, 6055, 2288, 21292, 3615, 6156, 47432, 36764, 33753, 2304, 6027, 16472, 7251, 30544, 2031, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 2031, 36764, 33753, 2304, 6027, 16472, 7251, 30544, 2031, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 502], "avg_logprob": -0.16178385416666666, "compression_ratio": 1.856060606060606, "no_speech_prob": 0.0, "words": [{"start": 306.62, "end": 307.1, "word": "4", "probability": 0.142578125}, {"start": 307.1, "end": 310.48, "word": " possibilities", "probability": 0.76708984375}, {"start": 310.48, "end": 314.78, "word": " يبقى", "probability": 0.937255859375}, {"start": 314.78, "end": 314.96, "word": " في", "probability": 0.8671875}, {"start": 314.96, "end": 315.54, "word": " عندي", "probability": 0.6033935546875}, {"start": 315.54, "end": 316.08, "word": " أربع", "probability": 0.7047526041666666}, {"start": 316.08, "end": 317.04, "word": " احتمالات", "probability": 0.95771484375}, {"start": 317.04, "end": 317.84, "word": " للدرجة", "probability": 0.9490966796875}, {"start": 317.84, "end": 318.42, "word": " الثانية", "probability": 0.8822021484375}, {"start": 318.42, "end": 319.98, "word": " احتمال", "probability": 0.9591064453125}, {"start": 319.98, "end": 320.36, "word": " ان", "probability": 0.473388671875}, {"start": 320.36, "end": 321.16, "word": " يكون", "probability": 0.973876953125}, {"start": 321.16, "end": 321.58, "word": " x", "probability": 0.51513671875}, {"start": 321.58, "end": 322.26, "word": " تربيع", "probability": 0.802001953125}, {"start": 322.26, "end": 322.92, "word": " فقط", "probability": 0.98681640625}, {"start": 322.92, "end": 325.34, "word": " واحتمال", "probability": 0.93603515625}, {"start": 325.34, "end": 325.66, "word": " ان", "probability": 0.85888671875}, {"start": 325.66, "end": 326.44, "word": " يكون", "probability": 0.987548828125}, {"start": 326.44, "end": 326.88, "word": " x", "probability": 0.9755859375}, {"start": 326.88, "end": 327.7, "word": " تربيع", "probability": 0.9349365234375}, {"start": 327.7, "end": 328.48, "word": " زائد", "probability": 0.8826497395833334}, {"start": 328.48, "end": 329.0, "word": " x", "probability": 0.88623046875}, {"start": 329.0, "end": 331.04, "word": " واحتمال", "probability": 0.9832763671875}, {"start": 331.04, "end": 331.4, "word": " ان", "probability": 0.8681640625}, {"start": 331.4, "end": 332.12, "word": " يكون", "probability": 0.99267578125}, {"start": 332.12, "end": 332.64, "word": " x", "probability": 0.9921875}, {"start": 332.64, "end": 333.54, "word": " تربيع", "probability": 0.9532470703125}, {"start": 333.54, "end": 334.7, "word": " زائد", "probability": 0.8274739583333334}, {"start": 334.7, "end": 335.1, "word": " 1", "probability": 0.712890625}], "temperature": 1.0}, {"id": 12, "seek": 36521, "start": 335.69, "end": 365.21, "text": "و احتمال ان يكون X تربية زائد X زائد واحد في ال X نجي للاحتمالات الأول يبقى الاحتمال الأول لو كان X تربية بقدر احلله X في X تمام؟ و لو كان لي احتمالي الثاني بقدر احلله X في X زائد واحد و لو كان لي احتمالي التالت بقدر احلله X زائد واحد", "tokens": [2407, 1975, 33753, 2304, 6027, 16472, 7251, 30544, 1783, 6055, 25513, 10632, 30767, 16373, 3215, 1783, 30767, 16373, 3215, 36764, 24401, 8978, 2423, 1783, 8717, 7435, 1829, 5296, 15040, 33753, 2304, 6027, 9307, 16247, 12610, 7251, 3555, 4587, 7578, 42963, 33753, 2304, 6027, 16247, 12610, 45164, 25961, 1783, 6055, 25513, 10632, 4724, 28543, 2288, 1975, 5016, 1211, 43761, 1783, 8978, 1783, 46811, 10943, 22807, 4032, 45164, 25961, 32239, 1975, 33753, 2304, 6027, 1829, 6024, 104, 7649, 1829, 4724, 28543, 2288, 1975, 5016, 1211, 43761, 1783, 8978, 1783, 30767, 16373, 3215, 36764, 24401, 4032, 45164, 25961, 32239, 1975, 33753, 2304, 6027, 1829, 16712, 6027, 2655, 4724, 28543, 2288, 1975, 5016, 1211, 43761, 1783, 30767, 16373, 3215, 36764, 24401], "avg_logprob": -0.1726694886209601, "compression_ratio": 2.5759493670886076, "no_speech_prob": 0.0, "words": [{"start": 335.69, "end": 336.25, "word": "و", "probability": 0.7236328125}, {"start": 336.25, "end": 337.05, "word": " احتمال", "probability": 0.80279541015625}, {"start": 337.05, "end": 337.51, "word": " ان", "probability": 0.662109375}, {"start": 337.51, "end": 338.35, "word": " يكون", "probability": 0.974609375}, {"start": 338.35, "end": 338.81, "word": " X", "probability": 0.397216796875}, {"start": 338.81, "end": 339.47, "word": " تربية", "probability": 0.7659505208333334}, {"start": 339.47, "end": 340.15, "word": " زائد", "probability": 0.6192220052083334}, {"start": 340.15, "end": 340.57, "word": " X", "probability": 0.98046875}, {"start": 340.57, "end": 341.25, "word": " زائد", "probability": 0.921875}, {"start": 341.25, "end": 341.61, "word": " واحد", "probability": 0.71728515625}, {"start": 341.61, "end": 342.25, "word": " في", "probability": 0.232421875}, {"start": 342.25, "end": 342.51, "word": " ال", "probability": 0.311767578125}, {"start": 342.51, "end": 342.97, "word": " X", "probability": 0.78515625}, {"start": 342.97, "end": 344.11, "word": " نجي", "probability": 0.80029296875}, {"start": 344.11, "end": 345.09, "word": " للاحتمالات", "probability": 0.8188069661458334}, {"start": 345.09, "end": 345.53, "word": " الأول", "probability": 0.845947265625}, {"start": 345.53, "end": 346.61, "word": " يبقى", "probability": 0.9378662109375}, {"start": 346.61, "end": 347.23, "word": " الاحتمال", "probability": 0.9722900390625}, {"start": 347.23, "end": 347.77, "word": " الأول", "probability": 0.796630859375}, {"start": 347.77, "end": 348.11, "word": " لو", "probability": 0.93212890625}, {"start": 348.11, "end": 348.39, "word": " كان", "probability": 0.9677734375}, {"start": 348.39, "end": 348.69, "word": " X", "probability": 0.98681640625}, {"start": 348.69, "end": 349.23, "word": " تربية", "probability": 0.96240234375}, {"start": 349.23, "end": 349.79, "word": " بقدر", "probability": 0.8585611979166666}, {"start": 349.79, "end": 350.75, "word": " احلله", "probability": 0.7469482421875}, {"start": 350.75, "end": 351.27, "word": " X", "probability": 0.947265625}, {"start": 351.27, "end": 351.49, "word": " في", "probability": 0.8798828125}, {"start": 351.49, "end": 351.95, "word": " X", "probability": 0.99658203125}, {"start": 351.95, "end": 354.03, "word": " تمام؟", "probability": 0.6468098958333334}, {"start": 354.03, "end": 354.19, "word": " و", "probability": 0.69873046875}, {"start": 354.19, "end": 354.41, "word": " لو", "probability": 0.94873046875}, {"start": 354.41, "end": 354.75, "word": " كان", "probability": 0.96044921875}, {"start": 354.75, "end": 354.89, "word": " لي", "probability": 0.337158203125}, {"start": 354.89, "end": 355.67, "word": " احتمالي", "probability": 0.9484375}, {"start": 355.67, "end": 356.05, "word": " الثاني", "probability": 0.85247802734375}, {"start": 356.05, "end": 356.63, "word": " بقدر", "probability": 0.9900716145833334}, {"start": 356.63, "end": 357.33, "word": " احلله", "probability": 0.9215087890625}, {"start": 357.33, "end": 357.83, "word": " X", "probability": 0.97509765625}, {"start": 357.83, "end": 358.01, "word": " في", "probability": 0.96728515625}, {"start": 358.01, "end": 358.35, "word": " X", "probability": 0.99609375}, {"start": 358.35, "end": 358.95, "word": " زائد", "probability": 0.9558919270833334}, {"start": 358.95, "end": 359.45, "word": " واحد", "probability": 0.93896484375}, {"start": 359.45, "end": 360.41, "word": " و", "probability": 0.927734375}, {"start": 360.41, "end": 360.69, "word": " لو", "probability": 0.9873046875}, {"start": 360.69, "end": 361.03, "word": " كان", "probability": 0.99365234375}, {"start": 361.03, "end": 361.17, "word": " لي", "probability": 0.94091796875}, {"start": 361.17, "end": 361.93, "word": " احتمالي", "probability": 0.9919921875}, {"start": 361.93, "end": 362.51, "word": " التالت", "probability": 0.9407552083333334}, {"start": 362.51, "end": 363.05, "word": " بقدر", "probability": 0.9915364583333334}, {"start": 363.05, "end": 363.69, "word": " احلله", "probability": 0.9390869140625}, {"start": 363.69, "end": 364.09, "word": " X", "probability": 0.99658203125}, {"start": 364.09, "end": 364.65, "word": " زائد", "probability": 0.9588216145833334}, {"start": 364.65, "end": 365.21, "word": " واحد", "probability": 0.984619140625}], "temperature": 1.0}, {"id": 13, "seek": 39440, "start": 365.56, "end": 394.4, "text": "X زائد واحد طبعا اللي تاخد X في X ب X ترابيعه زائد X و زايد X ب 2 X و احنا بنشتغل في Z2 يبقى ب Zero مع السلامة ماضلش الا واحد في واحد اليومين بواحد التلات احتمالات دول حللهم الى حاصل ضرب عاملين من الدرجة الأولى هل هذا ممكن؟", "tokens": [55, 30767, 16373, 3215, 36764, 24401, 23032, 3555, 3615, 995, 13672, 1829, 6055, 47283, 3215, 1783, 8978, 1783, 4724, 1783, 6055, 2288, 16758, 40228, 3224, 30767, 16373, 3215, 1783, 4032, 30767, 995, 25708, 1783, 4724, 568, 1783, 4032, 1975, 5016, 8315, 44945, 8592, 2655, 17082, 1211, 8978, 1176, 17, 7251, 3555, 4587, 7578, 4724, 17182, 20449, 21136, 37440, 3660, 19446, 11242, 1211, 8592, 42963, 36764, 24401, 8978, 36764, 24401, 45595, 20498, 9957, 4724, 14407, 24401, 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ال polynomial اللي عندنا على هذه هتلاقي لازم يبقى باقي، وأظن أن الباقي هو واحد صحيح، تمام؟ وبالتالي هذه لا تقسم من اللي فوق، يبقى باجي بقوله هذه by long division", "tokens": [44510, 11536, 4724, 995, 38436, 12399, 5296, 31377, 2304, 7251, 9566, 1211, 3615, 28239, 2655, 7435, 4724, 2304, 9957, 22807, 4724, 3555, 995, 38436, 12399, 7251, 3555, 4587, 7578, 45164, 12602, 995, 33753, 9122, 1829, 4117, 4032, 2304, 3794, 4117, 2655, 25062, 19528, 4032, 4587, 38251, 2655, 2423, 26110, 13672, 1829, 43242, 8315, 15844, 29538, 8032, 2655, 15040, 38436, 5296, 31377, 2304, 7251, 3555, 4587, 7578, 4724, 995, 38436, 12399, 36725, 19913, 1863, 14739, 29739, 995, 38436, 31439, 36764, 24401, 20328, 5016, 1829, 5016, 12399, 46811, 10943, 22807, 46599, 6027, 2655, 6027, 1829, 29538, 20193, 6055, 4587, 38251, 9154, 13672, 1829, 6156, 30543, 12399, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 29538, 538, 938, 10044], "avg_logprob": -0.18868172293951532, "compression_ratio": 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{"start": 527.99, "end": 528.31, "word": " لأ", "probability": 0.771728515625}, {"start": 528.31, "end": 528.79, "word": " لإنه", "probability": 0.65234375}, {"start": 528.79, "end": 529.27, "word": " حاصل", "probability": 0.9248046875}, {"start": 529.27, "end": 529.67, "word": " ضربه", "probability": 0.501708984375}, {"start": 529.67, "end": 530.49, "word": " ويحطينه", "probability": 0.35650634765625}, {"start": 530.49, "end": 530.77, "word": " 100", "probability": 0.274169921875}, {"start": 530.77, "end": 531.81, "word": " الدرجة", "probability": 0.9111328125}, {"start": 531.81, "end": 532.67, "word": " الخامسة", "probability": 0.978515625}, {"start": 532.67, "end": 533.35, "word": " يبقى", "probability": 0.8885498046875}, {"start": 533.35, "end": 533.73, "word": " هذا", "probability": 0.935546875}, {"start": 533.73, "end": 534.53, "word": " يقن", "probability": 0.628662109375}, {"start": 534.53, "end": 535.41, "word": " كذلك", "probability": 0.7976888020833334}, {"start": 535.41, "end": 536.11, "word": " now", "probability": 0.255126953125}, {"start": 536.11, "end": 537.29, "word": " factor", "probability": 0.73974609375}, {"start": 537.29, "end": 538.13, "word": " of", "probability": 0.9697265625}, {"start": 538.13, "end": 539.25, "word": " third", "probability": 0.92236328125}, {"start": 539.25, "end": 540.09, "word": " degree", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 19, "seek": 56887, "start": 542.33, "end": 568.87, "text": "ال degree يبقى ايش تفسيرنا لهذا الكلام ان ال F bar is irreducible على Z2 بس ضالت واحدة بشكل ان يكون ال degree ل F هي degree ل F bar يبقى الان بقى اللي بقوله since ال degree لل F هي نفس ال degree", "tokens": [6027, 4314, 7251, 3555, 4587, 7578, 1975, 1829, 8592, 6055, 36178, 13546, 8315, 46740, 15730, 2423, 28820, 10943, 16472, 2423, 479, 2159, 307, 16014, 769, 32128, 15844, 1176, 17, 4724, 3794, 48812, 6027, 2655, 36764, 24401, 3660, 4724, 8592, 28820, 16472, 7251, 30544, 2423, 4314, 5296, 479, 39896, 4314, 5296, 479, 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irreducible over زائد 2 هذا بدي يعطينا ايه؟", "tokens": [1211, 1211, 39184, 479, 2159, 13672, 1829, 39896, 6055, 3794, 995, 45865, 16490, 2304, 3794, 3660, 492, 362, 16472, 2423, 479, 2159, 295, 1783, 13672, 1829, 6055, 3794, 995, 45865, 1783, 5551, 10859, 9381, 16490, 2304, 3794, 3660, 30767, 16373, 3215, 1783, 6055, 2288, 16758, 10632, 30767, 16373, 3215, 36764, 24401, 307, 16014, 769, 32128, 670, 30767, 16373, 3215, 568, 23758, 4724, 16254, 37495, 9566, 1829, 8315, 1975, 1829, 3224, 22807], "avg_logprob": -0.2233072966337204, "compression_ratio": 1.414012738853503, "no_speech_prob": 0.0, "words": [{"start": 569.41, "end": 570.07, "word": "للـ", "probability": 0.8204752604166666}, {"start": 570.07, "end": 570.57, "word": " F", "probability": 0.5830078125}, {"start": 570.57, "end": 571.09, "word": " bar", "probability": 0.4521484375}, {"start": 571.09, "end": 571.33, "word": " اللي", "probability": 0.811767578125}, {"start": 571.33, "end": 571.65, "word": " هي", "probability": 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"word": " F", "probability": 0.67822265625}, {"start": 611.25, "end": 611.93, "word": " of", "probability": 0.86572265625}, {"start": 611.93, "end": 612.47, "word": " X", "probability": 0.9365234375}, {"start": 612.47, "end": 613.23, "word": " اللي", "probability": 0.77978515625}, {"start": 613.23, "end": 613.49, "word": " هي", "probability": 0.7373046875}, {"start": 613.49, "end": 614.23, "word": " تساوي", "probability": 0.9473876953125}, {"start": 614.23, "end": 614.77, "word": " X", "probability": 0.94921875}, {"start": 614.77, "end": 615.21, "word": " أُس", "probability": 0.606689453125}, {"start": 615.21, "end": 616.21, "word": " خمسة", "probability": 0.9478759765625}, {"start": 616.21, "end": 617.15, "word": " زائد", "probability": 0.8896484375}, {"start": 617.15, "end": 618.11, "word": " خمسة", "probability": 0.9879150390625}, {"start": 618.11, "end": 618.49, "word": " X", "probability": 0.97705078125}, {"start": 618.49, "end": 619.23, "word": " ترابيع", "probability": 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"text": "X تربيه في X تربيه هي X نص أربع وواحد في واحد هي واحد هذا موجب مع سالب لما نظر واحد هيطلع عكس التاني واحد بإشارة موجب وواحد بإشارة سالب لكن هل هذا موجود في Q يا بنات؟ لأ لإن الـQ is irrational مش rational الـQ ده set of rational number", "tokens": [55, 6055, 2288, 21292, 3224, 8978, 1783, 6055, 2288, 21292, 3224, 39896, 1783, 8717, 9381, 5551, 25513, 3615, 4032, 14407, 24401, 8978, 36764, 24401, 39896, 36764, 24401, 23758, 3714, 29245, 3555, 20449, 8608, 6027, 3555, 5296, 15042, 8717, 19913, 2288, 36764, 24401, 39896, 9566, 1211, 3615, 6225, 4117, 3794, 16712, 7649, 1829, 36764, 24401, 4724, 28814, 8592, 9640, 3660, 3714, 29245, 3555, 4032, 14407, 24401, 4724, 28814, 8592, 9640, 3660, 8608, 6027, 3555, 44381, 8032, 1211, 23758, 3714, 29245, 23328, 8978, 1249, 35186, 4724, 8315, 2655, 22807, 5296, 10721, 5296, 28814, 1863, 2423, 39184, 48, 307, 39914, 37893, 15090, 2423, 39184, 48, 11778, 3224, 992, 295, 15090, 1230], "avg_logprob": -0.2517201977038602, "compression_ratio": 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"temperature": 1.0}, {"id": 41, "seek": 120736, "start": 1179.93, "end": 1207.37, "text": "two polynomials وهذه ال polynomials موجودة في ارمان ردو سبل ارمان صحيح ولا لأ يبقى باجي بقوله this means that هذا يعني ان ال X مسارة زائد واحد is reduceable", "tokens": [20534, 22560, 12356, 37037, 24192, 2423, 6754, 77, 9220, 1124, 3714, 29245, 23328, 3660, 8978, 1975, 2288, 2304, 7649, 12602, 3215, 2407, 8608, 3555, 1211, 1975, 2288, 2304, 7649, 20328, 5016, 1829, 5016, 49429, 5296, 10721, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 341, 1355, 300, 23758, 37495, 22653, 16472, 2423, 1783, 47524, 9640, 3660, 30767, 16373, 3215, 36764, 24401, 307, 2182, 4176, 712], "avg_logprob": -0.47288602020810633, "compression_ratio": 1.380952380952381, "no_speech_prob": 0.0, "words": [{"start": 1179.93, "end": 1180.43, "word": "two", "probability": 0.28564453125}, {"start": 1180.43, "end": 1181.85, "word": " polynomials", "probability": 0.86181640625}, {"start": 1181.85, "end": 1182.33, 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الأولى", "probability": 0.98388671875}, {"start": 1620.85, "end": 1622.27, "word": " irreducible", "probability": 0.792236328125}, {"start": 1622.27, "end": 1622.91, "word": " كذلك", "probability": 0.9567057291666666}, {"start": 1622.91, "end": 1623.45, "word": " مالهاش", "probability": 0.8450927734375}, {"start": 1623.45, "end": 1624.13, "word": " تحليل", "probability": 0.985107421875}, {"start": 1624.13, "end": 1625.35, "word": " الدرجة", "probability": 0.9928385416666666}, {"start": 1625.35, "end": 1626.45, "word": " الأولى", "probability": 0.98876953125}, {"start": 1626.45, "end": 1626.99, "word": " يبقى", "probability": 0.8851318359375}, {"start": 1626.99, "end": 1627.33, "word": " هذا", "probability": 0.9560546875}, {"start": 1627.33, "end": 1627.73, "word": " بده", "probability": 0.468505859375}, {"start": 1627.73, "end": 1628.47, "word": " يعطينا", "probability": 0.970703125}, {"start": 1628.47, "end": 1629.11, "word": " ان", "probability": 0.412353515625}, {"start": 1629.11, 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"tokens": [2423, 479, 295, 1783, 13672, 1829, 47525, 11296, 6055, 3794, 995, 45865, 1783, 6055, 4117, 1829, 3555, 30767, 16373, 3215, 1783, 6055, 2288, 16758, 40228, 30767, 16373, 3215, 1783, 30767, 16373, 3215, 36764, 24401, 3714, 29245, 23328, 3660, 8978, 1176, 17, 295, 1783, 23032, 1829, 3555, 2464, 2423, 479, 295, 1783, 2464, 2423, 479, 295, 1783, 382], "avg_logprob": -0.2258890109329388, "compression_ratio": 1.4873949579831933, "no_speech_prob": 0.0, "words": [{"start": 1667.45, "end": 1667.85, "word": " ال", "probability": 0.2484130859375}, {"start": 1667.85, "end": 1668.25, "word": " F", "probability": 0.50341796875}, {"start": 1668.25, "end": 1668.69, "word": " of", "probability": 0.82421875}, {"start": 1668.69, "end": 1669.23, "word": " X", "probability": 0.9453125}, {"start": 1669.23, "end": 1670.09, "word": " اللي", "probability": 0.52032470703125}, {"start": 1670.09, "end": 1670.81, "word": " بدها", "probability": 0.69873046875}, {"start": 1670.81, "end": 1671.65, "word": " تساوي", "probability": 0.9510498046875}, {"start": 1671.65, "end": 1674.31, "word": " X", "probability": 0.95068359375}, {"start": 1674.31, "end": 1675.53, "word": " تكيب", "probability": 0.8043212890625}, {"start": 1675.53, "end": 1677.13, "word": " زائد", "probability": 0.773681640625}, {"start": 1677.13, "end": 1677.57, "word": " X", "probability": 0.99462890625}, {"start": 1677.57, "end": 1678.43, "word": " ترابيع", "probability": 0.6717529296875}, {"start": 1678.43, "end": 1679.47, "word": " زائد", "probability": 0.9222005208333334}, {"start": 1679.47, "end": 1679.81, "word": " X", "probability": 0.96875}, {"start": 1679.81, "end": 1680.31, "word": " زائد", "probability": 0.9781901041666666}, {"start": 1680.31, "end": 1680.99, "word": " واحد", "probability": 0.905517578125}, {"start": 1680.99, "end": 1682.91, "word": " موجودة", "probability": 0.9654541015625}, {"start": 1682.91, "end": 1683.29, "word": " في", "probability": 0.9716796875}, {"start": 1683.29, "end": 1685.23, "word": " Z2", "probability": 0.5780029296875}, {"start": 1685.23, "end": 1685.79, "word": " of", "probability": 0.8046875}, {"start": 1685.79, "end": 1686.23, "word": " X", "probability": 0.99609375}, {"start": 1686.23, "end": 1688.51, "word": " طيب", "probability": 0.9659830729166666}, {"start": 1688.51, "end": 1689.11, "word": " write", "probability": 0.5380859375}, {"start": 1689.11, "end": 1689.37, "word": " ال", "probability": 0.91943359375}, {"start": 1689.37, "end": 1689.61, "word": " F", "probability": 0.966796875}, {"start": 1689.61, "end": 1689.95, "word": " of", "probability": 0.97412109375}, {"start": 1689.95, "end": 1690.37, "word": " X", "probability": 0.99658203125}, {"start": 1690.37, "end": 1691.61, "word": " write", "probability": 0.7548828125}, {"start": 1691.61, "end": 1693.25, "word": " ال", "probability": 0.88525390625}, {"start": 1693.25, "end": 1693.61, "word": " F", "probability": 0.97509765625}, {"start": 1693.61, "end": 1694.09, "word": " of", "probability": 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{"start": 1703.18, "end": 1706.02, "word": " irreducible", "probability": 0.87548828125}, {"start": 1706.02, "end": 1707.9, "word": " pronoun", "probability": 0.7705078125}, {"start": 1707.9, "end": 1714.66, "word": " أنزلت", "probability": 0.711212158203125}], "temperature": 1.0}, {"id": 60, "seek": 175557, "start": 1727.15, "end": 1755.57, "text": "كم تحنات اليوم؟ نرجع لسؤالنا مرة ثانية قريبا كده ماعطيني polynomial و ال polynomial موجودة في Z2 وقولوا اكتب لل F of X as a product of reusable polynomials على Z2 السؤال هو هل هذا معناه ان ال F of X هذه", "tokens": [24793, 6055, 5016, 8315, 2655, 45595, 20498, 22807, 8717, 47341, 3615, 5296, 3794, 33604, 6027, 8315, 3714, 25720, 38637, 7649, 10632, 12174, 16572, 3555, 995, 9122, 3215, 3224, 19446, 3615, 9566, 9957, 1829, 26110, 4032, 2423, 26110, 3714, 29245, 23328, 3660, 8978, 1176, 17, 4032, 39648, 14407, 1975, 4117, 2655, 3555, 24976, 479, 295, 1783, 382, 257, 1674, 295, 41807, 22560, 12356, 15844, 1176, 17, 21136, 33604, 6027, 31439, 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" ماعطيني", "probability": 0.76279296875}, {"start": 1738.07, "end": 1738.65, "word": " polynomial", "probability": 0.693359375}, {"start": 1738.65, "end": 1738.99, "word": " و", "probability": 0.64892578125}, {"start": 1738.99, "end": 1739.13, "word": " ال", "probability": 0.72265625}, {"start": 1739.13, "end": 1739.67, "word": " polynomial", "probability": 0.91015625}, {"start": 1739.67, "end": 1740.29, "word": " موجودة", "probability": 0.974609375}, {"start": 1740.29, "end": 1740.45, "word": " في", "probability": 0.96826171875}, {"start": 1740.45, "end": 1741.13, "word": " Z2", "probability": 0.596435546875}, {"start": 1741.13, "end": 1742.15, "word": " وقولوا", "probability": 0.40966796875}, {"start": 1742.15, "end": 1742.69, "word": " اكتب", "probability": 0.9285888671875}, {"start": 1742.69, "end": 1742.89, "word": " لل", "probability": 0.3583984375}, {"start": 1742.89, "end": 1743.31, "word": " F", "probability": 0.8232421875}, {"start": 1743.31, "end": 1743.67, "word": " of", 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Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. Radiusable .. 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0.54638671875}, {"start": 3102.89, "end": 3103.57, "word": " و", "probability": 0.5439453125}, {"start": 3103.57, "end": 3104.03, "word": " Zero", "probability": 0.80908203125}, {"start": 3104.03, "end": 3105.09, "word": " إذا", "probability": 0.5599365234375}, {"start": 3105.09, "end": 3105.87, "word": " صارت", "probability": 0.9090169270833334}, {"start": 3105.87, "end": 3106.65, "word": " المثل", "probability": 0.653076171875}, {"start": 3106.65, "end": 3107.23, "word": " هذه", "probability": 0.82177734375}, {"start": 3107.23, "end": 3107.75, "word": " X", "probability": 0.97412109375}, {"start": 3107.75, "end": 3108.47, "word": " ترابيع", "probability": 0.8104248046875}, {"start": 3108.47, "end": 3109.39, "word": " زائد", "probability": 0.92236328125}, {"start": 3109.39, "end": 3109.89, "word": " X", "probability": 0.982421875}, {"start": 3109.89, "end": 3111.03, "word": " زائد", "probability": 0.9847005208333334}, {"start": 3111.03, "end": 3111.43, "word": " واحد", "probability": 0.978271484375}, {"start": 3111.43, "end": 3112.15, "word": " هل", "probability": 0.805419921875}, {"start": 3112.15, "end": 3112.81, "word": " الواحد", "probability": 0.9446614583333334}, {"start": 3112.81, "end": 3113.69, "word": " بيخليها", "probability": 0.851953125}, {"start": 3113.69, "end": 3114.39, "word": " صفر؟", "probability": 0.813720703125}], "temperature": 1.0}, {"id": 109, "seek": 314346, "start": 3114.8, "end": 3143.46, "text": "طبعاً لأ، التلاتة بيخليها صفر؟ لأ، يبقى ولا واحد فيهم بأصفار تمام؟ يبقى هنا صار the zeros zeros are one of one dct one تمام؟ and", "tokens": [9566, 3555, 3615, 995, 14111, 5296, 10721, 12399, 16712, 1211, 9307, 3660, 4724, 1829, 9778, 20292, 11296, 20328, 5172, 2288, 22807, 5296, 10721, 12399, 7251, 3555, 4587, 7578, 49429, 36764, 24401, 8978, 16095, 4724, 10721, 9381, 5172, 9640, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 34105, 20328, 9640, 264, 35193, 35193, 366, 472, 295, 472, 274, 349, 472, 46811, 10943, 22807, 293], "avg_logprob": -0.24429562924400208, "compression_ratio": 1.3943661971830985, "no_speech_prob": 0.0, "words": [{"start": 3114.8, "end": 3115.34, "word": "طبعاً", "probability": 0.95673828125}, {"start": 3115.34, "end": 3115.98, "word": " لأ،", "probability": 0.5937906901041666}, {"start": 3115.98, "end": 3117.82, "word": " التلاتة", "probability": 0.9288330078125}, {"start": 3117.82, "end": 3118.42, "word": " بيخليها", "probability": 0.9154296875}, {"start": 3118.42, "end": 3119.46, "word": " صفر؟", "probability": 0.800048828125}, {"start": 3119.46, "end": 3120.0, "word": " لأ،", "probability": 0.8234049479166666}, {"start": 3120.0, "end": 3120.38, "word": " يبقى", "probability": 0.96435546875}, {"start": 3120.38, "end": 3120.58, "word": " ولا", "probability": 0.87646484375}, {"start": 3120.58, "end": 3121.1, "word": " واحد", "probability": 0.994873046875}, {"start": 3121.1, "end": 3121.72, "word": " فيهم", "probability": 0.968017578125}, {"start": 3121.72, "end": 3122.88, "word": " بأصفار", "probability": 0.91787109375}, {"start": 3122.88, "end": 3124.1, "word": " تمام؟", "probability": 0.8238932291666666}, {"start": 3124.1, "end": 3124.84, "word": " يبقى", "probability": 0.9700927734375}, {"start": 3124.84, "end": 3125.4, "word": " هنا", "probability": 0.9931640625}, {"start": 3125.4, "end": 3126.4, "word": " صار", "probability": 0.912353515625}, {"start": 3126.4, "end": 3127.28, "word": " the", "probability": 0.181640625}, {"start": 3127.28, "end": 3128.22, "word": " zeros", "probability": 0.8291015625}, {"start": 3128.22, "end": 3132.22, "word": " zeros", "probability": 0.61865234375}, {"start": 3132.22, "end": 3133.84, "word": " are", "probability": 0.51220703125}, {"start": 3133.84, "end": 3135.18, "word": " one", "probability": 0.9033203125}, {"start": 3135.18, "end": 3136.1, "word": " of", "probability": 0.83203125}, {"start": 3136.1, "end": 3137.38, "word": " one", "probability": 0.354736328125}, {"start": 3137.38, "end": 3139.68, "word": " dct", "probability": 0.425567626953125}, {"start": 3139.68, "end": 3141.12, "word": " one", "probability": 0.88818359375}, {"start": 3141.12, "end": 3142.84, "word": " تمام؟", "probability": 0.752197265625}, {"start": 3142.84, "end": 3143.46, "word": " and", "probability": 0.6103515625}], "temperature": 1.0}, {"id": 110, "seek": 316742, "start": 3154.12, "end": 3167.42, "text": "طيب هنا انتهينا من هذا ال section وبعد غد ان شاء الله سنبدأ اخر section في المقرر", "tokens": [9566, 1829, 3555, 34105, 16472, 47395, 1829, 8315, 9154, 23758, 2423, 3541, 46599, 22488, 32771, 3215, 16472, 13412, 16606, 21984, 8608, 1863, 44510, 10721, 1975, 34740, 3541, 8978, 9673, 4587, 2288, 2288], "avg_logprob": -0.2921401515151515, "compression_ratio": 1.2222222222222223, "no_speech_prob": 0.0, "words": [{"start": 3154.12, "end": 3155.08, "word": "طيب", "probability": 0.5055745442708334}, {"start": 3155.08, "end": 3155.44, "word": " هنا", "probability": 0.65869140625}, {"start": 3155.44, "end": 3158.18, "word": " انتهينا", "probability": 0.83544921875}, {"start": 3158.18, "end": 3158.38, "word": " من", "probability": 0.9580078125}, {"start": 3158.38, "end": 3158.84, "word": " هذا", "probability": 0.48681640625}, {"start": 3158.84, "end": 3158.96, "word": " ال", "probability": 0.441650390625}, {"start": 3158.96, "end": 3159.3, "word": " section", "probability": 0.78369140625}, {"start": 3159.3, "end": 3160.58, "word": " وبعد", "probability": 0.7357177734375}, {"start": 3160.58, "end": 3161.02, "word": " غد", "probability": 0.789794921875}, {"start": 3161.02, "end": 3161.4, "word": " ان", "probability": 0.72509765625}, {"start": 3161.4, "end": 3161.8, "word": " شاء", "probability": 0.98046875}, {"start": 3161.8, "end": 3162.28, "word": " الله", "probability": 0.95751953125}, {"start": 3162.28, "end": 3163.7, "word": " سنبدأ", "probability": 0.97265625}, {"start": 3163.7, "end": 3164.48, "word": " اخر", "probability": 0.8154296875}, {"start": 3164.48, "end": 3165.24, "word": " section", "probability": 0.89599609375}, {"start": 3165.24, "end": 3166.18, "word": " في", "probability": 0.81689453125}, {"start": 3166.18, "end": 3167.42, "word": " المقرر", "probability": 0.9256591796875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3167.573375, "duration_after_vad": 3032.711249999987}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..757b1a038ca3966a9adb1d0a0a5cbbee73b70f2c
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU.srt
@@ -0,0 +1,1388 @@
+1
+00:00:21,480 --> 00:00:26,340
+بسم الله الرحمن الرحيم. المرة الماضية، احنا ابتدأنا
+
+2
+00:00:26,340 --> 00:00:31,820
+في introduction to ring. عرفنا الـring، أخدنا عليها
+
+3
+00:00:31,820 --> 00:00:36,940
+مجموعة من الأمثلة، واليوم إن شاء الله بنكمل الأمثلة
+
+4
+00:00:36,940 --> 00:00:42,180
+بالإضافة إلى بعض النظريات على اللي هو الـrings
+
+5
+00:00:42,180 --> 00:00:45,820
+أخدنا المرة الفاترة أربعة أمثلة، وهذا هو المثال
+
+6
+00:00:45,820 --> 00:00:49,300
+الخامس. بيقول: the set of all continuously valued
+
+7
+00:00:49,300 --> 00:00:53,730
+functions of a real variable whose graph
+
+8
+00:00:53,730 --> 00:00:58,030
+passes through the point (1, 0). يبقى احنا عندنا
+
+9
+00:00:58,030 --> 00:01:04,070
+مجموعة من الدوال الحقيقية اللي الرسم البياني لها
+
+10
+00:01:04,070 --> 00:01:10,110
+يمر بالنقطة (1, 0). يعني لو أخدنا محاور إحداثية
+
+11
+00:01:10,110 --> 00:01:15,470
+وقلنا هذا محور X، وهذا محور Y، النقطة هذه اللي هي
+
+12
+00:01:15,470 --> 00:01:21,880
+النقطة (1, 0). كل الدوال في متغير واحد، وهذا
+
+13
+00:01:21,880 --> 00:01:28,760
+المتغير متغير حقيقي التي تمر بهذه النقطة. الآن احنا
+
+14
+00:01:28,760 --> 00:01:35,000
+بنقول إن هذه commutative ring without unity. المرة
+
+15
+00:01:35,000 --> 00:01:38,520
+اللي فاتت الأمثلة قدامي كلها rings with unity. طبعا
+
+16
+00:01:38,520 --> 00:01:43,760
+الآن أنا هدعي إن هذا ring ما فيهوش unity. شو العملية
+
+17
+00:01:43,760 --> 00:01:48,300
+اللي عليها؟ عملية الجمع: f + g(a) = f(a) + g(a)
+
+18
+00:01:48,300 --> 00:01:54,700
+و f * g(a) = f(a) * g(a).
+
+19
+00:01:54,700 --> 00:02:00,360
+الآن لو جيت أقول لك الدالة f(x) = 1، هذه هي
+
+20
+00:02:00,360 --> 00:02:05,040
+constant function، والواحد لو ضربناه في أي دالة بيدي
+
+21
+00:02:05,040 --> 00:02:10,840
+يعطيني نفس الدالة. لكن السؤال: هذه ليش الـunity؟ مش
+
+22
+00:02:10,840 --> 00:02:16,880
+موجودة في هذه الـRing؟ الإجابة بسيطة جداً: إن منحنى
+
+23
+00:02:16,880 --> 00:02:24,620
+الدالة f(x) = 1 هو خط مستقيم يوازي محور
+
+24
+00:02:24,620 --> 00:02:30,740
+x. إذاً لا يمكن أن يمر بالنقطة (1, 0).
+
+25
+00:02:30,740 --> 00:02:37,280
+إذاً لو جيت رسمت الخط اللي عندنا هذا، هيطلع هيك، بهذا
+
+26
+00:02:37,280 --> 00:02:42,900
+الشكل. يبقى هذا الخط اللي هو main، اللي هو f(x)
+
+27
+00:02:42,900 --> 00:02:48,300
+يساوي واحد، لا يمكن أن يمر بهذه النقطة، وبالتالي هذه
+
+28
+00:02:48,300 --> 00:02:53,480
+الدالة مش موجودة في مجموعة هذه الدوال، وبالتالي هذه
+
+29
+00:02:53,480 --> 00:02:59,680
+ring without unity. طب ليش commutative؟ لأنه لو أخدنا
+
+30
+00:02:59,680 --> 00:03:05,100
+قيمتين للدالة f(a) و f(b)، فكل واحدة منهم عبارة
+
+31
+00:03:05,100 --> 00:03:09,340
+عن عدد حقيقي، واحنا بنعرف إن حاصل ضرب الأعداد
+
+32
+00:03:09,340 --> 00:03:15,840
+الحقيقية is commutative. يبقى هنا بقول: الـR is
+
+33
+00:03:15,840 --> 00:03:25,480
+commutative، أو the ring is commutative.
+
+34
+00:03:25,480 --> 00:03:28,660
+commutative
+
+35
+00:03:28,660 --> 00:03:33,280
+because الـ
+
+36
+00:03:33,280 --> 00:03:46,370
+f(a) and f(b) are real numbers. نظراً لأنهم أعداد
+
+37
+00:03:46,370 --> 00:03:50,670
+حقيقية، فهي commutative، يعني f(a) * f(b) = f(b) * f(a). وبالتالي ما فيها
+
+38
+00:03:50,670 --> 00:03:56,010
+مشكلة خالص. طيب، بدنا نروح الآن على Ring غير هذه الـ
+
+39
+00:04:01,530 --> 00:04:12,540
+rings، وهو مثال رقم 6. مثال رقم ستة بيقول:  لـ R1، و R2، و
+
+40
+00:04:12,540 --> 00:04:24,200
+لغاية الـ RN  rings. هذه عبارة عن حلقات. We
+
+41
+00:04:24,200 --> 00:04:25,500
+shall construct
+
+42
+00:04:33,610 --> 00:04:44,590
+a new ring. a new ring. بدنا
+
+43
+00:04:44,590 --> 00:04:52,350
+نكوّن من هذه الـrings ring جديدة as follow، كالتالي:
+
+44
+00:04:52,350 --> 00:05:02,010
+كيف؟ نعمل نقول: بدي آخذ الـR1 direct sum مع R
+
+45
+00:05:02,010 --> 00:05:12,340
+2 direct sum direct sum مع R N. تمام؟ من عناصر
+
+46
+00:05:12,340 --> 00:05:22,060
+هذه. كل العناصر على الشكل (A1, A2, ..., AN) بحيث الـAI
+
+47
+00:05:22,060 --> 00:05:31,300
+موجودة في الـRI. بالشكل اللي عندنا هذا. And we
+
+48
+00:05:31,300 --> 00:05:40,780
+form pairs for
+
+49
+00:05:40,780 --> 00:05:48,160
+addition and
+
+50
+00:05:48,160 --> 00:05:58,840
+multiplication. الجمع
+
+51
+00:05:58,840 --> 00:06:15,510
+وعملية الضرب component wise. from Poland Y that
+
+52
+00:06:15,510 --> 00:06:23,310
+is that is
+
+53
+00:06:23,310 --> 00:06:44,290
+(A1, A2,..., AN) + (B1, B2,..., BN) = (A1 + B1, A2 + B2,..., AN + BN).
+
+54
+00:06:44,290 --> 00:07:02,390
+(A1, A2,..., AN) * (B1, B2,..., BN) = (A1*B1, A2*B2,..., AN*BN).
+
+55
+00:07:02,390 --> 00:07:14,730
+This ring is called the direct
+
+56
+00:07:14,730 --> 00:07:33,700
+sum of R1, R2,..., RN.
+
+57
+00:07:33,700 --> 00:07:43,720
+R1, R2,..., RN.
+
+58
+00:08:18,300 --> 00:08:24,500
+المثال هذا يعني إن عندي مجموعة من الـrings: R1،
+
+59
+00:08:24,500 --> 00:08:29,900
+وR2، وR3، ولغاية RN. من الـrings هذه
+
+60
+00:08:29,900 --> 00:08:35,160
+بدي أكون ring جديدة، تمام؟ الـring الجديدة هذه شو
+
+61
+00:08:35,160 --> 00:08:42,040
+شكلها؟ يبقى: (R1, R2,..., RN)
+
+62
+00:08:42,040 --> 00:08:44,760
+(R1, R2,..., RN)
+
+63
+00:08:44,760 --> 00:08:47,270
+(R1, R2,..., RN) the set of all
+
+64
+00:08:47,270 --> 00:08:51,330
+n-tuples. هذه كنا في جبر حديث 1، اسمها
+
+65
+00:08:51,330 --> 00:08:57,170
+n-tuple. يعني جوس مكوّن من n من المركبات. الجوس
+
+66
+00:08:57,170 --> 00:09:02,050
+كله يعتبر عنصر واحد. العنصر الواحد عبارة عن مجموعة من
+
+67
+00:09:02,050 --> 00:09:09,510
+المركبات، تمام؟ بنسميها n-tuple، يعني جوس فيه n من
+
+68
+00:09:09,510 --> 00:09:16,270
+العناصر، تمام؟ بحيث الـAI موجود في RI. شو يعني؟ يعني
+
+69
+00:09:16,270 --> 00:09:23,390
+لو حطيت الـI بواحد، بيصير A1 موجود في R1، وA2 موجود
+
+70
+00:09:23,390 --> 00:09:29,590
+في R2، وA3 في R3، وAN موجود في RN. يعني من كل ring
+
+71
+00:09:29,590 --> 00:09:36,270
+بأخذ عنصر واحد فقط. مجموعة العناصر هذه كونت لي عنصر
+
+72
+00:09:36,270 --> 00:09:43,230
+واحد فقط في الـring الجديدة. طيب، عرفنا عليها عملية
+
+73
+00:09:43,230 --> 00:09:49,310
+العمليات. سميناها component wise. يعني إيه؟ جمع كل
+
+74
+00:09:49,310 --> 00:09:56,790
+عنصر مع نظيره، تمام؟ اضرب بضرب كل عنصر في نظيره. هذا
+
+75
+00:09:56,790 --> 00:10:02,630
+معنى الـaddition and multiplication component wise.
+
+76
+00:10:02,630 --> 00:10:08,310
+يعني كل عنصر مع نظيره رياضياً. بقول: هذا كل الـelement
+
+77
+00:10:08,310 --> 00:10:13,330
+الأول، وهذا الـelement الثاني، بدي أجمعهم. إذا بجمع
+
+78
+00:10:13,330 --> 00:10:19,590
+كل عنصر مع نظيره، يبقى A1 + B1 يمثل المركبة
+
+79
+00:10:19,590 --> 00:10:26,170
+الأولى، A2 + B2 يمثل المركبة الثانية، AN + BN
+
+80
+00:10:26,170 --> 00:10:31,670
+يمثل المركبة النونية. هذا الجمع. الضرب كذلك
+
+81
+00:10:31,670 --> 00:10:36,850
+component wise. بضرب كل عنصر مع نظيره من القوس
+
+82
+00:10:36,850 --> 00:10:41,610
+الثاني. فبالتالي بقول: هذا الجوس الأول ضرب الجوس الثاني
+
+83
+00:10:41,610 --> 00:10:50,750
+يبقى A1B1، العنصر الثاني A2B2، A3B3,..., ANBN. يبقى من
+
+84
+00:10:50,750 --> 00:10:57,310
+حاصل ضرب المركبات المتناظرة بيطلع عندي جوس جديد. هذا
+
+85
+00:10:57,310 --> 00:11:00,890
+الجوس الجديد موجود في R1 direct sum مع R2
+
+86
+00:11:00,890 --> 00:11:06,190
+direct sum مع R2...
+
+87
+00:11:06,190 --> 00:11:09,910
+direct sum...
+
+88
+00:11:09,910 --> 00:11:11,790
+مع R2... direct sum...
+
+89
+00:11:11,790 --> 00:11:12,110
+مع R2... direct sum...
+
+90
+00:11:12,110 --> 00:11:12,570
+مع R2... direct sum...
+
+91
+00:11:12,570 --> 00:11:12,610
+مع R2... direct sum...
+
+92
+00:11:12,610 --> 00:11:19,690
+مع R2.
+
+93
+00:11:19,690 --> 00:11:21,010
+direct sum...
+
+94
+00:11:21,010 --> 00:11:21,170
+مع R2... direct sum...
+
+95
+00:11:21,170 --> 00:11:22,510
+مع R2.
+
+96
+00:11:22,510 --> 00:11:22,550
+مع R2.
+
+97
+00:11:22,550 --> 00:11:22,670
+مع R2.
+
+98
+00:11:22,670 --> 00:11:27,370
+مع R2. يبقى هذه، وبتكون فيها unity
+
+99
+00:11:27,370 --> 00:11:33,110
+إذا كان كل ring من الـrings الأصلية فيها الـunity،
+
+100
+00:11:33,110 --> 00:11:39,230
+يبقى الـunity بتاع هذه الـring هو الـn-tuple
+
+101
+00:11:39,230 --> 00:11:45,810
+المكوّنة من الـunity بتاع كل ring، تمام؟ يبقى الـ
+
+102
+00:11:45,810 --> 00:11:51,650
+identity element، أو الـunity بتاع هذه الـring اللي
+
+103
+00:11:51,650 --> 00:11:56,880
+بتاعت الـdirect sum. العناصر... عنصر الوحدة فيها هو
+
+104
+00:11:56,880 --> 00:12:02,400
+المكوّن من عناصر الوحدة في كل من الـrings المختلفة.
+
+105
+00:12:02,400 --> 00:12:08,700
+تمام؟ هذا موضوع السؤال في الكتاب. الـR1، والـR
+
+106
+00:12:08,700 --> 00:12:15,120
+2، والـRN has a unity if and only if الـdirect
+
+107
+00:12:15,120 --> 00:12:20,560
+sum has a unity. يعني بنثبت البرهان في اتجاهين. أحد
+
+108
+00:12:20,560 --> 00:12:27,750
+أسئلة التمرين. طيب تمام. نعطي كمان مثال أخير، اللي هو
+
+109
+00:12:27,750 --> 00:12:35,070
+مثال رقم 7. مثال رقم 7 بيقول: consider the ring
+
+110
+00:12:35,070 --> 00:12:44,150
+Z, مجموعة الأعداد الصحيحة
+
+111
+00:12:44,150 --> 00:12:50,050
+عليها عملية الضرب، وعليها عملية الجمع زي ما أنت
+
+112
+00:12:50,050 --> 00:12:58,780
+شايفين، with two binary operations.
+
+113
+00:12:58,780 --> 00:13:08,480
+two binary operations defined by
+
+114
+00:13:08,480 --> 00:13:20,940
+المعرفة كالتالي: الـm + الـn = m + n - 1. و الـ
+
+115
+00:13:20,940 --> 00:13:29,580
+m * n = m + n - mn. لكل الـm والـ
+
+116
+00:13:29,580 --> 00:13:41,820
+n اللي موجودة في Z. find the
+
+117
+00:13:41,820 --> 00:13:49,760
+zero and unity.
+
+118
+00:13:50,430 --> 00:14:01,170
+سؤال تاني. قال: خلي مجموعة الأعداد الصحيحة، و
+
+119
+00:14:01,170 --> 00:14:05,370
+بنعرف عليها عمليتين ثنائيتين. العملية الأولى هي: m
+
+120
+00:14:05,370 --> 00:14:08,950
++ n = m + n -1. العملية هذه
+
+121
+00:14:27,370 --> 00:14:33,050
+سؤال مرة ثانية. قال: خلي مجموعة الأعداد الصحيحة، و
+
+122
+00:14:33,050 --> 00:14:39,490
+بنعرف عليها عمليتين ثنائيتين. العملية الأولى هي m
+
+123
+00:14:39,490 --> 00:14:46,150
++ n = m + n - 1.  العملية هذه
+
+124
+00:14:46,150 --> 00:14:51,670
++، وعليها دائرة ليست عملية الجمع العادية، ولكن
+
+125
+00:14:51,670 --> 00:14:57,770
+عملية هي عملية الجمع العادية مطروح منها واحد. عملية
+
+126
+00:14:57,770 --> 00:15:03,190
+الضرب مش عملية الضرب العادية، وإنما هي m * n = m + n - mn. يبقى هاي صارت
+
+127
+00:15:03,190 --> 00:15:09,990
+two binary operations. يبقى كل binary operation
+
+128
+00:15:09,990 --> 00:15:14,830
+بيصير عليها identity element و zero element. يختلف عن
+
+129
+00:15:14,830 --> 00:15:20,110
+مين؟ يختلف عن الـZ العادية، زي مثلاً في المصفوفة، في الـ
+
+130
+00:15:20,110 --> 00:15:26,190
+...في الـrings العادية بيجينا نقول الـunity 1،
+
+131
+00:15:26,190 --> 00:15:29,430
+تمام؟ لكن لو روحنا للمصفوفات بيجينا مصفوفة نظام
+
+132
+00:15:29,430 --> 00:15:33,950
+2 × 2، 1 0 0 1، اللي المحدد
+
+133
+00:15:33,950 --> 00:15:37,270
+بتاعها بيساوي واحد. صحيح؟ إذاً هنا تحت تأثير العملية
+
+134
+00:15:37,270 --> 00:15:42,390
+بتعرف مين هو الـzero element ومين هو الـunity.
+
+135
+00:15:42,390 --> 00:15:47,970
+تمام؟ لأنه بيقول: هذه ring فيها الـzero، فيها الـ
+
+136
+00:15:47,970 --> 00:15:51,850
+unity. بتعرف مين هو الـring والـunity. طبعاً الـZ دي
+
+137
+00:15:51,850 --> 00:15:56,020
+فيها مجموعة الأعداد الصحيحة الموجبة والسالبة والصفر،
+
+138
+00:15:56,020 --> 00:16:01,500
+تمام؟ بدنا نروح ونعرف مين هو الـZero Element. أنا
+
+139
+00:16:01,500 --> 00:16:09,160
+أدعي إن الـZero Element هو الواحد الصحيح. أدعيها
+
+140
+00:16:09,160 --> 00:16:15,540
+قد يكون وقد لا يكون. أتأكد. يبقى هنا بقول: The
+
+141
+00:16:15,540 --> 00:16:35,670
+unity is the zero element. الـunity هو الـ
+
+142
+00:16:35,670 --> 00:16:40,190
+zero element. آه، الـunity هو الـzero element. ليش؟
+
+143
+00:16:40,190 --> 00:16:45,270
+because أول
+
+144
+00:16:45,270 --> 00:16:51,510
+شيء، ما هو شرط الـunity؟ إن لو ضربته في عنصر يطلع
+
+145
+00:16:51,510 --> 00:16:58,700
+نفس العنصر، صح ولا لأ؟ يبقى هنا because آه، قلنا
+
+146
+00:16:58,700 --> 00:17:08,080
+because if m موجود في الـzero then الـunity
+
+147
+00:17:08,080 --> 00:17:13,900
+هو الـzero. إذا بدي آخذ الـm مضروبة في مين؟ في
+
+148
+00:17:13,900 --> 00:17:22,390
+الـzero، ينطلع الناتج يساوي m، بيكون فعلاً هذا هو. هذا
+
+149
+00:17:22,390 --> 00:17:28,070
+هو إيش؟ الـunity. طيب، هذا الكلام طبق على العملية اللي
+
+150
+00:17:28,070 --> 00:17:35,370
+عندنا. بده يساوي m + zero - m * zero. هذا جمع عادي وهذا ضرب عادي. بيطلع يساوي m +
+
+151
+00:17:35,370 --> 00:17:43,470
+zero - zero = m. يبقى فعلاً الـzero هو الـ
+
+152
+00:17:43,470 --> 00:17:51,900
+unity. لأن لما ضربنا في m، طلع النتيجة يساوي m. وبنفس الطريقة، الـzero * m برضه بدي يساوي m.
+
+153
+00:17:51,900 --> 00:17:57,480
+Similarly، الـ
+
+154
+00:17:57,480 --> 00:18:03,200
+zero * m بده يساوي m. يبقى بالأقل الـzero
+
+155
+00:18:03,200 --> 00:18:10,500
+هو الـunity. طيب، ضايل علينا الـzero element. The
+
+156
+00:18:10,500 --> 00:18:17,640
+zero element is one. يا سلام! واحد هو الصفر
+
+157
+00:18:17,640 --> 00:18:23,620
+بتاع الـring هذه؟ آه، ليش؟ ما هو لّا؟ لأ، أنا
+
+158
+00:18:23,620 --> 00:18:35,000
+بقول واحد هو zero. ليش؟ لأن تحت عملية الجمع بأجي
+
+159
+00:18:35,000 --> 00:18:40,660
+بقول أي element في الـZ + zero بتاعها بدي
+
+160
+00:18:40,660 --> 00:18:46,760
+يعطيني نفس الـelement، صح؟ يبقى أنا بدعي إن الواحد
+
+161
+00:18:46,760 --> 00:18:52,360
+يبقى الـm + الواحد بدي يعطيني m. إن حدث ذلك
+
+162
+00:18:52,360 --> 00:18:57,240
+يبقى فعلاً واحد هو العنصر الصفري لـring، على عكس ما
+
+163
+00:18:57,240 --> 00:19:04,340
+هو متوقع في دماغك. إن الـzero هو الـzero، والواحد هو
+
+164
+00:19:04,340 --> 00:19:09,560
+الـunit. لا، لا، مش صحيح هذا الكلام. يبقى كل شغلة
+
+165
+00:19:09,560 --> 00:19:13,820
+مرتبطة بالـbinary operation اللي معرفة على الـ
+
+166
+00:19:13,820 --> 00:19:18,040
+ring. يبقى هنا الـzero element is one. السبب because
+
+167
+00:19:18,040 --> 00:19:22,300
+if m موجود في Z، موجود في Z، then الـm + 1 = m.
+
+168
+00:19:22,300 --> 00:19:30,140
+...  يبقى هنا الـzero element is one. السبب because
+
+169
+00:19:30,140 --> 00:19:43,480
+if m موجود في Z، موجود في Z، then m + 1
+
+170
+00:19:43,480 --> 00:19:50,440
+= m.
+
+171
+00:19:50,440 --> 00:19:57,980
+...
+
+172
+00:19:57,980 --> 00:20:05,500
+...
+
+173
+00:20:05,500 --> 00:20:08,360
+...
+
+174
+00:20:08,360 --> 00:20:09,260
+...
+
+175
+00:20:09,260 --> 00:20:18,520
+... طيب، إن شاء الله نيجي الآن لأول نظرية على هذا
+
+176
+00:20:18,520 --> 00:20:28,940
+الموضوع. Theorem: if
+
+177
+00:20:28,940 --> 00:20:37,060
+R is a ring and
+
+178
+
+223
+00:25:52,100 --> 00:25:57,440
+فيهتم بأخذ سالب العنصر الآخر كما لو ضربته في -1
+
+224
+00:25:57,440 --> 00:26:03,340
+وهذا سالب ما هو حاصل الضرب a فيه. بدي أروح أثبت
+
+225
+00:26:03,340 --> 00:26:07,940
+صحة هذا الكلام بنفس الفكرة الآن يا بنات. لو جيت
+
+226
+00:26:07,940 --> 00:26:16,300
+قلت لك سالب a في b زائد a في b زائد a في
+
+227
+00:26:16,300 --> 00:26:23,790
+b قد ايش بتساوي؟ Zero. ممتاز جداً. طيب لو قلت لك a
+
+228
+00:26:23,790 --> 00:26:32,710
+في سالب b، a في سالب b بيكون هالشكل هذا اللي هو
+
+229
+00:26:32,710 --> 00:26:39,570
+a اللي هي الأولى هذه بدي أحاول أشوفها مع مين؟
+
+230
+00:26:39,570 --> 00:26:49,450
+مع b.  كده ايش بتعطيني؟ تمام؟ يبقى سالب a في b زائد a
+
+231
+00:26:49,450 --> 00:26:55,410
+في b بده يساوي zero. بدي اخذ الآن a في سالب b زائد
+
+232
+00:26:55,410 --> 00:27:01,770
+ab. في عندنا من خلال الـ distributive law بقدر أكتب
+
+233
+00:27:01,770 --> 00:27:11,790
+هذه a في (سالب b + b). مظبوطة؟ صح؟ طيب سالب b
+
+234
+00:27:11,790 --> 00:27:18,340
+زائد b بيعطيني الـ zero element. يبقى هذه صارت a في Zero.
+
+235
+00:27:18,340 --> 00:27:24,880
+طب a في Zero بتساوي Zero. يبقى هذه صارت بـ Zero من
+
+236
+00:27:24,880 --> 00:27:31,300
+part one من الحالة الأولى. طب من الحالتين الاثنين
+
+237
+00:27:31,300 --> 00:27:37,120
+هذول مع بعض، ايش ما أقدر أستنتج؟ هذا يساوي Zero وهذا
+
+238
+00:27:37,120 --> 00:27:42,720
+يساوي Zero. إذا الطرفين بيساوي بعض، يبقى بناءً عليه
+
+239
+00:27:42,880 --> 00:27:51,280
+اللي هو ناقص ab زائد ab بدي أساوي a في ناقص
+
+240
+00:27:51,280 --> 00:27:59,980
+b زائد ab. لو أضفت سالب العنصر هذا للطرفين، يعني
+
+241
+00:27:59,980 --> 00:28:05,940
+المعكوس الجمعي لـ ab، يعني سالب ab للطرفين، ايش
+
+242
+00:28:05,940 --> 00:28:13,800
+بضل عندنا يا بنات هنا؟ بضل a في ناقص b يساوي صفر. يساوي
+
+243
+00:28:13,800 --> 00:28:23,760
+ناقص a في b. مظبوط ايه؟  as in هذه هي هذه. صح؟ بنفس
+
+244
+00:28:23,760 --> 00:28:30,500
+الطريقة. يبقى similarly بنفس
+
+245
+00:28:30,500 --> 00:28:35,500
+الطريقة، we have أن
+
+246
+00:28:35,500 --> 00:28:46,780
+هيكون ناقص a في b بدي أساوي ناقص ab وهكذا. رأس الـ a
+
+247
+00:28:46,780 --> 00:28:54,700
+ناقص b يساوي ناقص a في b يساوي ناقص a في b وهو
+
+248
+00:28:54,700 --> 00:28:59,180
+المطلوب. النقطة
+
+249
+00:28:59,180 --> 00:29:06,340
+الثالثة. النقطة الثالثة بيقول سالب a في سالب b
+
+250
+00:29:06,340 --> 00:29:12,320
+تساوي ab. يجب أن أمسك الطرف الأيسر، وأحاول أوصله
+
+251
+00:29:12,320 --> 00:29:22,540
+للطرف الأيمن. يبقى هذه ناقص a في ناقص b، ويساوي. بدي
+
+252
+00:29:22,540 --> 00:29:30,000
+أستخدم الخاصية رقم اثنين. هذا element وهذا ناقص b
+
+253
+00:29:30,000 --> 00:29:38,480
+يبقى هذا الكلام بده يساوي ناقص (ناقص a في b). صحيح من
+
+254
+00:29:38,480 --> 00:29:48,500
+وين؟ من الخاصية رقم اثنين. يبقى هذا from part two. يبقى
+
+255
+00:29:48,500 --> 00:29:54,040
+هذا من part two. هذا الكلام يساوي هذه الناقص اللي
+
+256
+00:29:54,040 --> 00:30:02,540
+بره، وهذه من part two كذلك. يساوي الناقص لناقص a في
+
+257
+00:30:02,540 --> 00:30:10,820
+b برضه من وين؟ from part two. نفس الشيء. هذا الكلام
+
+258
+00:30:10,820 --> 00:30:15,340
+ناقص في ناقص a في b يعطينا زائد. يبقى هذا بدي
+
+259
+00:30:15,340 --> 00:30:22,060
+يعطينا a في b مباشرة. إذا ناقص a في ناقص b بدي
+
+260
+00:30:22,060 --> 00:30:29,680
+بيساوي a في b. النقطة الرابعة. النقطة الرابعة بدي
+
+261
+00:30:29,680 --> 00:30:37,420
+أخذ a في (b ناقص c). احنا
+
+262
+00:30:37,420 --> 00:30:43,960
+أخذنا على الـ ring العملية هذه صحيحة. a في (b زائد الـ
+
+263
+00:30:43,960 --> 00:30:50,740
+c) يساوي ab زائد ac. صح؟ تمام، بس الطرح ما أخذناهاش،
+
+264
+00:30:50,740 --> 00:30:56,920
+مظبوط؟ بدنا نثبتها صحيحة لعملية طرح عنصرين من
+
+265
+00:30:56,920 --> 00:31:02,840
+بعضهم مع التوزيع، يعني قانون التوزيع مش مع
+
+266
+00:31:02,840 --> 00:31:07,860
+الجمع فقط، الطرح كذلك. بدي أثبت صحته. هذا الكلام
+
+267
+00:31:07,860 --> 00:31:16,320
+بقدر أكدّه: a في (b زائد ناقص c). حد بيقدر يقول إن
+
+268
+00:31:16,320 --> 00:31:21,140
+كلامك مش مظبوط هذا؟ مظبوط. لأني حطيت ناقص في ناقص
+
+269
+00:31:21,140 --> 00:31:31,120
+طيب. هذا الكلام يساوي ab زائد a في ناقص c. هذا
+
+270
+00:31:31,120 --> 00:31:35,040
+مينابع من قانون الـ distributive law. يدخل على
+
+271
+00:31:35,040 --> 00:31:42,300
+الجمع ويدخل على الطرح. لكن هذه من part two من
+
+272
+00:31:42,300 --> 00:31:49,240
+part two. هي مقبولة تماماً. يساوي ناقص حاصل الضرب تبعه.
+
+273
+00:31:49,240 --> 00:31:59,740
+يبقى هذه يساوي ab ناقص ac من part two. أظن
+
+274
+00:31:59,740 --> 00:32:05,210
+هو المطلوب. خلصنا. يبقى تنفع لعملية الجمع والعملية
+
+275
+00:32:05,210 --> 00:32:11,850
+الطرح اللي هو خاصية التوزيع. بنفس الطريقة، similar
+
+276
+00:32:11,850 --> 00:32:21,190
+للو. مين؟ b ناقص c في a بيساوي؟ بيساوي مين؟
+
+277
+00:32:21,190 --> 00:32:28,390
+بيساوي ba ناقص ca. خلصنا النقطة
+
+278
+00:32:28,390 --> 00:32:34,950
+الرابعة. لنروح للنقطة الخامسة. أول أربع نقاط ما لهمش
+
+279
+00:32:34,950 --> 00:32:39,190
+دعوة إن الـ ring فيها unity أو لا unity. ما بتكون تكون
+
+280
+00:32:39,190 --> 00:32:45,090
+الخامسة الأساسية بأننا نشترط وجود الـ unity، يعني الـ
+
+281
+00:32:45,090 --> 00:32:49,930
+identity element في الـ ring.  فبتقول الخاصية
+
+282
+00:32:49,930 --> 00:32:55,530
+الخامسة اللي هو ناقص واحد في a بالمناسبة أنه
+
+283
+00:32:55,530 --> 00:33:04,110
+يساوي ناقص a. بدي ارجع لاستخدام الخاصية رقم اثنين.
+
+284
+00:33:04,110 --> 00:33:12,190
+ناقص واحد في a، الـ unity هو عنصر. يبقى الـ unity هو
+
+285
+00:33:12,190 --> 00:33:18,330
+عنصر موجود في الـ group. a ناقص واحد. يعني الخاصية
+
+286
+00:33:18,330 --> 00:33:26,690
+هذه. يبقى هذه ايش بتساوي؟ ناقص واحد في a. يبقى هذه
+
+287
+00:33:26,690 --> 00:33:33,390
+من part two. مظبوط؟ طيب الـ unity لما أنا أضربه في
+
+288
+00:33:33,390 --> 00:33:41,110
+عنصر يطلع نفس العنصر. إذا يساوي ناقص a وهو المطلوب.
+
+289
+00:33:41,110 --> 00:33:48,450
+خلصنا منها. الآن رقم ستة اللي هو ناقص واحد في ناقص
+
+290
+00:33:48,450 --> 00:33:53,970
+واحد. بدي أثبت إنه يساوي مين؟ يساوي واحد. طلعيني ليه الـ
+
+291
+00:33:53,970 --> 00:34:00,840
+system اللي بدنا نثبتها. طلعيني ليه ثلاثة. بدي اخذ a
+
+292
+00:34:00,840 --> 00:34:09,660
+تساوي b تساوي واحد. يبقى باجي بقول هذه تساوي واحد
+
+293
+00:34:09,660 --> 00:34:23,000
+from part three with a تساوي b تساوي واحد. وهو
+
+294
+00:34:23,000 --> 00:34:26,680
+المطلوب. طيب
+
+295
+00:34:27,510 --> 00:34:35,390
+بنجي لنظرية ثانية بدون اثباتها. ايش النظرية الثانية؟
+
+296
+00:34:35,390 --> 00:34:40,270
+فاكرين الـ group؟ وبجينا نجيب الـ identity element
+
+297
+00:34:40,270 --> 00:34:47,530
+صح؟ ومعكوس الـ element. طيب الـ unity هذا أو الـ
+
+298
+00:34:47,530 --> 00:34:51,110
+identity element في هالـ group أكثر من identity
+
+299
+00:34:51,110 --> 00:34:58,140
+element؟ وحيد. ما فيش... وهنا الـ ring وحيد. طيب معكوس
+
+300
+00:34:58,140 --> 00:35:05,280
+العنصر، وحيد. إذا كنا بنثبتهم في الجبر واحد،
+
+301
+00:35:05,280 --> 00:35:10,660
+بجينا بنثبت إن عندي two identity elements وبنحاول
+
+302
+00:35:10,660 --> 00:35:15,400
+نثبت إن الاثنين are equal. عندي two inverses وبنحاول
+
+303
+00:35:15,400 --> 00:35:20,260
+نثبت إن الاثنين are equal. وفعلاً أثبتنا هذا مع
+
+304
+00:35:20,260 --> 00:35:24,670
+الدكتور محمد. مظبوط. يبقى لا داعي لإعادة الإثبات
+
+305
+00:35:24,670 --> 00:35:28,890
+تماماً. من الأذكى ترجع إليه من دفترك أو من اللي أكثر
+
+306
+00:35:28,890 --> 00:35:39,130
+دقة. يبقى نظرية بتقول ما يأتي:  يا ربي. if
+
+307
+00:35:39,130 --> 00:35:48,310
+R is a ring with unity. if R is a ring with
+
+308
+00:35:48,310 --> 00:35:50,170
+unity
+
+309
+00:35:57,550 --> 00:36:06,990
+then the unity. then the unity is
+
+310
+00:36:06,990 --> 00:36:16,310
+unique. يكون وحيداً. هذه النقطة الأولى. النقطة الثانية:
+
+311
+00:36:16,310 --> 00:36:32,860
+if a. if. if they belong to a ring A الموجود في R
+
+312
+00:36:32,860 --> 00:36:40,720
+with multiplicative
+
+313
+00:36:40,720 --> 00:36:50,640
+inverse. with
+
+314
+00:36:50,640 --> 00:36:53,700
+multiplicative inverse
+
+315
+00:36:58,510 --> 00:37:03,950
+ثم هذا  يُنبسط
+
+316
+00:37:27,390 --> 00:37:35,050
+مرة ثانية بقول هذه if
+
+317
+00:37:35,050 --> 00:37:41,530
+R is a ring with unity, then the unity is unity
+
+318
+00:37:41,530 --> 00:37:47,730
+ما عنديش في الـ ring إلا unity وحيد فقط. لغى بعد هيك.
+
+319
+00:37:47,730 --> 00:37:52,670
+لو كان الـ a اللي موجود في الـ ring R إله معكوس، يعني
+
+320
+00:37:52,670 --> 00:37:57,890
+ايش سميناه؟ ايش سمينا هذا المضارب؟ unit. يبقى لو كان
+
+321
+00:37:57,890 --> 00:38:02,530
+unit يعني له معكوس، يبقى الـ unit هذا يكون وحيداً.
+
+322
+00:38:02,530 --> 00:38:07,690
+فالمعكوس الضربي multiplicative inverse له بيكون وحيداً.
+
+323
+00:38:07,690 --> 00:38:12,710
+ما فيهش غيره. البرهان نفس البرهان تبع الـ groups
+
+324
+00:38:12,710 --> 00:38:18,290
+بالضبط تماماً. لا زيادة ولا نقصان. يبقى لا داعي لتضيع
+
+325
+00:38:18,290 --> 00:38:23,650
+الوقت فيه. في عندنا ملاحظات هنا. يبقى lots
+
+326
+00:38:26,690 --> 00:38:36,790
+ملاحظة الأولى: if a و b و c موجودة في ring
+
+327
+00:38:36,790 --> 00:38:44,910
+R، وR is a ring and
+
+328
+00:38:44,910 --> 00:38:56,590
+a لا يساوي zero، then ab يساوي ac
+
+329
+00:38:56,590 --> 00:39:08,890
+does not imply أن b تساوي c. because... ايش السبب؟
+
+330
+00:39:38,990 --> 00:39:43,070
+مرة ثانية بقول لكم: لو عندي ثلاث عناصر وموجودة في
+
+331
+00:39:43,070 --> 00:39:48,130
+الـ ring R وكان الـ a لا يساوي زيرو وعندي معلومة
+
+332
+00:39:48,130 --> 00:39:54,050
+بتقول أن حاصل ضرب a في b بيساوي a في c. فهل هذا
+
+333
+00:39:54,050 --> 00:40:00,790
+يتطلب أن b تساوي c؟ الإجابة: قد يكون وقد لا يكون.
+
+334
+00:40:00,790 --> 00:40:08,520
+يبقى in general لا يكون. ليش؟ ليش؟ هل أنا قلت إنه
+
+335
+00:40:08,520 --> 00:40:14,580
+لأن a is a unit؟ لا. ما قلتش a is unit. ممكن
+
+336
+00:40:14,580 --> 00:40:20,180
+يكون أي رقم ولا يوجد له معكوس، يعني أي عنصر وهذا
+
+337
+00:40:20,180 --> 00:40:25,660
+العنصر ليس له معكوس. إذا لا يمكن من ab يساوي ac
+
+338
+00:40:25,660 --> 00:40:32,220
+أستنتج أن b تساوي c لأن a ممكن يكون
+
+339
+00:40:32,220 --> 00:40:42,050
+unit وممكن ما يكونش unit because... الإيه؟ may or may
+
+340
+00:40:42,050 --> 00:40:50,910
+not unit. يعني ممكن يكون له معكوس وممكن ما يكونش
+
+341
+00:40:50,910 --> 00:40:55,770
+له معكوس. لو إله معكوس، بضربه في المعادلة من جهة
+
+342
+00:40:55,770 --> 00:41:00,990
+اليسار. بظل b يساوي c. طب لو ما إلهوش معكوس؟ مش
+
+343
+00:41:00,990 --> 00:41:07,130
+ممكنية زي مين؟ زي اثنين وثلاثة في الـ Z6. اثنين
+
+344
+00:41:07,130 --> 00:41:13,010
+وثلاثة، اثنين في ثلاثة بستة، يعني قد ايش؟ Zero. صح
+
+345
+00:41:13,010 --> 00:41:18,450
+ولا لا؟ يبقى هل اثنين والثلاثة لهم معكوس؟ ولا
+
+346
+00:41:18,450 --> 00:41:23,130
+واحد منهم له معكوس؟ تمام؟ يبقى في هذه الحالة،
+
+347
+00:41:23,130 --> 00:41:28,350
+مدام ما إلهوش معكوس، ما أقدرش أقول إن a في b بده يساوي
+
+348
+00:41:28,350 --> 00:41:33,650
+a في c، يبقى b تساوي c. الأمر الثاني أو الملاحظة
+
+349
+00:41:33,650 --> 00:41:44,910
+الثانية: if a belongs to ring R where. و من
+
+350
+00:41:44,910 --> 00:41:57,370
+a تربيع بده يساوي a، we cannot say that لا
+
+351
+00:41:57,370 --> 00:42:02,780
+يمكن أو لا نستطيع أن نقول you cannot say that أن
+
+352
+00:42:02,780 --> 00:42:21,560
+a تساوي zero أو a تساوي واحد because... طيب
+
+353
+00:42:21,560 --> 00:42:27,380
+قبل ما نقول because في النهاية الشركة أنا بدي أفكر
+
+354
+00:42:27,870 --> 00:42:35,570
+بقول a تربيع تساوي a. أظن أن إذا قلت a تربيع ناقص
+
+355
+00:42:35,570 --> 00:42:41,370
+يساوي صفر، محدش بيعترض عليه. جت الـ distributive law.
+
+356
+00:42:41,370 --> 00:42:48,190
+قلت بقدر أقول a في (a ناقص واحد) يساوي صفر. هنا بتطوّروا
+
+357
+00:42:48,190 --> 00:42:54,950
+عليه، تقولوا اللي هو الـ ring هذه فيها unity. ما قلناش
+
+358
+00:42:54,950 --> 00:42:59,210
+فيها unity. يبقى هذه الخطوة اللي عملتها صح ولا غلط؟
+
+359
+00:42:59,210 --> 00:43:03,010
+صح إذا كان الـ ring فيها unity. غلط إذا الـ ring
+
+360
+00:43:03,010 --> 00:43:06,210
+ما فيهاش unity. يبقى هذا الكلام، بعيداً عن الله، حطه ع جنب.
+
+361
+00:43:06,210 --> 00:43:12,610
+مش صحيح. إذا لو كان هذا الكلام صحيح، بقوله: ممكن a
+
+362
+00:43:12,610 --> 00:43:18,150
+يساوي zero أو a تساوي واحد. لكن الواحد هذا مش
+
+363
+00:43:18,150 --> 00:43:22,810
+موجود في الـ ring. بيصير هذا الكلام ماله؟ غلط على طول.
+
+364
+00:43:22,810 --> 00:43:27,600
+النتيجة. يبقى هذا الكلام ايش؟ يساوي zero أو a يساوي
+
+365
+00:43:27,600 --> 00:43:35,340
+غلط. يبقى we say that أن
+
+366
+00:43:35,340 --> 00:43:40,760
+a تساوي zero أو a تساوي واحد. أنا ما بعرف ايش
+
+367
+00:43:40,760 --> 00:43:46,240
+قلنا with a. تلاقى we cannot say ايش؟  خليناها. بدأنا
+
+368
+00:43:46,240 --> 00:43:50,920
+نعملها. we cannot say. ما نقدرش نقول أن a تساوي zero أو
+
+369
+00:43:50,920 --> 00:44:04,070
+a تساوي واحد because they may or may not have
+
+370
+00:44:04,070 --> 00:44:10,830
+unity. يعني ممكن أن تكون فيها unity ويطلع الكلام
+
+371
+00:44:10,830 --> 00:44:14,550
+واضح، وممكن ما يكونش فيها unity. هنا ما شترطناش أن
+
+372
+00:44:14,550 --> 00:44:21,410
+يكون فيها unity. يبقى هذا الكلام ليس بالضرورة صحيح.
+
+373
+00:44:21,980 --> 00:44:26,900
+نجي لتعريف جديد. زي ما أخذنا في group بعد ما أخذنا
+
+374
+00:44:26,900 --> 00:44:30,640
+الـ subgroup، واحنا أخذنا ring بدنا نروح ناخذ sub
+
+375
+00:44:30,640 --> 00:44:36,660
+ring. يبقى definition هي
+
+376
+00:44:36,660 --> 00:44:47,740
+subset. هي subset S of a ring R is
+
+377
+00:44:55,900 --> 00:45:04,080
+is a subring of a ring R is
+
+378
+00:45:04,080 --> 00:45:16,440
+a subring
+
+379
+00:45:16,440 --> 00:45:21,280
+if S itself
+
+380
+00:45:25,230 --> 00:45:45,870
+is a ring under the operations on R. فده
+
+381
+00:45:45,870 --> 00:45:51,430
+نسميها
+
+382
+00:45:51,430 --> 00:45:58,490
+subring test. a
+
+383
+00:45:58,490 --> 00:46:02,450
+non-empty
+
+384
+00:46:02,450 --> 00:46:21,190
+a non-empty subset S of a ring R is a subring if
+
+385
+00:46:39,370 --> 00:46:40,770
+التعريف يقول
+
+386
+00:46:53,400 --> 00:46:57,840
+التعريف بيقول أن الـ subset S of a ring R بسميه sub
+
+387
+00:46:57,840 --> 00:47:04,560
+ring ما إذا كانت S نفسها بتظل ring تحت نفس
+
+388
+00:47:04,560 --> 00:47:09,860
+العمليات اللي على R. يعني إحنا عندنا ring كبيرة،
+
+389
+00:47:09,860 --> 00:47:14,600
+أخذنا منها شوية عناصر، تمام؟ العناصر هذه اللي جت الـ
+
+390
+00:47:14,600 --> 00:47:18,780
+ست خواص طبعتها الـ ring تنطبق عليها، إن حدث ذلك
+
+391
+00:47:18,780 --> 00:47:23,990
+بقول هذه sub ring. يعني بدي أثبت الست خواص. طيب يا
+
+392
+00:47
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1e6f7fc1d1a6d07f24959c9cabf7c40d85f89b1f
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU_postprocess.srt
@@ -0,0 +1,1604 @@
+1
+00:00:21,480 --> 00:00:26,340
+بسم الله الرحمن الرحيم المرة الماضية احنا ابتدأنا
+
+2
+00:00:26,340 --> 00:00:31,820
+في introduction to ring عرفنا ال ring أخدنا عليها
+
+3
+00:00:31,820 --> 00:00:36,940
+مجموعة من الأمثلة واليوم ان شاء الله بنكمل الأمثلة
+
+4
+00:00:36,940 --> 00:00:42,180
+بالاضافة إلى بعض النظريات على اللي هو ال rings
+
+5
+00:00:42,180 --> 00:00:45,820
+أخدنا المرة الفاترة أربعة أمثلة وهذا هو المثال
+
+6
+00:00:45,820 --> 00:00:49,300
+الخامس بيقول the set of all continuously valued
+
+7
+00:00:49,300 --> 00:00:53,730
+functionsof a real value because who the grass
+
+8
+00:00:53,730 --> 00:00:58,030
+passes through the point one وزيره يبقى احنا عندنا
+
+9
+00:00:58,030 --> 00:01:04,070
+مجموعة من الدوال الحقيقية اللي الرسم البياني اليها
+
+10
+00:01:04,070 --> 00:01:10,110
+يمر بالنقطة واحد وزيره يعني لو أخدنا محاول احداثية
+
+11
+00:01:10,110 --> 00:01:15,470
+وقلنا هذا محور X و هذا محور Y النقطة هذه اللي هي
+
+12
+00:01:15,470 --> 00:01:21,880
+النقطة واحد وزيره كل الدوالفي متغير واحد وهذا
+
+13
+00:01:21,880 --> 00:01:28,760
+المتغير متغير حقيقي التي تمر بهذه النقطة.الان احنا
+
+14
+00:01:28,760 --> 00:01:35,000
+بنقول ان هذه commutative ring without unity.المرة
+
+15
+00:01:35,000 --> 00:01:38,520
+اللي فات اللامتلة قدامي كلها rings with unity.طبعا
+
+16
+00:01:38,520 --> 00:01:43,760
+الان انا هدعي ان هذا ring مافيهاش unity.شو العملية
+
+17
+00:01:43,760 --> 00:01:48,300
+اللي عليها عملية الجامعة f زائد g of a يساوي f of
+
+18
+00:01:48,300 --> 00:01:54,700
+a زائد g of a والف في g of a يساوي f of a في g of
+
+19
+00:01:54,700 --> 00:02:00,360
+a الآن لو جيت أقولك الدلة f of x ساوي واحد هذه هي
+
+20
+00:02:00,360 --> 00:02:05,040
+constant function والواحد لو ضربناه في أي دلة بدي
+
+21
+00:02:05,040 --> 00:02:10,840
+يعطيني نفس الدلة لكن السؤال هذه ليش ال unity؟مش
+
+22
+00:02:10,840 --> 00:02:16,880
+موجود في هذه الـ Ring الإجابة بسيطة جدا ان منحنى
+
+23
+00:02:16,880 --> 00:02:24,620
+الدالة F of X يساوي 1 هو خط مستقيم يوازي يوازي
+
+24
+00:02:24,620 --> 00:02:30,740
+مين؟ يوازي محور X إذا لا يمكن أن يمر بالنقطة 1 و 0
+
+25
+00:02:30,740 --> 00:02:37,280
+إذا لو ليترسمت الخط اللي عندنا هذا أفضي هيك بهذا
+
+26
+00:02:37,280 --> 00:02:42,900
+الشكليبقى هذا الخط اللي هو main اللي هو f of x
+
+27
+00:02:42,900 --> 00:02:48,300
+يساوي واحد لايمكن ان يمر بهذه النقطة وبالتالي هذه
+
+28
+00:02:48,300 --> 00:02:53,480
+الدالة مش موجودة في مجموعة هذه الدوال وبالتالي هذه
+
+29
+00:02:53,480 --> 00:02:59,680
+ring with unity طب ليش commutative؟ لأنه لو أخدنا
+
+30
+00:02:59,680 --> 00:03:05,100
+قيمتين للدالة f of a وf of b فكل واحدة منهم عبارة
+
+31
+00:03:05,100 --> 00:03:09,340
+عن قدد حقيقيو احنا بنعرف ان حاصل ضرب الاعداد
+
+32
+00:03:09,340 --> 00:03:15,840
+الحقيقية is commutative يبقى هنا بقول ال R is
+
+33
+00:03:15,840 --> 00:03:25,480
+commutative او the ring is commutative
+
+34
+00:03:25,480 --> 00:03:28,660
+commutative
+
+35
+00:03:28,660 --> 00:03:33,280
+because ال
+
+36
+00:03:33,280 --> 00:03:46,370
+F of Aand f of b are real numbers نظرا لأنهم أعداد
+
+37
+00:03:46,370 --> 00:03:50,670
+حقيقية فهي composite فهي community يعني f of a في
+
+38
+00:03:50,670 --> 00:03:56,010
+f of b هي f of b في main في f of a وبالتالي مافيها
+
+39
+00:03:56,010 --> 00:04:01,530
+مشكلة خالص طيب بدنا نروح الآن على ring غير هذه ال
+
+40
+00:04:01,530 --> 00:04:12,540
+rings وهو مثال رقم 6مثال رقم ستة بيقول لل R1 وR2 و
+
+41
+00:04:12,540 --> 00:04:24,200
+لغاية ال RN بي رينز بي رينز هذه عبارة عن حلقات we
+
+42
+00:04:24,200 --> 00:04:25,500
+shall construct
+
+43
+00:04:33,610 --> 00:04:44,590
+we shall construct a new ring a a new ring بدنا
+
+44
+00:04:44,590 --> 00:04:52,350
+نكوّن من هذه ال rings رينج جديدة as follow كالتالي
+
+45
+00:04:52,350 --> 00:05:02,010
+كيف نجم نقول بدي أخد ال R واحد direct sum مع R
+
+46
+00:05:02,010 --> 00:05:12,340
+اتنينdirect sum direct sum مع R N تمام من علاصر
+
+47
+00:05:12,340 --> 00:05:22,060
+هذه كل العلاصر على الشكل A1 و A2 و A N بحيث ال AI
+
+48
+00:05:22,060 --> 00:05:31,300
+موجودة في ال R I بالشكل اللي عندنا هذا and peer
+
+49
+00:05:31,300 --> 00:05:40,780
+formوبنكون pair for and
+
+50
+00:05:40,780 --> 00:05:48,160
+pair for addition and
+
+51
+00:05:48,160 --> 00:05:58,840
+multiplication الجمع
+
+52
+00:05:58,840 --> 00:06:15,510
+وعملية الدرب component wisefrom Poland Y that
+
+53
+00:06:15,510 --> 00:06:23,310
+is that is
+
+54
+00:06:23,310 --> 00:06:44,290
+A1 و A2 و AN زائد B1و B2 و DN مدرسة A1 زي B1 A2 زي
+
+55
+00:06:44,290 --> 00:07:02,390
+B2 و AN زي BN ال A1 و ال A2 و ال AN مضروبة في B1و
+
+56
+00:07:02,390 --> 00:07:14,730
+B2 و BN بدي سامع A1 B1 A2
+
+57
+00:07:14,730 --> 00:07:33,700
+B2 و AN BN this ring this ring is calledthe direct
+
+58
+00:07:33,700 --> 00:07:43,720
+sum of
+
+59
+00:07:43,720 --> 00:07:51,200
+R1 وR2 وRN
+
+60
+00:08:18,300 --> 00:08:24,500
+المثال هذا يعني ان عندي مجموعة من ال rings ر واحد
+
+61
+00:08:24,500 --> 00:08:29,900
+و ر اتنين و ر ثلاثة و لغاية ر ان من ال rings هذه
+
+62
+00:08:29,900 --> 00:08:35,160
+بدي اكوّل ring جديدة تمام ال ring الجديدة هذي شو
+
+63
+00:08:35,160 --> 00:08:42,040
+شكلها يبقى روحت ر واحد رتو رتو رتو رتو رتو رتو رتو
+
+64
+00:08:42,040 --> 00:08:44,760
+رتو رتو رتو رتو رتو رتو رتو رتو رتو رتو رتو رتو
+
+65
+00:08:44,760 --> 00:08:47,270
+رتو رتو رتو رتو رتو رتو رتو رتوthe set of all
+
+66
+00:08:47,270 --> 00:08:51,330
+innituples هذه كنت في جبر حديث واحد اسمها
+
+67
+00:08:51,330 --> 00:08:57,170
+innituple يعني جوس مركب من ان من المركبات الجوس
+
+68
+00:08:57,170 --> 00:09:02,050
+كله يعتبر عنصر واحد العنصر واحد عبارة عن مجموعة من
+
+69
+00:09:02,050 --> 00:09:09,510
+المركبات تمام؟ بنسميها innituple يعني جوس في ان من
+
+70
+00:09:09,510 --> 00:09:16,270
+العناصر تمام؟بحيث ال AI موجود في RI شو يعني؟ يعني
+
+71
+00:09:16,270 --> 00:09:23,390
+لو حطيت ال I بواحد بصير A1 موجود في R1 و A2 موجود
+
+72
+00:09:23,390 --> 00:09:29,590
+في R2 و A3 في R3 و AN موجود في RN يعني من كل ring
+
+73
+00:09:29,590 --> 00:09:36,270
+باخد عنصر واحد فقط مجموعة العناصر هذه كونت لي عنصر
+
+74
+00:09:36,270 --> 00:09:43,230
+واحد فقط في ال ring الجديدةطيب عرفت عليها عملية
+
+75
+00:09:43,230 --> 00:09:49,310
+العملية سميت component wise يعني إذا جمع بلج مع كل
+
+76
+00:09:49,310 --> 00:09:56,790
+عنصر مع نظيره تمام اضرب بضرب كل عنصر في نظيري هذا
+
+77
+00:09:56,790 --> 00:10:02,630
+معنى ال addition and multiplication component wise
+
+78
+00:10:02,630 --> 00:10:08,310
+يعني كل عنصر مع نظيره رياضيابقول هذا كل ال element
+
+79
+00:10:08,310 --> 00:10:13,330
+الأول وهذا ال element التاني بدي أجمعهم إذا بجمع
+
+80
+00:10:13,330 --> 00:10:19,590
+كل عنصر مع نظيره يبقى a1 زائد b1 يمثل المراكبة
+
+81
+00:10:19,590 --> 00:10:26,170
+الأولى a2 زائد b2 يمثل المراكبة التانية an زائد bn
+
+82
+00:10:26,170 --> 00:10:31,670
+يمثل المراكبة النونية هذا الجمعالضرب كذلك
+
+83
+00:10:31,670 --> 00:10:36,850
+component wise بضرب كل عنصر مع نظيره من القوس
+
+84
+00:10:36,850 --> 00:10:41,610
+الثاني فبالي بقول هذا الجوس الأول ضرب الجوس الثاني
+
+85
+00:10:41,610 --> 00:10:50,750
+يبقى a1 b1 العنصر التاني a2 b2 a3 b3 am bm يبقى من
+
+86
+00:10:50,750 --> 00:10:57,310
+حاصر ضرب المركبات المتنظرة بطلع عندي جوس جديدهذا
+
+87
+00:10:57,310 --> 00:11:00,890
+ال course جديد موجود في ال R1 direct sum مع R2
+
+88
+00:11:00,890 --> 00:11:06,190
+direct sum مع R2 direct sum مع R2
+
+89
+00:11:06,190 --> 00:11:09,910
+direct sum
+
+90
+00:11:09,910 --> 00:11:11,790
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+91
+00:11:11,790 --> 00:11:12,110
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+92
+00:11:12,110 --> 00:11:12,570
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+93
+00:11:12,570 --> 00:11:12,610
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+94
+00:11:12,610 --> 00:11:19,690
+مع R2 direct sum مع R2
+
+95
+00:11:19,690 --> 00:11:21,010
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+96
+00:11:21,010 --> 00:11:21,170
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+97
+00:11:21,170 --> 00:11:22,510
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+98
+00:11:22,510 --> 00:11:22,550
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+99
+00:11:22,550 --> 00:11:22,670
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+100
+00:11:22,670 --> 00:11:27,370
+direct sum مع R2يبقى هذه وبتاش بيكون فيها unity
+
+101
+00:11:27,370 --> 00:11:33,110
+إذا كان كل ring من ال rings الأصلية فيها ال unity
+
+102
+00:11:33,110 --> 00:11:39,230
+يبقى ال unity تبع هذه ال ring هو ال N تيوبل
+
+103
+00:11:39,230 --> 00:11:45,810
+المكوّلة من ال unity تبع كل ring تمام؟ يبقى ال
+
+104
+00:11:45,810 --> 00:11:51,650
+identity element أو ال unity تبع هذه ال ring اللي
+
+105
+00:11:51,650 --> 00:11:56,880
+تبعت ال direct sunالعناصر انصر الوحدة فيها هو
+
+106
+00:11:56,880 --> 00:12:02,400
+المكون من العناصر الوحدة في كل من الرنج المختلفة
+
+107
+00:12:02,400 --> 00:12:08,700
+تمام؟ هذا موضوع السؤال في الكتاب ال R واحد وال R
+
+108
+00:12:08,700 --> 00:12:15,120
+اتنين وال R N has a unity if and only if ال direct
+
+109
+00:12:15,120 --> 00:12:20,560
+sum has a unity يعني بنثبت البرهان في اتجاهين أحد
+
+110
+00:12:20,560 --> 00:12:27,750
+أسئلة التمرينطيب تمام نعطي كمان مثال أخير اللي هو
+
+111
+00:12:27,750 --> 00:12:35,070
+مثال رقم 7 مثال رقم 7 بيقول consider the ring
+
+112
+00:12:35,070 --> 00:12:44,150
+consider the ring اللي هي z مجموعة الأعداد الصحيحة
+
+113
+00:12:44,150 --> 00:12:50,050
+عليها عملية الضرب و عليها عملية الجمع زي ما انت
+
+114
+00:12:50,050 --> 00:12:58,780
+شايفين withtwo binary operations
+
+115
+00:12:58,780 --> 00:13:08,480
+two binary operations defined by defined by
+
+116
+00:13:08,480 --> 00:13:20,940
+المعرفة كالتالي ال a زائد او ال m زائد ال nالـ M
+
+117
+00:13:20,940 --> 00:13:29,580
+زائد ال N يساوي ال M زائد ال N ناقص واحد and ال M
+
+118
+00:13:29,580 --> 00:13:41,820
+بطل N يساوي ال M زائد ال N ناقص M في N لكل ال M و
+
+119
+00:13:41,820 --> 00:13:49,760
+ال N اللي موجودة في Z find the
+
+120
+00:13:50,430 --> 00:14:01,170
+زيرو بزيرو الوضع ومجموعة
+
+121
+00:14:01,170 --> 00:14:05,370
+الرمز ومجموعة
+
+122
+00:14:05,370 --> 00:14:08,950
+هذا الرمز
+
+123
+00:14:27,370 --> 00:14:33,050
+سؤال مرة تانية قال خلّي مجموعة الأعداد الصحيحة و
+
+124
+00:14:33,050 --> 00:14:39,490
+بنعرف عليها عمليتين ثنائيتين العملية الأولى هي M
+
+125
+00:14:39,490 --> 00:14:46,150
+زائد ال N يساوي M زائد N ناقص واحد العملية هذه
+
+126
+00:14:46,150 --> 00:14:51,670
+زائد و عليها دائرة ليست عملية الجمع العادية ولكن
+
+127
+00:14:51,670 --> 00:14:57,770
+عمليا هي عملية الجمع العادية مطروح منها واحدعملية
+
+128
+00:14:57,770 --> 00:15:03,190
+الضرب مش عملية الضرب عادية وانما هي M زائد ال N
+
+129
+00:15:03,190 --> 00:15:09,990
+ناقص عملية الضرب العادية لل M في N يبقى هاي صارت
+
+130
+00:15:09,990 --> 00:15:14,830
+two binary operations يبقى كل binary operation
+
+131
+00:15:14,830 --> 00:15:20,110
+بصير علها identity element و zero element يختلف عن
+
+132
+00:15:20,110 --> 00:15:26,190
+مين يختلف عن الداني زي مثلك في المصوفة في الفي ال
+
+133
+00:15:26,190 --> 00:15:29,430
+.. في ال ranks العادية بيجينا نقول ال unity واحد
+
+134
+00:15:29,430 --> 00:15:33,950
+تمام؟ لكن لو روحنا للمصففات بيجيناها مصففة نظام
+
+135
+00:15:33,950 --> 00:15:37,270
+اتنين في اتنين واحد zero zero واحد اللي المحدد
+
+136
+00:15:37,270 --> 00:15:42,390
+تبعها متوسط واحد صحيح اذا هنا تحت تأثير العملية
+
+137
+00:15:42,390 --> 00:15:47,970
+بتعرف مين هو ال zero element ومين هو من ال unity
+
+138
+00:15:47,970 --> 00:15:51,850
+تمام؟ لإنه بيقول هذه ring فيها ال zero فيها ال
+
+139
+00:15:51,850 --> 00:15:56,020
+unity بتعرف مين هو ال ring و ال unityطبعا الـ Z دي
+
+140
+00:15:56,020 --> 00:16:01,500
+في مجموعة العداد الصحيحة الموجبة والسالبة والصفر
+
+141
+00:16:01,500 --> 00:16:09,160
+تمام؟ بدنا نروح و نعرف مين هو الـ Zero Element أنا
+
+142
+00:16:09,160 --> 00:16:15,540
+أدعي أن الـ Zero Element هو الواحد الصحيح أدعيها
+
+143
+00:16:15,540 --> 00:16:21,720
+قد يكون و قد لا يكون أتأكد يبقى هنا بقولهم The
+
+144
+00:16:21,720 --> 00:16:35,670
+unityas unity is the zero element ال unity هو ال
+
+145
+00:16:35,670 --> 00:16:40,190
+zero element اه ال unity هو ال zero element ليش؟
+
+146
+00:16:40,190 --> 00:16:45,270
+because اول
+
+147
+00:16:45,270 --> 00:16:51,510
+شيء ما هو شرط ال unity ان لو ضربته في عنصر يطلع
+
+148
+00:16:51,510 --> 00:16:58,700
+نفس عنصر صح ولا لا؟يبقى هنا because اه قلنا
+
+149
+00:16:58,700 --> 00:17:08,080
+because if ال M موجودة في ال zero then ال unity
+
+150
+00:17:08,080 --> 00:17:13,900
+good هو ال zero اذا بدي اخد ال M مضروبة في من؟ في
+
+151
+00:17:13,900 --> 00:17:22,390
+ال zero انطلع الناتج يساوي M بيكون فعلا هذا هوهذا
+
+152
+00:17:22,390 --> 00:17:28,070
+هو إيش ال unity طيب هذا الكلام طبق للعملية اللي
+
+153
+00:17:28,070 --> 00:17:35,370
+عندنا بده يساوي ال M زائد ال zero ناقص ال M في ال
+
+154
+00:17:35,370 --> 00:17:43,470
+zero هذا جمع عادي و هذا ضرب عادي يفجأ يساوي M زائد
+
+155
+00:17:43,470 --> 00:17:51,900
+Zero ناقص ال Zero و يساوي Mيبقى فعلا ال zero هو ال
+
+156
+00:17:51,900 --> 00:17:57,480
+unity لأن لما ضربنا في M طلع النتيجة يساوي 100 M
+
+157
+00:17:57,480 --> 00:18:03,200
+وبنفس الطريقة ال zero ضرب ال M برضه بدي يساوي 100
+
+158
+00:18:03,200 --> 00:18:10,500
+M Similarly ال
+
+159
+00:18:10,500 --> 00:18:17,640
+zero ضرب ال M بدي يساوي Mيبقى بالأقل عليه الـ zero
+
+160
+00:18:17,640 --> 00:18:23,620
+هو ال unity طيب ضايل علينا ال zero element the
+
+161
+00:18:23,620 --> 00:18:35,000
+zero element is one يا سلام عجوز؟ واحد هو الصفر
+
+162
+00:18:35,000 --> 00:18:40,660
+تبع ال ring هذه؟ اه ليش مليش ما هوش لا؟ لا لأ انا
+
+163
+00:18:40,660 --> 00:18:46,760
+قاعد واحد هو zero ليش؟لأن تحت عملية الجامعة باجي
+
+164
+00:18:46,760 --> 00:18:52,360
+بقول أي element في ال Z زائد ال zero تبعها بدي
+
+165
+00:18:52,360 --> 00:18:57,240
+يعطيني نفس ال element صح؟ يبقى أنا بدعي ان الواحد
+
+166
+00:18:57,240 --> 00:19:04,340
+يبقى ال M زائد الواحد بدي يعطيني جداش M ان حدث ذلك
+
+167
+00:19:04,340 --> 00:19:09,560
+يبقى فعلا واحد هو العنصر الصفري ل ring على عكس ما
+
+168
+00:19:09,560 --> 00:19:13,820
+هو مطوع في دماغكإن ال zero هو ال zero والواحد هو
+
+169
+00:19:13,820 --> 00:19:18,040
+ال unit لا لا مش صحيح هذا الخلاب يبقى كل شغلة
+
+170
+00:19:18,040 --> 00:19:22,300
+مرتبطة بال binary operation اللي مخطوطة على ال
+
+171
+00:19:22,300 --> 00:19:30,140
+ring يبقى هنا ال zero element is one السبب because
+
+172
+00:19:30,140 --> 00:19:43,480
+if M موجودة في Z موجودة في Z then ال Mزائد الواحد
+
+173
+00:19:43,480 --> 00:19:50,440
+زائد
+
+174
+00:19:50,440 --> 00:19:57,980
+الواحد زائد الواحد زائد الواحد زائد الواحد زائد
+
+175
+00:19:57,980 --> 00:20:05,500
+الواحد زائد الواحد زائد الواحد زائد الواحد زائد
+
+176
+00:20:05,500 --> 00:20:08,360
+الواحد زائد الواحد زائد الواحد زائد الواحد زائد
+
+177
+00:20:08,360 --> 00:20:09,260
+الواحد زائد الواحد زائد الواحد زائد الواحد زائد
+
+178
+00:20:09,260 --> 00:20:18,520
+الواحدطيب اننا نيجي الأن لأول نظرية على هذا
+
+179
+00:20:18,520 --> 00:20:28,940
+الموضوع theorem if
+
+180
+00:20:28,940 --> 00:20:37,060
+R is a ring and
+
+181
+00:20:46,600 --> 00:20:57,640
+ثم نمر واحد ال a في ال zero ساوي zero دي ساوي zero
+
+182
+00:20:57,640 --> 00:21:07,060
+في a دي ساوي zero نمر اتنين ال a ناقص b ساوي ناقص
+
+183
+00:21:07,060 --> 00:21:18,220
+a في ال b ساوي ناقص a في bنقطة التالتة ناقص a في
+
+184
+00:21:18,220 --> 00:21:28,920
+ناقص b يسوي ab النقطة الرابعة a في b ناقص c يسوي
+
+185
+00:21:28,920 --> 00:21:40,600
+ab ناقص ac و ال b ناقص c في a يسوي ba ناقص ca
+
+186
+00:21:43,140 --> 00:21:47,360
+الـ A is
+
+187
+00:21:47,360 --> 00:21:56,880
+a ring with unity لو كانت هذه ال ring فيها unity
+
+188
+00:21:56,880 --> 00:22:07,700
+then رقم خمسة اللي هو سالب واحد في A دو سوى سالب A
+
+189
+00:22:07,700 --> 00:22:23,520
+رقم ستة سالب واحدبسالف واحد يساوي واحد الامر
+
+190
+00:22:23,520 --> 00:22:29,120
+يجب ان انا على اول نظرية على موضوع ال ring النظرية
+
+191
+00:22:29,120 --> 00:22:34,880
+بتقول اه ال ring وفي عندى خت تلت عناصر عشوائيا
+
+192
+00:22:34,880 --> 00:22:40,460
+موجودة في هذا ال ring هي ال a والb والc يرجعبدي
+
+193
+00:22:40,460 --> 00:22:47,140
+أثبت صحة الستة اللي هو more than أو الستة حالات
+
+194
+00:22:47,140 --> 00:22:51,740
+اللي قلناها طبعا الناظر الأول وهلها بيقولها ما هي
+
+195
+00:22:51,740 --> 00:22:55,100
+مديهي ايه في zero هي في zero في ايه في zero طبيعي
+
+196
+00:22:55,100 --> 00:22:59,540
+طبيعي هدف ال real numbers بس في ال group في ال
+
+197
+00:22:59,540 --> 00:23:02,880
+rings اللي هو موضوع دراستنا يمكن يكون الكلام مش
+
+198
+00:23:02,880 --> 00:23:08,160
+صحيح فمشان يكون صحيح بنروح نثبت صحته حتى نعتمده
+
+199
+00:23:08,160 --> 00:23:15,110
+بعد ذلكالان بدأجي للحالة الاولى الحالة الاولى بدي
+
+200
+00:23:15,110 --> 00:23:21,690
+اثبت ان a في zero هو zero في a وهو يساوي zero لذلك
+
+201
+00:23:21,690 --> 00:23:28,810
+لو جيت قلت لك خديلي a في zero زائد zero هذا الكلام
+
+202
+00:23:28,810 --> 00:23:34,470
+لو جيت فاكته حسب ال distributive law يبقى هذا a في
+
+203
+00:23:34,470 --> 00:23:42,790
+zero زائد a في zeroلو أخدت نفس المقدار A في Zero
+
+204
+00:23:42,790 --> 00:23:48,770
+زائد Zero نفس حاصنة ضارب و روحت مافكتش زي قبل بال
+
+205
+00:23:48,770 --> 00:23:52,790
+Distributive load و روحت قول Zero زائد Zero جدن
+
+206
+00:23:52,790 --> 00:24:02,130
+Zero يبقى هذا صار A في Zero تمام؟ من اتنين هدول مع
+
+207
+00:24:02,130 --> 00:24:07,500
+بعض الطرف الشمال هو الطرف الشماليبقى الطرف اليمين
+
+208
+00:24:07,500 --> 00:24:13,700
+هو الطرف اليمين يبقى ال A في Zero زائد ال A في
+
+209
+00:24:13,700 --> 00:24:20,360
+Zero بده ساوي ال A في Zero لو أضفنا سالب هذا
+
+210
+00:24:20,360 --> 00:24:28,260
+العنصر للطرفين يعني سارعين دي A في Zero زائد A في
+
+211
+00:24:28,260 --> 00:24:35,000
+Zero ناقص A في Zero بده ساوي A Zero ناقص A Zero
+
+212
+00:24:35,730 --> 00:24:42,710
+الان هذا ال element قداش بيطلع ال zero صح ولا لأ
+
+213
+00:24:42,710 --> 00:24:49,350
+يبقى صار a note زائد ال zero بده يساوي zero مش a
+
+214
+00:24:49,350 --> 00:24:54,770
+note ايه في zero وليس a note ايه في zero يبقى معنى
+
+215
+00:24:54,770 --> 00:25:00,790
+هذا الكلام ان ال a في zero بده يساوي قداش zero
+
+216
+00:25:00,790 --> 00:25:06,370
+يبقى أثبت لهالطرف هذا بدي أثبت الطرف هذا زي هذا
+
+217
+00:25:06,370 --> 00:25:14,010
+بالضبط تماما إذا بروح بقوله similarly بنفس الطريقة
+
+218
+00:25:14,010 --> 00:25:24,110
+zero في a بدي ساوي zero يبقى دص وهكذا اللي هو ال a
+
+219
+00:25:24,110 --> 00:25:32,980
+في zero بدي ساوي zero في a بدي ساويبدي يساوي zero
+
+220
+00:25:32,980 --> 00:25:40,140
+و هو المطلوب بدي اجيلا نمره اتنين من النظرية بقول
+
+221
+00:25:40,140 --> 00:25:45,440
+ال A في ناقص B يساوي ناقص A في B يساوي ناقص ال برة
+
+222
+00:25:45,440 --> 00:25:52,100
+و ال B مع بعض يعني لو كان عندي سلب العنصر و ضربت A
+
+223
+00:25:52,100 --> 00:25:57,440
+فيهتماما سالب العنصر الآخر كما لو ضربته في بيه
+
+224
+00:25:57,440 --> 00:26:03,340
+وهذا سالب اللي هو حاصل الضرب a بيه بدى أروح أثبت
+
+225
+00:26:03,340 --> 00:26:07,940
+صحة هذا الكلام بنفس الفكرة الآن يا بنات لو جيت
+
+226
+00:26:07,940 --> 00:26:16,300
+قولتلك سالب a بيه زائد ال a في ال b زائد ال a في
+
+227
+00:26:16,300 --> 00:26:23,790
+ال b قدش انها تاني؟ Zero ممتاز جداطب لو قلتلك ال A
+
+228
+00:26:23,790 --> 00:26:32,710
+في سالب B ال A في سالب B بقاله الشكل هذا اللي هو
+
+229
+00:26:32,710 --> 00:26:39,570
+ال A اللي هي الأولى هذى بدي أحاول أشوفها مع مين؟
+
+230
+00:26:39,570 --> 00:26:49,450
+مع ال B كدهش بتعطيني تمام؟ يبقى سالب A في Bزائد a
+
+231
+00:26:49,450 --> 00:26:55,410
+في b بده يساوي zero بدي أخد الآن a في سالف b زائد
+
+232
+00:26:55,410 --> 00:27:01,770
+ab في عندنا من خلال ال distributive law بقدر أكتب
+
+233
+00:27:01,770 --> 00:27:11,790
+هذه هي a في سالف b زائد b مظبوطة؟ صح؟ طيب السالف b
+
+234
+00:27:11,790 --> 00:27:18,340
+زائد b بجد ال zero elementيبقى هذه صارت A في Zero
+
+235
+00:27:18,340 --> 00:27:24,880
+طب ال A في Zero بقدرش Zero يبقى هذه صارت ب Zero من
+
+236
+00:27:24,880 --> 00:27:31,300
+part one من الحالة الأولى طب من الحالتين الأثنين
+
+237
+00:27:31,300 --> 00:27:37,120
+هذول مع بعض ايش ماقدر أستنتج هذا يساوي Zero و هذا
+
+238
+00:27:37,120 --> 00:27:42,720
+يساوي Zero إذا الطرفين بيساوي بعض يبقى بناء العليل
+
+239
+00:27:42,880 --> 00:27:51,280
+اللي هو ناقص a b زائد ال a b بدي ساوي ال a في ناقص
+
+240
+00:27:51,280 --> 00:27:59,980
+b زائد ال a b لو أضفت سالب العنصر هذا للطرفين يعني
+
+241
+00:27:59,980 --> 00:28:05,940
+المعكوس الجمعي لل a b يعني سالب a b للطرفين إيش
+
+242
+00:28:05,940 --> 00:28:13,800
+بضلنا يا بنات هنا بضل a في ناقص b يساوي 100يساوي
+
+243
+00:28:13,800 --> 00:28:23,760
+ناقص a في b مظبوط ايه؟ as in هذه هي هذه صح؟ بنفس
+
+244
+00:28:23,760 --> 00:28:30,500
+الطريقة يبقى similarly بنفس
+
+245
+00:28:30,500 --> 00:28:35,500
+الطريقة we have انه
+
+246
+00:28:35,500 --> 00:28:46,780
+هيكون ناقص a في b بدي ساوي ناقص abوهكذا راس ال A
+
+247
+00:28:46,780 --> 00:28:54,700
+ناقص B يساوي ناقص A في B يساوي ناقص A في B وهو
+
+248
+00:28:54,700 --> 00:28:59,180
+المطلوب النقطة
+
+249
+00:28:59,180 --> 00:29:06,340
+التالتة النقطة التالتة بيقول سالب A في سالب B
+
+250
+00:29:06,340 --> 00:29:12,320
+تساوي AB يجب أن أمسك الطرف الأيسرو احاول اوصله
+
+251
+00:29:12,320 --> 00:29:22,540
+لطرف الايمد يبقى هذه ناقص a في ناقص b ويساوي بدى
+
+252
+00:29:22,540 --> 00:29:30,000
+استخدم الخاصية رقم اتنين هذا element وهذا ناقص b
+
+253
+00:29:30,000 --> 00:29:38,480
+يبقى هذا الكلام بده يساوي ناقص ناقص a في b صحيح من
+
+254
+00:29:38,480 --> 00:29:48,500
+وين؟الخاصية رقم اتنين يبقى هذا from part two يبقى
+
+255
+00:29:48,500 --> 00:29:54,040
+هذا من part two هذا الكلام يساوي هذه الناقص اللي
+
+256
+00:29:54,040 --> 00:30:02,540
+برا وهذه من part two كذلك يساوي الناقص لناقص a في
+
+257
+00:30:02,540 --> 00:30:10,820
+b برضه من وين from part two نفس الشيءهذا الكلام
+
+258
+00:30:10,820 --> 00:30:15,340
+ناقص في ناقص a في b يعطينا زائد يبقى هذا بدي
+
+259
+00:30:15,340 --> 00:30:22,060
+يعطينا a في b مباشرة إذا ناقص a في ناقص b بدي
+
+260
+00:30:22,060 --> 00:30:29,680
+بيساوي a في b النقطة الرابعة النقطة الرابعة بدي
+
+261
+00:30:29,680 --> 00:30:37,420
+أخد a في b ناقص ال c احنا
+
+262
+00:30:37,420 --> 00:30:43,960
+أخدنا على ال ringالعملية هذه صحيحة A في B زائد الـ
+
+263
+00:30:43,960 --> 00:30:50,740
+C يساوي AB زائد AC صح؟ تمام، بس النقص ماخنهاش،
+
+264
+00:30:50,740 --> 00:30:56,920
+مظبوط؟ بدنا نثبتها صحيحة لعملية طرح أنصرين من
+
+265
+00:30:56,920 --> 00:31:02,840
+بعضهم مع التوزيع، يعني قانون التوزيع مش مع
+
+266
+00:31:02,840 --> 00:31:07,860
+الجماعة، الطرح كذلك، بدي أثبت صحته، هذا الكلام
+
+267
+00:31:07,860 --> 00:31:16,320
+بقدر أكدهA في B زائد لناقص C حد بيقدر أقول إن
+
+268
+00:31:16,320 --> 00:31:21,140
+كلامك مش مظبوط هذا؟ مظبوط لأني زاد في ناقص في ناقص
+
+269
+00:31:21,140 --> 00:31:31,120
+طيب هذا الكلام يساوي AB زائد A في ناقص C هذا
+
+270
+00:31:31,120 --> 00:31:35,040
+مينابع ناقص قانون الـ distributive law يدخل على
+
+271
+00:31:35,040 --> 00:31:42,300
+الجامعة يدخل لا على الجامعةلكن هذه من part two من
+
+272
+00:31:42,300 --> 00:31:49,240
+part two هي مقبض تماما يساوي ناقص حاصل الضرب تبعه
+
+273
+00:31:49,240 --> 00:31:59,740
+يبقى هذه يساوي a في b ناقص a في c من part two أظن
+
+274
+00:31:59,740 --> 00:32:05,210
+هو المطلوب، خلصنا، يبقى تنفع لعملية الجمعوالعملية
+
+275
+00:32:05,210 --> 00:32:11,850
+الطرح اللي هو خاصية التوزيع بنفس الطريقة similar
+
+276
+00:32:11,850 --> 00:32:21,190
+الو مين بي ناقص ال C في ال A بيساوي بيساوي مين
+
+277
+00:32:21,190 --> 00:32:28,390
+بيساوي بي في ال A ناقص ال C في ال A خلصنا النقطة
+
+278
+00:32:28,390 --> 00:32:34,950
+الرابعة لنروح للنقطة الخامسةأول أربع نقاط مالهمش
+
+279
+00:32:34,950 --> 00:32:39,190
+دعوة ال ring فيها unity و لا unity ما تكون تكون
+
+280
+00:32:39,190 --> 00:32:45,090
+الخامسة الاساسة باننا نشترق وجود ال unity يعني ال
+
+281
+00:32:45,090 --> 00:32:49,930
+identity element في ال ring ا فبتقول الخاصية
+
+282
+00:32:49,930 --> 00:32:55,530
+الخامسة اللي هو ناقص واحد في ايه بالمناسبة انه
+
+283
+00:32:55,530 --> 00:33:04,110
+يساوي ناقص ايه بدي ارجع لاستخدامالخاصية رقم اتنين
+
+284
+00:33:04,110 --> 00:33:12,190
+ناقص واحد في ايه ال unity هو عنصر يبقى ال unity هو
+
+285
+00:33:12,190 --> 00:33:18,330
+عنصر موجود في ال group ايه ناقص واحد يعني الخاصية
+
+286
+00:33:18,330 --> 00:33:26,690
+هذه يبقى هذه ايش بتتساوي ناقص واحد في ايه يبقى هذه
+
+287
+00:33:26,690 --> 00:33:33,390
+من part two مظبوط؟طب ال unity لما أنا أضربه في
+
+288
+00:33:33,390 --> 00:33:41,110
+عنصر يطلع نفسي عنصر إذا يساوي ناقص A وهو المطلوب
+
+289
+00:33:41,110 --> 00:33:48,450
+خلصنا منه الآن رقم ستة اللي هو ناقص واحد في ناقص
+
+290
+00:33:48,450 --> 00:33:53,970
+واحد بدي أثبت إنه يساوي مين؟ يساوي طلعيني ليه ال
+
+291
+00:33:53,970 --> 00:34:00,840
+system اللي بدنا نثبتها طلعيني ليه تلاتةبدي أخد a
+
+292
+00:34:00,840 --> 00:34:09,660
+تساوي b تساوي واحد يبقى باجي بقول هذه تساوي واحد
+
+293
+00:34:09,660 --> 00:34:23,000
+from part a three with a تساوي ال b تساوي واحد وهو
+
+294
+00:34:23,000 --> 00:34:26,680
+المطلوب طيب
+
+295
+00:34:27,510 --> 00:34:35,390
+بنجي لنظرية ثانية دون اثباتها ايش النظرية التانية؟
+
+296
+00:34:35,390 --> 00:34:40,270
+فاكرين ال group؟ و بجينا نجيب ال identity element
+
+297
+00:34:40,270 --> 00:34:47,530
+صح؟ و معكوس ال element طيب ال unity هذا او ال
+
+298
+00:34:47,530 --> 00:34:51,110
+identity element في هال group اكتر من ال identity
+
+299
+00:34:51,110 --> 00:34:58,140
+element؟ وحيد مافيش .. و هنا ال ring وحيد طيبمعكوس
+
+300
+00:34:58,140 --> 00:35:05,280
+العنصر، وحيد، إذا كانت بجينا نثبتهم في الجبر واحد،
+
+301
+00:35:05,280 --> 00:35:10,660
+بجينا بنثبت ان عندي two identity elements و بنحاول
+
+302
+00:35:10,660 --> 00:35:15,400
+نكون اتنين are equal عندي two inverses و بنحاول
+
+303
+00:35:15,400 --> 00:35:20,260
+نثبت ان اتنين are equal و فعلا أثبتنا هذا مع
+
+304
+00:35:20,260 --> 00:35:24,670
+الدكتور محمدمظبوط يبقى لا داعي ليه تكرار الإتباه
+
+305
+00:35:24,670 --> 00:35:28,890
+تماما من الذكية ترجعيله من دفترك أو من اللي اكتر
+
+306
+00:35:28,890 --> 00:35:39,130
+يبقى نظرية بتقول ما يأتي سويا يا ربي if
+
+307
+00:35:39,130 --> 00:35:48,310
+الار is a ring with unity if الار is a ring with
+
+308
+00:35:48,310 --> 00:35:50,170
+unity
+
+309
+00:35:57,550 --> 00:36:06,990
+then the unity then the unity is
+
+310
+00:36:06,990 --> 00:36:16,310
+unique يكون وحيدا هذا النقطة الأولى النقطة التانية
+
+311
+00:36:16,310 --> 00:36:32,860
+if ايه if if they belongto a ring A الموجود في R
+
+312
+00:36:32,860 --> 00:36:40,720
+with multiplicative
+
+313
+00:36:40,720 --> 00:36:50,640
+inverse with
+
+314
+00:36:50,640 --> 00:36:53,700
+multiplicative inverse
+
+315
+00:36:58,510 --> 00:37:03,950
+ثم هذا انبسط
+
+316
+00:37:27,390 --> 00:37:35,050
+مرة تانية بقول هذه if
+
+317
+00:37:35,050 --> 00:37:41,530
+R is a ring with unity then the unity is unity
+
+318
+00:37:41,530 --> 00:37:47,730
+ماعنديش فى ال ring إلا unity وحيد فقط لغى بعد هيك
+
+319
+00:37:47,730 --> 00:37:52,670
+لو كان ال A اللى موجود فى ال ring R إله معكوس يعني
+
+320
+00:37:52,670 --> 00:37:57,890
+إيش سمناه؟ إيش سمناه المضارف هذه؟ unitيبقى لو كان
+
+321
+00:37:57,890 --> 00:38:02,530
+unit يعني له معكوس يبقى ال unit هذا يكون وحيدا
+
+322
+00:38:02,530 --> 00:38:07,690
+فالمعكوس المطبق negative inverse له بيكون وحيد
+
+323
+00:38:07,690 --> 00:38:12,710
+مافيهش غيره البرهان نفس البرهان تبع ال groups
+
+324
+00:38:12,710 --> 00:38:18,290
+بالضبط تماما لا زيادة ولا نقصان يبقى لا داعي لتضيع
+
+325
+00:38:18,290 --> 00:38:23,650
+الوقت فيه في عندنا ملاحظات هنا يبقى lots
+
+326
+00:38:26,690 --> 00:38:36,790
+ملاحظة الأولى if ال A و ال B و ال C موجودة فى ring
+
+327
+00:38:36,790 --> 00:38:44,910
+R و ال R is a ring and
+
+328
+00:38:44,910 --> 00:38:56,590
+ال A ضماء equal to zero then ال A فى Bبساوي A بC
+
+329
+00:38:56,590 --> 00:39:08,890
+ضغمة imply أن ال B تساوي C because .. إيش السبب؟
+
+330
+00:39:38,990 --> 00:39:43,070
+مرة تانية بقولوا لو عندي ثلاث علاقات وموجودات في
+
+331
+00:39:43,070 --> 00:39:48,130
+ال ring R وكان ال A لا يساوي زيرو وعندي معلومة
+
+332
+00:39:48,130 --> 00:39:54,050
+بتقول انه حاصل ضرب A في B بيساوي A في C فهل هذا
+
+333
+00:39:54,050 --> 00:40:00,790
+يتطلب انه B تساوي C؟ الإجابة قد يكون وقد لا يكون
+
+334
+00:40:00,790 --> 00:40:08,520
+يبقى in general لا يكون ليش؟ ليش؟ هل أنا قلتإنه
+
+335
+00:40:08,520 --> 00:40:14,580
+ليه ال a is a unit؟ لأ ماقلتش ال a is unit ممكن
+
+336
+00:40:14,580 --> 00:40:20,180
+يكون أي رقم ولا يوجد له معكوس يعني أي عنصر وهذا
+
+337
+00:40:20,180 --> 00:40:25,660
+العنصر ليس له معكوس إذا لا يمكن ال a بيساوي a c
+
+338
+00:40:25,660 --> 00:40:32,220
+أستنتج ان ال b تساوي من ال c لإن ال a ممكن يكون
+
+339
+00:40:32,220 --> 00:40:42,050
+unit وممكن مايكونش unit becauseالإيه؟ may or may
+
+340
+00:40:42,050 --> 00:40:50,910
+not unit يعني ممكن يكون له معكوس وممكن ليه مايكونش
+
+341
+00:40:50,910 --> 00:40:55,770
+له معكوس لو إله معكوس بضربه في المعادلة من جهة
+
+342
+00:40:55,770 --> 00:41:00,990
+الشمال بظل النبي يسويسي طب لو مانوش معكوس مش
+
+343
+00:41:00,990 --> 00:41:07,130
+ممكنية زي مين؟زي اتنين و تلاتة في الـ Z، six اتنين
+
+344
+00:41:07,130 --> 00:41:13,010
+و تلاتة، اتنين في تلاتة بستة يعني كداش؟ Zero صح
+
+345
+00:41:13,010 --> 00:41:18,450
+ولا لا؟ يبقى هل اتنين والتلاتة اللي هم معكوز؟ ولا
+
+346
+00:41:18,450 --> 00:41:23,130
+واحد فيهم اللي معكوز؟ تمام؟ يبقى في هذه الحالة،
+
+347
+00:41:23,130 --> 00:41:28,350
+مدام ما لهش معكوز، ماقدرش اقول ان ا في B بده يساوي
+
+348
+00:41:28,350 --> 00:41:33,650
+ا في C، يبقى الـ B تساوي Cالامر الثاني او الملاحظة
+
+349
+00:41:33,650 --> 00:41:44,910
+الثانية if ال a belongs to ring R when اللي و من
+
+350
+00:41:44,910 --> 00:41:57,370
+ال a تربيع بده ساوي ال a we cannot say that لا
+
+351
+00:41:57,370 --> 00:42:02,780
+يمكن او لا نستطيع ان نقولو you cannot say that ان
+
+352
+00:42:02,780 --> 00:42:21,560
+ال a تساوي zero or ال a تساوي ال واحد because طيب
+
+353
+00:42:21,560 --> 00:42:27,380
+قبل ما نقول because في نهاية الشركة انا بدي افكر
+
+354
+00:42:27,870 --> 00:42:35,570
+بقول a تربية تساول a اظن ان اذا قلت a تربية ناقص
+
+355
+00:42:35,570 --> 00:42:41,370
+يساوي 0 محدش بيعترض عليه جتنا ال distributive law
+
+356
+00:42:41,370 --> 00:42:48,190
+قلت بقدر اقول a في a ناقص واحد يساوي 0 هنا بتطوروا
+
+357
+00:42:48,190 --> 00:42:54,950
+عليه تقولوا اللي هو ال ring هذي فيها unity ماجليش
+
+358
+00:42:54,950 --> 00:42:59,210
+فيها unityيبقى هذا الخطوة اللي عملتها صح ولا غلط؟
+
+359
+00:42:59,210 --> 00:43:03,010
+صح إذا كان ال ring فيها unity غلط إذا ال ring
+
+360
+00:43:03,010 --> 00:43:06,210
+فيهاش unity يبقى هذا الكلام يبعد لك الله حطه ع شجة
+
+361
+00:43:06,210 --> 00:43:12,610
+مش صحيح إذا لو كان هذا الكلام صحيح بقوله ممكن a
+
+362
+00:43:12,610 --> 00:43:18,150
+يساوي zero أو ال a تساوي واحد لكن الواحد هذا مش
+
+363
+00:43:18,150 --> 00:43:22,810
+موجود في ال ring بصير هذا الكلام ماله غلط على طول
+
+364
+00:43:22,810 --> 00:43:27,600
+القطريبقى هذا الكلام ايه يساوي zero او ايه يساوي
+
+365
+00:43:27,600 --> 00:43:35,340
+غلط يبقى we say that ان
+
+366
+00:43:35,340 --> 00:43:40,760
+ال a تساوي zero او ال a تساوي واحد انا ماعرف ايش
+
+367
+00:43:40,760 --> 00:43:46,240
+قلنا with a تلاقى we cannot say ايه نخيناها بدأوا
+
+368
+00:43:46,240 --> 00:43:50,920
+نعملها we cannot say نقدرش نقول ان a تساوي zero او
+
+369
+00:43:50,920 --> 00:44:04,070
+a تساوي واحدbecause they are may or may not have
+
+370
+00:44:04,070 --> 00:44:10,830
+unity يعني ممكن ان تكون فيها unity ويطلع الكلام
+
+371
+00:44:10,830 --> 00:44:14,550
+واضح وممكن مايكونش فيها unity هنا ماشترطناش ان
+
+372
+00:44:14,550 --> 00:44:21,410
+يكون فيها unity يبقى هذا الكلام ليس بالضرورة صحيح
+
+373
+00:44:21,980 --> 00:44:26,900
+نجي للألة تعريف جديد زي ما أخدته group بعد أخدته
+
+374
+00:44:26,900 --> 00:44:30,640
+ال sub group و أحنا أخدنا ring بدنا نروح ناخد sub
+
+375
+00:44:30,640 --> 00:44:36,660
+ring يبقى definition هي
+
+376
+00:44:36,660 --> 00:44:47,740
+subset هي subset S of subset
+
+377
+00:44:55,900 --> 00:45:04,080
+is of a ring R is
+
+378
+00:45:04,080 --> 00:45:16,440
+a sub ring
+
+379
+00:45:16,440 --> 00:45:21,280
+if ال S itself
+
+380
+00:45:25,230 --> 00:45:45,870
+is appearing نفسها under the operations on R فده
+
+381
+00:45:45,870 --> 00:45:51,430
+نسميها
+
+382
+00:45:51,430 --> 00:45:58,490
+sub ringtest a
+
+383
+00:45:58,490 --> 00:46:02,450
+non-empty
+
+384
+00:46:02,450 --> 00:46:21,190
+a non-empty subset S of a ring A is a subring F
+
+385
+00:46:39,370 --> 00:46:40,770
+التعريف يقول
+
+386
+00:46:53,400 --> 00:46:57,840
+التعريف بيقول ان ال subset S of a ring R بسميه sub
+
+387
+00:46:57,840 --> 00:47:04,560
+ring ما إذا كانت ال S نفسها بتظلها ring تحت نفس
+
+388
+00:47:04,560 --> 00:47:09,860
+العمليات اللي على R يعني احنا عندنا ring كبيرة،
+
+389
+00:47:09,860 --> 00:47:14,600
+خدنا منها شوية عناصر، تمام؟ العناصر هذه اللي جت ال
+
+390
+00:47:14,600 --> 00:47:18,780
+6 خواص طبعتها ال ring ينطبقوا عليها إن حدث ذلك
+
+391
+00:47:18,780 --> 00:47:23,990
+بقول هذه sub ring يعني بدي أثبت ال 6 خواصطيب يا
+
+392
+00:47:23,990 --> 00:47:28,090
+طلع هذه قصة طويلة، كان كل مرة بدي أسوي هيك، فراعوا
+
+393
+00:47:28,090 --> 00:47:33,590
+العلماء اكتشفوا هالشغلة هذه، سموها Subring Test إن
+
+394
+00:47:33,590 --> 00:47:39,750
+الـS صبست من أرض، بقول عنها Subring إذا حققت دي مش
+
+395
+00:47:39,750 --> 00:47:45,110
+ستة وإنما تلاتة خواصة، non-empty أخدت أي عنصرين
+
+396
+00:47:45,110 --> 00:47:48,710
+فيما بينهم، ولقيت الفرق فيما بينهم ما موجود في S
+
+397
+00:47:48,710 --> 00:47:53,780
+وحصل ضربه ما موجود كذلك في Sالمرة القادمة ان شاء
+
+398
+00:47:53,780 --> 00:47:59,140
+الله بنروح نخبط هذه النظرية لذلك بنقولك روحي مريلي
+
+399
+00:47:59,140 --> 00:48:03,320
+على القرآن اللي في الكتاب مرة سريعة بس يكون عندك
+
+400
+00:48:03,320 --> 00:48:08,520
+فكرة حتى و احنا بنشرح هنا تستمع بهذا الكلام ثم بعد
+
+401
+00:48:08,520 --> 00:48:13,340
+ذلك بناخد أمثلة عليها ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..942c23a884565a092eb6ccb470c19bb7f6cc6fbf
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/68aSoYPVPJU_raw.srt
@@ -0,0 +1,1616 @@
+1
+00:00:21,480 --> 00:00:26,340
+بسم الله الرحمن الرحيم المرة الماضية احنا ابتدأنا
+
+2
+00:00:26,340 --> 00:00:31,820
+في introduction to ring عرفنا ال ring أخدنا عليها
+
+3
+00:00:31,820 --> 00:00:36,940
+مجموعة من الأمثلة واليوم ان شاء الله بنكمل الأمثلة
+
+4
+00:00:36,940 --> 00:00:42,180
+بالاضافة إلى بعض النظريات على اللي هو ال rings
+
+5
+00:00:42,180 --> 00:00:45,820
+أخدنا المرة الفاترة أربعة أمثلة وهذا هو المثال
+
+6
+00:00:45,820 --> 00:00:49,300
+الخامس بيقول the set of all continuously valued
+
+7
+00:00:49,300 --> 00:00:53,730
+functionsof a real value because who the grass
+
+8
+00:00:53,730 --> 00:00:58,030
+passes through the point one وزيره يبقى احنا عندنا
+
+9
+00:00:58,030 --> 00:01:04,070
+مجموعة من الدوال الحقيقية اللي الرسم البياني اليها
+
+10
+00:01:04,070 --> 00:01:10,110
+يمر بالنقطة واحد وزيره يعني لو أخدنا محاول احداثية
+
+11
+00:01:10,110 --> 00:01:15,470
+وقلنا هذا محور X و هذا محور Y النقطة هذه اللي هي
+
+12
+00:01:15,470 --> 00:01:21,880
+النقطة واحد وزيره كل الدوالفي متغير واحد وهذا
+
+13
+00:01:21,880 --> 00:01:28,760
+المتغير متغير حقيقي التي تمر بهذه النقطة.الان احنا
+
+14
+00:01:28,760 --> 00:01:35,000
+بنقول ان هذه commutative ring without unity.المرة
+
+15
+00:01:35,000 --> 00:01:38,520
+اللي فات اللامتلة قدامي كلها rings with unity.طبعا
+
+16
+00:01:38,520 --> 00:01:43,760
+الان انا هدعي ان هذا ring مافيهاش unity.شو العملية
+
+17
+00:01:43,760 --> 00:01:48,300
+اللي عليها عملية الجامعة f زائد g of a يساوي f of
+
+18
+00:01:48,300 --> 00:01:54,700
+a زائد g of a والف في g of a يساوي f of a في g of
+
+19
+00:01:54,700 --> 00:02:00,360
+a الآن لو جيت أقولك الدلة f of x ساوي واحد هذه هي
+
+20
+00:02:00,360 --> 00:02:05,040
+constant function والواحد لو ضربناه في أي دلة بدي
+
+21
+00:02:05,040 --> 00:02:10,840
+يعطيني نفس الدلة لكن السؤال هذه ليش ال unity؟مش
+
+22
+00:02:10,840 --> 00:02:16,880
+موجود في هذه الـ Ring الإجابة بسيطة جدا ان منحنى
+
+23
+00:02:16,880 --> 00:02:24,620
+الدالة F of X يساوي 1 هو خط مستقيم يوازي يوازي
+
+24
+00:02:24,620 --> 00:02:30,740
+مين؟ يوازي محور X إذا لا يمكن أن يمر بالنقطة 1 و 0
+
+25
+00:02:30,740 --> 00:02:37,280
+إذا لو ليترسمت الخط اللي عندنا هذا أفضي هيك بهذا
+
+26
+00:02:37,280 --> 00:02:42,900
+الشكليبقى هذا الخط اللي هو main اللي هو f of x
+
+27
+00:02:42,900 --> 00:02:48,300
+يساوي واحد لايمكن ان يمر بهذه النقطة وبالتالي هذه
+
+28
+00:02:48,300 --> 00:02:53,480
+الدالة مش موجودة في مجموعة هذه الدوال وبالتالي هذه
+
+29
+00:02:53,480 --> 00:02:59,680
+ring with unity طب ليش commutative؟ لأنه لو أخدنا
+
+30
+00:02:59,680 --> 00:03:05,100
+قيمتين للدالة f of a وf of b فكل واحدة منهم عبارة
+
+31
+00:03:05,100 --> 00:03:09,340
+عن قدد حقيقيو احنا بنعرف ان حاصل ضرب الاعداد
+
+32
+00:03:09,340 --> 00:03:15,840
+الحقيقية is commutative يبقى هنا بقول ال R is
+
+33
+00:03:15,840 --> 00:03:25,480
+commutative او the ring is commutative
+
+34
+00:03:25,480 --> 00:03:28,660
+commutative
+
+35
+00:03:28,660 --> 00:03:33,280
+because ال
+
+36
+00:03:33,280 --> 00:03:46,370
+F of Aand f of b are real numbers نظرا لأنهم أعداد
+
+37
+00:03:46,370 --> 00:03:50,670
+حقيقية فهي composite فهي community يعني f of a في
+
+38
+00:03:50,670 --> 00:03:56,010
+f of b هي f of b في main في f of a وبالتالي مافيها
+
+39
+00:03:56,010 --> 00:04:01,530
+مشكلة خالص طيب بدنا نروح الآن على ring غير هذه ال
+
+40
+00:04:01,530 --> 00:04:12,540
+rings وهو مثال رقم 6مثال رقم ستة بيقول لل R1 وR2 و
+
+41
+00:04:12,540 --> 00:04:24,200
+لغاية ال RN بي رينز بي رينز هذه عبارة عن حلقات we
+
+42
+00:04:24,200 --> 00:04:25,500
+shall construct
+
+43
+00:04:33,610 --> 00:04:44,590
+we shall construct a new ring a a new ring بدنا
+
+44
+00:04:44,590 --> 00:04:52,350
+نكوّن من هذه ال rings رينج جديدة as follow كالتالي
+
+45
+00:04:52,350 --> 00:05:02,010
+كيف نجم نقول بدي أخد ال R واحد direct sum مع R
+
+46
+00:05:02,010 --> 00:05:12,340
+اتنينdirect sum direct sum مع R N تمام من علاصر
+
+47
+00:05:12,340 --> 00:05:22,060
+هذه كل العلاصر على الشكل A1 و A2 و A N بحيث ال AI
+
+48
+00:05:22,060 --> 00:05:31,300
+موجودة في ال R I بالشكل اللي عندنا هذا and peer
+
+49
+00:05:31,300 --> 00:05:40,780
+formوبنكون pair for and
+
+50
+00:05:40,780 --> 00:05:48,160
+pair for addition and
+
+51
+00:05:48,160 --> 00:05:58,840
+multiplication الجمع
+
+52
+00:05:58,840 --> 00:06:15,510
+وعملية الدرب component wisefrom Poland Y that
+
+53
+00:06:15,510 --> 00:06:23,310
+is that is
+
+54
+00:06:23,310 --> 00:06:44,290
+A1 و A2 و AN زائد B1و B2 و DN مدرسة A1 زي B1 A2 زي
+
+55
+00:06:44,290 --> 00:07:02,390
+B2 و AN زي BN ال A1 و ال A2 و ال AN مضروبة في B1و
+
+56
+00:07:02,390 --> 00:07:14,730
+B2 و BN بدي سامع A1 B1 A2
+
+57
+00:07:14,730 --> 00:07:33,700
+B2 و AN BN this ring this ring is calledthe direct
+
+58
+00:07:33,700 --> 00:07:43,720
+sum of
+
+59
+00:07:43,720 --> 00:07:51,200
+R1 وR2 وRN
+
+60
+00:08:18,300 --> 00:08:24,500
+المثال هذا يعني ان عندي مجموعة من ال rings ر واحد
+
+61
+00:08:24,500 --> 00:08:29,900
+و ر اتنين و ر ثلاثة و لغاية ر ان من ال rings هذه
+
+62
+00:08:29,900 --> 00:08:35,160
+بدي اكوّل ring جديدة تمام ال ring الجديدة هذي شو
+
+63
+00:08:35,160 --> 00:08:42,040
+شكلها يبقى روحت ر واحد رتو رتو رتو رتو رتو رتو رتو
+
+64
+00:08:42,040 --> 00:08:44,760
+رتو رتو رتو رتو رتو رتو رتو رتو رتو رتو رتو رتو
+
+65
+00:08:44,760 --> 00:08:47,270
+رتو رتو رتو رتو رتو رتو رتو رتوthe set of all
+
+66
+00:08:47,270 --> 00:08:51,330
+innituples هذه كنت في جبر حديث واحد اسمها
+
+67
+00:08:51,330 --> 00:08:57,170
+innituple يعني جوس مركب من ان من المركبات الجوس
+
+68
+00:08:57,170 --> 00:09:02,050
+كله يعتبر عنصر واحد العنصر واحد عبارة عن مجموعة من
+
+69
+00:09:02,050 --> 00:09:09,510
+المركبات تمام؟ بنسميها innituple يعني جوس في ان من
+
+70
+00:09:09,510 --> 00:09:16,270
+العناصر تمام؟بحيث ال AI موجود في RI شو يعني؟ يعني
+
+71
+00:09:16,270 --> 00:09:23,390
+لو حطيت ال I بواحد بصير A1 موجود في R1 و A2 موجود
+
+72
+00:09:23,390 --> 00:09:29,590
+في R2 و A3 في R3 و AN موجود في RN يعني من كل ring
+
+73
+00:09:29,590 --> 00:09:36,270
+باخد عنصر واحد فقط مجموعة العناصر هذه كونت لي عنصر
+
+74
+00:09:36,270 --> 00:09:43,230
+واحد فقط في ال ring الجديدةطيب عرفت عليها عملية
+
+75
+00:09:43,230 --> 00:09:49,310
+العملية سميت component wise يعني إذا جمع بلج مع كل
+
+76
+00:09:49,310 --> 00:09:56,790
+عنصر مع نظيره تمام اضرب بضرب كل عنصر في نظيري هذا
+
+77
+00:09:56,790 --> 00:10:02,630
+معنى ال addition and multiplication component wise
+
+78
+00:10:02,630 --> 00:10:08,310
+يعني كل عنصر مع نظيره رياضيابقول هذا كل ال element
+
+79
+00:10:08,310 --> 00:10:13,330
+الأول وهذا ال element التاني بدي أجمعهم إذا بجمع
+
+80
+00:10:13,330 --> 00:10:19,590
+كل عنصر مع نظيره يبقى a1 زائد b1 يمثل المراكبة
+
+81
+00:10:19,590 --> 00:10:26,170
+الأولى a2 زائد b2 يمثل المراكبة التانية an زائد bn
+
+82
+00:10:26,170 --> 00:10:31,670
+يمثل المراكبة النونية هذا الجمعالضرب كذلك
+
+83
+00:10:31,670 --> 00:10:36,850
+component wise بضرب كل عنصر مع نظيره من القوس
+
+84
+00:10:36,850 --> 00:10:41,610
+الثاني فبالي بقول هذا الجوس الأول ضرب الجوس الثاني
+
+85
+00:10:41,610 --> 00:10:50,750
+يبقى a1 b1 العنصر التاني a2 b2 a3 b3 am bm يبقى من
+
+86
+00:10:50,750 --> 00:10:57,310
+حاصر ضرب المركبات المتنظرة بطلع عندي جوس جديدهذا
+
+87
+00:10:57,310 --> 00:11:00,890
+ال course جديد موجود في ال R1 direct sum مع R2
+
+88
+00:11:00,890 --> 00:11:06,190
+direct sum مع R2 direct sum مع R2
+
+89
+00:11:06,190 --> 00:11:09,910
+direct sum
+
+90
+00:11:09,910 --> 00:11:11,790
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+91
+00:11:11,790 --> 00:11:12,110
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+92
+00:11:12,110 --> 00:11:12,110
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+93
+00:11:12,110 --> 00:11:12,570
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+94
+00:11:12,570 --> 00:11:12,570
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+95
+00:11:12,570 --> 00:11:12,610
+مع R2 direct sum مع R2 direct sum مع R2 direct sum
+
+96
+00:11:12,610 --> 00:11:19,690
+مع R2 direct sum مع R2
+
+97
+00:11:19,690 --> 00:11:21,010
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+98
+00:11:21,010 --> 00:11:21,170
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+99
+00:11:21,170 --> 00:11:22,510
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+100
+00:11:22,510 --> 00:11:22,510
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+101
+00:11:22,510 --> 00:11:22,550
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+102
+00:11:22,550 --> 00:11:22,670
+direct sum مع R2 direct sum مع R2 direct sum مع R2
+
+103
+00:11:22,670 --> 00:11:27,370
+direct sum مع R2يبقى هذه وبتاش بيكون فيها unity
+
+104
+00:11:27,370 --> 00:11:33,110
+إذا كان كل ring من ال rings الأصلية فيها ال unity
+
+105
+00:11:33,110 --> 00:11:39,230
+يبقى ال unity تبع هذه ال ring هو ال N تيوبل
+
+106
+00:11:39,230 --> 00:11:45,810
+المكوّلة من ال unity تبع كل ring تمام؟ يبقى ال
+
+107
+00:11:45,810 --> 00:11:51,650
+identity element أو ال unity تبع هذه ال ring اللي
+
+108
+00:11:51,650 --> 00:11:56,880
+تبعت ال direct sunالعناصر انصر الوحدة فيها هو
+
+109
+00:11:56,880 --> 00:12:02,400
+المكون من العناصر الوحدة في كل من الرنج المختلفة
+
+110
+00:12:02,400 --> 00:12:08,700
+تمام؟ هذا موضوع السؤال في الكتاب ال R واحد وال R
+
+111
+00:12:08,700 --> 00:12:15,120
+اتنين وال R N has a unity if and only if ال direct
+
+112
+00:12:15,120 --> 00:12:20,560
+sum has a unity يعني بنثبت البرهان في اتجاهين أحد
+
+113
+00:12:20,560 --> 00:12:27,750
+أسئلة التمرينطيب تمام نعطي كمان مثال أخير اللي هو
+
+114
+00:12:27,750 --> 00:12:35,070
+مثال رقم 7 مثال رقم 7 بيقول consider the ring
+
+115
+00:12:35,070 --> 00:12:44,150
+consider the ring اللي هي z مجموعة الأعداد الصحيحة
+
+116
+00:12:44,150 --> 00:12:50,050
+عليها عملية الضرب و عليها عملية الجمع زي ما انت
+
+117
+00:12:50,050 --> 00:12:58,780
+شايفين withtwo binary operations
+
+118
+00:12:58,780 --> 00:13:08,480
+two binary operations defined by defined by
+
+119
+00:13:08,480 --> 00:13:20,940
+المعرفة كالتالي ال a زائد او ال m زائد ال nالـ M
+
+120
+00:13:20,940 --> 00:13:29,580
+زائد ال N يساوي ال M زائد ال N ناقص واحد and ال M
+
+121
+00:13:29,580 --> 00:13:41,820
+بطل N يساوي ال M زائد ال N ناقص M في N لكل ال M و
+
+122
+00:13:41,820 --> 00:13:49,760
+ال N اللي موجودة في Z find the
+
+123
+00:13:50,430 --> 00:14:01,170
+زيرو بزيرو الوضع ومجموعة
+
+124
+00:14:01,170 --> 00:14:05,370
+الرمز ومجموعة
+
+125
+00:14:05,370 --> 00:14:08,950
+هذا الرمز
+
+126
+00:14:27,370 --> 00:14:33,050
+سؤال مرة تانية قال خلّي مجموعة الأعداد الصحيحة و
+
+127
+00:14:33,050 --> 00:14:39,490
+بنعرف عليها عمليتين ثنائيتين العملية الأولى هي M
+
+128
+00:14:39,490 --> 00:14:46,150
+زائد ال N يساوي M زائد N ناقص واحد العملية هذه
+
+129
+00:14:46,150 --> 00:14:51,670
+زائد و عليها دائرة ليست عملية الجمع العادية ولكن
+
+130
+00:14:51,670 --> 00:14:57,770
+عمليا هي عملية الجمع العادية مطروح منها واحدعملية
+
+131
+00:14:57,770 --> 00:15:03,190
+الضرب مش عملية الضرب عادية وانما هي M زائد ال N
+
+132
+00:15:03,190 --> 00:15:09,990
+ناقص عملية الضرب العادية لل M في N يبقى هاي صارت
+
+133
+00:15:09,990 --> 00:15:14,830
+two binary operations يبقى كل binary operation
+
+134
+00:15:14,830 --> 00:15:20,110
+بصير علها identity element و zero element يختلف عن
+
+135
+00:15:20,110 --> 00:15:26,190
+مين يختلف عن الداني زي مثلك في المصوفة في الفي ال
+
+136
+00:15:26,190 --> 00:15:29,430
+.. في ال ranks العادية بيجينا نقول ال unity واحد
+
+137
+00:15:29,430 --> 00:15:33,950
+تمام؟ لكن لو روحنا للمصففات بيجيناها مصففة نظام
+
+138
+00:15:33,950 --> 00:15:37,270
+اتنين في اتنين واحد zero zero واحد اللي المحدد
+
+139
+00:15:37,270 --> 00:15:42,390
+تبعها متوسط واحد صحيح اذا هنا تحت تأثير العملية
+
+140
+00:15:42,390 --> 00:15:47,970
+بتعرف مين هو ال zero element ومين هو من ال unity
+
+141
+00:15:47,970 --> 00:15:51,850
+تمام؟ لإنه بيقول هذه ring فيها ال zero فيها ال
+
+142
+00:15:51,850 --> 00:15:56,020
+unity بتعرف مين هو ال ring و ال unityطبعا الـ Z دي
+
+143
+00:15:56,020 --> 00:16:01,500
+في مجموعة العداد الصحيحة الموجبة والسالبة والصفر
+
+144
+00:16:01,500 --> 00:16:09,160
+تمام؟ بدنا نروح و نعرف مين هو الـ Zero Element أنا
+
+145
+00:16:09,160 --> 00:16:15,540
+أدعي أن الـ Zero Element هو الواحد الصحيح أدعيها
+
+146
+00:16:15,540 --> 00:16:21,720
+قد يكون و قد لا يكون أتأكد يبقى هنا بقولهم The
+
+147
+00:16:21,720 --> 00:16:35,670
+unityas unity is the zero element ال unity هو ال
+
+148
+00:16:35,670 --> 00:16:40,190
+zero element اه ال unity هو ال zero element ليش؟
+
+149
+00:16:40,190 --> 00:16:45,270
+because اول
+
+150
+00:16:45,270 --> 00:16:51,510
+شيء ما هو شرط ال unity ان لو ضربته في عنصر يطلع
+
+151
+00:16:51,510 --> 00:16:58,700
+نفس عنصر صح ولا لا؟يبقى هنا because اه قلنا
+
+152
+00:16:58,700 --> 00:17:08,080
+because if ال M موجودة في ال zero then ال unity
+
+153
+00:17:08,080 --> 00:17:13,900
+good هو ال zero اذا بدي اخد ال M مضروبة في من؟ في
+
+154
+00:17:13,900 --> 00:17:22,390
+ال zero انطلع الناتج يساوي M بيكون فعلا هذا هوهذا
+
+155
+00:17:22,390 --> 00:17:28,070
+هو إيش ال unity طيب هذا الكلام طبق للعملية اللي
+
+156
+00:17:28,070 --> 00:17:35,370
+عندنا بده يساوي ال M زائد ال zero ناقص ال M في ال
+
+157
+00:17:35,370 --> 00:17:43,470
+zero هذا جمع عادي و هذا ضرب عادي يفجأ يساوي M زائد
+
+158
+00:17:43,470 --> 00:17:51,900
+Zero ناقص ال Zero و يساوي Mيبقى فعلا ال zero هو ال
+
+159
+00:17:51,900 --> 00:17:57,480
+unity لأن لما ضربنا في M طلع النتيجة يساوي 100 M
+
+160
+00:17:57,480 --> 00:18:03,200
+وبنفس الطريقة ال zero ضرب ال M برضه بدي يساوي 100
+
+161
+00:18:03,200 --> 00:18:10,500
+M Similarly ال
+
+162
+00:18:10,500 --> 00:18:17,640
+zero ضرب ال M بدي يساوي Mيبقى بالأقل عليه الـ zero
+
+163
+00:18:17,640 --> 00:18:23,620
+هو ال unity طيب ضايل علينا ال zero element the
+
+164
+00:18:23,620 --> 00:18:35,000
+zero element is one يا سلام عجوز؟ واحد هو الصفر
+
+165
+00:18:35,000 --> 00:18:40,660
+تبع ال ring هذه؟ اه ليش مليش ما هوش لا؟ لا لأ انا
+
+166
+00:18:40,660 --> 00:18:46,760
+قاعد واحد هو zero ليش؟لأن تحت عملية الجامعة باجي
+
+167
+00:18:46,760 --> 00:18:52,360
+بقول أي element في ال Z زائد ال zero تبعها بدي
+
+168
+00:18:52,360 --> 00:18:57,240
+يعطيني نفس ال element صح؟ يبقى أنا بدعي ان الواحد
+
+169
+00:18:57,240 --> 00:19:04,340
+يبقى ال M زائد الواحد بدي يعطيني جداش M ان حدث ذلك
+
+170
+00:19:04,340 --> 00:19:09,560
+يبقى فعلا واحد هو العنصر الصفري ل ring على عكس ما
+
+171
+00:19:09,560 --> 00:19:13,820
+هو مطوع في دماغكإن ال zero هو ال zero والواحد هو
+
+172
+00:19:13,820 --> 00:19:18,040
+ال unit لا لا مش صحيح هذا الخلاب يبقى كل شغلة
+
+173
+00:19:18,040 --> 00:19:22,300
+مرتبطة بال binary operation اللي مخطوطة على ال
+
+174
+00:19:22,300 --> 00:19:30,140
+ring يبقى هنا ال zero element is one السبب because
+
+175
+00:19:30,140 --> 00:19:43,480
+if M موجودة في Z موجودة في Z then ال Mزائد الواحد
+
+176
+00:19:43,480 --> 00:19:50,440
+زائد
+
+177
+00:19:50,440 --> 00:19:57,980
+الواحد زائد الواحد زائد الواحد زائد الواحد زائد
+
+178
+00:19:57,980 --> 00:20:05,500
+الواحد زائد الواحد زائد الواحد زائد الواحد زائد
+
+179
+00:20:05,500 --> 00:20:08,360
+الواحد زائد الواحد زائد الواحد زائد الواحد زائد
+
+180
+00:20:08,360 --> 00:20:09,260
+الواحد زائد الواحد زائد الواحد زائد الواحد زائد
+
+181
+00:20:09,260 --> 00:20:18,520
+الواحدطيب اننا نيجي الأن لأول نظرية على هذا
+
+182
+00:20:18,520 --> 00:20:28,940
+الموضوع theorem if
+
+183
+00:20:28,940 --> 00:20:37,060
+R is a ring and
+
+184
+00:20:46,600 --> 00:20:57,640
+ثم نمر واحد ال a في ال zero ساوي zero دي ساوي zero
+
+185
+00:20:57,640 --> 00:21:07,060
+في a دي ساوي zero نمر اتنين ال a ناقص b ساوي ناقص
+
+186
+00:21:07,060 --> 00:21:18,220
+a في ال b ساوي ناقص a في bنقطة التالتة ناقص a في
+
+187
+00:21:18,220 --> 00:21:28,920
+ناقص b يسوي ab النقطة الرابعة a في b ناقص c يسوي
+
+188
+00:21:28,920 --> 00:21:40,600
+ab ناقص ac و ال b ناقص c في a يسوي ba ناقص ca
+
+189
+00:21:43,140 --> 00:21:47,360
+الـ A is
+
+190
+00:21:47,360 --> 00:21:56,880
+a ring with unity لو كانت هذه ال ring فيها unity
+
+191
+00:21:56,880 --> 00:22:07,700
+then رقم خمسة اللي هو سالب واحد في A دو سوى سالب A
+
+192
+00:22:07,700 --> 00:22:23,520
+رقم ستة سالب واحدبسالف واحد يساوي واحد الامر
+
+193
+00:22:23,520 --> 00:22:29,120
+يجب ان انا على اول نظرية على موضوع ال ring النظرية
+
+194
+00:22:29,120 --> 00:22:34,880
+بتقول اه ال ring وفي عندى خت تلت عناصر عشوائيا
+
+195
+00:22:34,880 --> 00:22:40,460
+موجودة في هذا ال ring هي ال a والb والc يرجعبدي
+
+196
+00:22:40,460 --> 00:22:47,140
+أثبت صحة الستة اللي هو more than أو الستة حالات
+
+197
+00:22:47,140 --> 00:22:51,740
+اللي قلناها طبعا الناظر الأول وهلها بيقولها ما هي
+
+198
+00:22:51,740 --> 00:22:55,100
+مديهي ايه في zero هي في zero في ايه في zero طبيعي
+
+199
+00:22:55,100 --> 00:22:59,540
+طبيعي هدف ال real numbers بس في ال group في ال
+
+200
+00:22:59,540 --> 00:23:02,880
+rings اللي هو موضوع دراستنا يمكن يكون الكلام مش
+
+201
+00:23:02,880 --> 00:23:08,160
+صحيح فمشان يكون صحيح بنروح نثبت صحته حتى نعتمده
+
+202
+00:23:08,160 --> 00:23:15,110
+بعد ذلكالان بدأجي للحالة الاولى الحالة الاولى بدي
+
+203
+00:23:15,110 --> 00:23:21,690
+اثبت ان a في zero هو zero في a وهو يساوي zero لذلك
+
+204
+00:23:21,690 --> 00:23:28,810
+لو جيت قلت لك خديلي a في zero زائد zero هذا الكلام
+
+205
+00:23:28,810 --> 00:23:34,470
+لو جيت فاكته حسب ال distributive law يبقى هذا a في
+
+206
+00:23:34,470 --> 00:23:42,790
+zero زائد a في zeroلو أخدت نفس المقدار A في Zero
+
+207
+00:23:42,790 --> 00:23:48,770
+زائد Zero نفس حاصنة ضارب و روحت مافكتش زي قبل بال
+
+208
+00:23:48,770 --> 00:23:52,790
+Distributive load و روحت قول Zero زائد Zero جدن
+
+209
+00:23:52,790 --> 00:24:02,130
+Zero يبقى هذا صار A في Zero تمام؟ من اتنين هدول مع
+
+210
+00:24:02,130 --> 00:24:07,500
+بعض الطرف الشمال هو الطرف الشماليبقى الطرف اليمين
+
+211
+00:24:07,500 --> 00:24:13,700
+هو الطرف اليمين يبقى ال A في Zero زائد ال A في
+
+212
+00:24:13,700 --> 00:24:20,360
+Zero بده ساوي ال A في Zero لو أضفنا سالب هذا
+
+213
+00:24:20,360 --> 00:24:28,260
+العنصر للطرفين يعني سارعين دي A في Zero زائد A في
+
+214
+00:24:28,260 --> 00:24:35,000
+Zero ناقص A في Zero بده ساوي A Zero ناقص A Zero
+
+215
+00:24:35,730 --> 00:24:42,710
+الان هذا ال element قداش بيطلع ال zero صح ولا لأ
+
+216
+00:24:42,710 --> 00:24:49,350
+يبقى صار a note زائد ال zero بده يساوي zero مش a
+
+217
+00:24:49,350 --> 00:24:54,770
+note ايه في zero وليس a note ايه في zero يبقى معنى
+
+218
+00:24:54,770 --> 00:25:00,790
+هذا الكلام ان ال a في zero بده يساوي قداش zero
+
+219
+00:25:00,790 --> 00:25:06,370
+يبقى أثبت لهالطرف هذا بدي أثبت الطرف هذا زي هذا
+
+220
+00:25:06,370 --> 00:25:14,010
+بالضبط تماما إذا بروح بقوله similarly بنفس الطريقة
+
+221
+00:25:14,010 --> 00:25:24,110
+zero في a بدي ساوي zero يبقى دص وهكذا اللي هو ال a
+
+222
+00:25:24,110 --> 00:25:32,980
+في zero بدي ساوي zero في a بدي ساويبدي يساوي zero
+
+223
+00:25:32,980 --> 00:25:40,140
+و هو المطلوب بدي اجيلا نمره اتنين من النظرية بقول
+
+224
+00:25:40,140 --> 00:25:45,440
+ال A في ناقص B يساوي ناقص A في B يساوي ناقص ال برة
+
+225
+00:25:45,440 --> 00:25:52,100
+و ال B مع بعض يعني لو كان عندي سلب العنصر و ضربت A
+
+226
+00:25:52,100 --> 00:25:57,440
+فيهتماما سالب العنصر الآخر كما لو ضربته في بيه
+
+227
+00:25:57,440 --> 00:26:03,340
+وهذا سالب اللي هو حاصل الضرب a بيه بدى أروح أثبت
+
+228
+00:26:03,340 --> 00:26:07,940
+صحة هذا الكلام بنفس الفكرة الآن يا بنات لو جيت
+
+229
+00:26:07,940 --> 00:26:16,300
+قولتلك سالب a بيه زائد ال a في ال b زائد ال a في
+
+230
+00:26:16,300 --> 00:26:23,790
+ال b قدش انها تاني؟ Zero ممتاز جداطب لو قلتلك ال A
+
+231
+00:26:23,790 --> 00:26:32,710
+في سالب B ال A في سالب B بقاله الشكل هذا اللي هو
+
+232
+00:26:32,710 --> 00:26:39,570
+ال A اللي هي الأولى هذى بدي أحاول أشوفها مع مين؟
+
+233
+00:26:39,570 --> 00:26:49,450
+مع ال B كدهش بتعطيني تمام؟ يبقى سالب A في Bزائد a
+
+234
+00:26:49,450 --> 00:26:55,410
+في b بده يساوي zero بدي أخد الآن a في سالف b زائد
+
+235
+00:26:55,410 --> 00:27:01,770
+ab في عندنا من خلال ال distributive law بقدر أكتب
+
+236
+00:27:01,770 --> 00:27:11,790
+هذه هي a في سالف b زائد b مظبوطة؟ صح؟ طيب السالف b
+
+237
+00:27:11,790 --> 00:27:18,340
+زائد b بجد ال zero elementيبقى هذه صارت A في Zero
+
+238
+00:27:18,340 --> 00:27:24,880
+طب ال A في Zero بقدرش Zero يبقى هذه صارت ب Zero من
+
+239
+00:27:24,880 --> 00:27:31,300
+part one من الحالة الأولى طب من الحالتين الأثنين
+
+240
+00:27:31,300 --> 00:27:37,120
+هذول مع بعض ايش ماقدر أستنتج هذا يساوي Zero و هذا
+
+241
+00:27:37,120 --> 00:27:42,720
+يساوي Zero إذا الطرفين بيساوي بعض يبقى بناء العليل
+
+242
+00:27:42,880 --> 00:27:51,280
+اللي هو ناقص a b زائد ال a b بدي ساوي ال a في ناقص
+
+243
+00:27:51,280 --> 00:27:59,980
+b زائد ال a b لو أضفت سالب العنصر هذا للطرفين يعني
+
+244
+00:27:59,980 --> 00:28:05,940
+المعكوس الجمعي لل a b يعني سالب a b للطرفين إيش
+
+245
+00:28:05,940 --> 00:28:13,800
+بضلنا يا بنات هنا بضل a في ناقص b يساوي 100يساوي
+
+246
+00:28:13,800 --> 00:28:23,760
+ناقص a في b مظبوط ايه؟ as in هذه هي هذه صح؟ بنفس
+
+247
+00:28:23,760 --> 00:28:30,500
+الطريقة يبقى similarly بنفس
+
+248
+00:28:30,500 --> 00:28:35,500
+الطريقة we have انه
+
+249
+00:28:35,500 --> 00:28:46,780
+هيكون ناقص a في b بدي ساوي ناقص abوهكذا راس ال A
+
+250
+00:28:46,780 --> 00:28:54,700
+ناقص B يساوي ناقص A في B يساوي ناقص A في B وهو
+
+251
+00:28:54,700 --> 00:28:59,180
+المطلوب النقطة
+
+252
+00:28:59,180 --> 00:29:06,340
+التالتة النقطة التالتة بيقول سالب A في سالب B
+
+253
+00:29:06,340 --> 00:29:12,320
+تساوي AB يجب أن أمسك الطرف الأيسرو احاول اوصله
+
+254
+00:29:12,320 --> 00:29:22,540
+لطرف الايمد يبقى هذه ناقص a في ناقص b ويساوي بدى
+
+255
+00:29:22,540 --> 00:29:30,000
+استخدم الخاصية رقم اتنين هذا element وهذا ناقص b
+
+256
+00:29:30,000 --> 00:29:38,480
+يبقى هذا الكلام بده يساوي ناقص ناقص a في b صحيح من
+
+257
+00:29:38,480 --> 00:29:48,500
+وين؟الخاصية رقم اتنين يبقى هذا from part two يبقى
+
+258
+00:29:48,500 --> 00:29:54,040
+هذا من part two هذا الكلام يساوي هذه الناقص اللي
+
+259
+00:29:54,040 --> 00:30:02,540
+برا وهذه من part two كذلك يساوي الناقص لناقص a في
+
+260
+00:30:02,540 --> 00:30:10,820
+b برضه من وين from part two نفس الشيءهذا الكلام
+
+261
+00:30:10,820 --> 00:30:15,340
+ناقص في ناقص a في b يعطينا زائد يبقى هذا بدي
+
+262
+00:30:15,340 --> 00:30:22,060
+يعطينا a في b مباشرة إذا ناقص a في ناقص b بدي
+
+263
+00:30:22,060 --> 00:30:29,680
+بيساوي a في b النقطة الرابعة النقطة الرابعة بدي
+
+264
+00:30:29,680 --> 00:30:37,420
+أخد a في b ناقص ال c احنا
+
+265
+00:30:37,420 --> 00:30:43,960
+أخدنا على ال ringالعملية هذه صحيحة A في B زائد الـ
+
+266
+00:30:43,960 --> 00:30:50,740
+C يساوي AB زائد AC صح؟ تمام، بس النقص ماخنهاش،
+
+267
+00:30:50,740 --> 00:30:56,920
+مظبوط؟ بدنا نثبتها صحيحة لعملية طرح أنصرين من
+
+268
+00:30:56,920 --> 00:31:02,840
+بعضهم مع التوزيع، يعني قانون التوزيع مش مع
+
+269
+00:31:02,840 --> 00:31:07,860
+الجماعة، الطرح كذلك، بدي أثبت صحته، هذا الكلام
+
+270
+00:31:07,860 --> 00:31:16,320
+بقدر أكدهA في B زائد لناقص C حد بيقدر أقول إن
+
+271
+00:31:16,320 --> 00:31:21,140
+كلامك مش مظبوط هذا؟ مظبوط لأني زاد في ناقص في ناقص
+
+272
+00:31:21,140 --> 00:31:31,120
+طيب هذا الكلام يساوي AB زائد A في ناقص C هذا
+
+273
+00:31:31,120 --> 00:31:35,040
+مينابع ناقص قانون الـ distributive law يدخل على
+
+274
+00:31:35,040 --> 00:31:42,300
+الجامعة يدخل لا على الجامعةلكن هذه من part two من
+
+275
+00:31:42,300 --> 00:31:49,240
+part two هي مقبض تماما يساوي ناقص حاصل الضرب تبعه
+
+276
+00:31:49,240 --> 00:31:59,740
+يبقى هذه يساوي a في b ناقص a في c من part two أظن
+
+277
+00:31:59,740 --> 00:32:05,210
+هو المطلوب، خلصنا، يبقى تنفع لعملية الجمعوالعملية
+
+278
+00:32:05,210 --> 00:32:11,850
+الطرح اللي هو خاصية التوزيع بنفس الطريقة similar
+
+279
+00:32:11,850 --> 00:32:21,190
+الو مين بي ناقص ال C في ال A بيساوي بيساوي مين
+
+280
+00:32:21,190 --> 00:32:28,390
+بيساوي بي في ال A ناقص ال C في ال A خلصنا النقطة
+
+281
+00:32:28,390 --> 00:32:34,950
+الرابعة لنروح للنقطة الخامسةأول أربع نقاط مالهمش
+
+282
+00:32:34,950 --> 00:32:39,190
+دعوة ال ring فيها unity و لا unity ما تكون تكون
+
+283
+00:32:39,190 --> 00:32:45,090
+الخامسة الاساسة باننا نشترق وجود ال unity يعني ال
+
+284
+00:32:45,090 --> 00:32:49,930
+identity element في ال ring ا فبتقول الخاصية
+
+285
+00:32:49,930 --> 00:32:55,530
+الخامسة اللي هو ناقص واحد في ايه بالمناسبة انه
+
+286
+00:32:55,530 --> 00:33:04,110
+يساوي ناقص ايه بدي ارجع لاستخدامالخاصية رقم اتنين
+
+287
+00:33:04,110 --> 00:33:12,190
+ناقص واحد في ايه ال unity هو عنصر يبقى ال unity هو
+
+288
+00:33:12,190 --> 00:33:18,330
+عنصر موجود في ال group ايه ناقص واحد يعني الخاصية
+
+289
+00:33:18,330 --> 00:33:26,690
+هذه يبقى هذه ايش بتتساوي ناقص واحد في ايه يبقى هذه
+
+290
+00:33:26,690 --> 00:33:33,390
+من part two مظبوط؟طب ال unity لما أنا أضربه في
+
+291
+00:33:33,390 --> 00:33:41,110
+عنصر يطلع نفسي عنصر إذا يساوي ناقص A وهو المطلوب
+
+292
+00:33:41,110 --> 00:33:48,450
+خلصنا منه الآن رقم ستة اللي هو ناقص واحد في ناقص
+
+293
+00:33:48,450 --> 00:33:53,970
+واحد بدي أثبت إنه يساوي مين؟ يساوي طلعيني ليه ال
+
+294
+00:33:53,970 --> 00:34:00,840
+system اللي بدنا نثبتها طلعيني ليه تلاتةبدي أخد a
+
+295
+00:34:00,840 --> 00:34:09,660
+تساوي b تساوي واحد يبقى باجي بقول هذه تساوي واحد
+
+296
+00:34:09,660 --> 00:34:23,000
+from part a three with a تساوي ال b تساوي واحد وهو
+
+297
+00:34:23,000 --> 00:34:26,680
+المطلوب طيب
+
+298
+00:34:27,510 --> 00:34:35,390
+بنجي لنظرية ثانية دون اثباتها ايش النظرية التانية؟
+
+299
+00:34:35,390 --> 00:34:40,270
+فاكرين ال group؟ و بجينا نجيب ال identity element
+
+300
+00:34:40,270 --> 00:34:47,530
+صح؟ و معكوس ال element طيب ال unity هذا او ال
+
+301
+00:34:47,530 --> 00:34:51,110
+identity element في هال group اكتر من ال identity
+
+302
+00:34:51,110 --> 00:34:58,140
+element؟ وحيد مافيش .. و هنا ال ring وحيد طيبمعكوس
+
+303
+00:34:58,140 --> 00:35:05,280
+العنصر، وحيد، إذا كانت بجينا نثبتهم في الجبر واحد،
+
+304
+00:35:05,280 --> 00:35:10,660
+بجينا بنثبت ان عندي two identity elements و بنحاول
+
+305
+00:35:10,660 --> 00:35:15,400
+نكون اتنين are equal عندي two inverses و بنحاول
+
+306
+00:35:15,400 --> 00:35:20,260
+نثبت ان اتنين are equal و فعلا أثبتنا هذا مع
+
+307
+00:35:20,260 --> 00:35:24,670
+الدكتور محمدمظبوط يبقى لا داعي ليه تكرار الإتباه
+
+308
+00:35:24,670 --> 00:35:28,890
+تماما من الذكية ترجعيله من دفترك أو من اللي اكتر
+
+309
+00:35:28,890 --> 00:35:39,130
+يبقى نظرية بتقول ما يأتي سويا يا ربي if
+
+310
+00:35:39,130 --> 00:35:48,310
+الار is a ring with unity if الار is a ring with
+
+311
+00:35:48,310 --> 00:35:50,170
+unity
+
+312
+00:35:57,550 --> 00:36:06,990
+then the unity then the unity is
+
+313
+00:36:06,990 --> 00:36:16,310
+unique يكون وحيدا هذا النقطة الأولى النقطة التانية
+
+314
+00:36:16,310 --> 00:36:32,860
+if ايه if if they belongto a ring A الموجود في R
+
+315
+00:36:32,860 --> 00:36:40,720
+with multiplicative
+
+316
+00:36:40,720 --> 00:36:50,640
+inverse with
+
+317
+00:36:50,640 --> 00:36:53,700
+multiplicative inverse
+
+318
+00:36:58,510 --> 00:37:03,950
+ثم هذا انبسط
+
+319
+00:37:27,390 --> 00:37:35,050
+مرة تانية بقول هذه if
+
+320
+00:37:35,050 --> 00:37:41,530
+R is a ring with unity then the unity is unity
+
+321
+00:37:41,530 --> 00:37:47,730
+ماعنديش فى ال ring إلا unity وحيد فقط لغى بعد هيك
+
+322
+00:37:47,730 --> 00:37:52,670
+لو كان ال A اللى موجود فى ال ring R إله معكوس يعني
+
+323
+00:37:52,670 --> 00:37:57,890
+إيش سمناه؟ إيش سمناه المضارف هذه؟ unitيبقى لو كان
+
+324
+00:37:57,890 --> 00:38:02,530
+unit يعني له معكوس يبقى ال unit هذا يكون وحيدا
+
+325
+00:38:02,530 --> 00:38:07,690
+فالمعكوس المطبق negative inverse له بيكون وحيد
+
+326
+00:38:07,690 --> 00:38:12,710
+مافيهش غيره البرهان نفس البرهان تبع ال groups
+
+327
+00:38:12,710 --> 00:38:18,290
+بالضبط تماما لا زيادة ولا نقصان يبقى لا داعي لتضيع
+
+328
+00:38:18,290 --> 00:38:23,650
+الوقت فيه في عندنا ملاحظات هنا يبقى lots
+
+329
+00:38:26,690 --> 00:38:36,790
+ملاحظة الأولى if ال A و ال B و ال C موجودة فى ring
+
+330
+00:38:36,790 --> 00:38:44,910
+R و ال R is a ring and
+
+331
+00:38:44,910 --> 00:38:56,590
+ال A ضماء equal to zero then ال A فى Bبساوي A بC
+
+332
+00:38:56,590 --> 00:39:08,890
+ضغمة imply أن ال B تساوي C because .. إيش السبب؟
+
+333
+00:39:38,990 --> 00:39:43,070
+مرة تانية بقولوا لو عندي ثلاث علاقات وموجودات في
+
+334
+00:39:43,070 --> 00:39:48,130
+ال ring R وكان ال A لا يساوي زيرو وعندي معلومة
+
+335
+00:39:48,130 --> 00:39:54,050
+بتقول انه حاصل ضرب A في B بيساوي A في C فهل هذا
+
+336
+00:39:54,050 --> 00:40:00,790
+يتطلب انه B تساوي C؟ الإجابة قد يكون وقد لا يكون
+
+337
+00:40:00,790 --> 00:40:08,520
+يبقى in general لا يكون ليش؟ ليش؟ هل أنا قلتإنه
+
+338
+00:40:08,520 --> 00:40:14,580
+ليه ال a is a unit؟ لأ ماقلتش ال a is unit ممكن
+
+339
+00:40:14,580 --> 00:40:20,180
+يكون أي رقم ولا يوجد له معكوس يعني أي عنصر وهذا
+
+340
+00:40:20,180 --> 00:40:25,660
+العنصر ليس له معكوس إذا لا يمكن ال a بيساوي a c
+
+341
+00:40:25,660 --> 00:40:32,220
+أستنتج ان ال b تساوي من ال c لإن ال a ممكن يكون
+
+342
+00:40:32,220 --> 00:40:42,050
+unit وممكن مايكونش unit becauseالإيه؟ may or may
+
+343
+00:40:42,050 --> 00:40:50,910
+not unit يعني ممكن يكون له معكوس وممكن ليه مايكونش
+
+344
+00:40:50,910 --> 00:40:55,770
+له معكوس لو إله معكوس بضربه في المعادلة من جهة
+
+345
+00:40:55,770 --> 00:41:00,990
+الشمال بظل النبي يسويسي طب لو مانوش معكوس مش
+
+346
+00:41:00,990 --> 00:41:07,130
+ممكنية زي مين؟زي اتنين و تلاتة في الـ Z، six اتنين
+
+347
+00:41:07,130 --> 00:41:13,010
+و تلاتة، اتنين في تلاتة بستة يعني كداش؟ Zero صح
+
+348
+00:41:13,010 --> 00:41:18,450
+ولا لا؟ يبقى هل اتنين والتلاتة اللي هم معكوز؟ ولا
+
+349
+00:41:18,450 --> 00:41:23,130
+واحد فيهم اللي معكوز؟ تمام؟ يبقى في هذه الحالة،
+
+350
+00:41:23,130 --> 00:41:28,350
+مدام ما لهش معكوز، ماقدرش اقول ان ا في B بده يساوي
+
+351
+00:41:28,350 --> 00:41:33,650
+ا في C، يبقى الـ B تساوي Cالامر الثاني او الملاحظة
+
+352
+00:41:33,650 --> 00:41:44,910
+الثانية if ال a belongs to ring R when اللي و من
+
+353
+00:41:44,910 --> 00:41:57,370
+ال a تربيع بده ساوي ال a we cannot say that لا
+
+354
+00:41:57,370 --> 00:42:02,780
+يمكن او لا نستطيع ان نقولو you cannot say that ان
+
+355
+00:42:02,780 --> 00:42:21,560
+ال a تساوي zero or ال a تساوي ال واحد because طيب
+
+356
+00:42:21,560 --> 00:42:27,380
+قبل ما نقول because في نهاية الشركة انا بدي افكر
+
+357
+00:42:27,870 --> 00:42:35,570
+بقول a تربية تساول a اظن ان اذا قلت a تربية ناقص
+
+358
+00:42:35,570 --> 00:42:41,370
+يساوي 0 محدش بيعترض عليه جتنا ال distributive law
+
+359
+00:42:41,370 --> 00:42:48,190
+قلت بقدر اقول a في a ناقص واحد يساوي 0 هنا بتطوروا
+
+360
+00:42:48,190 --> 00:42:54,950
+عليه تقولوا اللي هو ال ring هذي فيها unity ماجليش
+
+361
+00:42:54,950 --> 00:42:59,210
+فيها unityيبقى هذا الخطوة اللي عملتها صح ولا غلط؟
+
+362
+00:42:59,210 --> 00:43:03,010
+صح إذا كان ال ring فيها unity غلط إذا ال ring
+
+363
+00:43:03,010 --> 00:43:06,210
+فيهاش unity يبقى هذا الكلام يبعد لك الله حطه ع شجة
+
+364
+00:43:06,210 --> 00:43:12,610
+مش صحيح إذا لو كان هذا الكلام صحيح بقوله ممكن a
+
+365
+00:43:12,610 --> 00:43:18,150
+يساوي zero أو ال a تساوي واحد لكن الواحد هذا مش
+
+366
+00:43:18,150 --> 00:43:22,810
+موجود في ال ring بصير هذا الكلام ماله غلط على طول
+
+367
+00:43:22,810 --> 00:43:27,600
+القطريبقى هذا الكلام ايه يساوي zero او ايه يساوي
+
+368
+00:43:27,600 --> 00:43:35,340
+غلط يبقى we say that ان
+
+369
+00:43:35,340 --> 00:43:40,760
+ال a تساوي zero او ال a تساوي واحد انا ماعرف ايش
+
+370
+00:43:40,760 --> 00:43:46,240
+قلنا with a تلاقى we cannot say ايه نخيناها بدأوا
+
+371
+00:43:46,240 --> 00:43:50,920
+نعملها we cannot say نقدرش نقول ان a تساوي zero او
+
+372
+00:43:50,920 --> 00:44:04,070
+a تساوي واحدbecause they are may or may not have
+
+373
+00:44:04,070 --> 00:44:10,830
+unity يعني ممكن ان تكون فيها unity ويطلع الكلام
+
+374
+00:44:10,830 --> 00:44:14,550
+واضح وممكن مايكونش فيها unity هنا ماشترطناش ان
+
+375
+00:44:14,550 --> 00:44:21,410
+يكون فيها unity يبقى هذا الكلام ليس بالضرورة صحيح
+
+376
+00:44:21,980 --> 00:44:26,900
+نجي للألة تعريف جديد زي ما أخدته group بعد أخدته
+
+377
+00:44:26,900 --> 00:44:30,640
+ال sub group و أحنا أخدنا ring بدنا نروح ناخد sub
+
+378
+00:44:30,640 --> 00:44:36,660
+ring يبقى definition هي
+
+379
+00:44:36,660 --> 00:44:47,740
+subset هي subset S of subset
+
+380
+00:44:55,900 --> 00:45:04,080
+is of a ring R is
+
+381
+00:45:04,080 --> 00:45:16,440
+a sub ring
+
+382
+00:45:16,440 --> 00:45:21,280
+if ال S itself
+
+383
+00:45:25,230 --> 00:45:45,870
+is appearing نفسها under the operations on R فده
+
+384
+00:45:45,870 --> 00:45:51,430
+نسميها
+
+385
+00:45:51,430 --> 00:45:58,490
+sub ringtest a
+
+386
+00:45:58,490 --> 00:46:02,450
+non-empty
+
+387
+00:46:02,450 --> 00:46:21,190
+a non-empty subset S of a ring A is a subring F
+
+388
+00:46:39,370 --> 00:46:40,770
+التعريف يقول
+
+389
+00:46:53,400 --> 00:46:57,840
+التعريف بيقول ان ال subset S of a ring R بسميه sub
+
+390
+00:46:57,840 --> 00:47:04,560
+ring ما إذا كانت ال S نفسها بتظلها ring تحت نفس
+
+391
+00:47:04,560 --> 00:47:09,860
+العمليات اللي على R يعني احنا عندنا ring كبيرة،
+
+392
+00:47:09,860 --> 00:47:14,600
+خدنا منها شوية عناصر، تمام؟ العناصر هذه اللي جت ال
+
+393
+00:47:14,600 --> 00:47:18,780
+6 خواص طبعتها ال ring ينطبقوا عليها إن حدث ذلك
+
+394
+00:47:18,780 --> 00:47:23,990
+بقول هذه sub ring يعني بدي أثبت ال 6 خواصطيب يا
+
+395
+00:47:23,990 --> 00:47:28,090
+طلع هذه قصة طويلة، كان كل مرة بدي أسوي هيك، فراعوا
+
+396
+00:47:28,090 --> 00:47:33,590
+العلماء اكتشفوا هالشغلة هذه، سموها Subring Test إن
+
+397
+00:47:33,590 --> 00:47:39,750
+الـS صبست من أرض، بقول عنها Subring إذا حققت دي مش
+
+398
+00:47:39,750 --> 00:47:45,110
+ستة وإنما تلاتة خواصة، non-empty أخدت أي عنصرين
+
+399
+00:47:45,110 --> 00:47:48,710
+فيما بينهم، ولقيت الفرق فيما بينهم ما موجود في S
+
+400
+00:47:48,710 --> 00:47:53,780
+وحصل ضربه ما موجود كذلك في Sالمرة القادمة ان شاء
+
+401
+00:47:53,780 --> 00:47:59,140
+الله بنروح نخبط هذه النظرية لذلك بنقولك روحي مريلي
+
+402
+00:47:59,140 --> 00:48:03,320
+على القرآن اللي في الكتاب مرة سريعة بس يكون عندك
+
+403
+00:48:03,320 --> 00:48:08,520
+فكرة حتى و احنا بنشرح هنا تستمع بهذا الكلام ثم بعد
+
+404
+00:48:08,520 --> 00:48:13,340
+ذلك بناخد أمثلة عليها ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..cde8b5f08053496463785e42fdd1ab67ddf8a255
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4.srt
@@ -0,0 +1,1119 @@
+1
+00:00:20,920 --> 00:00:26,780
+بسم الله الرحمن الرحيم نبدأ اليوم Chapter جديد
+
+2
+00:00:26,780 --> 00:00:30,780
+اللي هو Chapter 18 اللي هو divisibility in
+
+3
+00:00:30,780 --> 00:00:36,120
+integral domains يعني القسمة داخل الـ integral
+
+4
+00:00:36,120 --> 00:00:41,760
+domains أو التحليل داخل الـ integral domains في
+
+5
+00:00:41,760 --> 00:00:46,840
+عندنا ثلاثة تعريفات أساسية للبدأ في هذا الـ Chapter هي
+
+6
+00:00:46,840 --> 00:00:52,180
+الثلاثة تعريفات قدامنا بنحاول نقرأها ونفهم مفهوم كل
+
+7
+00:00:52,180 --> 00:00:57,440
+تعريف من التعريفات الثلاثة. التعريف الأول بيقول two
+
+8
+00:00:57,440 --> 00:01:02,500
+elements here and here وما حط الشرط عليهم صفر غير
+
+9
+00:01:02,500 --> 00:01:06,660
+صفر units ما يعني أي two elements موجودات في الـ
+
+10
+00:01:06,660 --> 00:01:11,520
+integral domain D بيقول الـ are called associates
+
+11
+00:01:11,520 --> 00:01:18,420
+اتنين هدول بيكونوا مرتبطين مع بعض إذا كان واحد
+
+12
+00:01:18,420 --> 00:01:25,700
+منهم قدرت أكتبه حاصل ضرب الثاني في element ثاني الـ
+
+13
+00:01:25,700 --> 00:01:31,060
+element الثاني اللي هو u هذا is a unit يعني الـ a
+
+14
+00:01:31,060 --> 00:01:35,740
+بده يتساوي b مضروباً في unit و الـ unit هذا من الـ
+
+15
+00:01:35,740 --> 00:01:40,540
+integral domain اللي عليه إن حدث ذلك يبقى بقول الـ
+
+16
+00:01:40,540 --> 00:01:45,320
+a و الـ b are associates يبقى اتنين مرتبطين مع بعض
+
+17
+00:01:45,320 --> 00:01:50,410
+تماماً. التعريف الثاني بيقول a non-zero element of an
+
+18
+00:01:50,410 --> 00:01:55,750
+integral domain دي بيحط شرط أن العنصر غير صفر لكن
+
+19
+00:01:55,750 --> 00:02:02,270
+في التعريف الأول ما حطش هذا الشرط طبعاً يبقى a non
+
+20
+00:02:02,270 --> 00:02:06,230
+-zero element of an integral domain دي is called
+
+21
+00:02:06,230 --> 00:02:12,350
+irreducible يعني لا يمكن أفككه إلى حاصل ضرب two
+
+22
+00:02:12,350 --> 00:02:18,760
+elements أو أحلله إلى حاصل ضرب two elements إذا كان
+
+23
+00:02:18,760 --> 00:02:27,340
+الـ a not a unit يبقى هذا الشرط أساسي أن الـ a is not
+
+24
+00:02:27,340 --> 00:02:31,980
+a unit هذه النقطة الأولى، النقطة الثانية الـ
+
+25
+00:02:31,980 --> 00:02:38,940
+عنصرين p و c موجودة في p with الـ a يساوي حاصل ضرب
+
+26
+00:02:38,940 --> 00:02:44,950
+p في c يبقى الشرط الثاني لو لقيت عنصرين حاصل
+
+27
+00:02:44,950 --> 00:02:50,610
+ضربهما يساوي الـ element a اللي هو غير الصفري و اللي
+
+28
+00:02:50,610 --> 00:02:55,390
+هو الـ irreducible يبقى الـ p و الـ c واحدة منهم لازم
+
+29
+00:02:55,390 --> 00:03:03,670
+تكون a unit طيب يبقى هنا العنصر بقول عنه
+
+30
+00:03:03,670 --> 00:03:10,250
+irreducible إذا تحقق شرطان: الشرط الأول أن الـ a is
+
+31
+00:03:10,250 --> 00:03:16,470
+not a unit تمام، الشرط الثاني لو لقيت حاصل ضرب عنصرين
+
+32
+00:03:16,470 --> 00:03:21,870
+يساوي هذا العنصر معناته واحد فيهم لازم يكون a unit
+
+33
+00:03:21,870 --> 00:03:27,530
+الـ a مش unit هدول واحد منهم بده يكون ماله؟ بده يكون
+
+34
+00:03:27,530 --> 00:03:33,390
+is a unit هذا معنى الـ irreducible الآن ننتقل إلى
+
+35
+00:03:33,390 --> 00:03:37,740
+التعريف الثالث، برضه non zero element in integral
+
+36
+00:03:37,740 --> 00:03:44,840
+domain D is called a prime.  A prime is associated to irreducible. A prime
+
+37
+00:03:44,840 --> 00:03:49,520
+التعريف الثالث يبقى بتقول عنه A prime إذا
+
+38
+00:03:49,520 --> 00:03:55,000
+تحقق شرطان: الشرط الأولاني برضه قالوا ما هوش unit
+
+39
+00:03:55,000 --> 00:04:00,720
+زي الحالة الأولى من التعريف الثاني، والشرط
+
+40
+00:04:00,720 --> 00:04:05,810
+الثاني لو كان a بيقسم الـ b في الـ c يبقى بده يقسم
+
+41
+00:04:05,810 --> 00:04:13,490
+أحدهما يا إما بيقسم الـ b يا إما بيقسم الـ c نبدأ
+
+42
+00:04:13,490 --> 00:04:21,130
+نعطي بعض الأمثلة البسيطة. فمثلاً لو جيت قُلت أنا بدي
+
+43
+00:04:21,130 --> 00:04:29,850
+آخذ الـ Z is an integral domain صحيح؟ اه it is an
+
+44
+00:04:29,850 --> 00:04:35,820
+integral domain تمام؟ لو وجد حاصل ضرب عنصرين n يساوي
+
+45
+00:04:35,820 --> 00:04:41,360
+صفر، ليس يمكن أن يحدث ذلك إلا إذا كان أحدهما يساوي
+
+46
+00:04:41,360 --> 00:04:48,180
+صفر على الأقل. يبقى أنا عندي Z an integral domain
+
+47
+00:04:48,180 --> 00:04:53,680
+طيب بدي أشوف أحكاية الـ irreducible و الـ
+
+48
+00:04:53,680 --> 00:04:58,720
+irreducible لو رحت أخدت any integer n
+
+49
+00:05:01,030 --> 00:05:08,850
+مرتبط مع مين؟ مرتبط مع نفسه ومع -n مظبوط؟ طيب
+
+50
+00:05:08,850 --> 00:05:14,090
+ليش؟ مرتبط مع نفسه لأنه لا يوجد units في Z إلا
+
+51
+00:05:14,090 --> 00:05:20,050
+اثنين: الواحد و الـ -1، مظبوط؟ يبقى الـ n بقدر
+
+52
+00:05:20,050 --> 00:05:25,750
+أكتبه 1 × n والـ -n بقدر أكتبه -1 × n
+
+53
+00:05:25,750 --> 00:05:31,470
+تمام؟ يبقى صار مين؟ صار -n يساوي -1 × n
+
+54
+00:05:31,470 --> 00:05:37,550
+و الـ -1 is a unit والواحد is a unit
+
+55
+00:05:37,550 --> 00:05:44,670
+كذلك. يبقى هذا طبقاً للتعريف الأول: integral domain والـ
+
+56
+00:05:44,670 --> 00:05:49,290
+a و b موجودات فيها، يبقى اتنين associated إذا كان
+
+57
+00:05:49,290 --> 00:05:53,910
+واحد كتبتها بدلالة الثاني بس اللي بدي أضرب فيه
+
+58
+00:05:53,910 --> 00:05:58,670
+بده يكون إيش؟ بده يكون unit تمام؟ مش أي رقم، كويس. طيب المثال اللي احنا سمعناه فبنروح
+
+59
+00:05:58,670 --> 00:06:04,250
+نسجله مشان ما يضيع علينا واحنا بنذكر يبقى
+
+60
+00:06:04,250 --> 00:06:09,910
+النقطة الأولى بدي آخذ every non-zero integer every
+
+61
+00:06:09,910 --> 00:06:15,670
+non-zero integer in
+
+62
+00:06:15,670 --> 00:06:24,530
+Z has exactly  has exactly بالضبط has exactly two
+
+63
+00:06:27,670 --> 00:06:38,110
+associates. has exactly two
+
+64
+00:06:38,110 --> 00:06:43,590
+associates
+
+65
+00:06:43,590 --> 00:06:47,690
+in
+
+66
+00:06:47,690 --> 00:06:52,590
+Z اللي
+
+67
+00:06:52,590 --> 00:07:03,060
+هم مين؟ الـ n و الـ -n because the
+
+68
+00:07:03,060 --> 00:07:19,880
+only units in Z اللي هو ±1 that is
+
+69
+00:07:19,880 --> 00:07:23,600
+in Z
+
+70
+00:07:25,060 --> 00:07:32,960
+بده يساوي 1 × n و الـ -n يساوي -1 × n
+
+71
+00:07:32,960 --> 00:07:43,860
+لكل الـ n الموجودة في Z.
+
+72
+00:07:44,120 --> 00:07:50,560
+طيب المثال الثاني، المثال
+
+73
+00:07:50,560 --> 00:07:59,410
+الثاني بيقول the irreducible elements the irreducible
+
+74
+00:07:59,410 --> 00:08:05,770
+elements
+
+75
+00:08:05,770 --> 00:08:20,030
+in Z are just the
+
+76
+00:08:20,030 --> 00:08:22,010
+أعداد صحيحة
+
+77
+00:08:32,660 --> 00:08:39,420
+مين يا بنات؟ من العناصر الموجودة في Z اللي
+
+78
+00:08:39,420 --> 00:08:45,440
+ما أقدرش أحللها إلا إذا كان قلت العنصر فيه unit.
+
+79
+00:08:46,420 --> 00:08:50,680
+الأعداد الأولية الممتازة جداً. يبقى الأعداد الأولية زائد مين؟ يكون
+
+80
+00:08:50,680 --> 00:08:53,860
+2، 3، 5، 7، 11، 13،
+
+81
+00:08:53,860 --> 00:08:58,930
+17، 19، إلى آخره. يبقى هدول هم الـ
+
+82
+00:08:58,930 --> 00:09:09,350
+prime integers يبقى just the prime integers لأن الـ
+
+83
+00:09:09,350 --> 00:09:14,330
+prime integers لا يقسم إلا على نفسه وعلى الواحد
+
+84
+00:09:14,330 --> 00:09:18,550
+الصحيح because
+
+85
+00:09:18,550 --> 00:09:25,150
+the only divisors
+
+86
+00:09:27,070 --> 00:09:40,050
+the only divisors of a prime p أو
+
+87
+00:09:40,050 --> 00:09:49,610
+-p و ±1،  Its Associates and
+
+88
+00:09:49,610 --> 00:09:52,410
+Associates and
+
+89
+00:09:54,880 --> 00:10:05,800
+±1 اللي هم الـ units Z يبقى الـ units
+
+90
+00:10:05,800 --> 00:10:15,760
+الموجودة في Z الـ p
+
+91
+00:10:15,760 --> 00:10:30,520
+is not a unit ما هوش unit والـ p بدها تساوي 1
+
+92
+00:10:30,520 --> 00:10:45,040
+مضروبة في p هذا بدي أعطيك واحد is a unit يبقى
+
+93
+00:10:45,040 --> 00:10:49,980
+المثال الثاني بيقول the irreducible elements في Z
+
+94
+00:10:49,980 --> 00:10:55,910
+هم بالضبط الـ prime numbers تمام؟ الـ prime مرة
+
+95
+00:10:55,910 --> 00:11:01,110
+بيحط له الرمز p، ليش؟ لأن الـ only divisor of
+
+96
+00:11:01,110 --> 00:11:06,070
+الـ prime p له الـ p و الـ -p و الـ 1 و الـ -1
+
+97
+00:11:06,070 --> 00:11:10,570
+ما فيش غيرهم، فلو قلت الـ p و الـ -p هدول الـ
+
+98
+00:11:10,570 --> 00:11:18,130
+associates طبقاً للتعريف الأول، تمام؟ و... وكذلك الـ
+
+99
+00:11:18,130 --> 00:11:24,060
+units اللي هم ±1، ليش؟ لأنه لما نيجي
+
+100
+00:11:24,060 --> 00:11:30,220
+على الـ irreducible تعريفه يبقى هو non-zero integer هذا
+
+101
+00:11:30,220 --> 00:11:35,600
+بنسميه irreducible إذا كان not a unit يبقى قولنا هنا الـ p
+
+102
+00:11:35,600 --> 00:11:41,060
+not a unit ما هوش unit تمام؟ and whenever وإذا كان
+
+103
+00:11:41,060 --> 00:11:46,620
+حاصل ضربهما بده يساوي هذا الـ element يبقى واحد منهم
+
+104
+00:11:46,620 --> 00:11:52,840
+بده يكون هو عبارة عن unit طيب نيجي لأول ملاحظة في
+
+105
+00:11:52,840 --> 00:12:02,640
+هذا الـ section يبقى remark بيقول
+
+106
+00:12:02,640 --> 00:12:09,880
+let a belong to
+
+107
+00:12:09,880 --> 00:12:11,260
+an integral domain
+
+108
+00:12:21,550 --> 00:12:31,130
+و الـ a لا تساوي صفر، الـ a لا تساوي صفر، ثم الـ a is a
+
+109
+00:12:31,130 --> 00:12:40,870
+prime. الـ a is a prime if and only if if and only
+
+110
+00:12:40,870 --> 00:12:49,010
+if the principal ideal generated by a is a prime
+
+111
+00:12:49,010 --> 00:12:50,650
+ideal
+
+112
+00:13:03,930 --> 00:13:10,310
+D مرة ثانية، أخذنا عنصر a مولد في الـ integral
+
+113
+00:13:10,310 --> 00:13:15,630
+domain D والعنصر a لا يساوي صفر يبقى non-zero
+
+114
+00:13:15,630 --> 00:13:20,290
+element زي ما اشتغلناها في التعريفات الاتنين دول non-
+
+115
+00:13:20,290 --> 00:13:25,550
+zero element، قال الـ a is a prime يبقى هذا بده
+
+116
+00:13:25,550 --> 00:13:29,090
+يكون prime number if and only if الـ principal
+
+117
+00:13:29,090 --> 00:13:34,750
+ideal generated by a is a prime ideal يبقى البرهان
+
+118
+00:13:34,750 --> 00:13:42,330
+بده يصير باتجاهين يبقى برجع بقول assume افترض
+
+119
+00:13:42,330 --> 00:13:49,630
+أن الـ a is a prime إيش بده نطبق هنا بنات؟ إنه هذا
+
+120
+00:13:49,630 --> 00:13:55,090
+هو prime ideal. طب هذا احنا عارفين إنه هو ideal
+
+121
+00:13:55,090 --> 00:13:59,470
+لأن الـ principal ideal generated by a إيش؟ يبقى we
+
+122
+00:13:59,470 --> 00:14:11,010
+know that. We know that أن هذا is an ideal اللي
+
+123
+00:14:11,010 --> 00:14:17,540
+بيضل علينا نثبت إيش؟ يبقى بآخذ عنصرين في D، أفرض أن
+
+124
+00:14:17,540 --> 00:14:23,040
+حاصل ضربهما موجود في الـ ideal دي، إذا قلت أثبت أن
+
+125
+00:14:23,040 --> 00:14:27,840
+أحدهما موجود في هذا الـ ideal بصير الـ ideal هذا a
+
+126
+00:14:27,840 --> 00:14:32,820
+prime مش هيك بنعرف الـ prime ideal يبقى بروح بقول له
+
+127
+00:14:32,820 --> 00:14:40,200
+let الـ x و الـ y موجودة وين؟ في الـ integral domain D
+
+128
+00:14:40,200 --> 00:14:49,760
+such that بحيث أن الـ xy موجودة في الـ principal
+
+129
+00:14:49,760 --> 00:14:55,780
+ideal generated by a إيش بدي أحاول أثبت؟ بدي أحاول
+
+130
+00:14:55,780 --> 00:15:01,160
+أثبت أن الـ x موجود في هذا الـ ideal أو الـ y موجود
+
+131
+00:15:01,160 --> 00:15:05,660
+في هذا الـ ideal. أن جربنا يبقى على طول الخط بصير الـ
+
+132
+00:15:05,660 --> 00:15:11,180
+ideal هذا prime ideal وبكون برهنة لإتجاه الأول
+
+133
+00:15:14,780 --> 00:15:20,020
+من خلال تعريف الـ principal ideal، الـ xy شبه
+
+134
+00:15:20,020 --> 00:15:29,740
+ما أقدر أكتبها a × b يبقى هذا a × b for some b
+
+135
+00:15:29,740 --> 00:15:37,580
+الموجودة وين؟ في الـ integral domain D كويس؟
+
+136
+00:15:37,580 --> 00:15:44,500
+فمعنى هذا الكلام أن a تقسم الـ xy صح ولا لا
+
+137
+00:15:44,860 --> 00:15:55,280
+يبقى هنا  أن الـ a تقسم الـ x × y. طيب احنا فاهمين و
+
+138
+00:15:55,280 --> 00:16:01,300
+هذا  يعيش  في  prime،  ليه  prime  هذا الثاني هو
+
+139
+00:16:01,300 --> 00:16:06,260
+التعريف الثاني لل prime، لو كانت a تقسم هذا يبقى
+
+140
+00:16:06,260 --> 00:16:18,750
+هتقسم أحدهما. يبقى this means then الـ a بتقسم الـ x أو الـ a
+
+141
+00:16:18,750 --> 00:16:28,030
+بتقسم الـ y. طيب مدام الـ a بتقسم الـ x أو الـ a بتقسم
+
+142
+00:16:28,030 --> 00:16:33,710
+الـ y يبقى بدنا نشوف إيش بدنا نستنتج من هذا الكلام
+
+143
+00:16:33,710 --> 00:16:39,890
+من هذا الكلام نستنتج أن الـ x بدها تساوي الـ a في عنصر
+
+144
+00:16:39,890 --> 00:16:48,790
+آخر، يبقى هذا بدي يعطينا إن الـ x بدها تساوي a مثلاً
+
+145
+00:16:48,790 --> 00:17:02,670
+في b1 تمام Or الـ y بدها تساوي مثلاً a في b2 و الـ b1
+
+146
+00:17:02,670 --> 00:17:14,470
+و الـ b2 موجودة في D، و الـ b1 و الـ b2 موجودة في. طيب
+
+147
+00:17:14,470 --> 00:17:22,430
+ما هو تفسيرك لهذا؟ الـ x يساوي a × عنصر ثاني
+
+148
+00:17:22,430 --> 00:17:26,650
+يبقى في الـ principal ideal generated by a أو الـ y
+
+149
+00:17:26,650 --> 00:17:30,830
+موجود في الـ principal ideal generated يبقى هنا
+
+150
+00:17:30,830 --> 00:17:36,730
+this means this
+
+151
+00:17:36,730 --> 00:17:46,240
+means that هذا يعني أن الـ x belongs to the
+
+152
+00:17:46,240 --> 00:17:52,740
+principal ideal generated by a أو الـ y belong to
+
+153
+00:17:52,740 --> 00:17:56,580
+the principal ideal generated by a إيش معنى هذا
+
+154
+00:17:56,580 --> 00:18:02,680
+الكلام أن هذا الـ ideal is a prime هذا بده يعطينا
+
+155
+00:18:02,680 --> 00:18:14,260
+الـ ideal اللي عندنا هذا is a prime ideal in D يبقى
+
+156
+00:18:14,260 --> 00:18:18,040
+انتهينا من الاتجاه الأول، بما نروح للاتجاه الثاني
+
+157
+00:18:18,040 --> 00:18:27,940
+بروح بقول إيش؟ converse تمام، يبقى assume that
+
+158
+00:18:27,940 --> 00:18:34,620
+نفترض أن الـ principal ideal generated by a is
+
+159
+00:18:34,620 --> 00:18:39,320
+a prime ideal
+
+160
+00:18:44,670 --> 00:18:52,730
+prime اه صحيح prime ideal بنفترض
+
+161
+00:18:52,730 --> 00:19:04,590
+هذا is a prime ideal indeed إيش بدنا نثبت؟ أن الـ a
+
+162
+00:19:04,590 --> 00:19:10,230
+في حد ذاتها is a prime، not a unit بدنا نثبت أن الـ a is
+
+163
+00:19:10,230 --> 00:19:15,330
+a prime. لو رجعنا هنا معناته بدنا نثبت نقطتين
+
+164
+00:19:15,330 --> 00:19:22,270
+النقطة الأولى بدنا نثبت أن هذا is not a unit هذه
+
+165
+00:19:22,270 --> 00:19:27,950
+واحدة، والثانية لو أخذنا a بتقسم b × c يبقى يا
+
+166
+00:19:27,950 --> 00:19:35,390
+إما الـ a بتقسم b يا إما الـ a بتقسم c يا إما الـ a بتقسم
+
+167
+00:19:35,390 --> 00:19:41,800
+من a to c يبقى بدأت بتشغيل team يبقى نجي للشغل
+
+168
+00:19:41,800 --> 00:19:47,360
+قال لي هذا نفرضه prime ideal السؤال هو ممكن
+
+169
+00:19:47,360 --> 00:19:55,240
+الـ a تكون unit؟
+
+170
+00:19:55,240 --> 00:20:01,640
+ممكن الـ a تكون unit؟ السؤال لسه ممكن؟ ممنوع، بدنا نعرف ليش،
+
+171
+00:20:01,640 --> 00:20:14,020
+كويس؟ يبقى هنا بنقول معناه الـ a is not a unit هو
+
+172
+00:20:14,020 --> 00:20:25,980
+الشرط الأول because السبب because if الـ a is a unit
+
+173
+00:20:25,980 --> 00:20:30,800
+then الـ 1
+
+174
+00:20:30,800 --> 00:20:35,960
+الصحيح بيكون مولد في هذا الـ principal ولا لا؟ لأن
+
+175
+00:20:35,960 --> 00:20:42,640
+الـ a unit كل العناصر بتبقى موجودة فيه، مظبوط؟ يبقى
+
+176
+00:20:42,640 --> 00:20:50,920
+هنا then الـ 1 belong to الـ a فأخذنا remark
+
+177
+00:20:50,920 --> 00:20:56,980
+صغيرة، لو الـ ideal احتوى على unity تبع الـ ring،
+
+178
+00:20:56,980 --> 00:21:02,520
+يبقى الـ ideal بتساوي الـ ring كلها، مظبوط؟ يبقى
+
+179
+00:21:02,520 --> 00:21:08,050
+then هذا بده يع
+
+223
+00:26:45,460 --> 00:26:59,650
+the square of a prime by the square of a prime on
+
+224
+00:26:59,650 --> 00:27:08,510
+the integral domain on
+
+225
+00:27:08,510 --> 00:27:17,590
+the integral domain اللي هو Z of √D مين هو
+
+226
+00:27:17,590 --> 00:27:26,490
+هذا؟ كل العناصر a + b√D بحيث الـ a و الـ b
+
+227
+00:27:26,490 --> 00:27:36,930
+أعداد صحيحة. Define a function
+
+228
+00:27:36,930 --> 00:27:48,610
+عرف الدالة من Z of √D إلى Z+
+
+229
+00:27:51,040 --> 00:28:02,580
+by N(a + b√D) = |a² - b²D|. N(a + b√D)
+
+230
+00:28:02,580 --> 00:28:10,460
+= |a² - b²D|.  بدل ساوي absolute value للـ a تربيع ناقص
+
+231
+00:28:10,460 --> 00:28:17,900
+b² تربيع. Then النقطة
+
+232
+00:28:17,900 --> 00:28:27,680
+الأولى: N(x) = 0 if and only if x = 0.
+
+233
+00:28:27,680 --> 00:28:35,700
+= 0. النقطة الثانية: N(x)
+
+234
+00:28:35,700 --> 00:28:44,800
+= y  if N(xy) = N(x)N(y)
+
+235
+00:28:44,800 --> 00:28:54,340
+لكل الـ x والـ y اللي موجودة في Z of the square
+
+236
+00:28:54,340 --> 00:28:59,880
+root of D. النقطة
+
+237
+00:28:59,880 --> 00:29:13,300
+الثالثة: x is a unit if and only if N(x) =
+
+238
+00:29:13,300 --> 00:29:13,800
+1.
+
+239
+00:29:17,500 --> 00:29:30,920
+الرابعة: if N(x) = a'
+
+240
+00:29:30,920 --> 00:29:40,160
+is a prime, then x is irreducible.
+
+241
+00:29:40,160 --> 00:29:44,020
+is irreducible.
+
+242
+00:30:12,470 --> 00:30:18,440
+طبعاً الكتاب  ترى كلّ كنت تفرّح للرياضيّة، وأنتم طبعاً
+
+243
+00:30:18,440 --> 00:30:24,640
+قارئين، يبقى ممكن تقولوا إنهم أنتم طبعاً، طيب ما
+
+244
+00:30:24,640 --> 00:30:28,460
+علينا نجي
+
+245
+00:30:28,460 --> 00:30:33,560
+نرجع لنصّ الـ remark اللي هنا، يقول:  الـ D موجودة في
+
+246
+00:30:33,560 --> 00:30:38,580
+الـ Z و الـ D لا يساوي الواحد، وفي نفس الوقت D is
+
+247
+00:30:38,580 --> 00:30:44,060
+not divisible by the square of a prime. يعني لو أخذنا
+
+248
+00:30:44,060 --> 00:30:49,230
+عدد أولي وربعناه، يبقى هذا الـ element لا يُقسم به
+
+249
+00:30:49,230 --> 00:30:54,110
+بمربع العدد الأولي، عشان أقول على الـ integral domain
+
+250
+00:30:54,110 --> 00:30:59,390
+هذا المعرف بهذا الشكل. بدي أعرف function من الـ
+
+251
+00:30:59,390 --> 00:31:03,810
+integral domain هذا إلى مجموعة الأعداد الصحيحة
+
+252
+00:31:03,810 --> 00:31:10,670
+الموجبة، سالب ما عنده صفر، ما عنده،  بقلل N هي
+
+253
+00:31:10,670 --> 00:31:16,910
+function من Z of D إلى Z+، by إن لما تأثر على
+
+254
+00:31:16,910 --> 00:31:23,610
+الـ element اللي هنا، بده يساوي المربع الأول ناقص
+
+255
+00:31:23,610 --> 00:31:28,790
+D في المربع الثاني، المربع هذا، بطل اللي يربط على
+
+256
+00:31:28,790 --> 00:31:33,830
+الـ D، وهذا الـ D اللي هي الـ D  الثالثة. فيه عندي
+
+257
+00:31:33,830 --> 00:31:38,430
+أربع نقاط. النقطة الأولى: N(x) = 0 if and only if x = 0.
+
+258
+00:31:38,430 --> 00:31:44,640
+x = 0. N(x) = N(x)N(y) لكل
+
+259
+00:31:44,640 --> 00:31:50,260
+x, y الموجودة في Z of √D. النقطة الثالثة: x
+
+260
+00:31:50,260 --> 00:31:55,360
+زيونة، if N(x) = 1.
+
+261
+00:31:55,360 --> 00:32:01,440
+is defined that x is irreducible على مين؟ على Z يبقى
+
+262
+00:32:01,440 --> 00:32:06,180
+كلّه على التعريف اللي عنده ده، وليه دالك؟ مضيت شمسه
+
+263
+00:32:06,180 --> 00:32:11,300
+التعريف، وخلتها حتى لو تحضرها، متى لازم أقوله، نمسك
+
+264
+00:32:11,300 --> 00:32:19,630
+الأولى، يبقى N(x) = 0 if and only if بدي
+
+265
+00:32:19,630 --> 00:32:25,190
+أمشي لغاية ما أوصل إلى x = 0.  طب الـ
+
+266
+00:32:25,190 --> 00:32:30,450
+N(x)  الـ x اللي موجودة يبقى شكلها a + b
+
+267
+00:32:30,450 --> 00:32:43,010
+√D. يبقى N(a + b√D) = 0 هذا
+
+268
+00:32:43,010 --> 00:32:49,610
+الكلام صحيح if and only if هذا اللي هو الـ absolute
+
+269
+00:32:49,610 --> 00:32:59,650
+value للـ a تربيع ناقص b تربيع يساوي zero. طيب
+
+270
+00:32:59,650 --> 00:33:07,690
+هذا الكلام صحيح إذا كان a تربيع ناقص الـ D b
+
+271
+00:33:07,690 --> 00:33:15,950
+تربيع يساوي zero. مظبوط؟ صح؟ طيب، أليس هذا فرق بين
+
+272
+00:33:15,950 --> 00:33:23,330
+المربعين؟ يبقى الـ  بقدر أقول والتانية اللي هو
+
+273
+00:33:23,330 --> 00:33:32,490
+الـ a - b√D في الـ a + b√D
+
+274
+00:33:32,490 --> 00:33:38,020
+بده يساوي zero. طب احنا بنشتغل فيه؟ في integral
+
+275
+00:33:38,020 --> 00:33:43,320
+domain، وحاصل ضرب عنصرين يساوي zero يبقى ولا حد
+
+276
+00:33:43,320 --> 00:33:49,520
+منهم بده يساوي zero. مظبوط؟ يبقى هذا الكلام صحيح if
+
+277
+00:33:49,520 --> 00:33:56,540
+and only if a - b√D = 0 أو
+
+278
+00:33:56,540 --> 00:34:03,400
+a + b√D = 0. ليش هذا
+
+279
+00:34:03,400 --> 00:34:14,530
+since D is an integral domain.
+
+280
+00:34:14,530 --> 00:34:17,930
+طيب
+
+281
+00:34:17,930 --> 00:34:25,950
+الكلام هذا صحيح if and only if الأولاري بقدر أقول
+
+282
+00:34:25,950 --> 00:34:38,940
+a = b√D أو a = -b√D. هذا الكلام صحيح if and only if شكل الـ x اللي
+
+283
+00:34:38,940 --> 00:34:47,900
+موجودة في الـ integral domain هذا بده يساوي a +
+
+284
+00:34:47,900 --> 00:34:54,040
+b√D. مظبوط؟ طيب هنا الـ a  بداشأنا بها ب جذر اتنين
+
+285
+00:34:54,040 --> 00:35:05,030
+صح،  يفقد بده يساوي الـ a + a اللي هو بقدّاش؟
+
+286
+00:35:05,030 --> 00:35:13,750
+ب 2a أو الـ x بده يساوي a - a  مش الـ a - b
+
+287
+00:35:13,750 --> 00:35:25,790
+√2. يبقى بده أشيل هذه a زي ... أيها يا بني،
+
+288
+00:35:25,790 --> 00:35:32,320
+هذه واحدة وهي ثانية، مش عندنا a زي b√D, x
+
+289
+00:35:32,320 --> 00:35:38,580
+خلت الـ a زي ... b√D, b√D هذه خطأ
+
+290
+00:35:38,580 --> 00:35:45,760
+طبيعيّة، تمام؟ يبقى b√D، طب أنا عندي b√D
+
+291
+00:35:45,760 --> 00:35:51,580
+بـ a يبقى شلتها وحطّيت مكانها a و a بـ 2a أو الـ x
+
+292
+00:35:51,580 --> 00:35:58,820
+من النقطة الثانية بتأخذ هذا، يبقى الـ a كما هي
+
+293
+00:35:58,820 --> 00:36:04,980
+و الثّانية b√D  بـ -a، هذا -a يجعله
+
+294
+00:36:04,980 --> 00:36:12,380
+يساوي zero. يبقى هذه هو المطلوب، خلاص خلصناها من
+
+295
+00:36:12,380 --> 00:36:18,320
+الجهود، كم؟
+
+296
+00:36:22,270 --> 00:36:27,310
+قال ماشي، الحين هي هذه أو هذه، تمام؟ يبقى هذه و
+
+297
+00:36:27,310 --> 00:36:31,370
+هذه يبقى stop أيضا طبيعي، واحدة منهم، أنا بدي أخد
+
+298
+00:36:31,370 --> 00:36:39,010
+x = 0، تمام؟ يكفيني ذلك، تمام؟ طيب، النقطة؟
+
+299
+00:36:39,010 --> 00:36:44,270
+النقطة بسيطة جداً، لو سألتي، بتقول لك هذا شو؟
+
+300
+00:36:44,270 --> 00:36:49,010
+بتقول لي هذا هو الشرط الثاني من شروط الـ homomorphism
+
+301
+00:36:49,490 --> 00:36:54,970
+يبقى أنا بأبدأ وأخليك تكملّي أنت في الدار لحالك كيف
+
+302
+00:36:54,970 --> 00:37:02,810
+بدنا نبدأ سؤال. شوف الحين N(xy) يبقى N
+
+303
+00:37:02,810 --> 00:37:07,970
+أنا بده أشيل الـ x وأحطها from الـ integral
+
+304
+00:37:07,970 --> 00:37:16,790
+domain هذا، يبقى إيش بده يصير؟ أيوة a + b√D
+
+305
+00:37:16,790 --> 00:37:27,420
+× c + e√D. بتكتر ضربها حتى
+
+306
+00:37:27,420 --> 00:37:34,420
+تقدر تبقيّش اللي عندك. النقطة هذه، يبقى هذا بتساوي N
+
+307
+00:37:34,420 --> 00:37:47,110
+(ac + beD) هذه مع هذه، وهذه مع هذه. طريقة
+
+308
+00:37:47,110 --> 00:37:59,290
+تظهر الآن a مع الأخيرة يبقى ae + bd
+
+309
+00:37:59,290 --> 00:38:08,190
+√D, كلّه في جذر الـ D. يبقى
+
+310
+00:38:08,190 --> 00:38:16,080
+M يؤثر على هذا، يبقى المربع الأول ناقص D في
+
+311
+00:38:16,080 --> 00:38:22,280
+المربع الثاني. يبقى هذا الكلام في الـ  D  اللي هو
+
+312
+00:38:22,280 --> 00:38:31,660
+ac + beD الكل تربيع as absolute value ناقص
+
+313
+00:38:31,660 --> 00:38:42,330
+D في ae + bc الكل تربيع، بالمثل، بدّك تروح
+
+314
+00:38:42,330 --> 00:38:50,030
+تجيبي N(x) في N(y). يبقى جاهزة كده، إيش بده
+
+315
+00:38:50,030 --> 00:39:00,090
+يصير؟ الـ N(a + b√D) فاهمين؟ في الـ N
+
+316
+00:39:00,090 --> 00:39:11,970
+اللي هو c + e√D. هذا بالطريقة الـ
+
+317
+00:39:11,970 --> 00:39:19,930
+absolute value a تربيع ناقص D b تربيع مضروب في
+
+318
+00:39:19,930 --> 00:39:31,730
+مين؟ في الـ c تربيع ناقص D e تربيع. الحين مطلوب
+
+319
+00:39:31,730 --> 00:39:38,980
+إنّك تثبتي أنّ الاتنين هدول are equal، يبقى بيك تروح
+
+320
+00:39:38,980 --> 00:39:44,880
+تضرب، تفكي هذه، تفكي هذه، تفكي هذه، حتلاقي اتنين متساويين
+
+321
+00:39:44,880 --> 00:39:54,340
+مع بعض، يبقى هدول are equal،  قدّ البني آدم  check عليهم
+
+322
+00:39:54,340 --> 00:40:03,790
+شيك عليهم، تمام؟ بقى النقطتين للمرّة القادمة، إن شاء
+
+323
+00:40:03,790 --> 00:40:05,090
+الله تعالى.
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/71X_6BKpq-I_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/71X_6BKpq-I_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..90e09e0071d3ca42f6e39f54f0437cfcb796bb36
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/71X_6BKpq-I_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4874, "start": 20.82, "end": 48.74, "text": "بسم الله الرحمن الرحيم اليوم ان شاء الله نكمل ما ابتدأنا به المرة الماضية اخر حاجة المرة الماضية اخذنا نظرية واخدنا علي ذلك كمثال النظرية كانت نظرية ال division algorithm فقلنا لو عندنا function f و function ثانية g او polynomial f of x", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 16472, 13412, 16606, 21984, 8717, 24793, 1211, 19446, 48127, 2655, 3215, 10721, 8315, 39627, 9673, 25720, 9673, 46958, 10632, 1975, 34740, 11331, 26108, 3660, 9673, 25720, 9673, 46958, 10632, 1975, 9778, 8848, 8315, 8717, 19913, 2288, 10632, 4032, 47283, 3215, 8315, 25894, 29910, 23275, 9122, 2304, 12984, 6027, 28239, 19913, 2288, 10632, 25961, 2655, 8717, 19913, 2288, 10632, 2423, 10044, 9284, 6156, 4587, 1211, 8315, 45164, 43242, 8315, 2445, 283, 4032, 2445, 38637, 7649, 10632, 290, 1975, 2407, 26110, 283, 295, 2031], "avg_logprob": -0.12300531978302813, "compression_ratio": 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بناخد ثلاث نتائج النتيجة الأولى تقول ما يدى يبقى crawleries one النتيجة الأولى", "tokens": [2407, 38251, 1829, 8315, 2423, 497, 295, 1783, 39896, 9673, 9957, 3215, 2288, 7251, 3555, 4587, 7578, 29538, 19753, 34740, 8717, 19913, 2288, 10632, 9122, 2655, 3555, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 8978, 3714, 5016, 46958, 25720, 45595, 20498, 16472, 13412, 16606, 21984, 47525, 8315, 8717, 47283, 3215, 1045, 13999, 1918, 530, 15844, 29538, 28239, 19913, 2288, 10632, 44945, 47283, 3215, 38637, 1211, 5718, 104, 8717, 2655, 16373, 7435, 28239, 31371, 7435, 3660, 16247, 12610, 7578, 6055, 39648, 19446, 7251, 3215, 7578, 7251, 3555, 4587, 7578, 13999, 1918, 530, 472, 28239, 31371, 7435, 3660, 16247, 12610, 7578], "avg_logprob": -0.22906249791383743, "compression_ratio": 1.7980295566502462, "no_speech_prob": 0.0, "words": [{"start": 75.38, "end": 76.32, "word": "وسمينا", "probability": 0.8367919921875}, {"start": 76.32, "end": 76.58, "word": " ال", "probability": 0.77587890625}, 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0.879638671875}, {"start": 836.63, "end": 839.15, "word": " افترض", "probability": 0.9158935546875}, {"start": 839.15, "end": 840.09, "word": " ان", "probability": 0.931640625}, {"start": 840.09, "end": 840.47, "word": " ال", "probability": 0.6171875}, {"start": 840.47, "end": 840.87, "word": " X", "probability": 0.65966796875}, {"start": 840.87, "end": 841.61, "word": " ماقص", "probability": 0.66729736328125}, {"start": 841.61, "end": 841.91, "word": " ال", "probability": 0.962890625}, {"start": 841.91, "end": 842.29, "word": " A", "probability": 0.77587890625}, {"start": 842.29, "end": 843.43, "word": " is", "probability": 0.64111328125}, {"start": 843.43, "end": 844.39, "word": " a", "probability": 0.9228515625}, {"start": 844.39, "end": 845.79, "word": " factor", "probability": 0.87744140625}, {"start": 845.79, "end": 847.21, "word": " of", "probability": 0.96875}, {"start": 847.21, "end": 848.29, "word": " ال", "probability": 0.52001953125}, {"start": 848.29, "end": 848.71, 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counting", "probability": 0.625}, {"start": 1034.4, "end": 1036.44, "word": " multiplicity", "probability": 0.973876953125}], "temperature": 1.0}, {"id": 36, "seek": 109550, "start": 1069.6, "end": 1095.5, "text": "القرناميال مرة تانية بيقول القرناميال من الدرجة اللينية على field وليس على قرناميال لينك رينك ولا على إنتجر الدمين على field ال three cronaries على field has at most أكثر ما يمكن بيكون in zeros counting multiplicity إيش عن ال count؟", "tokens": [6027, 4587, 2288, 1863, 10943, 1829, 6027, 3714, 25720, 6055, 7649, 10632, 4724, 1829, 39648, 25062, 2288, 1863, 10943, 1829, 6027, 9154, 32748, 47341, 3660, 13672, 9957, 10632, 15844, 2519, 4032, 20292, 3794, 15844, 12174, 2288, 1863, 10943, 1829, 6027, 5296, 9957, 4117, 12602, 9957, 4117, 49429, 15844, 11933, 29399, 7435, 2288, 32748, 2304, 9957, 15844, 2519, 2423, 1045, 941, 266, 4889, 15844, 2519, 575, 412, 881, 5551, 4117, 49115, 19446, 7251, 43020, 4724, 1829, 30544, 294, 35193, 13251, 17596, 507, 11933, 1829, 8592, 18871, 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That is", "tokens": [3224, 2407, 34105, 300, 2423, 479, 295, 1783, 3714, 29245, 23328, 3660, 8978, 4238, 479, 295, 1783, 13, 11778, 1211, 30543, 31371, 8032, 39648, 3224, 479, 13, 2423, 479, 295, 1783, 307, 257, 4314, 472, 13, 663, 307], "avg_logprob": -0.2742387958062001, "compression_ratio": 1.105263157894737, "no_speech_prob": 0.0, "words": [{"start": 1155.19, "end": 1155.59, "word": "هو", "probability": 0.894287109375}, {"start": 1155.59, "end": 1155.95, "word": " هنا", "probability": 0.97412109375}, {"start": 1155.95, "end": 1156.97, "word": " that", "probability": 0.1622314453125}, {"start": 1156.97, "end": 1158.11, "word": " ال", "probability": 0.83154296875}, {"start": 1158.11, "end": 1158.43, "word": " F", "probability": 0.74951171875}, {"start": 1158.43, "end": 1158.91, "word": " of", "probability": 0.9521484375}, {"start": 1158.91, "end": 1159.43, "word": " X", "probability": 0.93994140625}, {"start": 1159.43, "end": 1160.95, "word": " موجودة", "probability": 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"word": " هكتبلك،", "probability": 0.8482259114583334}, {"start": 2085.45, "end": 2086.15, "word": " أوضحلك", "probability": 0.8128662109375}, {"start": 2086.15, "end": 2086.59, "word": " إياها", "probability": 0.9803059895833334}, {"start": 2086.59, "end": 2087.41, "word": " كذلك", "probability": 0.9708658854166666}, {"start": 2087.41, "end": 2088.97, "word": " بمثال", "probability": 0.885986328125}], "temperature": 1.0}, {"id": 70, "seek": 210891, "start": 2089.09, "end": 2108.91, "text": "يعني يا بنات الكرولري هذه ليست صحيحة إلا على الفيل، فغير الفيل ماهياش صحيحة. ربي خليني أكتب المراحة وهذه، ريمان. كرولري تلاتة", "tokens": [40228, 22653, 35186, 4724, 8315, 2655, 33251, 2288, 12610, 16572, 29538, 32239, 14851, 20328, 5016, 1829, 5016, 3660, 11933, 15040, 15844, 27188, 26895, 12399, 6156, 17082, 13546, 27188, 26895, 19446, 3224, 1829, 33599, 20328, 5016, 1829, 5016, 3660, 13, 12602, 21292, 16490, 1211, 9957, 1829, 5551, 4117, 2655, 3555, 9673, 23557, 5016, 3660, 37037, 24192, 12399, 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2185.68, "word": " zeros", "probability": 0.91357421875}, {"start": 2185.68, "end": 2186.62, "word": " and", "probability": 0.869140625}, {"start": 2186.62, "end": 2187.82, "word": " the", "probability": 0.4599609375}, {"start": 2187.82, "end": 2188.8, "word": " six", "probability": 0.74365234375}], "temperature": 1.0}, {"id": 73, "seek": 224329, "start": 2214.03, "end": 2243.29, "text": "ده سؤال التاريخ ال six هدفين؟ لأ لأ هذا integral domain لإنه في zero divisors و لا فيش فيه zero يبقى كمان مش مش مش مش integral domain لكن polynomial ring صح يبقى ده polynomial ring ماشي لعين يبقى مادام ring يعني ليست field و ليست integral domain", "tokens": [3215, 3224, 8608, 33604, 6027, 2423, 2655, 9640, 1829, 9778, 2423, 2309, 8032, 3215, 5172, 9957, 22807, 5296, 10721, 5296, 10721, 23758, 11573, 9274, 5296, 28814, 1863, 3224, 8978, 4018, 25974, 830, 4032, 20193, 8978, 8592, 8978, 3224, 4018, 7251, 3555, 4587, 7578, 9122, 2304, 7649, 37893, 37893, 37893, 37893, 11573, 9274, 44381, 26110, 4875, 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{"start": 2218.33, "end": 2218.69, "word": " هذا", "probability": 0.302001953125}, {"start": 2218.69, "end": 2219.09, "word": " integral", "probability": 0.6162109375}, {"start": 2219.09, "end": 2219.65, "word": " domain", "probability": 0.93212890625}, {"start": 2219.65, "end": 2220.83, "word": " لإنه", "probability": 0.70947265625}, {"start": 2220.83, "end": 2221.01, "word": " في", "probability": 0.8818359375}, {"start": 2221.01, "end": 2221.69, "word": " zero", "probability": 0.43310546875}, {"start": 2221.69, "end": 2222.53, "word": " divisors", "probability": 0.79931640625}, {"start": 2222.53, "end": 2222.67, "word": " و", "probability": 0.53515625}, {"start": 2222.67, "end": 2222.75, "word": " لا", "probability": 0.759765625}, {"start": 2222.75, "end": 2223.01, "word": " فيش", "probability": 0.480224609375}, {"start": 2223.01, "end": 2223.27, "word": " فيه", "probability": 0.44677734375}, {"start": 2223.27, "end": 2223.47, "word": " zero", "probability": 0.2459716796875}, {"start": 2223.47, "end": 2224.53, "word": " يبقى", "probability": 0.7390594482421875}, {"start": 2224.53, "end": 2225.13, "word": " كمان", "probability": 0.9537760416666666}, {"start": 2225.13, "end": 2225.63, "word": " مش", "probability": 0.9873046875}, {"start": 2225.63, "end": 2226.93, "word": " مش", "probability": 0.69482421875}, {"start": 2226.93, "end": 2228.23, "word": " مش", "probability": 0.984375}, {"start": 2228.23, "end": 2228.67, "word": " مش", "probability": 0.8525390625}, {"start": 2228.67, "end": 2229.17, "word": " integral", "probability": 0.71630859375}, {"start": 2229.17, "end": 2229.73, "word": " domain", "probability": 0.970703125}, {"start": 2229.73, "end": 2230.45, "word": " لكن", "probability": 0.85791015625}, {"start": 2230.45, "end": 2230.83, "word": " polynomial", "probability": 0.9560546875}, {"start": 2230.83, "end": 2231.53, "word": " ring", "probability": 0.95263671875}, {"start": 2231.53, "end": 2232.39, "word": " صح", "probability": 0.97412109375}, {"start": 2232.39, "end": 2233.15, "word": " يبقى", "probability": 0.8843994140625}, {"start": 2233.15, "end": 2233.45, "word": " ده", "probability": 0.642822265625}, {"start": 2233.45, "end": 2233.79, "word": " polynomial", "probability": 0.966796875}, {"start": 2233.79, "end": 2234.31, "word": " ring", "probability": 0.990234375}, {"start": 2234.31, "end": 2234.75, "word": " ماشي", "probability": 0.8142903645833334}, {"start": 2234.75, "end": 2235.05, "word": " لعين", "probability": 0.59912109375}, {"start": 2235.05, "end": 2235.75, "word": " يبقى", "probability": 0.9149169921875}, {"start": 2235.75, "end": 2236.45, "word": " مادام", "probability": 0.5811360677083334}, {"start": 2236.45, "end": 2237.21, "word": " ring", "probability": 0.9140625}, {"start": 2237.21, "end": 2239.17, "word": " يعني", "probability": 0.71484375}, {"start": 2239.17, "end": 2240.81, "word": " ليست", "probability": 0.58251953125}, {"start": 2240.81, "end": 2241.29, "word": " field", "probability": 0.88427734375}, {"start": 2241.29, "end": 2241.85, "word": " و", "probability": 0.95166015625}, {"start": 2241.85, "end": 2242.29, "word": " ليست", "probability": 0.766845703125}, {"start": 2242.29, "end": 2242.83, "word": " integral", "probability": 0.830078125}, {"start": 2242.83, "end": 2243.29, "word": " domain", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 74, "seek": 227046, "start": 2243.58, "end": 2270.46, "text": "تعالى نشوف هذه في إيها كام حل في Z6 أنا بتدعي إنهم مين أربعة حلول، إيش أربعة حلول؟ طيب على أصل Z6 هم Zero، واحد واثنين، ثلاثة، أربعة وخمسة، تمام؟ هل ال Zero بخبري هذه الحل؟ ال Zero بعدين جاوب اتنين، يبقى ال Zero ليس أحد الحلول، طيب نجرب", "tokens": [2655, 3615, 6027, 7578, 8717, 8592, 38688, 29538, 8978, 11933, 1829, 11296, 9122, 10943, 11331, 1211, 8978, 1176, 21, 41850, 39894, 3215, 3615, 1829, 36145, 16095, 3714, 9957, 5551, 25513, 27884, 11331, 1211, 12610, 12399, 11933, 1829, 8592, 5551, 25513, 27884, 11331, 1211, 12610, 22807, 23032, 1829, 3555, 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"probability": 0.9591471354166666}, {"start": 2252.12, "end": 2253.3, "word": " حلول؟", "probability": 0.9637451171875}, {"start": 2253.3, "end": 2253.64, "word": " طيب", "probability": 0.95947265625}, {"start": 2253.64, "end": 2253.84, "word": " على", "probability": 0.8056640625}, {"start": 2253.84, "end": 2254.1, "word": " أصل", "probability": 0.812255859375}, {"start": 2254.1, "end": 2254.84, "word": " Z6", "probability": 0.937744140625}, {"start": 2254.84, "end": 2255.16, "word": " هم", "probability": 0.786376953125}, {"start": 2255.16, "end": 2255.76, "word": " Zero،", "probability": 0.4940185546875}, {"start": 2255.76, "end": 2256.3, "word": " واحد", "probability": 0.91259765625}, {"start": 2256.3, "end": 2257.26, "word": " واثنين،", "probability": 0.7636311848958334}, {"start": 2257.26, "end": 2258.12, "word": " ثلاثة،", "probability": 0.8228352864583334}, {"start": 2258.12, "end": 2258.5, "word": " أربعة", "probability": 0.9270833333333334}, {"start": 2258.5, "end": 2259.66, "word": " وخمسة،", "probability": 0.914794921875}, {"start": 2259.66, "end": 2260.56, "word": " تمام؟", "probability": 0.9171549479166666}, {"start": 2260.56, "end": 2260.94, "word": " هل", "probability": 0.987060546875}, {"start": 2260.94, "end": 2261.18, "word": " ال", "probability": 0.95068359375}, {"start": 2261.18, "end": 2261.72, "word": " Zero", "probability": 0.51806640625}, {"start": 2261.72, "end": 2262.92, "word": " بخبري", "probability": 0.61981201171875}, {"start": 2262.92, "end": 2263.34, "word": " هذه", "probability": 0.8603515625}, {"start": 2263.34, "end": 2264.68, "word": " الحل؟", "probability": 0.84033203125}, {"start": 2264.68, "end": 2265.02, "word": " ال", "probability": 0.64404296875}, {"start": 2265.02, "end": 2265.2, "word": " Zero", "probability": 0.923828125}, {"start": 2265.2, "end": 2265.58, "word": " بعدين", "probability": 0.666748046875}, {"start": 2265.58, "end": 2265.9, "word": " جاوب", "probability": 0.7557779947916666}, {"start": 2265.9, "end": 2266.46, "word": " اتنين،", "probability": 0.85458984375}, {"start": 2266.46, "end": 2266.62, "word": " يبقى", "probability": 0.9390869140625}, {"start": 2266.62, "end": 2266.78, "word": " ال", "probability": 0.95361328125}, {"start": 2266.78, "end": 2267.12, "word": " Zero", "probability": 0.93017578125}, {"start": 2267.12, "end": 2267.98, "word": " ليس", "probability": 0.95703125}, {"start": 2267.98, "end": 2268.44, "word": " أحد", "probability": 0.92041015625}, {"start": 2268.44, "end": 2269.64, "word": " الحلول،", "probability": 0.8946533203125}, {"start": 2269.64, "end": 2269.88, "word": " طيب", "probability": 0.9383138020833334}, {"start": 2269.88, "end": 2270.46, "word": " نجرب", "probability": 0.970703125}], "temperature": 1.0}, {"id": 75, "seek": 230010, "start": 2271.54, "end": 2300.1, "text": "الواحد هو حل ولا لا؟ واحد تقريبا تلاتة في واحد زي دين يبقى ايه؟ ستة يعني جدرس. Zero في زي ستة يبقى الواحد أحد الحلوين. As for zeros in that case أي أنواع. الواحد هو اتنين، اربعة، تلاتة، ستة،", "tokens": [6027, 14407, 24401, 31439, 11331, 1211, 49429, 20193, 22807, 36764, 24401, 6055, 4587, 16572, 3555, 995, 6055, 1211, 9307, 3660, 8978, 36764, 24401, 30767, 1829, 11778, 9957, 7251, 3555, 4587, 7578, 1975, 1829, 3224, 22807, 8608, 2655, 3660, 37495, 22653, 10874, 3215, 2288, 3794, 13, 17182, 8978, 30767, 1829, 8608, 2655, 3660, 7251, 3555, 4587, 7578, 2423, 14407, 24401, 5551, 24401, 21542, 1211, 2407, 9957, 13, 1018, 337, 35193, 294, 300, 1389, 36632, 14739, 14407, 3615, 13, 2423, 14407, 24401, 31439, 1975, 2655, 1863, 9957, 12399, 1975, 25513, 27884, 12399, 6055, 1211, 9307, 3660, 12399, 8608, 2655, 3660, 12399], "avg_logprob": -0.37062501043081286, "compression_ratio": 1.6578947368421053, "no_speech_prob": 0.0, "words": [{"start": 2271.54, "end": 2272.2, "word": "الواحد", "probability": 0.9513346354166666}, {"start": 2272.2, "end": 2272.44, "word": " هو", "probability": 0.95703125}, {"start": 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{"start": 2298.96, "end": 2300.1, "word": " ستة،", "probability": 0.9134521484375}], "temperature": 1.0}, {"id": 76, "seek": 232977, "start": 2300.15, "end": 2329.77, "text": "واربع عشرة واتنين زيك يبقى كمان احد الحلول طيب اربع اربع في اربع ستة عشر تلاتة في اربع اتناش وستاش تمانية وعشرين واتنين تلاتين بالفعل ستة وستة وتلاتين اه احد الحلول I and Rams", "tokens": [2407, 9640, 3555, 3615, 6225, 8592, 25720, 4032, 9307, 1863, 9957, 30767, 1829, 4117, 7251, 3555, 4587, 7578, 9122, 2304, 7649, 1975, 24401, 21542, 1211, 12610, 23032, 1829, 3555, 1975, 25513, 3615, 1975, 25513, 3615, 8978, 1975, 25513, 3615, 8608, 2655, 3660, 6225, 46309, 6055, 1211, 9307, 3660, 8978, 1975, 25513, 3615, 1975, 2655, 1863, 33599, 4032, 14851, 33599, 46811, 7649, 10632, 4032, 3615, 46309, 9957, 4032, 9307, 1863, 9957, 6055, 1211, 9307, 9957, 20666, 5172, 30241, 8608, 2655, 3660, 4032, 14851, 3660, 34683, 1211, 9307, 9957, 1975, 3224, 1975, 24401, 21542, 1211, 12610, 286, 293, 28990], "avg_logprob": 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"probability": 0.9368489583333334}, {"start": 2310.01, "end": 2310.15, "word": " في", "probability": 0.7314453125}, {"start": 2310.15, "end": 2310.67, "word": " اربع", "probability": 0.9676106770833334}, {"start": 2310.67, "end": 2311.63, "word": " ستة", "probability": 0.7626953125}, {"start": 2311.63, "end": 2311.99, "word": " عشر", "probability": 0.611572265625}, {"start": 2311.99, "end": 2312.91, "word": " تلاتة", "probability": 0.8839111328125}, {"start": 2312.91, "end": 2313.05, "word": " في", "probability": 0.94384765625}, {"start": 2313.05, "end": 2313.31, "word": " اربع", "probability": 0.8723958333333334}, {"start": 2313.31, "end": 2314.03, "word": " اتناش", "probability": 0.7364501953125}, {"start": 2314.03, "end": 2315.29, "word": " وستاش", "probability": 0.7976888020833334}, {"start": 2315.29, "end": 2316.09, "word": " تمانية", "probability": 0.96044921875}, {"start": 2316.09, "end": 2316.81, "word": " وعشرين", "probability": 0.911865234375}, {"start": 2316.81, "end": 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"temperature": 1.0}, {"id": 77, "seek": 235719, "start": 2331.58, "end": 2357.2, "text": "خمسة في خمسة، خمسة وعشرين، خمسة في تلاتة، خمس عشر، خمسة واربعين، اربعين واتنين، نين واربعين، تكسب ع ستة؟ أه سبعة وستة واتنين واربعين. يبقى من الاستبعدنا؟ استبعدنا الـ Zero واستبعدنا التلاتة. هل يترى التلاتة هي أحد، هي الـ Zero لهذه التلاتة على الجهود؟", "tokens": [9778, 2304, 3794, 3660, 8978, 16490, 2304, 3794, 3660, 12399, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 12399, 16490, 2304, 3794, 3660, 8978, 6055, 1211, 9307, 3660, 12399, 16490, 2304, 3794, 6225, 46309, 12399, 16490, 2304, 3794, 3660, 4032, 9640, 3555, 3615, 9957, 12399, 1975, 25513, 3615, 9957, 4032, 9307, 1863, 9957, 12399, 8717, 9957, 4032, 9640, 3555, 3615, 9957, 12399, 6055, 4117, 35457, 6225, 8608, 2655, 3660, 22807, 5551, 3224, 8608, 3555, 27884, 4032, 14851, 3660, 4032, 9307, 1863, 9957, 4032, 9640, 3555, 3615, 9957, 13, 7251, 3555, 4587, 7578, 9154, 42963, 14851, 3555, 22488, 8315, 22807, 44713, 3555, 22488, 8315, 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هو واحد إذا النتيجة هذه كلها تساوي واحدة هذا يا بنات جيبناها من نظرية De Moivre يعني بتقدر تقول اللي بين جسينك De Moivre's theory مش عشوائي يعني مش فاهم يبقى أصبح", "tokens": [5172, 10721, 4587, 2288, 10721, 2423, 1433, 16247, 9778, 13546, 4032, 10874, 1829, 3555, 46811, 10943, 4032, 10874, 1829, 3555, 46811, 10943, 31767, 5172, 2288, 13672, 1829, 31439, 36764, 24401, 11933, 15730, 28239, 31371, 7435, 3660, 29538, 28242, 11296, 6055, 3794, 995, 45865, 36764, 24401, 3660, 23758, 35186, 4724, 8315, 2655, 10874, 1829, 3555, 8315, 11296, 9154, 8717, 19913, 2288, 10632, 1346, 3335, 592, 265, 37495, 22653, 39894, 28543, 2288, 6055, 39648, 13672, 1829, 49374, 10874, 3794, 9957, 4117, 1346, 3335, 592, 265, 311, 5261, 37893, 6225, 8592, 2407, 16373, 1829, 37495, 22653, 37893, 6156, 995, 16095, 7251, 3555, 4587, 7578, 5551, 9381, 49628], "avg_logprob": -0.3434523923056466, "compression_ratio": 1.6712962962962963, "no_speech_prob": 0.0, "words": [{"start": 2744.72, "end": 2745.28, "word": 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{"start": 3104.81, "end": 3105.03, "word": " a", "probability": 0.947265625}, {"start": 3105.03, "end": 3105.51, "word": " principle", "probability": 0.54150390625}, {"start": 3105.51, "end": 3105.95, "word": " ideal", "probability": 0.79052734375}, {"start": 3105.95, "end": 3106.65, "word": " generated", "probability": 0.8857421875}, {"start": 3106.65, "end": 3107.23, "word": " by", "probability": 0.9765625}, {"start": 3107.23, "end": 3107.63, "word": " ان", "probability": 0.482666015625}, {"start": 3107.63, "end": 3108.65, "word": " خلصنا", "probability": 0.81585693359375}, {"start": 3108.65, "end": 3109.47, "word": " يبقى", "probability": 0.97509765625}, {"start": 3109.47, "end": 3109.97, "word": " زد", "probability": 0.797607421875}, {"start": 3109.97, "end": 3110.39, "word": " is", "probability": 0.8974609375}, {"start": 3110.39, "end": 3110.85, "word": " a", "probability": 0.9775390625}, {"start": 3110.85, "end": 3111.51, "word": " principle", "probability": 0.92822265625}, {"start": 3111.51, "end": 3112.57, "word": " ideal", "probability": 0.890625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3116.744875, "duration_after_vad": 2894.3343749999885}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/71X_6BKpq-I_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/71X_6BKpq-I_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..be06b8c8784b7eb55395ba4892034649ec120d6d
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/71X_6BKpq-I_raw.srt
@@ -0,0 +1,1568 @@
+1
+00:00:20,820 --> 00:00:26,740
+بسم الله الرحمن الرحيم اليوم ان شاء الله نكمل ما
+
+2
+00:00:26,740 --> 00:00:31,200
+ابتدأنا به المرة الماضية اخر حاجة المرة الماضية
+
+3
+00:00:31,200 --> 00:00:36,640
+اخذنا نظرية واخدنا علي ذلك كمثال النظرية كانت
+
+4
+00:00:36,640 --> 00:00:41,500
+نظرية ال division algorithm فقلنا لو عندنا
+
+5
+00:00:41,500 --> 00:00:48,740
+function f و function ثانية g او polynomial f of x
+
+6
+00:00:49,090 --> 00:00:56,030
+و polynomial تانية g of x جسمنا اتنين على بعض بصير
+
+7
+00:00:56,030 --> 00:01:01,110
+المعادلة اللي هي f of x او ال polynomial of f of x
+
+8
+00:01:01,110 --> 00:01:06,750
+على الشكل اللي عندنا له f of x يسوى g of x في ال q
+
+9
+00:01:06,750 --> 00:01:13,350
+of x زائد ال r of x سمينا ال q of x اللي هو ال
+
+10
+00:01:13,350 --> 00:01:21,700
+quotientوسمينا ال R of X هي الميندر يبقى هذه آخر
+
+11
+00:01:21,700 --> 00:01:26,880
+نظرية كتبناها المرة الماضية في محاضرة اليوم ان شاء
+
+12
+00:01:26,880 --> 00:01:30,900
+الله بدنا ناخد three crawleries على هذه النظرية
+
+13
+00:01:30,900 --> 00:01:37,700
+بناخد ثلاث نتائج النتيجة الأولى تقول ما يدى يبقى
+
+14
+00:01:37,700 --> 00:01:48,120
+crawleries one النتيجة الأولىلت ال F بي A field لت
+
+15
+00:01:48,120 --> 00:01:58,820
+ال F بي A field وال A element موجود في ال field F
+
+16
+00:01:58,820 --> 00:02:08,880
+and ال F of X موجودة في ال field capital F of X
+
+17
+00:02:08,880 --> 00:02:14,720
+يعني Polynomial فيالـ polynomials كلهم اللي
+
+18
+00:02:14,720 --> 00:02:22,700
+بيكونوله فيه capital F of X then ال F of X is the
+
+19
+00:02:22,700 --> 00:02:33,480
+remainder is the remainder يبقى هو الباقي in the
+
+20
+00:02:33,480 --> 00:02:38,900
+division division
+
+21
+00:02:38,900 --> 00:02:53,540
+of F of Xباي اكس ناقص ال a نبقى
+
+22
+00:02:53,540 --> 00:02:59,920
+هو دي
+
+23
+00:02:59,920 --> 00:03:05,380
+اول نتيجة على ال division algorithm نظرية المرة
+
+24
+00:03:05,380 --> 00:03:09,640
+الماضية بيقول ياخدلي field عبارة عن ال F عبارة عن
+
+25
+00:03:09,640 --> 00:03:15,760
+ال Vالـ A element موجود في هذا الـ field ال F of X
+
+26
+00:03:15,760 --> 00:03:21,520
+موجودة في ال .. ال field تبع ال polynomial كلهم
+
+27
+00:03:21,520 --> 00:03:28,760
+اللي سمته CAP فال F of X من ال F of A يبقى لو
+
+28
+00:03:28,760 --> 00:03:33,380
+عوضنا بال X مكانها بال A تبعتي ال field هذا
+
+29
+00:03:33,380 --> 00:03:40,040
+بيعطينا ال remainder الذي ينتجالنتيجة ده ليه قسمة
+
+30
+00:03:40,040 --> 00:03:48,260
+ال F of X على ال X ناقص ال A يبقى الان بروح بقوله
+
+31
+00:03:48,260 --> 00:03:59,060
+from the division algorithm theorem
+
+32
+00:03:59,060 --> 00:04:05,660
+we have ال
+
+33
+00:04:05,660 --> 00:04:14,250
+F of Xلأن بدا تساوي ال X ناقص ال A هيطلع لنا
+
+34
+00:04:14,250 --> 00:04:23,030
+polynomial تانية Q of X زائد ال remainder R of X
+
+35
+00:04:23,030 --> 00:04:31,570
+وال R of X قد تكون Zero او ال degree تبعتها اقل من
+
+36
+00:04:31,570 --> 00:04:31,910
+100
+
+37
+00:04:35,790 --> 00:04:44,690
+و ال R of X بده يساوي Zero او ال degree لل R of X
+
+38
+00:04:44,690 --> 00:04:51,990
+اقل من من ال degree لل X ناقص اللي اللي هو مقسوم
+
+39
+00:04:51,990 --> 00:04:58,790
+عليه يعني درجة الباقي يكون اقل من درجة اللي مقسوم
+
+40
+00:04:58,790 --> 00:05:05,950
+عليه اللي هو ال X ناقص الليطب المقصوم عليه من
+
+41
+00:05:05,950 --> 00:05:12,330
+الدرجة الأولى يبقى ثابت يبقى هناك أقل منه يبقى
+
+42
+00:05:12,330 --> 00:05:21,490
+فاجي بقوله since ال X ناقص ال A is of degree one
+
+43
+00:05:21,490 --> 00:05:29,950
+هذا معدلة من الدرجة الأولى we have ان ال R of X
+
+44
+00:05:29,950 --> 00:05:40,060
+بده تساوي zero or8 degree لل R of X less than 8
+
+45
+00:05:40,060 --> 00:05:48,020
+degree لل X ماقص ال A طب لو كانت ال R of X يساوي
+
+46
+00:05:48,020 --> 00:05:54,760
+Zero أليس هذا constant؟ طب لو كانت ال degree لل R
+
+47
+00:05:54,760 --> 00:06:03,150
+of X أقل من واحد ايش أقل من واحد يعني Zeroوأي حاجة
+
+48
+00:06:03,150 --> 00:06:08,550
+مفعول الـ O Zero اللي هو صحيح ولا لأ يبقى على كلا
+
+49
+00:06:08,550 --> 00:06:14,210
+الأمرين ال R of X constant ولا variable؟ constant
+
+50
+00:06:14,210 --> 00:06:26,230
+يبقى بروح بقوله in both cases في كلا الحالتين ال R
+
+51
+00:06:26,230 --> 00:06:29,070
+of X is constant
+
+52
+00:06:33,460 --> 00:06:42,480
+طيب خلينا نجرب ناخد ال F of A بدأت ساوي ال A ناقص
+
+53
+00:06:42,480 --> 00:06:52,880
+ال A ل Q of A زائد ال R of A ال A ناقص ال A ب Zero
+
+54
+00:06:52,880 --> 00:07:04,350
+ل Q of A زائد ال R of A هذا كله قداشب Zero يبقى
+
+55
+00:07:04,350 --> 00:07:15,030
+هذا بيساوي Zero زائد ال R of A Zero زائد ال R of A
+
+56
+00:07:15,030 --> 00:07:24,230
+هذا معناته الرمين ده R of A بيساوي ال F of A وهو R
+
+57
+00:07:24,230 --> 00:07:30,290
+اخر يبقى الكرولري هذا بيقول ال F of A هو الرمين ده
+
+58
+00:07:30,510 --> 00:07:37,310
+عندما نقسم F of X على مين على X ناحس L. ابقى من
+
+59
+00:07:37,310 --> 00:07:42,630
+الأنفا صاعدا الرمين ده بدي يسوي F of A بس خدوا
+
+60
+00:07:42,630 --> 00:07:48,690
+بالكوا احنا بنشتغل في fields لا في integral domain
+
+61
+00:07:48,690 --> 00:07:54,410
+ولا في polynomial rings. نشتغل في fields. فيكرو
+
+62
+00:07:54,410 --> 00:07:55,230
+الريتنين.
+
+63
+00:08:02,100 --> 00:08:08,060
+رولر اتنين بتقول ما يأتي let ال F be A field نفس
+
+64
+00:08:08,060 --> 00:08:19,420
+المعقية اللي فوق let ال F be A field وال
+
+65
+00:08:19,420 --> 00:08:29,120
+A موجودة في capital F and ال F of X موجودة في
+
+66
+00:08:29,120 --> 00:08:44,010
+capitalf of x then ال a is a ال
+
+67
+00:08:44,010 --> 00:08:55,570
+a is a zero of ال f of x if and only if ال x ناقص
+
+68
+00:08:55,570 --> 00:09:07,800
+ال a is a factorof the F of X.إذا كان فاكتر لمين
+
+69
+00:09:07,800 --> 00:09:18,040
+لل F of X؟البنانيين
+
+70
+00:09:18,040 --> 00:09:23,000
+البرهين البرومي مرة
+
+71
+00:09:23,000 --> 00:09:27,520
+تانية المعلومات تبع الكرولر الأولى هي نفس
+
+72
+00:09:27,520 --> 00:09:32,580
+المعلومات تبع الكرولر التانيةالـ F field element A
+
+73
+00:09:32,580 --> 00:09:37,400
+موجود في F F of X polynomial موجودة في ال set of
+
+74
+00:09:37,400 --> 00:09:43,720
+all polynomials على ال field F then ال A بسميه
+
+75
+00:09:43,720 --> 00:09:50,400
+Zero لدال ال F، إيش يعني Zero؟ الرقم اللي يجعل أو
+
+76
+00:09:50,400 --> 00:09:57,380
+العمصر اللي يجعل التالة F تساوي صفر هذا صحيح عشان
+
+77
+00:09:57,380 --> 00:10:03,800
+دول Fال X ناقص هنا الرقم is a factor of X أحد
+
+78
+00:10:03,800 --> 00:10:12,760
+عوامل من ال F of X طيب احنا شو اللي عنا؟ عنا ال F
+
+79
+00:10:12,760 --> 00:10:23,060
+of X بده يساوي طلعولي كويس هنا قلنا ال X ناقص ال A
+
+80
+00:10:23,060 --> 00:10:32,930
+في ال Q of Xزائد ال remainder of X طب من crawler
+
+81
+00:10:32,930 --> 00:10:43,490
+هو ان ال remainder كده؟ F of A يبقى بطء ولكن بطء
+
+82
+00:10:43,490 --> 00:10:49,930
+from crawler when
+
+83
+00:10:49,930 --> 00:11:01,760
+ال F of A isvery mean ده هذا
+
+84
+00:11:01,760 --> 00:11:08,180
+بده يعطينا مين؟ هذا بده يعطينا ان ال F of X بده
+
+85
+00:11:08,180 --> 00:11:17,100
+يساوي مين؟ ال X ناقص ال A في ال Q of X زائد ال F
+
+86
+00:11:17,100 --> 00:11:26,350
+of A وسميليها هذه ايش؟ معادلة رقم واحدحتى لو أنا
+
+87
+00:11:26,350 --> 00:11:32,630
+مابدهتش الشغل بدي أبدأ ال a is a zero of f of x
+
+88
+00:11:32,630 --> 00:11:36,990
+إذا كان ال x ناقص ال a is a factor يبقى f and
+
+89
+00:11:36,990 --> 00:11:43,190
+don't leave بيخلي البرهان يصير اتجاهي بدي أجي أخد
+
+90
+00:11:43,190 --> 00:11:55,010
+اتجاهي الأول هروح أقوله assume افترض أنه assumeإن
+
+91
+00:11:55,010 --> 00:12:04,930
+الـ A is A Zero Assume الـ A is A Zero of the
+
+92
+00:12:04,930 --> 00:12:14,950
+function F of X اللي موجودة في كابتن F of X Then
+
+93
+00:12:14,950 --> 00:12:21,830
+الـ
+
+94
+00:12:21,830 --> 00:12:28,970
+A هو Zeroمدام ال A هو Zero يبقى ال F of A بذات
+
+95
+00:12:28,970 --> 00:12:36,690
+ساوي كده؟ Zero يبقى لان ال F of A بذات ساوي Zero
+
+96
+00:12:36,690 --> 00:12:46,530
+هذا بدي أقولك إنه equation one take take the form
+
+97
+00:12:46,530 --> 00:12:56,750
+يصبح شكلها على الشكل التاليإن ال F of X بدي يساوي
+
+98
+00:12:56,750 --> 00:13:05,610
+ال X ناقص ال A في ال Q of X F of A بيساوي Zero
+
+99
+00:13:05,610 --> 00:13:12,510
+لأنه أحد الحلول أو ال Zero لل function يبقى بناء
+
+100
+00:13:12,510 --> 00:13:18,670
+عليه صلة ال F of X من معدل واحد يا X ناقص ال A في
+
+101
+00:13:18,670 --> 00:13:27,080
+ال Q of Xما تفسيرك لهذه العبارة x نقص ال a is a
+
+102
+00:13:27,080 --> 00:13:35,780
+factor يفجر هذا يعطينا ان ال x نقص ال a is a
+
+103
+00:13:35,780 --> 00:13:48,240
+factor of the polynomial f of x عظم ما هو المطلوب؟
+
+104
+00:13:48,950 --> 00:13:54,670
+المطلوب الثاني Conversely
+
+105
+00:13:54,670 --> 00:14:08,710
+Assume افترض ان ال X ماقص ال A is a factor of ال F
+
+106
+00:14:08,710 --> 00:14:14,890
+of X then ال
+
+107
+00:14:14,890 --> 00:14:27,010
+F of X تساويال X ناقص ال A في ال Q of X أكتف جيد
+
+108
+00:14:27,010 --> 00:14:32,930
+ال remainder؟ لأ لإيش؟ لأنه جاي العامل عامل يعني
+
+109
+00:14:32,930 --> 00:14:39,430
+قسمة بدون باقي الباقي صفر خلاص بتخلص القسمة يبقى
+
+110
+00:14:39,430 --> 00:14:45,010
+أنا جاي ال X ناقص ال A هو factor من factors تبعتي
+
+111
+00:14:45,010 --> 00:14:50,370
+ده ال F of Xفجبنا نعليه طبقا لـDivision Algorithm
+
+112
+00:14:50,370 --> 00:14:56,190
+بقول ان ال F of X بده يساوي ال X ناقص ال A في ال Q
+
+113
+00:14:56,190 --> 00:15:02,370
+of X طب انا ايش بده اثبت؟ بده اثبت ان ال A هو Zero
+
+114
+00:15:02,370 --> 00:15:10,830
+لده ال F طيب، اذا هذا الكلام بده يخللي ان ال F of
+
+115
+00:15:10,830 --> 00:15:19,620
+A بده يساوي ال A ناقص ال Aفي الـ Q of A هذا بيدري
+
+116
+00:15:19,620 --> 00:15:24,880
+يعطينا Zero في الـ Q of A و اللي هو بيدري يسويها
+
+117
+00:15:24,880 --> 00:15:32,340
+Zero الآن هذا بيدري يعطيك ان ال F of A تسوي Zero
+
+118
+00:15:32,340 --> 00:15:39,180
+ايش تفسيرك لهذه العبارة ان ال A هو حل هذه المعادلة
+
+119
+00:15:39,180 --> 00:15:47,770
+او ال A is A Zero for the function F of Xيبقى هدف
+
+120
+00:15:47,770 --> 00:16:02,370
+يعطينا ان ال A is easy for the polynomial ال
+
+121
+00:16:02,370 --> 00:16:09,210
+F of X هو المفترض كمان
+
+122
+00:16:09,210 --> 00:16:10,110
+قريه تلاتة
+
+123
+00:16:23,030 --> 00:16:30,050
+بقول لي ايه ال polynomial of
+
+124
+00:16:30,050 --> 00:16:47,630
+degree n polynomial degree n over a field over
+
+125
+00:16:47,630 --> 00:17:04,480
+a field has at mostas at most n as at most n zeros
+
+126
+00:17:04,480 --> 00:17:14,400
+counting multiplicity counting counting
+
+127
+00:17:14,400 --> 00:17:16,440
+multiplicity
+
+128
+00:17:49,600 --> 00:17:55,380
+القرناميال مرة تانية بيقول القرناميال من الدرجة
+
+129
+00:17:55,380 --> 00:18:00,460
+اللينية على field وليس على قرناميال لينك رينك ولا
+
+130
+00:18:00,460 --> 00:18:04,840
+على إنتجر الدمين على field ال three cronaries على
+
+131
+00:18:04,840 --> 00:18:11,620
+field has at most أكثر ما يمكن بيكون in zeros
+
+132
+00:18:11,620 --> 00:18:19,440
+counting multiplicity إيش عن ال count؟مش عد؟ عد
+
+133
+00:18:19,440 --> 00:18:28,580
+يعني حساب multiplicity تكرار يعني يعني بدي يكون
+
+134
+00:18:28,580 --> 00:18:35,460
+أقصى تكرار للحلول هو قداش على أقصى ما يكون in الذي
+
+135
+00:18:35,460 --> 00:18:42,880
+يساوي درجة من ال polynomial يعني داخل ال field عدد
+
+136
+00:18:42,880 --> 00:18:49,460
+الحلولبدو يساوي الاص تبع مين ال polynomial او ال
+
+137
+00:18:49,460 --> 00:18:55,160
+degree تبع ال polynomial هي اللي بيقول الابن انجل
+
+138
+00:18:55,160 --> 00:19:00,760
+بره انصحت هذا الكلام يبقى انا بدي اخد polynomial
+
+139
+00:19:00,760 --> 00:19:09,680
+موجودة في فيل اللي هو F يبقى بالتالي هقوله لا ال F
+
+140
+00:19:09,680 --> 00:19:12,420
+هي ايه فيل؟
+
+141
+00:19:15,190 --> 00:19:24,290
+هو هنا that ال F of X موجودة في capital F of X.
+
+142
+00:19:28,130 --> 00:19:37,930
+دلوقتي هقوله F. ال F of X is a degree one.
+
+143
+00:19:39,770 --> 00:19:40,790
+That is
+
+144
+00:19:45,330 --> 00:19:52,910
+الـ F of X بده يسوى AX زائد B معادلة من الدرجة
+
+145
+00:19:52,910 --> 00:19:59,270
+الأولى لما سويها بصفرة كمحل بلقيلها واحد يبقى جد
+
+146
+00:19:59,270 --> 00:20:10,870
+مين جد درجة المعادلة يبقى then ال F has exactly
+
+147
+00:20:10,870 --> 00:20:14,410
+one
+
+148
+00:20:15,570 --> 00:20:22,790
+zero دلوقت وانا zero يعني ايش قصدك تقول قصدي اقول
+
+149
+00:20:22,790 --> 00:20:29,410
+ان عددي الحلول طلع جد درجة مين جد درجة ال
+
+150
+00:20:29,410 --> 00:20:35,650
+polynomial في حالة ما تكون درجتها واحد صحيح طب
+
+151
+00:20:35,650 --> 00:20:39,710
+نكبر شوية فبتدعي اقول هنا
+
+152
+00:20:45,110 --> 00:21:04,490
+that ان ال F of X has degree N and ال A is a zero
+
+153
+00:21:04,490 --> 00:21:10,630
+of multiplicity
+
+154
+00:21:10,630 --> 00:21:13,390
+K
+
+155
+00:21:16,040 --> 00:21:30,880
+in the field capital F of X then ال F of X بده
+
+156
+00:21:30,880 --> 00:21:39,600
+يكون شكلها ال X ناقص ال A to the power K في ال Q
+
+157
+00:21:39,600 --> 00:21:44,060
+of X ماعنديش
+
+158
+00:21:44,060 --> 00:21:50,270
+remainderلأنه جايل F of X الدرجة تبع التهادى ويلها
+
+159
+00:21:50,270 --> 00:21:57,530
+Zero of multiplicity K بدون Remember فخليني أدور
+
+160
+00:21:57,530 --> 00:22:02,750
+على الدرجة تبع التهادى أشوف إيش تساوي مش هذه تساوي
+
+161
+00:22:02,750 --> 00:22:09,890
+هذه صح إذا الدرجة تهادى تساوي الدرجة تهادى طيب
+
+162
+00:22:09,890 --> 00:22:19,270
+يبقى ال degree لل F of Xبدي يساوي ال degree لمن لل
+
+163
+00:22:19,270 --> 00:22:27,770
+X ناقص ال A to the power K في ال Q of X هذا الكلام
+
+164
+00:22:27,770 --> 00:22:36,090
+بدي يساوي أليس هو ال degree لل X ناقص ال A to the
+
+165
+00:22:36,090 --> 00:22:45,570
+power K زائد ال degree تبع ال Q of Xلما أنا بدي
+
+166
+00:22:45,570 --> 00:22:50,670
+polynomial و polynomial مضربات في بعض بدي قداش
+
+167
+00:22:50,670 --> 00:22:56,230
+درجة ال polynomial الكبيرة يبقى درجة الأولى زائد
+
+168
+00:22:56,230 --> 00:23:01,650
+درجة مين الثانية يبقى هاي درجة الأولى زائد درجة
+
+169
+00:23:01,650 --> 00:23:08,870
+الثانية قداش درجة ال F of X قررتها
+
+170
+00:23:08,870 --> 00:23:17,940
+قداش N يبقى ال N تساويقدرش درجة القوس هذا كيه لو
+
+171
+00:23:17,940 --> 00:23:24,900
+فكته اعلى قوس عند كيه يبقى من الدرجة رقم كيه زائد
+
+172
+00:23:24,900 --> 00:23:34,600
+ال degree لمن للي q of x بناء عليه ال degree ال
+
+173
+00:23:34,600 --> 00:23:44,130
+degree لمن للي q of x بده تساوي ال nنقص ال K من
+
+174
+00:23:44,130 --> 00:23:50,650
+الأكبر ال N و الله K يعني K أصغر يبقى بقدر أقوله
+
+175
+00:23:50,650 --> 00:23:59,710
+well K أقل من أو تساوي ال N خليلي
+
+176
+00:23:59,710 --> 00:24:05,850
+هالمعلومة عندكم على شج نزمان يبقى هذه اعتبريها رقم
+
+177
+00:24:05,850 --> 00:24:10,050
+واحد كويس
+
+178
+00:24:10,960 --> 00:24:19,400
+بدا لي افترض ان عندي حل تاني لو zero تاني ليه
+
+179
+00:24:19,400 --> 00:24:25,240
+حكاية ال a لان مش كل ال polynomial بيقول عندي x
+
+180
+00:24:25,240 --> 00:24:28,660
+ناقص ليه to the power k والتاني ال polynomial تاني
+
+181
+00:24:28,660 --> 00:24:34,120
+مالهاش حلول يمكن ألاقي كمان حل ويمكن ألاقي كمان حل
+
+182
+00:24:34,120 --> 00:24:39,040
+مختلف ويطلع عندي تلت أربع حلول مختلفة هذا
+
+183
+00:24:39,040 --> 00:24:44,010
+multiplicity kهذا multiplicity كوان يعني يمكن يطلع
+
+184
+00:24:44,010 --> 00:24:48,730
+اتنين هذا multiplicity one يبقى قص مفيش غيره مش كل
+
+185
+00:24:48,730 --> 00:24:56,810
+احتمالات هذه واردة اذا باجي بقول بدي اختار ال ال
+
+186
+00:24:56,810 --> 00:25:08,930
+بي بي ازرع of the polynomial polynomial
+
+187
+00:25:08,930 --> 00:25:23,010
+FF of X with P لا تساوي A in the field ال field
+
+188
+00:25:23,010 --> 00:25:31,010
+اللي لأ هذا بيساوي الشرط طيب مدام حل يبقى F of P
+
+189
+00:25:31,010 --> 00:25:39,270
+قداش تساوي Zero إذا هذا هيحقق المعدل الأصلي اللي
+
+190
+00:25:39,270 --> 00:25:49,780
+عندنا هذاthen ال F of B يساوي B ناقص ال A to the
+
+191
+00:25:49,780 --> 00:26:03,400
+power K في ال Q of B لخاطر
+
+192
+00:26:03,400 --> 00:26:09,920
+قبل هذه أعمل شغلة هذه يا بنات في الأول ممكن تكون
+
+193
+00:26:10,100 --> 00:26:14,880
+الـ Q of X كونستانت وممكن ما تكونش كونستانت خلينا
+
+194
+00:26:14,880 --> 00:26:20,540
+ناخد احتمال الاول قبل الخطوات خلينا قبل الخطوات
+
+195
+00:26:20,540 --> 00:26:26,280
+ناخد هذا الاحتمال لكي يكون شغلنا امركز باجي بقول
+
+196
+00:26:26,280 --> 00:26:38,280
+يسمين هذه star يبقى from star if ال Q of X is
+
+197
+00:26:38,280 --> 00:26:39,260
+كونستانت
+
+198
+00:26:42,550 --> 00:26:47,350
+لما يصير constant يبقى ال degree تبع ال F كم بتكون
+
+199
+00:26:47,350 --> 00:26:50,410
+K
+
+200
+00:26:50,410 --> 00:26:58,110
+لإن أنا مثلا مغيرش من ال degree يبقى constant then
+
+201
+00:26:58,110 --> 00:27:12,510
+ال degree ل ال F of X بده ساوي اللي هو K that isن
+
+202
+00:27:12,510 --> 00:27:21,390
+تساوي K يبقى الـ N تساوي مين؟ اللي هو الـ K طيب
+
+203
+00:27:21,390 --> 00:27:29,030
+إذا لما الـ N تساوي K يبقى كأنه صار عدد الحلول
+
+204
+00:27:29,030 --> 00:27:36,190
+يساوي قداشر؟ يساوي N اللي هو K itself يبقى هنا
+
+205
+00:27:36,190 --> 00:27:50,330
+بقول صار the numberare zeros are if is in تساوي K
+
+206
+00:27:50,330 --> 00:27:59,170
+يبقى بالطبع تماما الان بتاجي اقوله let ال B be a
+
+207
+00:27:59,170 --> 00:28:08,890
+zero for the polynomial polynomial
+
+208
+00:28:08,890 --> 00:28:11,450
+F of X
+
+209
+00:28:13,950 --> 00:28:32,010
+اللي موجودة اللي موجودة في capital F of X او
+
+210
+00:28:32,010 --> 00:28:38,730
+بقدر اقول افترضي بعدين هذا لحظة شوية احنا خدنا انه
+
+211
+00:28:38,730 --> 00:28:45,600
+ال Q of X is constant الحالة التاليةif Q of X is
+
+212
+00:28:45,600 --> 00:28:54,540
+not constant لو ماكناش كل أصل بدي أفرض بيه let ال
+
+213
+00:28:54,540 --> 00:29:02,960
+V be a 0 for the polynomial
+
+214
+00:29:13,680 --> 00:29:20,800
+ال F of B بده يساوي طبعاً اتة بي بي A zero for the
+
+215
+00:29:20,800 --> 00:29:31,240
+polynomial F of X with ال B لا تساوي ال A ال B
+
+216
+00:29:31,240 --> 00:29:44,710
+بتساويش ال A انه ال F. Then F of B يساوي ال Bناقص
+
+217
+00:29:44,710 --> 00:29:59,390
+ال A ال B ناقص ال A to the power K ثمين في ال Q of
+
+218
+00:29:59,390 --> 00:30:08,090
+B يبقى شيلنا كل X وحطينا مكانها B مدام B هو عبارة
+
+219
+00:30:08,090 --> 00:30:17,750
+عن Zero يبقى Sinceالو ال F of B يساوي Zero لإن ال
+
+220
+00:30:17,750 --> 00:30:31,650
+B Zero لل F because ال B is a Zero for F we have
+
+221
+00:30:31,650 --> 00:30:41,470
+ان ال F of B بدي ساوي Zero هذا بدي يعطينا ان ال
+
+222
+00:30:41,470 --> 00:30:49,600
+Zeroبدي يساوي ال B ناقص ال A to the power K في ال
+
+223
+00:30:49,600 --> 00:30:56,320
+Q order السؤال هو هل ممكن ال course هذا يسوي Zero
+
+224
+00:30:56,320 --> 00:31:04,460
+؟ لأ هذا ممكن يسوي Zero صحيح ليش ان عندنا field
+
+225
+00:31:04,460 --> 00:31:11,900
+اتنين ال D لايمكن ان تسوي ال A يرجع هذا بدي يعطينا
+
+226
+00:31:12,200 --> 00:31:22,880
+إن ال EQ of B بدها تساوي Zero Because ال
+
+227
+00:31:22,880 --> 00:31:36,440
+B لا تساوي ال A and ال F is تحفيز طيب
+
+228
+00:31:36,440 --> 00:31:46,210
+طلعوا لي هنا ال EQ of Bتساوي Zero واطلعولي لدرجة
+
+229
+00:31:46,210 --> 00:31:53,090
+ال Q تساوي N ناقص K يبقى هذه المعادلة لها كام حل
+
+230
+00:31:53,090 --> 00:32:01,910
+على أكتر ما يمكن الدرجة تبعتها N ناقص K أقصى درجة
+
+231
+00:32:01,910 --> 00:32:07,830
+عندها N ناقص K وعند ال Q of B بدأت تساوي Zero واني
+
+232
+00:32:07,830 --> 00:32:13,300
+بقدرة اللي قلت افترض بيهحال او اترث بيه zero تلاقى
+
+233
+00:32:13,300 --> 00:32:18,420
+Q تسوى zero يبقى قداش اقصى ما يمكن عندي من الحلول
+
+234
+00:32:18,420 --> 00:32:23,800
+الناقص K مش درجة ال degree الناقص K صح ولا لأ مش
+
+235
+00:32:23,800 --> 00:32:30,920
+الدرجة ال Q اقصى ماعندي الناقص K و ال Q of بيبدو
+
+236
+00:32:30,920 --> 00:32:37,440
+سواء اذا ال Q of X اقصى الحلول لها اللي هو الناقص
+
+237
+00:32:37,440 --> 00:32:45,580
+K مظبوطيبقى هنا بجي بقوله هذا بدي يعطينا ايش؟ بدي
+
+238
+00:32:45,580 --> 00:32:59,600
+يعطينا the most zeros of a Q of X بدي تساوي zero
+
+239
+00:32:59,600 --> 00:33:03,380
+is N ناقص الفيه
+
+240
+00:33:24,240 --> 00:33:30,840
+طيب الآن أنا بدى أدور على الحلول تبعت من تبعت الـ
+
+241
+00:33:30,840 --> 00:33:37,940
+F قولنا هذا بيجيبلي قداش K من الحلول وهذا بيجيبلي
+
+242
+00:33:37,940 --> 00:33:44,840
+قداش N ناقص K من الحلول يبقى مجموعة الحلول بصير
+
+243
+00:33:44,840 --> 00:33:56,850
+على الشكل التالف يبقى the zeros of Fat most بدها
+
+244
+00:33:56,850 --> 00:34:05,470
+تساوي الأولاني K والتاني N ناقص ال K يساوي كده؟
+
+245
+00:34:05,470 --> 00:34:14,290
+يساوي N فنطلع من هذا الكلام بما يأتي على بالك الله
+
+246
+00:34:14,290 --> 00:34:22,490
+لو كنت بشتغل في field دجج أيه معناه كلام؟لو كنت
+
+247
+00:34:22,490 --> 00:34:29,710
+بشتغل في field فعدد الحلول لل polynomial يساوي
+
+248
+00:34:29,710 --> 00:34:35,350
+درجة ال polynomial لكن لو ماكانش field، الكلام مش
+
+249
+00:34:35,350 --> 00:34:40,990
+صحيح، الكلام ده ممكن يطلع عدد حلول أكتر من مين،
+
+250
+00:34:40,990 --> 00:34:45,450
+أكتر من أنا، هكتبلك إياها، بصي صبر شوية، هكتبلك،
+
+251
+00:34:45,450 --> 00:34:51,150
+أوضحلك إياها كذلك بمثاليعني يا بنات الكرولري هذه
+
+252
+00:34:51,150 --> 00:34:58,090
+ليست صحيحة إلا على الفيل، فغير الفيل ماهياش صحيحة.
+
+253
+00:34:58,470 --> 00:35:02,430
+ربي خليني أكتب المراحة وهذه، ريمان.
+
+254
+00:35:06,710 --> 00:35:08,910
+كرولري تلاتة
+
+255
+00:35:26,740 --> 00:35:39,060
+but not true but not true لكنها ليست صحيحة for
+
+256
+00:35:39,060 --> 00:35:46,660
+pronomial ring for polynomial ring
+
+257
+00:35:46,660 --> 00:35:52,480
+لكنها ليست صحيحة للpronomial ring for example
+
+258
+00:35:52,480 --> 00:35:55,840
+كتوضيح for example
+
+259
+00:35:59,640 --> 00:36:10,820
+ف ال F of X يسار X ترابيع زائد تلاتة X زائد اتنين
+
+260
+00:36:10,820 --> 00:36:28,800
+then ال F has four zeros four zeros and the six
+
+261
+00:36:54,030 --> 00:36:59,090
+ده سؤال التاريخ ال six هدفين؟ لأ لأ هذا integral
+
+262
+00:36:59,090 --> 00:37:03,470
+domain لإنه في zero divisors و لا فيش فيه zero
+
+263
+00:37:03,470 --> 00:37:10,450
+يبقى كمان مش مش مش مش integral domain لكن
+
+264
+00:37:10,450 --> 00:37:14,750
+polynomial ring صح يبقى ده polynomial ring ماشي
+
+265
+00:37:14,750 --> 00:37:22,290
+لعين يبقى مادام ring يعني ليست field و ليست
+
+266
+00:37:22,290 --> 00:37:27,580
+integral domainتعالى نشوف هذه في إيها كام حل في Z6
+
+267
+00:37:27,580 --> 00:37:33,640
+أنا بتدعي إنهم مين أربعة حلول، إيش أربعة حلول؟ طيب
+
+268
+00:37:33,640 --> 00:37:38,500
+على أصل Z6 هم Zero، واحد واثنين، ثلاثة، أربعة
+
+269
+00:37:38,500 --> 00:37:45,200
+وخمسة، تمام؟ هل ال Zero بخبري هذه الحل؟ ال Zero
+
+270
+00:37:45,200 --> 00:37:49,880
+بعدين جاوب اتنين، يبقى ال Zero ليس أحد الحلول، طيب
+
+271
+00:37:49,880 --> 00:37:56,880
+نجربالواحد هو حل ولا لا؟ واحد تقريبا تلاتة في واحد
+
+272
+00:37:56,880 --> 00:38:02,280
+زي دين يبقى ايه؟ ستة يعني جدرس. Zero في زي ستة
+
+273
+00:38:02,280 --> 00:38:09,700
+يبقى الواحد أحد الحلوين. As for zeros in that case
+
+274
+00:38:09,700 --> 00:38:16,560
+أي أنواع. الواحد هو اتنين،
+
+275
+00:38:16,560 --> 00:38:24,970
+اربعة، تلاتة، ستة،واربع عشرة واتنين زيك يبقى كمان
+
+276
+00:38:24,970 --> 00:38:33,050
+احد الحلول طيب اربع اربع في اربع ستة عشر تلاتة في
+
+277
+00:38:33,050 --> 00:38:39,970
+اربع اتناش وستاش تمانية وعشرين واتنين تلاتين
+
+278
+00:38:39,970 --> 00:38:49,770
+بالفعل ستة وستة وتلاتين اه احد الحلول I and Rams
+
+279
+00:38:51,580 --> 00:38:57,740
+خمسة في خمسة، خمسة وعشرين، خمسة في تلاتة، خمس عشر،
+
+280
+00:38:57,740 --> 00:39:01,500
+خمسة واربعين، اربعين واتنين، نين واربعين، تكسب ع
+
+281
+00:39:01,500 --> 00:39:05,820
+ستة؟ أه سبعة وستة واتنين واربعين. يبقى من
+
+282
+00:39:05,820 --> 00:39:09,940
+الاستبعدنا؟ استبعدنا الـ Zero واستبعدنا التلاتة.
+
+283
+00:39:10,320 --> 00:39:16,420
+هل يترى التلاتة هي أحد، هي الـ Zero لهذه التلاتة
+
+284
+00:39:16,420 --> 00:39:20,300
+على الجهود؟تسعة و تسعة و تسعة و تسعة و تسعة و تسعة
+
+285
+00:39:20,300 --> 00:39:20,960
+و تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و
+
+286
+00:39:20,960 --> 00:39:21,500
+تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و
+
+287
+00:39:21,500 --> 00:39:23,340
+تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و
+
+288
+00:39:23,340 --> 00:39:25,160
+تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و
+
+289
+00:39:25,160 --> 00:39:27,420
+تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و
+
+290
+00:39:27,420 --> 00:39:29,840
+تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و
+
+291
+00:39:29,840 --> 00:39:38,820
+تسعة و تسعة و تسعة و تسعة و تسعة و تسعة و تسعة
+
+292
+00:39:38,820 --> 00:39:42,300
+و تسعة
+
+293
+00:39:42,300 --> 00:39:49,050
+والدرجة تبعتي ال paranormal تساوي عدد الحلول بطل
+
+294
+00:39:49,050 --> 00:39:53,170
+يصير عندنا فيه اللي بيبقى الدرجة بتختلف عن عدد
+
+295
+00:39:53,170 --> 00:39:57,350
+الحلول، تمام؟ دائما الحلول أكبر من الدرجة إذا
+
+296
+00:39:57,350 --> 00:40:02,910
+ماكنتش فيه؟ أيه أكبر؟ يعني عندك أربعة حلول والدرجة
+
+297
+00:40:02,910 --> 00:40:07,750
+التانية، لأن لو بدأ أشغل أنا وياك بلغة معلوماتنا
+
+298
+00:40:07,750 --> 00:40:12,770
+القديمة، بدناش نشتغل جبر، المعادلة هذه لكم حالة؟
+
+299
+00:40:14,660 --> 00:40:20,100
+حلين؟ سالب واحد وسالب اتنين صح ولا ده؟ والله اتنين
+
+300
+00:40:20,100 --> 00:40:26,380
+و واحد تمام؟ إذا هذه ملهاش الا حلين لكن احنا
+
+301
+00:40:26,380 --> 00:40:30,260
+بنشتغل و أنا مابنشتغلش في الخلق بنشتغل في ring
+
+302
+00:40:30,260 --> 00:40:36,000
+يعني احنا مقيدين بال ring Z6 ماخل ذلك ماليش علاقة
+
+303
+00:40:36,000 --> 00:40:41,240
+فيه تمام؟ هذه لما تيجي تحل ليها بصير X زي اتنين في
+
+304
+00:40:41,240 --> 00:40:45,440
+X زي واحد يسوى Zeroيبقى يكسب ناقص اتنين ويكسب ناقص
+
+305
+00:40:45,440 --> 00:40:49,600
+واحدة هذا على ال real line بس احنا مش على ال real
+
+306
+00:40:49,600 --> 00:40:54,180
+line احنا بنشتغل داخل ال ring Z6 اللي لا هي
+
+307
+00:40:54,180 --> 00:41:01,020
+integral domain ولا هي كمان field طيب نعطي كمان
+
+308
+00:41:01,020 --> 00:41:05,560
+مثال example
+
+309
+00:41:05,560 --> 00:41:06,640
+find
+
+310
+00:41:26,600 --> 00:41:38,260
+x in minus one هاذي
+
+311
+00:41:38,260 --> 00:41:44,040
+ايش مناورة يا بنات بدنا zeros تبع x in minus one
+
+312
+00:41:44,040 --> 00:41:50,160
+ممكن احطها بشكل اخر هذي اقول x in minus one بده
+
+313
+00:41:50,160 --> 00:41:58,070
+يسوى zero مين هيالعناصر ها اللي هي أعداد مُركّبة
+
+314
+00:41:58,070 --> 00:42:04,330
+اللي بدي أتحقق لهذه المعادة يعني هذه المعادة لا
+
+315
+00:42:04,330 --> 00:42:11,670
+بقدر أقول في نهاية الشهر ان X يساوي واحد هذه بد ال
+
+316
+00:42:11,670 --> 00:42:17,310
+X باخد الجذر النوني للواحد الصحيح خليني أرجعكوا
+
+317
+00:42:17,310 --> 00:42:22,140
+بالذاكرة للغراء للثانوية العامةأخدت الجذور
+
+318
+00:42:22,140 --> 00:42:27,940
+التكعيبية للواحدة الصحية مظبوط يبقى احنا عندنا X
+
+319
+00:42:27,940 --> 00:42:33,160
+تكعيب تساوي واحد عن X تكعيب ناقص واحد بنحللها فالق
+
+320
+00:42:33,160 --> 00:42:38,620
+بين المكعبين X ناقص واحد في X تربية زايد X زايد
+
+321
+00:42:38,620 --> 00:42:43,240
+واحد الأولى بتعطيني X تساوي واحد التانية بتعطيني
+
+322
+00:42:43,240 --> 00:42:53,330
+جذرين تخيليين ومترافقين صح؟يبقى هذه أعداد مُركّبة
+
+323
+00:42:53,330 --> 00:42:59,730
+يبقى صار عندي جذور مُركّبة المعادلة هذه لها حل
+
+324
+00:42:59,730 --> 00:43:06,010
+واحد حقيقي وهي X يساوي واحد باقي الحلول أعداد
+
+325
+00:43:06,010 --> 00:43:13,010
+مُركّبة يعني هذه المسألة هذه المسألة الحلول تبعها
+
+326
+00:43:13,010 --> 00:43:21,090
+بدتكون أفضل كده؟ كده اتوقعوا؟ أكترلأن ال complex
+
+327
+00:43:21,090 --> 00:43:27,390
+number is a field. فمتازة. يبدأ هذه عيلها عدد من
+
+328
+00:43:27,390 --> 00:43:35,790
+الحلول يساوي N. بس في حل رئيسي من خلاله بجيب كل
+
+329
+00:43:35,790 --> 00:43:41,810
+الحلول. بدنا ندور من هو الحل الرئيسي. بجينا بنقول
+
+330
+00:43:41,810 --> 00:43:47,070
+let omega تسوي كذا. W والله omega بتفارقش عننا.
+
+331
+00:43:47,670 --> 00:43:56,380
+يبقى العددوميجا و الله w يسوى cosine اتنين باي على
+
+332
+00:43:56,380 --> 00:44:11,660
+M زائد I sine اتنين باي على M تمام؟
+
+333
+00:44:11,660 --> 00:44:19,950
+طب بترفع اتنين كأسحطلهم أُس العدد N طبعاً N
+
+334
+00:44:19,950 --> 00:44:26,870
+Positive Integer يبقى بالدرجة يقولوا W أُس N يسوى
+
+335
+00:44:26,870 --> 00:44:37,470
+Cos 2 Pi على N زائد I Sin 2 Pi على M to the power
+
+336
+00:44:37,470 --> 00:44:44,990
+N حد فيكم ماخدتش مادة ال Complex Value واخدتها
+
+337
+00:44:44,990 --> 00:44:54,040
+يعنيطيب الحمد لله ذلك ما كنا نبعد نطلق لنظرية دي
+
+338
+00:44:54,040 --> 00:44:59,820
+موافقة يرجى ال N بنزل على الزاوية تمام؟ يرجى هذا
+
+339
+00:44:59,820 --> 00:45:12,600
+بيصير Cos N 2 Pi على N زائد I Sin N 2 Pi على N
+
+340
+00:45:12,600 --> 00:45:21,190
+ممتاز جدايبقى هذا الكلام بده يساوي ان مع ان بصير
+
+341
+00:45:21,190 --> 00:45:30,530
+cosine اتنين by زائد I sine اتنين by ان بتروح
+
+342
+00:45:30,530 --> 00:45:37,510
+معايا جيب ال 360 جيب
+
+343
+00:45:37,510 --> 00:45:43,370
+الشيطانات جيب ال 360 هو جيب السفر جيب السفر في
+
+344
+00:45:43,370 --> 00:45:50,320
+قرداجةفأقرأ ال term الأخير و جيب تمام و جيب تمام
+
+345
+00:45:50,320 --> 00:45:55,220
+الصفر اللي هو واحد إذا النتيجة هذه كلها تساوي
+
+346
+00:45:55,220 --> 00:46:00,720
+واحدة هذا يا بنات جيبناها من نظرية De Moivre يعني
+
+347
+00:46:00,720 --> 00:46:09,520
+بتقدر تقول اللي بين جسينك De Moivre's theory مش
+
+348
+00:46:09,520 --> 00:46:17,460
+عشوائي يعني مش فاهم يبقى أصبحالـ W قص M يساوي كده
+
+349
+00:46:17,460 --> 00:46:23,760
+طيب وليس الـ W هو أحد الحلول أو هو الـ Zero
+
+350
+00:46:23,760 --> 00:46:38,420
+للمعادلة يبقى هنا الـ W هو A Zero of the equation
+
+351
+00:46:38,420 --> 00:46:44,580
+X to the power M يساوي واحدةطب احنا قلنا ال six
+
+352
+00:46:44,580 --> 00:46:49,860
+complex numbers is a field يبقى من الدرجة النونية
+
+353
+00:46:49,860 --> 00:46:59,220
+عند n من الحلول يبقى بروح بقوله the zeros of the x
+
+354
+00:46:59,220 --> 00:47:06,120
+to the power n بتساوي الواحد are انا هتدعي ان واحد
+
+355
+00:47:06,120 --> 00:47:14,800
+و W و W تربيه و W تكييفو W أُس N ناقص واحد جديش
+
+356
+00:47:14,800 --> 00:47:24,080
+عددهم N طيب ليش هدول الحلول لإن واحد أس N يبقى
+
+357
+00:47:24,080 --> 00:47:32,480
+واحد أحد الحلول يبقى هنا because واحد
+
+358
+00:47:32,480 --> 00:47:40,250
+أس N يساوي واحد هدول بداخل واحد عشوائي منهموثبتح
+
+359
+00:47:40,250 --> 00:47:44,090
+نثبتنا ان ال W هنا أحد الحلول بدي أجيب لك كمان
+
+360
+00:47:44,090 --> 00:47:53,530
+واحد غير ال W ناخد W تكيب يبقى N ال W تكيب to the
+
+361
+00:47:53,530 --> 00:48:00,070
+power N إذا طلعت بواحد يبقى بصير ال W تكيب هي أحد
+
+362
+00:48:00,070 --> 00:48:11,020
+الحلول يبقى هذا W أس 3 Nيبقى W أُس M تكريم ال W
+
+363
+00:48:11,020 --> 00:48:18,100
+أُس M قداش عندنا تكريم واحد يبقى واحد تكريم هو
+
+364
+00:48:18,100 --> 00:48:24,420
+واحد يبقى هذون مجموعة الحلول للمعادلة اللي عندنا
+
+365
+00:48:24,420 --> 00:48:30,340
+حيث W اللي هي فاضمها في الأول اللي هو على الشكل
+
+366
+00:48:30,340 --> 00:48:36,090
+اللي عندنا انايبقى الـ W هي اللي جابتلي كل باقي
+
+367
+00:48:36,090 --> 00:48:41,690
+الحلول يبقى الـ W هذه بسميها ال primitive zero او
+
+368
+00:48:41,690 --> 00:48:46,570
+ال primitive solution لمين لهذه المعادلة اعطيكيها
+
+369
+00:48:46,570 --> 00:48:56,010
+على شكل definition W definition above
+
+370
+00:48:56,010 --> 00:49:01,270
+complex W
+
+371
+00:49:03,740 --> 00:49:08,600
+is called the
+
+372
+00:49:08,600 --> 00:49:14,500
+primitive is
+
+373
+00:49:14,500 --> 00:49:21,580
+called the primitive infruit infruit
+
+374
+00:49:21,580 --> 00:49:29,620
+of unity ليش؟
+
+375
+00:49:29,620 --> 00:49:34,320
+لأن هذا جاب لي .. يعني هذا هو الحل الرئيسيأو الحل
+
+376
+00:49:34,320 --> 00:49:40,500
+الاقتدائي لكل الحلول البنى عليه كمان definition
+
+377
+00:49:40,500 --> 00:49:50,520
+اخرى a principle ideal domain a principle ideal
+
+378
+00:49:50,520 --> 00:50:02,380
+domain اللى هديله الرمز PID is an integral domain
+
+379
+00:50:02,790 --> 00:50:12,730
+is an integral domain R
+
+380
+00:50:12,730 --> 00:50:26,050
+in which every ideal in which every ideal has the
+
+381
+00:50:26,050 --> 00:50:36,220
+form has the formعالى الشكل اللى هو main principle
+
+382
+00:50:36,220 --> 00:50:45,500
+ID generated by A كل ال R A بحيث ال R موجودة في A
+
+383
+00:50:45,500 --> 00:50:57,220
+for some ال A اللى موجودة في R مرّط
+
+384
+00:50:57,220 --> 00:51:03,040
+علينا شغل زيك يا بنات؟مرة علينا، طب واحدة فيكم
+
+385
+00:51:03,040 --> 00:51:09,440
+بتقدر تجيبلي مثال؟
+
+386
+00:51:09,440 --> 00:51:18,740
+ها تقوللي هاي ring و هاي فيها ideal و هاي integral
+
+387
+00:51:18,740 --> 00:51:25,480
+domain و كل ideal فيه is a principle مكتوب معاكم،
+
+388
+00:51:25,480 --> 00:51:32,610
+بس يالا تقدر تجيبه في الأول integral domain؟اللي
+
+389
+00:51:32,610 --> 00:51:37,070
+هم يعني زد مجموعة الاعداد الصحية الذهبية التجارة
+
+390
+00:51:37,070 --> 00:51:40,410
+الدولية مافيها zero divisor ايه الشكل ال ideal
+
+391
+00:51:40,410 --> 00:51:45,950
+فيها ان في زد ان في زد is a principle ideal
+
+392
+00:51:45,950 --> 00:51:52,570
+generated by ان خلصنا يبقى زد is a principle ideal
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..568d5dee07d063f4b6e6a42c2cd7c3ada491c371
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_raw.json
@@ -0,0 +1 @@
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then ال capital P of X لprinciple هذا بده يساوي zero or", "tokens": [47, 401, 2534, 47429, 13412, 2407, 21136, 3555, 3555, 570, 498, 430, 295, 1783, 307, 5754, 550, 2423, 4238, 430, 295, 1783, 5296, 1424, 21961, 781, 23758, 47525, 3224, 7251, 3794, 995, 45865, 4018, 420], "avg_logprob": -0.3676215393675698, "compression_ratio": 1.0956521739130434, "no_speech_prob": 0.0, "words": [{"start": 219.81, "end": 221.21, "word": "Polynomial", "probability": 0.579986572265625}, {"start": 221.21, "end": 222.61, "word": " شو", "probability": 0.82568359375}, {"start": 222.61, "end": 223.13, "word": " السبب", "probability": 0.9811197916666666}, {"start": 223.13, "end": 224.37, "word": " because", "probability": 0.20458984375}, {"start": 224.37, "end": 228.27, "word": " if", "probability": 0.75634765625}, {"start": 228.27, "end": 229.73, "word": " P", "probability": 0.8408203125}, {"start": 229.73, "end": 230.05, "word": " of", "probability": 0.685546875}, {"start": 230.05, "end": 230.45, "word": " 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"probability": 0.6241455078125}, {"start": 309.63, "end": 310.63, "word": " بقوله", "probability": 0.8680013020833334}, {"start": 310.63, "end": 311.25, "word": " now", "probability": 0.48388671875}, {"start": 311.25, "end": 312.69, "word": " want", "probability": 0.4658203125}, {"start": 312.69, "end": 313.07, "word": " to", "probability": 0.98681640625}, {"start": 313.07, "end": 313.71, "word": " show", "probability": 0.96728515625}, {"start": 313.71, "end": 317.59, "word": " that", "probability": 0.912109375}, {"start": 317.59, "end": 319.97, "word": " ان", "probability": 0.771484375}, {"start": 319.97, "end": 320.31, "word": " ال", "probability": 0.607421875}, {"start": 320.31, "end": 320.75, "word": " P", "probability": 0.98046875}, {"start": 320.75, "end": 321.57, "word": " of", "probability": 0.9794921875}, {"start": 321.57, "end": 322.11, "word": " X", "probability": 0.99365234375}, {"start": 322.11, "end": 323.11, "word": " is", "probability": 0.96875}, {"start": 323.11, "end": 324.61, "word": " irreducible", "probability": 0.9573567708333334}, {"start": 324.61, "end": 327.49, "word": " over", "probability": 0.8515625}, {"start": 327.49, "end": 327.85, "word": " X", "probability": 0.970703125}], "temperature": 1.0}, {"id": 12, "seek": 36043, "start": 333.87, "end": 360.43, "text": "الشفتر هذا كل البرهين كانت في ال contradiction وماحدش أحسن من حد و هذه تلحقهم كمان يبقى هقوله assume نعم يبقى هنا هقوله assume ان ال P of X is reducible تمام يبقى reducible over F", "tokens": [6027, 8592, 5172, 2655, 2288, 23758, 28242, 2423, 26890, 3224, 9957, 25961, 2655, 8978, 2423, 34937, 4032, 15042, 24401, 8592, 5551, 5016, 3794, 1863, 9154, 11331, 3215, 4032, 29538, 6055, 1211, 5016, 4587, 16095, 9122, 2304, 7649, 7251, 3555, 4587, 7578, 8032, 39648, 3224, 6552, 8717, 25957, 7251, 3555, 4587, 7578, 34105, 8032, 39648, 3224, 6552, 16472, 2423, 430, 295, 1783, 307, 2783, 32128, 46811, 10943, 7251, 3555, 4587, 7578, 2783, 32128, 670, 479], "avg_logprob": 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{"start": 340.81, "end": 341.19, "word": " حد", "probability": 0.970703125}, {"start": 341.19, "end": 341.37, "word": " و", "probability": 0.6064453125}, {"start": 341.37, "end": 341.67, "word": " هذه", "probability": 0.263427734375}, {"start": 341.67, "end": 342.49, "word": " تلحقهم", "probability": 0.87626953125}, {"start": 342.49, "end": 342.85, "word": " كمان", "probability": 0.9295247395833334}, {"start": 342.85, "end": 343.11, "word": " يبقى", "probability": 0.8375244140625}, {"start": 343.11, "end": 343.63, "word": " هقوله", "probability": 0.5662434895833334}, {"start": 343.63, "end": 344.11, "word": " assume", "probability": 0.8486328125}, {"start": 344.11, "end": 344.59, "word": " نعم", "probability": 0.56396484375}, {"start": 344.59, "end": 345.83, "word": " يبقى", "probability": 0.94873046875}, {"start": 345.83, "end": 346.21, "word": " هنا", "probability": 0.98095703125}, {"start": 346.21, "end": 347.09, "word": " هقوله", "probability": 0.9488932291666666}, {"start": 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"probability": 0.88818359375}], "temperature": 1.0}, {"id": 13, "seek": 39099, "start": 362.49, "end": 390.99, "text": "فماش اللي بده يحصل يبقى then ال P of X هذه حد ساوي ال G of X في ال H of X where حيث ال G of X و ال H of X موجودات في capital F of X and", "tokens": [5172, 2304, 33599, 13672, 1829, 47525, 3224, 7251, 5016, 36520, 7251, 3555, 4587, 7578, 550, 2423, 430, 295, 1783, 29538, 11331, 3215, 8608, 995, 45865, 2423, 460, 295, 1783, 8978, 2423, 389, 295, 1783, 689, 11331, 1829, 12984, 2423, 460, 295, 1783, 4032, 2423, 389, 295, 1783, 3714, 29245, 23328, 9307, 8978, 4238, 479, 295, 1783, 293], "avg_logprob": -0.20757004207578197, "compression_ratio": 1.3925925925925926, "no_speech_prob": 0.0, "words": [{"start": 362.49, "end": 362.91, "word": "فماش", "probability": 0.6128743489583334}, {"start": 362.91, "end": 363.07, "word": " اللي", "probability": 0.876708984375}, {"start": 363.07, "end": 363.33, "word": " بده", "probability": 0.691650390625}, {"start": 363.33, "end": 363.99, 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" و", "probability": 0.5791015625}, {"start": 382.59, "end": 382.81, "word": " ال", "probability": 0.68994140625}, {"start": 382.81, "end": 383.23, "word": " H", "probability": 0.9814453125}, {"start": 383.23, "end": 383.73, "word": " of", "probability": 0.97216796875}, {"start": 383.73, "end": 384.17, "word": " X", "probability": 0.998046875}, {"start": 384.17, "end": 385.73, "word": " موجودات", "probability": 0.87109375}, {"start": 385.73, "end": 386.07, "word": " في", "probability": 0.71923828125}, {"start": 386.07, "end": 387.95, "word": " capital", "probability": 0.293701171875}, {"start": 387.95, "end": 388.73, "word": " F", "probability": 0.93359375}, {"start": 388.73, "end": 389.21, "word": " of", "probability": 0.96728515625}, {"start": 389.21, "end": 389.73, "word": " X", "probability": 0.99755859375}, {"start": 389.73, "end": 390.99, "word": " and", "probability": 0.7578125}], "temperature": 1.0}, {"id": 14, "seek": 41738, "start": 392.04, "end": 417.38, "text": "R of lower degree ايش يعني lower degree يعني درجة كل واحدة فيهم من GH اقل من درجة من P of X ممتاز جدا يبقى الآن صار عندنا شبنان صار عندنا P of X", "tokens": [49, 295, 3126, 4314, 1975, 1829, 8592, 37495, 22653, 3126, 4314, 37495, 22653, 11778, 47341, 3660, 28242, 36764, 24401, 3660, 8978, 16095, 9154, 40690, 1975, 4587, 1211, 9154, 11778, 47341, 3660, 9154, 430, 295, 1783, 3714, 2304, 2655, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 6024, 48506, 20328, 9640, 43242, 8315, 13412, 3555, 1863, 7649, 20328, 9640, 43242, 8315, 430, 295, 1783], "avg_logprob": -0.25124006706570823, "compression_ratio": 1.5384615384615385, "no_speech_prob": 0.0, "words": [{"start": 392.04, "end": 393.02, "word": "R", "probability": 0.28955078125}, {"start": 393.02, "end": 394.36, "word": " of", "probability": 0.71435546875}, {"start": 394.36, "end": 396.1, "word": " lower", "probability": 0.443115234375}, {"start": 396.1, "end": 397.08, "word": " degree", "probability": 0.9677734375}, {"start": 397.08, "end": 401.84, "word": " ايش", "probability": 0.5895589192708334}, {"start": 401.84, "end": 402.1, "word": " يعني", "probability": 0.893310546875}, {"start": 402.1, "end": 402.46, "word": " lower", "probability": 0.77001953125}, {"start": 402.46, "end": 402.98, "word": " degree", "probability": 0.99462890625}, {"start": 402.98, "end": 404.22, "word": " يعني", "probability": 0.81396484375}, {"start": 404.22, "end": 404.88, "word": " درجة", "probability": 0.9658203125}, {"start": 404.88, "end": 405.26, "word": " كل", "probability": 0.96044921875}, {"start": 405.26, "end": 405.82, "word": " واحدة", "probability": 0.9786783854166666}, {"start": 405.82, "end": 406.24, "word": " فيهم", "probability": 0.900634765625}, {"start": 406.24, "end": 406.5, "word": " من", "probability": 0.89599609375}, {"start": 406.5, "end": 406.82, "word": " GH", "probability": 0.403564453125}, {"start": 406.82, "end": 408.12, "word": " اقل", "probability": 0.8314615885416666}, {"start": 408.12, "end": 408.48, "word": " من", "probability": 0.994140625}, {"start": 408.48, "end": 409.08, "word": " درجة", "probability": 0.9850260416666666}, {"start": 409.08, "end": 409.44, "word": " من", "probability": 0.2294921875}, {"start": 409.44, "end": 410.44, "word": " P", "probability": 0.67138671875}, {"start": 410.44, "end": 410.98, "word": " of", "probability": 0.78857421875}, {"start": 410.98, "end": 411.34, "word": " X", "probability": 0.9091796875}, {"start": 411.34, "end": 412.04, "word": " ممتاز", "probability": 0.9166259765625}, {"start": 412.04, "end": 412.44, "word": " جدا", "probability": 0.97314453125}, {"start": 412.44, "end": 413.58, "word": " يبقى", "probability": 0.946533203125}, {"start": 413.58, "end": 413.96, "word": " الآن", "probability": 0.6063232421875}, {"start": 413.96, "end": 414.26, "word": " صار", "probability": 0.79345703125}, {"start": 414.26, "end": 414.66, "word": " عندنا", "probability": 0.58331298828125}, {"start": 414.66, "end": 415.3, "word": " شبنان", "probability": 0.7391357421875}, {"start": 415.3, "end": 415.94, "word": " صار", "probability": 0.94189453125}, {"start": 415.94, "end": 416.48, "word": " عندنا", "probability": 0.9833984375}, {"start": 416.48, "end": 416.74, "word": " P", "probability": 0.97412109375}, {"start": 416.74, "end": 417.06, "word": " of", "probability": 0.970703125}, {"start": 417.06, "end": 417.38, "word": " X", "probability": 0.99560546875}], "temperature": 1.0}, {"id": 15, "seek": 44543, "start": 417.67, "end": 445.43, "text": "يساوي حاصل ضرب two polynomials تمام ليش ان ال P of X ليست constant polynomial إذا كتبناها على حاصل الضرب وكل واحدة فيهم درجتها أقل من درجة مين أقل من درجة P of X طيب بتكتب هالجملة هذه وشوف والي صح ولا غلط أنا أزعم الآن", "tokens": [1829, 3794, 995, 45865, 11331, 33546, 1211, 48812, 25513, 732, 22560, 12356, 46811, 10943, 32239, 8592, 16472, 2423, 430, 295, 1783, 32239, 14851, 5754, 26110, 11933, 15730, 9122, 2655, 3555, 8315, 11296, 15844, 11331, 33546, 1211, 6024, 114, 25513, 4032, 28820, 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هى", "tokens": [10721, 1829, 2407, 3660, 46811, 10943, 23032, 1829, 3555, 6024, 48506, 20328, 9640, 14407, 8032, 3215, 12610, 1975, 2655, 1863, 9957, 25993, 9154, 45030, 11242, 29538, 25993, 9154, 29538, 37037, 24192, 25993, 9154, 29538, 46811, 10943, 22807, 47525, 3224, 9640, 1829, 6024, 48506, 1975, 9778, 3215, 28242, 36764, 24401, 3660, 9154, 11296, 15844, 1975, 1829, 8592, 6156, 9640, 11242, 22807, 6156, 9640, 11242, 16472, 2423, 8665, 7348, 10833, 538, 430, 295, 1783, 307, 257, 49336, 7348, 4032, 4117, 2655, 3555, 8315, 3224, 9122, 2655, 3555, 8315, 3224, 8032, 7578], "avg_logprob": -0.2734374900658925, "compression_ratio": 1.561904761904762, "no_speech_prob": 0.0, "words": [{"start": 561.23, "end": 562.05, "word": "أيوة", "probability": 0.81280517578125}, {"start": 562.05, "end": 562.85, "word": " تمام", "probability": 0.981201171875}, {"start": 562.85, "end": 564.79, "word": " طيب", "probability": 0.9226888020833334}, {"start": 564.79, "end": 565.79, "word": " الآن", 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"probability": 0.65966796875}, {"start": 585.89, "end": 586.63, "word": " ID", "probability": 0.88525390625}, {"start": 586.63, "end": 587.81, "word": " وكتبناه", "probability": 0.9034016927083334}, {"start": 587.81, "end": 588.57, "word": " كتبناه", "probability": 0.96494140625}, {"start": 588.57, "end": 588.91, "word": " هى", "probability": 0.440185546875}], "temperature": 1.0}, {"id": 21, "seek": 61689, "start": 589.39, "end": 616.89, "text": "مدام maximum لو عندى العبارة هذه يبقى يا إما هذه تساوي هذه أو هذه تساوي هذه صح يبقى باجي بقوله بما أنه يبقى since the principle ideal generated by P of X is maximum we have أحد أمرين", "tokens": [2304, 3215, 10943, 6674, 45164, 43242, 7578, 18863, 3555, 9640, 3660, 29538, 7251, 3555, 4587, 7578, 35186, 11933, 15042, 29538, 6055, 3794, 995, 45865, 29538, 34051, 29538, 6055, 3794, 995, 45865, 29538, 20328, 5016, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 4724, 15042, 14739, 3224, 7251, 3555, 4587, 7578, 1670, 264, 8665, 7157, 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ideal، domain تمام؟ يبقى ال ideal هذا زي ولد ب polynomial وولد تكون على سبيل المثال g of x إذن هديها بقدر أصيها صياغة جديدة", "tokens": [2304, 19913, 3555, 2407, 9566, 22807, 8717, 19913, 23557, 5296, 28814, 1863, 2423, 479, 6225, 3555, 9640, 3660, 18871, 2519, 7251, 3555, 4587, 7578, 36632, 7157, 307, 257, 8665, 32239, 8592, 22807, 5296, 33456, 2423, 2519, 6225, 3555, 9640, 3660, 18871, 8665, 12399, 7157, 12399, 9274, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 2423, 7157, 8032, 8848, 995, 30767, 1829, 4032, 1211, 3215, 4724, 26110, 4032, 12610, 3215, 6055, 30544, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 290, 295, 2031, 11933, 8848, 1863, 8032, 16254, 11296, 4724, 28543, 2288, 5551, 9381, 1829, 11296, 20328, 1829, 5718, 118, 3660, 10874, 16254, 41891], "avg_logprob": -0.2386642091122328, "compression_ratio": 1.5454545454545454, "no_speech_prob": 0.0, "words": [{"start": 1180.75, "end": 1181.77, "word": "مظبوط؟", "probability": 0.8102620442708334}, {"start": 1181.77, "end": 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"end": 1201.29, "word": " g", "probability": 0.2344970703125}, {"start": 1201.29, "end": 1201.63, "word": " of", "probability": 0.49609375}, {"start": 1201.63, "end": 1201.95, "word": " x", "probability": 0.87939453125}, {"start": 1201.95, "end": 1203.09, "word": " إذن", "probability": 0.70068359375}, {"start": 1203.09, "end": 1204.47, "word": " هديها", "probability": 0.5494791666666666}, {"start": 1204.47, "end": 1205.73, "word": " بقدر", "probability": 0.9275716145833334}, {"start": 1205.73, "end": 1206.55, "word": " أصيها", "probability": 0.7767333984375}, {"start": 1206.55, "end": 1207.57, "word": " صياغة", "probability": 0.91982421875}, {"start": 1207.57, "end": 1208.17, "word": " جديدة", "probability": 0.9747721354166666}], "temperature": 1.0}, {"id": 43, "seek": 123553, "start": 1208.47, "end": 1235.53, "text": "الجهد ده بده يعطينا ان ال principle ID generated by P of X subset من ال principle ID generated by G of X subset من capital F of X طيب تعالى نشوف الآن اش اللي بده يحصل 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0.494140625}, {"start": 1234.61, "end": 1235.53, "word": " نثبته؟", "probability": 0.8732421875}], "temperature": 1.0}, {"id": 44, "seek": 126489, "start": 1236.43, "end": 1264.89, "text": "بنثبت ان ال ideal is maximum يعني بدي أثبت ان اتنين هذول بتساوى او اتنين هذول بتساوى تمام؟ نيجي للحالة الأول الآن بدي اثبت ان اتنين هذول بيتساوى ان امكن ذلك تمام؟ طب احنا في حاجة كتبناها ومستفدناش منها ال radio set", "tokens": [3555, 1863, 12984, 3555, 2655, 16472, 2423, 7157, 307, 6674, 37495, 22653, 4724, 16254, 5551, 12984, 3555, 2655, 16472, 1975, 2655, 1863, 9957, 8032, 8848, 12610, 39894, 3794, 995, 2407, 7578, 1975, 2407, 1975, 2655, 1863, 9957, 8032, 8848, 12610, 39894, 3794, 995, 2407, 7578, 46811, 10943, 22807, 8717, 1829, 7435, 1829, 24976, 5016, 6027, 3660, 16247, 12610, 6024, 48506, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 1975, 2655, 1863, 9957, 8032, 8848, 12610, 4724, 36081, 3794, 995, 2407, 7578, 16472, 1975, 43020, 29910, 23275, 46811, 10943, 22807, 23032, 3555, 1975, 5016, 8315, 8978, 11331, 26108, 3660, 9122, 2655, 3555, 8315, 11296, 4032, 2304, 14851, 5172, 3215, 1863, 33599, 9154, 11296, 2423, 6477, 992], "avg_logprob": -0.24605978934661202, "compression_ratio": 1.8717948717948718, "no_speech_prob": 0.0, "words": [{"start": 1236.43, "end": 1237.25, "word": "بنثبت", "probability": 0.663037109375}, {"start": 1237.25, "end": 1237.41, "word": " ان", "probability": 0.59130859375}, {"start": 1237.41, "end": 1237.59, "word": " ال", "probability": 0.86474609375}, {"start": 1237.59, "end": 1238.15, "word": " ideal", "probability": 0.759765625}, {"start": 1238.15, "end": 1238.59, "word": " is", "probability": 0.88525390625}, {"start": 1238.59, "end": 1239.23, "word": " maximum", "probability": 0.82421875}, {"start": 1239.23, "end": 1240.07, "word": " يعني", "probability": 0.82177734375}, {"start": 1240.07, "end": 1240.37, "word": " بدي", "probability": 0.669677734375}, {"start": 1240.37, "end": 1240.91, "word": " أثبت", "probability": 0.892578125}, {"start": 1240.91, "end": 1241.11, "word": " ان", "probability": 0.810546875}, {"start": 1241.11, "end": 1241.61, "word": " اتنين", "probability": 0.8798828125}, {"start": 1241.61, "end": 1242.01, "word": " هذول", "probability": 0.8603515625}, {"start": 1242.01, "end": 1242.87, "word": " بتساوى", "probability": 0.7587890625}, {"start": 1242.87, "end": 1243.39, "word": " او", "probability": 0.731689453125}, {"start": 1243.39, "end": 1243.99, "word": " اتنين", "probability": 0.9832763671875}, {"start": 1243.99, "end": 1244.41, "word": " هذول", "probability": 0.98291015625}, {"start": 1244.41, "end": 1245.49, "word": " بتساوى", "probability": 0.9701171875}, {"start": 1245.49, "end": 1246.53, "word": " تمام؟", "probability": 0.6378173828125}, {"start": 1246.53, "end": 1246.83, "word": " نيجي", "probability": 0.80322265625}, {"start": 1246.83, "end": 1247.91, "word": " للحالة", "probability": 0.947021484375}, {"start": 1247.91, "end": 1248.59, "word": " الأول", "probability": 0.84765625}, {"start": 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{"start": 1258.15, "end": 1258.49, "word": " احنا", "probability": 0.97314453125}, {"start": 1258.49, "end": 1258.79, "word": " في", "probability": 0.9013671875}, {"start": 1258.79, "end": 1259.53, "word": " حاجة", "probability": 0.9759114583333334}, {"start": 1259.53, "end": 1260.77, "word": " كتبناها", "probability": 0.9935546875}, {"start": 1260.77, "end": 1261.61, "word": " ومستفدناش", "probability": 0.8580147879464286}, {"start": 1261.61, "end": 1262.15, "word": " منها", "probability": 0.99365234375}, {"start": 1262.15, "end": 1262.81, "word": " ال", "probability": 0.429931640625}, {"start": 1262.81, "end": 1264.45, "word": " radio", "probability": 0.04534912109375}, {"start": 1264.45, "end": 1264.89, "word": " set", "probability": 0.2484130859375}], "temperature": 1.0}, {"id": 45, "seek": 129020, "start": 1265.98, "end": 1290.2, "text": "أخدنا إن الـ P-O-Fix is irreducible. حتى الآن لم نستفد منها شيء. مظبوط؟ طيب، هذه نرجع لقبل شوية. إيش اللي أخدناها قبل شوية؟ أخدناها شيء؟ لأ ما أخدناها شيء، اتفقتنا بس للاتجاهين الأول.", "tokens": [10721, 9778, 3215, 8315, 36145, 2423, 39184, 430, 12, 46, 12, 37, 970, 307, 16014, 769, 32128, 13, 11331, 49975, 6024, 48506, 32767, 8717, 14851, 5172, 3215, 9154, 11296, 44049, 38207, 13, 3714, 19913, 3555, 2407, 9566, 22807, 23032, 1829, 3555, 12399, 29538, 8717, 47341, 3615, 5296, 4587, 36150, 13412, 2407, 10632, 13, 11933, 1829, 8592, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 12174, 36150, 13412, 2407, 10632, 22807, 5551, 9778, 3215, 8315, 11296, 44049, 38207, 22807, 5296, 10721, 19446, 5551, 9778, 3215, 8315, 11296, 44049, 38207, 12399, 1975, 2655, 5172, 38149, 8315, 4724, 3794, 24976, 9307, 7435, 40294, 9957, 16247, 12610, 13], "avg_logprob": -0.21995192766189575, "compression_ratio": 1.6062176165803108, "no_speech_prob": 0.0, "words": [{"start": 1265.9799999999998, "end": 1266.8999999999999, "word": "أخدنا", "probability": 0.9195556640625}, {"start": 1266.8999999999999, "end": 1267.82, "word": " إن", "probability": 0.35107421875}, {"start": 1267.82, "end": 1268.12, "word": " الـ", "probability": 0.7841796875}, {"start": 1268.12, "end": 1268.28, "word": " P", "probability": 0.33349609375}, {"start": 1268.28, "end": 1268.5, "word": "-O", "probability": 0.44539642333984375}, {"start": 1268.5, "end": 1268.86, "word": "-Fix", "probability": 0.6570638020833334}, {"start": 1268.86, "end": 1269.28, "word": " is", "probability": 0.7392578125}, {"start": 1269.28, "end": 1270.3, "word": " irreducible.", "probability": 0.93994140625}, {"start": 1270.74, "end": 1271.08, "word": " حتى", "probability": 0.8681640625}, {"start": 1271.08, "end": 1271.46, "word": " الآن", "probability": 0.86181640625}, {"start": 1271.46, "end": 1271.7, "word": " لم", "probability": 0.904296875}, {"start": 1271.7, "end": 1272.4, "word": " نستفد", "probability": 0.8424072265625}, {"start": 1272.4, "end": 1273.06, "word": " منها", "probability": 0.989013671875}, {"start": 1273.06, "end": 1273.76, "word": " شيء.", "probability": 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let f of x ده ساول x تكعيب مثلا زائد x زائد واحد هاي polynomial وهنا let كمان let الفيه let z اتنين بيه الفيه", "tokens": [23328, 995, 7251, 39648, 14407, 718, 283, 295, 2031, 11778, 3224, 8608, 995, 12610, 2031, 6055, 4117, 3615, 1829, 3555, 50113, 15040, 30767, 16373, 3215, 2031, 30767, 16373, 3215, 36764, 24401, 8032, 47302, 26110, 37037, 8315, 718, 9122, 2304, 7649, 718, 27188, 1829, 3224, 718, 710, 1975, 2655, 1863, 9957, 4724, 1829, 3224, 27188, 1829, 3224], "avg_logprob": -0.43037281956589013, "compression_ratio": 1.4015151515151516, "no_speech_prob": 0.0, "words": [{"start": 2908.69, "end": 2909.25, "word": "ودا", "probability": 0.35589599609375}, {"start": 2909.25, "end": 2909.97, "word": " يقولوا", "probability": 0.5691731770833334}, {"start": 2909.97, "end": 2910.51, "word": " let", "probability": 0.82568359375}, {"start": 2910.51, "end": 2912.01, "word": " f", "probability": 0.385986328125}, {"start": 2912.01, "end": 2912.47, "word": " of", "probability": 0.28857421875}, 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"seek": 302557, "start": 2996.69, "end": 3025.57, "text": "يبقى بقى دي بقوله by the above theorem the principle ideal generated by the highest maximal مدام maximal هذا الآل بده يعطينا ان z2 modulo هذا ال ideal", "tokens": [1829, 3555, 4587, 7578, 4724, 4587, 7578, 11778, 1829, 4724, 39648, 3224, 538, 264, 3673, 20904, 264, 8665, 7157, 10833, 538, 264, 6343, 49336, 3714, 3215, 10943, 49336, 23758, 6024, 95, 1211, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 710, 17, 1072, 13455, 23758, 2423, 7157], "avg_logprob": -0.38829786726768983, "compression_ratio": 1.3450704225352113, "no_speech_prob": 0.0, "words": [{"start": 2996.69, "end": 2997.51, "word": "يبقى", "probability": 0.8118896484375}, {"start": 2997.51, "end": 2997.85, "word": " بقى", "probability": 0.6365559895833334}, {"start": 2997.85, "end": 2997.95, "word": " دي", "probability": 0.52783203125}, {"start": 2997.95, "end": 2998.71, "word": " بقوله", "probability": 0.8575846354166666}, {"start": 2998.71, "end": 2999.11, "word": " 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0.9638671875}, {"start": 3127.23, "end": 3127.23, "word": " لسه", "probability": 0.9894205729166666}, {"start": 3127.23, "end": 3127.23, "word": " من", "probability": 0.919921875}, {"start": 3127.23, "end": 3127.23, "word": " هنا؟", "probability": 0.972412109375}, {"start": 3127.23, "end": 3127.23, "word": " انا", "probability": 0.841552734375}, {"start": 3127.23, "end": 3127.23, "word": " بسأل", "probability": 0.973876953125}, {"start": 3127.23, "end": 3127.23, "word": " لسه", "probability": 0.9899088541666666}, {"start": 3127.23, "end": 3127.23, "word": " من", "probability": 0.97314453125}, {"start": 3127.23, "end": 3127.23, "word": " هنا؟", "probability": 0.979736328125}, {"start": 3127.23, "end": 3127.23, "word": " انا", "probability": 0.75244140625}, {"start": 3127.23, "end": 3127.43, "word": " بسأل", "probability": 0.9776611328125}, {"start": 3127.43, "end": 3127.83, "word": " لسه", "probability": 0.9892578125}, {"start": 3127.83, "end": 3127.83, "word": " من", "probability": 0.97802734375}, {"start": 3127.83, "end": 3127.83, "word": " هنا؟", "probability": 0.98095703125}, {"start": 3127.83, "end": 3127.83, "word": " انا", "probability": 0.786376953125}, {"start": 3127.83, "end": 3127.83, "word": " بسأل", "probability": 0.9842529296875}, {"start": 3127.83, "end": 3127.83, "word": " لسه", "probability": 0.9895833333333334}, {"start": 3127.83, "end": 3127.83, "word": " من", "probability": 0.9794921875}, {"start": 3127.83, "end": 3127.83, "word": " هنا؟", "probability": 0.97900390625}, {"start": 3127.83, "end": 3127.83, "word": " انا", "probability": 0.856689453125}, {"start": 3127.83, "end": 3127.83, "word": " بسأل", "probability": 0.9873046875}, {"start": 3127.83, "end": 3127.83, "word": " لسه", "probability": 0.9899088541666666}, {"start": 3127.83, "end": 3127.83, "word": " من", "probability": 0.98046875}, {"start": 3127.83, "end": 3127.83, "word": " هنا؟", "probability": 0.9775390625}, {"start": 3127.83, "end": 3127.83, "word": " انا", "probability": 0.8935546875}, {"start": 3127.83, "end": 3127.83, "word": " بسأل", "probability": 0.98876953125}, {"start": 3127.83, "end": 3127.83, "word": " لسه", "probability": 0.9900716145833334}, {"start": 3127.83, "end": 3127.83, "word": " من", "probability": 0.9814453125}, {"start": 3127.83, "end": 3127.83, "word": " هنا؟", "probability": 0.9755859375}, {"start": 3127.83, "end": 3127.83, "word": " انا", "probability": 0.91259765625}, {"start": 3127.83, "end": 3127.83, "word": " بسأل", "probability": 0.9903564453125}, {"start": 3127.83, "end": 3127.83, "word": " لسه", "probability": 0.9908854166666666}, {"start": 3127.83, "end": 3127.83, "word": " من", "probability": 0.982421875}, {"start": 3127.83, "end": 3127.83, "word": " هنا؟", "probability": 0.974609375}, {"start": 3127.83, "end": 3127.83, "word": " انا", "probability": 0.9287109375}, {"start": 3127.83, "end": 3127.83, "word": " بسأل", "probability": 0.9913330078125}, {"start": 3127.83, "end": 3127.83, "word": " لسه", "probability": 0.9915364583333334}, {"start": 3127.83, "end": 3127.83, "word": " من", "probability": 0.98486328125}, {"start": 3127.83, "end": 3127.83, "word": " هنا؟", "probability": 0.973388671875}, {"start": 3127.83, "end": 3127.83, "word": " انا", "probability": 0.92919921875}, {"start": 3127.83, "end": 3127.83, "word": " بسأل", "probability": 0.9915771484375}, {"start": 3127.83, "end": 3127.83, "word": " لسه", "probability": 0.9915364583333334}, {"start": 3127.83, "end": 3127.83, "word": " من", "probability": 0.98583984375}, {"start": 3127.83, "end": 3127.83, "word": " هنا؟", "probability": 0.97216796875}, {"start": 3127.83, "end": 3127.83, "word": " انا", "probability": 0.932861328125}, {"start": 3127.83, "end": 3127.83, "word": " بسأل", "probability": 0.991943359375}, {"start": 3127.83, "end": 3128.77, "word": " لسه", "probability": 0.9915364583333334}, {"start": 3128.77, "end": 3128.77, "word": " من", "probability": 0.98681640625}, {"start": 3128.77, "end": 3128.77, "word": " هنا؟", "probability": 0.973388671875}, {"start": 3128.77, "end": 3128.87, "word": " انا", "probability": 0.93505859375}, {"start": 3128.87, "end": 3129.37, "word": " بسأل", "probability": 0.992431640625}, {"start": 3129.37, "end": 3129.47, "word": " لسه", "probability": 0.9908854166666666}, {"start": 3129.47, "end": 3129.47, "word": " من", "probability": 0.98779296875}, {"start": 3129.47, "end": 3129.95, "word": " هنا؟", "probability": 0.974609375}, {"start": 3129.95, "end": 3130.49, "word": " انا", "probability": 0.940185546875}, {"start": 3130.49, "end": 3130.89, "word": " بسأل", "probability": 0.9927978515625}, {"start": 3130.89, "end": 3131.37, "word": " لسه", "probability": 0.990234375}, {"start": 3131.37, "end": 3131.61, "word": " من", "probability": 0.98828125}, {"start": 3131.61, "end": 3131.69, "word": " هنا؟", "probability": 0.975341796875}, {"start": 3131.69, "end": 3133.21, "word": " انا", "probability": 0.94775390625}, {"start": 3133.21, "end": 3133.57, "word": " بسأل", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9a2b3ad2750f11890d65664dc3805379d5485c4f
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_raw.srt
@@ -0,0 +1,1808 @@
+1
+00:00:20,960 --> 00:00:25,780
+بسم الله الرحمن الرحيم مواصل اليوم ما ابتدأناه في
+
+2
+00:00:25,780 --> 00:00:31,800
+المقابلات السابقة وهذه هي اخر نظرية في هذا ال
+
+3
+00:00:31,800 --> 00:00:38,760
+chapter ان شاء الله تبارك وتعالى نص النظرية كتالي
+
+4
+00:00:38,760 --> 00:00:44,520
+بناخد ال F عبارة عن fields ال P of X polynomial في
+
+5
+00:00:44,520 --> 00:00:50,430
+كارتن F of Xالـprinciple ideal generated by P of X
+
+6
+00:00:50,430 --> 00:00:55,970
+is maximum ideal في capital F of X if and only if
+
+7
+00:00:55,970 --> 00:01:02,610
+P of X عبارة عن الـreducible عالميا على F فالورحان
+
+8
+00:01:02,610 --> 00:01:07,810
+بده يصير في اتجاهين بسبب وجود ال F and only if
+
+9
+00:01:07,810 --> 00:01:13,230
+الأن بناخد الاتجاه الأول و بعد أن ننتهي منه ننتقل
+
+10
+00:01:13,230 --> 00:01:19,620
+الى الاتجاه الثانيالاتجاه الأول بدي افترض ان ال P
+
+11
+00:01:19,620 --> 00:01:25,460
+of X موجودة في capital F of X و P of X هو عبارة عن
+
+12
+00:01:25,460 --> 00:01:33,820
+maximal ID يبقى let ال P of X موجودة في capital F
+
+13
+00:01:33,820 --> 00:01:42,840
+of X such that بحيث ان ال P of X لprinciple ID
+
+14
+00:01:42,840 --> 00:01:51,550
+generated by P of Xis a maximal ideal
+
+15
+00:01:51,550 --> 00:01:56,970
+in capital
+
+16
+00:01:56,970 --> 00:02:01,890
+F of X قبل
+
+17
+00:02:01,890 --> 00:02:07,730
+ما اكمل اروح ال P of X is irreducible بدي اسألي
+
+18
+00:02:07,730 --> 00:02:09,090
+السؤال التالت
+
+19
+00:02:14,980 --> 00:02:21,860
+السؤال هو هل ممكن ال P of X تكون كونستان؟ لأ، في
+
+20
+00:02:21,860 --> 00:02:27,060
+الشمكانية السبب أنه إذا كانت P of X عبارة عن
+
+21
+00:02:27,060 --> 00:02:32,700
+كونستان بالprinciple ideal generated by X يا إما
+
+22
+00:02:32,700 --> 00:02:39,660
+Zero فقط يا إما كل capital F of Xليش؟ انه constant
+
+23
+00:02:39,660 --> 00:02:43,440
+polynomial any constant .. any non-zero constant
+
+24
+00:02:43,440 --> 00:02:49,460
+polynomial is a unit ومدام unit بديه يجيب لمين؟ كل
+
+25
+00:02:49,460 --> 00:02:54,620
+عناصر اللي هو ال capital F of X والسؤال هو هل ال
+
+26
+00:02:54,620 --> 00:03:00,740
+capital F of X is maximal؟ لأ لإن هي تناقض مع مين؟
+
+27
+00:03:00,740 --> 00:03:05,720
+مع ال proper any prime ideal أو maximal ideal is
+
+28
+00:03:05,720 --> 00:03:10,370
+properيبقى ليه يمكن ال P of X تبقى constant
+
+29
+00:03:10,370 --> 00:03:15,910
+polynomial خلينا نكتب المعلومة هذه مشان تلزج في
+
+30
+00:03:15,910 --> 00:03:22,490
+دماغنا لإن ربما تلزم و احنا نشترك يبقى P of X is
+
+31
+00:03:22,490 --> 00:03:31,010
+maximal ideal هنا بنكتب note that لاحظي ان ال P of
+
+32
+00:03:31,010 --> 00:03:35,410
+X is non constant
+
+33
+00:03:39,810 --> 00:03:48,270
+Polynomial شو السبب because if
+
+34
+00:03:48,270 --> 00:03:59,190
+P of X is constant then ال
+
+35
+00:03:59,190 --> 00:04:06,090
+capital P of X لprinciple هذا بده يساوي zero or
+
+36
+00:04:08,430 --> 00:04:16,230
+الـP of X is a unit وهذه
+
+37
+00:04:16,230 --> 00:04:22,030
+ستجعل الـprinciple ideal generated by P of X يكون
+
+38
+00:04:22,030 --> 00:04:40,890
+كابتل F of X and neither Zero nor F of Xis maximum
+
+39
+00:04:40,890 --> 00:04:44,670
+لا
+
+40
+00:04:44,670 --> 00:04:49,370
+هذا maximum ولا هذا maximum إذا ضروري ال P of X ما
+
+41
+00:04:49,370 --> 00:04:55,150
+تكونش constant طبعا بتبقى polynomial لكنها ليست
+
+42
+00:04:55,150 --> 00:05:01,810
+constant الآن هذه بس مجرد ملاحظة كان جملة اعتراضية
+
+43
+00:05:01,810 --> 00:05:06,790
+و بدنا نيجي إيشبدنا نثبت ان ال P of X is
+
+44
+00:05:06,790 --> 00:05:17,590
+irreducible يبقى الأن بقوله now want to show that
+
+45
+00:05:17,590 --> 00:05:27,850
+ان ال P of X is irreducible over X
+
+46
+00:05:33,870 --> 00:05:38,790
+الشفتر هذا كل البرهين كانت في ال contradiction
+
+47
+00:05:38,790 --> 00:05:43,630
+وماحدش أحسن من حد و هذه تلحقهم كمان يبقى هقوله
+
+48
+00:05:43,630 --> 00:05:51,230
+assume نعم يبقى هنا هقوله assume ان ال P of X is
+
+49
+00:05:51,230 --> 00:05:56,510
+reducible تمام
+
+50
+00:05:56,510 --> 00:06:06,150
+يبقى reducible over Fفماش اللي بده يحصل يبقى then
+
+51
+00:06:06,150 --> 00:06:15,810
+ال P of X هذه حد ساوي ال G of X في ال H of X where
+
+52
+00:06:15,810 --> 00:06:29,210
+حيث ال G of X و ال H of X موجودات في capital F of
+
+53
+00:06:29,210 --> 00:06:41,840
+X andR of lower degree ايش
+
+54
+00:06:41,840 --> 00:06:46,820
+يعني lower degree يعني درجة كل واحدة فيهم من GH
+
+55
+00:06:46,820 --> 00:06:54,260
+اقل من درجة من P of X ممتاز جدا يبقى الآن صار
+
+56
+00:06:54,260 --> 00:07:00,030
+عندنا شبنان صار عندنا P of Xيساوي حاصل ضرب two
+
+57
+00:07:00,030 --> 00:07:06,730
+polynomials تمام ليش ان ال P of X ليست constant
+
+58
+00:07:06,730 --> 00:07:11,670
+polynomial إذا كتبناها على حاصل الضرب وكل واحدة
+
+59
+00:07:11,670 --> 00:07:19,370
+فيهم درجتها أقل من درجة مين أقل من درجة P of X طيب
+
+60
+00:07:19,370 --> 00:07:24,710
+بتكتب هالجملة هذه وشوف والي صح ولا غلط أنا أزعم
+
+61
+00:07:24,710 --> 00:07:32,720
+الآنإن ال principle ideal generated by P of X هو
+
+62
+00:07:32,720 --> 00:07:39,820
+subset من ال principle ideal generated by G of X
+
+63
+00:07:39,820 --> 00:07:50,780
+هذه أقل من أو subset من اللي هو capital F of X طب
+
+64
+00:07:50,780 --> 00:07:57,060
+نمشي واحدة واحدة غطيت هذه هذه صحيحة؟هذه ما حد
+
+65
+00:07:57,060 --> 00:08:01,340
+يشيلوا عليها ترى تمام طيب ضالة تالت هل ال
+
+66
+00:08:01,340 --> 00:08:06,440
+principle ideal generated by P of X subset من ال G
+
+67
+00:08:06,440 --> 00:08:12,060
+of X طبقا لهذه المعادلة؟
+
+68
+00:08:12,060 --> 00:08:20,640
+في شكك؟ طيب سانوزيل الشك سانوزيل الشك main subset
+
+69
+00:08:20,640 --> 00:08:29,310
+من التانية 2Z دهوالله أربعة زد صبشت
+
+70
+00:08:29,310 --> 00:08:34,910
+تمام اليمين أربعة زد أصغر من اتنين زد و الله أكبر
+
+71
+00:08:34,910 --> 00:08:42,210
+أصغر تمام يبقى اتنين زد هي الرقم تبعها صغير بس
+
+72
+00:08:42,210 --> 00:08:49,270
+الأربعة زد رقمها أكبر يبقى صارت صارت مين صارت
+
+73
+00:08:49,270 --> 00:08:55,560
+الأربعة زد صبشت من مينمن اتنين زد رغم انهم اربعة
+
+74
+00:08:55,560 --> 00:09:02,180
+اكبر من من اكبر من اتنين على ضوء هذه ممكن ان نفهم
+
+75
+00:09:02,180 --> 00:09:07,000
+ان ال P of X ال principle ideal اصغر من ال
+
+76
+00:09:07,000 --> 00:09:12,820
+principle ideal generated by اللي هو G of X اي
+
+77
+00:09:12,820 --> 00:09:19,860
+واحدة ثانية هو ال P of X maximum ولا لا maximum
+
+78
+00:09:21,230 --> 00:09:28,390
+أيوة تمام طيب الآن صاروا هدول اتنين subset من بعض
+
+79
+00:09:28,390 --> 00:09:34,290
+هذه subset من هذه وهذه subset من هذه تمام؟ بدهاري
+
+80
+00:09:34,290 --> 00:09:41,410
+الآن اخد كل واحدة منها على ايش فارض؟ فارض ان ال
+
+81
+00:09:41,410 --> 00:09:46,630
+principle ID generated by P of X is a maximal ID
+
+82
+00:09:46,630 --> 00:09:52,270
+وكتبناه كتبناه هىمدام maximum لو عندى العبارة هذه
+
+83
+00:09:52,270 --> 00:09:59,270
+يبقى يا إما هذه تساوي هذه أو هذه تساوي هذه صح يبقى
+
+84
+00:09:59,270 --> 00:10:04,930
+باجي بقوله بما أنه يبقى since the principle ideal
+
+85
+00:10:04,930 --> 00:10:16,890
+generated by P of X is maximum we have أحد أمرين
+
+86
+00:10:17,350 --> 00:10:22,610
+الأمر الأول يا إما ال principle ideal generated by
+
+87
+00:10:22,610 --> 00:10:27,650
+P of X بده يساوي ال principle ideal generated by G
+
+88
+00:10:27,650 --> 00:10:34,310
+of X or ال principle ideal generated by G of X بده
+
+89
+00:10:34,310 --> 00:10:43,470
+يساوي capital F of X كله طب بتاخد كل حالة منهم
+
+90
+00:10:43,470 --> 00:10:51,960
+وشوف إيش بتعطينيالان لو كان F F اللي هو ال
+
+91
+00:10:51,960 --> 00:10:57,080
+principle ideal generated by P of X بده يساوي ال
+
+92
+00:10:57,080 --> 00:11:02,120
+principle ideal generated by G of X ما هي العلاقة
+
+93
+00:11:02,120 --> 00:11:13,280
+بين درجة ال P ودرجة ال G؟ وبعد يبقى then اللي هو
+
+94
+00:11:13,280 --> 00:11:27,200
+درجةالـ P of X بدها تساوي درجة الـ G of X تمام؟
+
+95
+00:11:27,200 --> 00:11:31,420
+لسه .. بدنا نجيب الباقي لسه في احتمال تاني يعني
+
+96
+00:11:31,420 --> 00:11:34,840
+انت بدك تنفي .. بدك تنفي الاحتمالين مش تنفي واحد و
+
+97
+00:11:34,840 --> 00:11:39,580
+التاني لا لأن احنا بنقول يا إما هذا يا إما هذا في
+
+98
+00:11:39,580 --> 00:11:44,150
+التساوي إذا بدنا نروح للحالة الثانيةيبقى باجي
+
+99
+00:11:44,150 --> 00:11:50,370
+بقوله هنا F ال principle ideal generated by G of X
+
+100
+00:11:50,370 --> 00:11:58,530
+بده ساوي capital F of X هذا حد فيكم بتقدر تقولي
+
+101
+00:11:58,530 --> 00:12:06,870
+يبقى G of X شو درجتها؟ كونصا صحيح يبقى ال G of X
+
+102
+00:12:06,870 --> 00:12:11,150
+بده تكون كونصا لأن هذه كل ال field اللي عندنا
+
+103
+00:12:11,530 --> 00:12:18,890
+Constant يعني unit صح يبقى مدام unit هي من الدرجة
+
+104
+00:12:18,890 --> 00:12:26,710
+الصفرية هتكون على طول الخط يبقى then ال degree لل
+
+105
+00:12:26,710 --> 00:12:34,250
+G بده يساوي zero يعني هذا يا بنات مش ممكن ال
+
+106
+00:12:34,250 --> 00:12:37,730
+principle ideal generated by G of X يساوي ال F of
+
+107
+00:12:37,730 --> 00:12:43,320
+X إلا إذا كانالـ g of x is constant مدام constant
+
+108
+00:12:43,320 --> 00:12:50,000
+يبقى unit مدام constant إذا ال degree تبعته تساوي
+
+109
+00:12:50,000 --> 00:12:55,200
+zero طب مدام ال degree تبعته تساوي zero إيش مضل
+
+110
+00:12:55,200 --> 00:13:05,520
+عندنا بصير عندنا ال degree ال degree لمن
+
+111
+00:13:05,520 --> 00:13:14,750
+لل g of xبدها تساوي ال degree أبصر لمين ال degree
+
+112
+00:13:14,750 --> 00:13:20,930
+ل G تساوي Zero يبقاش مضلع لنا ال degree ل P بدها
+
+113
+00:13:20,930 --> 00:13:24,630
+تساوي ال degree ل G كمان والله إيش احنا أخدنا هذه
+
+114
+00:13:24,630 --> 00:13:29,630
+في الأول بدنا نجيب التاني ال degree ل G بدها تساوي
+
+115
+00:13:29,630 --> 00:13:34,170
+ال degree ل H بس
+
+116
+00:13:34,170 --> 00:13:38,040
+خمس استغل شوية واحدة واحدةالحين احنا خدنا الحالة
+
+117
+00:13:38,040 --> 00:13:41,560
+الأولى ال principle ideal يسوي اذا ال degree ل P
+
+118
+00:13:41,560 --> 00:13:45,300
+بديه يسوي ال degree ل G الحالة التانية صارت ال
+
+119
+00:13:45,300 --> 00:13:51,380
+degree ل G Zero يبقى ال G هذه صارت constant يبقى
+
+120
+00:13:51,380 --> 00:13:56,160
+بصير ال degree ل P تسوي مين ال degree ل H يبقى ال
+
+121
+00:13:56,160 --> 00:14:03,920
+degree على P ال degree ل P ل P of X بديه يسوي ال
+
+122
+00:14:03,920 --> 00:14:10,810
+degree ل Hطب اتطلعيله للاتنين مع بعض هذا
+
+123
+00:14:10,810 --> 00:14:16,090
+contradiction ولا لا؟ هذه قالت ال degree ل P هي
+
+124
+00:14:16,090 --> 00:14:20,770
+degree ل G وهذا قالت ال degree ل P هي degree ل H و
+
+125
+00:14:20,770 --> 00:14:27,010
+degree ل P وH are of lower degree than P of X
+
+126
+00:14:27,010 --> 00:14:33,110
+تناقض ولا لا؟ يعني على كلا الحالتين صار عندي تناقض
+
+127
+00:14:33,470 --> 00:14:41,130
+يبقى هذا Contradiction هو
+
+128
+00:14:41,130 --> 00:14:50,650
+Contradicts تخليني أضحى Contradicts that ان ال G
+
+129
+00:14:50,650 --> 00:15:02,250
+of X and ال H of X are of lower degree than
+
+130
+00:15:03,600 --> 00:15:08,300
+الـ P of X تمام؟
+
+131
+00:15:08,300 --> 00:15:13,760
+ايوة طالع لما قلنا هنا قلنا where الـ R of lower
+
+132
+00:15:13,760 --> 00:15:18,200
+degree طلعوا بضريتين زي بعض يبقى هذا التناقض ما
+
+133
+00:15:18,200 --> 00:15:23,620
+الذي جاء بهذا التناقض؟ الفرض الخاطئ ما هو الفرض
+
+134
+00:15:23,620 --> 00:15:30,680
+الخاطئ؟ ان فرقت ان ال P of X is reducible
+
+135
+00:15:34,250 --> 00:15:38,950
+هذا فرضنا ان ال P of X is irreducible يبقى هذا
+
+136
+00:15:38,950 --> 00:15:44,230
+الفرض الخاطق إذا وصلنا إلى هنا يبقى باجي بقوله
+
+137
+00:15:44,230 --> 00:15:55,950
+Thus وهكذا ال P of X is irreducible over
+
+138
+00:15:55,950 --> 00:16:04,550
+اللي هو ال F نمشي .. نمشيالاتجاه المعاكس يبقى
+
+139
+00:16:04,550 --> 00:16:19,630
+conversely assume that ان ال P of X is irreducible
+
+140
+00:16:19,630 --> 00:16:23,870
+over F
+
+141
+00:16:30,110 --> 00:16:33,390
+ان ال principle ideal generated by P of X is
+
+142
+00:16:33,390 --> 00:16:41,490
+maximum يبقى انا want to show that
+
+143
+00:16:41,490 --> 00:16:46,790
+بدنا نحاول نثبت ان ال principle ideal generated by
+
+144
+00:16:46,790 --> 00:16:53,750
+P of X is maximum طيب
+
+145
+00:16:54,690 --> 00:16:59,930
+كيف كنا بنثبت ال ideal عبارة عن maximum؟ بطريقة
+
+146
+00:16:59,930 --> 00:17:06,090
+تانية النظرية و التعريف مظبوط لو قدرنا نثبت ان ال
+
+147
+00:17:06,090 --> 00:17:12,670
+factor ring عبارة عن field يبقى ال principle ideal
+
+148
+00:17:12,670 --> 00:17:17,710
+اللي نتج منها هو maximum يا أما التعريف طب روح
+
+149
+00:17:17,710 --> 00:17:25,390
+ناخد التعريف يبقى لان بداجي أقول له لأالـ I be an
+
+150
+00:17:25,390 --> 00:17:37,450
+ideal in الهميم in ال capital F of X such that و
+
+151
+00:17:37,450 --> 00:17:44,990
+بحيث أن ال P of X ال principle ideal generated by
+
+152
+00:17:44,990 --> 00:17:52,220
+P of X سبسط من I و I في الحقيقة سبسط من مينمن
+
+153
+00:17:52,220 --> 00:17:57,680
+capital F of X طرد
+
+154
+00:17:57,680 --> 00:18:02,340
+انه عندي ideal I بحيث ال principle ideal generated
+
+155
+00:18:02,340 --> 00:18:08,300
+by P of X ب subset من I و I subset من capital F of
+
+156
+00:18:08,300 --> 00:18:12,960
+X يبقى مطموض مننا نثبت ان ال principle ideal
+
+157
+00:18:12,960 --> 00:18:18,800
+generated by P of X هو I او ال I يساوي ال field
+
+158
+00:18:19,390 --> 00:18:24,510
+مظبوط ان اثبتنا ذلك بصير ال I is maximum. السؤال
+
+159
+00:18:24,510 --> 00:18:32,150
+هو ال F عبارة عن ايه؟ Field. هي في رأس المثل. ال F
+
+160
+00:18:32,150 --> 00:18:38,150
+عبارة عن field. مدام field. Any ideal في هذا ال
+
+161
+00:18:38,150 --> 00:18:44,590
+field عبارة عن ايه؟principal ideal خدناها نظرية
+
+162
+00:18:44,590 --> 00:18:49,330
+قبل ذلك إذا ال F هي عبارة عن field يبقى any ideal
+
+163
+00:18:49,330 --> 00:18:55,270
+عبارة عن principal ideal يبقى باجي بقول هنا since
+
+164
+00:18:55,270 --> 00:19:07,910
+ال F is a field يبقى any ideal
+
+165
+00:19:10,060 --> 00:19:15,760
+ال F is a principle ايش
+
+166
+00:19:15,760 --> 00:19:21,720
+معناه هذا الكلام هذا معناه ان ال I اللي عندنا هي
+
+167
+00:19:21,720 --> 00:19:33,200
+principle ideal generated by G of X for some G
+
+168
+00:19:33,200 --> 00:19:42,730
+of X اللي موجودة في capital F of Xمظبوط؟ نظرا لإن
+
+169
+00:19:42,730 --> 00:19:47,630
+ال F عبارة عن field يبقى أي ideal is a principle
+
+170
+00:19:47,630 --> 00:19:51,630
+ليش؟ لأن ال field عبارة عن principle، ideal،
+
+171
+00:19:51,630 --> 00:19:58,150
+domain تمام؟ يبقى ال ideal هذا زي ولد ب polynomial
+
+172
+00:19:58,150 --> 00:20:05,730
+وولد تكون على سبيل المثال g of x إذن هديها بقدر
+
+173
+00:20:05,730 --> 00:20:11,170
+أصيها صياغة جديدةالجهد ده بده يعطينا ان ال
+
+174
+00:20:11,170 --> 00:20:17,030
+principle ID generated by P of X subset من ال
+
+175
+00:20:17,030 --> 00:20:22,650
+principle ID generated by G of X subset من capital
+
+176
+00:20:22,650 --> 00:20:29,630
+F of X طيب
+
+177
+00:20:29,630 --> 00:20:34,610
+تعالى نشوف الآن اش اللي بده يحصل احنا اش اللي بنا
+
+178
+00:20:34,610 --> 00:20:40,910
+نثبته؟بنثبت ان ال ideal is maximum يعني بدي أثبت
+
+179
+00:20:40,910 --> 00:20:46,530
+ان اتنين هذول بتساوى او اتنين هذول بتساوى تمام؟
+
+180
+00:20:46,530 --> 00:20:52,550
+نيجي للحالة الأول الآن بدي اثبت ان اتنين هذول
+
+181
+00:20:52,550 --> 00:21:00,770
+بيتساوى ان امكن ذلك تمام؟ طب احنا في حاجة كتبناها
+
+182
+00:21:00,770 --> 00:21:09,280
+ومستفدناش منها ال radio setأخدنا إن الـ P-O-Fix is
+
+183
+00:21:09,280 --> 00:21:16,360
+irreducible. حتى الآن لم نستفد منها شيء. مظبوط؟
+
+184
+00:21:16,360 --> 00:21:22,740
+طيب، هذه نرجع لقبل شوية. إيش اللي أخدناها قبل
+
+185
+00:21:22,740 --> 00:21:28,940
+شوية؟ أخدناها شيء؟ لأ ما أخدناها شيء، اتفقتنا بس
+
+186
+00:21:28,940 --> 00:21:33,710
+للاتجاهين الأول.طيب يبقى ال F of X اللي عندنا هذه
+
+187
+00:21:33,710 --> 00:21:40,430
+is irreducible وين بتلزم؟ بدياها طيب نرجع الآن ال
+
+188
+00:21:40,430 --> 00:21:46,570
+P of X هذا subset من هذه بستفيد منها شغلة ما هي
+
+189
+00:21:46,570 --> 00:21:52,490
+الشغلة هذه؟ ال P of X موجودة في ال principle ideal
+
+190
+00:21:52,490 --> 00:21:59,380
+generated by P of X حد بتقدر ينكر هذا؟طيب هذه ال
+
+191
+00:21:59,380 --> 00:22:06,100
+subset من هذه هذا معناته ان ال P of X موجودة في ال
+
+192
+00:22:06,100 --> 00:22:11,520
+principle ideal generated by G of X صحيح ولا لأ؟
+
+193
+00:22:11,520 --> 00:22:20,940
+طيب هذا معناه ان ال P of X شو شكل العنصر هنا؟ G of
+
+194
+00:22:20,940 --> 00:22:25,840
+X مضروب في Pronomial تاني حسب تعريف ال principle
+
+195
+00:22:25,840 --> 00:22:32,660
+ideal مظبوط؟يبقى هذا ال P of X بده يساوي ال G of X
+
+196
+00:22:32,660 --> 00:22:43,640
+ب H of X for او بلاش for و ال H of X هذي موجودة في
+
+197
+00:22:43,640 --> 00:22:49,600
+capital F of X هذا
+
+198
+00:22:49,600 --> 00:22:58,250
+الفرق انه هذا irreducible اذا طلعت منكتناقض؟ لأ مش
+
+199
+00:22:58,250 --> 00:23:04,930
+تناقض ايوة هذا اللي بدنا نوصله يبقى هذا الكلام
+
+200
+00:23:04,930 --> 00:23:10,650
+صحيح في حالة واحدة انه ممكن تكون ال G of X
+
+201
+00:23:10,650 --> 00:23:17,870
+constant او ال H of X constant صح ولا لا؟ يبقى هذا
+
+202
+00:23:17,870 --> 00:23:24,310
+بني بقول since بما ان ال P of X is
+
+203
+00:23:28,230 --> 00:23:37,610
+irreducible over if we have ان ال g of x constant
+
+204
+00:23:37,610 --> 00:23:44,310
+او ال h of x constant we have ان ال g of x is
+
+205
+00:23:44,310 --> 00:23:51,510
+constant or ال h of x is constant
+
+206
+00:23:54,640 --> 00:24:01,520
+تمام ؟ الى ان نمشي الحالة الأولى لو كانت ال g of x
+
+207
+00:24:01,520 --> 00:24:06,600
+is constant لو
+
+208
+00:24:06,600 --> 00:24:12,400
+كانت ال g of x ممتاز
+
+209
+00:24:12,400 --> 00:24:19,590
+جدا لو كانت ال g of x constant يبقى هذا معناهإن ال
+
+210
+00:24:19,590 --> 00:24:24,890
+principle ideal generated by g of x بتسوي capital
+
+211
+00:24:24,890 --> 00:24:32,590
+F of X كله صح لأنه unit مظبوط يبقى هذا هجيبلي
+
+212
+00:24:32,590 --> 00:24:37,550
+capital F و ناخد الحالة التانية الحالة التانية لو
+
+213
+00:24:37,550 --> 00:24:45,930
+كانت ال H of X is constant يبقى is constant
+
+214
+00:24:49,250 --> 00:24:56,610
+طلع اليه ال H of X constant ليبقى إيش مضال عندنا؟
+
+215
+00:24:56,610 --> 00:24:59,710
+ال principle ideal generated by P of X هو ال
+
+216
+00:24:59,710 --> 00:25:03,150
+principle ideal generated by G of X لأن هذا
+
+217
+00:25:03,150 --> 00:25:09,890
+constant ليبقى then ال principle ideal generated
+
+218
+00:25:09,890 --> 00:25:18,450
+by P of X هولـ principal ideal generated by g of
+
+219
+00:25:18,450 --> 00:25:26,530
+x. إيش معنى هذا الكلام؟ ال P of X maximum. يبقى من
+
+220
+00:25:26,530 --> 00:25:35,290
+الإتنين هذول بستنتج ل principal id generated by P
+
+221
+00:25:35,290 --> 00:25:40,710
+of X ماله is maximum.
+
+222
+00:25:44,520 --> 00:25:45,500
+وهو المطلوب.
+
+223
+00:25:48,120 --> 00:25:52,040
+خليني أرجعك النظرية مرة تانية بس على السريع مشان
+
+224
+00:25:52,040 --> 00:25:56,560
+أثبت المعلومة لإن دوخناكوا شوية. ابقى ركزي معايا
+
+225
+00:25:56,560 --> 00:26:02,140
+حتى ترسخ النظرية. النظرية بيقول ياخد F فيه وخد P
+
+226
+00:26:02,140 --> 00:26:05,760
+of X في capital F of X. from the principle ID
+
+227
+00:26:05,760 --> 00:26:10,280
+generated by P of X عبارة عن maximum ID if and
+
+228
+00:26:10,280 --> 00:26:14,690
+only if P of X is irreducible.بدأ امشي الانتجاه
+
+229
+00:26:14,690 --> 00:26:19,330
+هنا ماخد P of X موجودة في capital F of X بحيث ال
+
+230
+00:26:19,330 --> 00:26:26,350
+capital P of X is maximal ideal هذا الكلام صحيح لو
+
+231
+00:26:26,350 --> 00:26:32,350
+كانت ال P of X لا تساوي constant لأن لو كانت ال P
+
+232
+00:26:32,350 --> 00:26:37,750
+of X constant يبقى هذا بدي أعطيني أحد أمرين يا إما
+
+233
+00:26:37,750 --> 00:26:43,090
+ال zero ideals يا إما الفيل نفسه وعلى كل الأمرين
+
+234
+00:26:43,410 --> 00:26:49,250
+مشي proper وبالتالي ماهواش maximum إذا لازم تكون
+
+235
+00:26:49,250 --> 00:26:57,670
+polynomial وليس constant تمام نيجي لغاية فرضت ان
+
+236
+00:26:57,670 --> 00:27:06,950
+ال P of X is maximum كويس بدنا نحاول نثبت ان P of
+
+237
+00:27:06,950 --> 00:27:12,430
+X is irreduciblewant to show is irreducible بدي
+
+238
+00:27:12,430 --> 00:27:16,890
+ابرهن بالتناقض وان افرض الكلام مش صحيح مش صحيح
+
+239
+00:27:16,890 --> 00:27:21,950
+يعني ايش يعني reducible مدام reducible اذا بقدر
+
+240
+00:27:21,950 --> 00:27:26,610
+اكتبه على شكل حاصل ضرب two polynomials of lower
+
+241
+00:27:26,610 --> 00:27:31,190
+degree الدرجة تبعتهم اقل في نفس ال field اللي هو
+
+242
+00:27:31,190 --> 00:27:37,610
+capital F of X طيب الان ال ideal اللي عندكsubset
+
+243
+00:27:37,610 --> 00:27:41,430
+من ال ideal subset من ال field الأصلي أو من ال
+
+244
+00:27:41,430 --> 00:27:47,610
+ring الأصلي الآن هذا maximum مدار maximum يبقى يا
+
+245
+00:27:47,610 --> 00:27:52,610
+هدول اتنين بتساوي يا اتنين هدول بتساوي هاي التساوي
+
+246
+00:27:52,610 --> 00:27:57,030
+أو هذا ناخد التساوي الأول انطلع اتنين هدول بتساوي
+
+247
+00:27:57,030 --> 00:28:02,950
+وبتنين نفس الدرجة يبقى صلة ال degree تبعت ال P
+
+248
+00:28:02,950 --> 00:28:11,100
+تساويالـ Degree تبع الـ G لو كان الـ G of X بدري
+
+249
+00:28:11,100 --> 00:28:15,700
+يسوي الـ capital F of X يبقى ال degree ل G Zero
+
+250
+00:28:15,700 --> 00:28:21,020
+لانه بيصير constant وبالتالي بيولد لي جميع عناصر
+
+251
+00:28:21,020 --> 00:28:25,080
+الفيه إذا ان ال degree بتسوي Zero هذا مع ال degree
+
+252
+00:28:25,080 --> 00:28:29,540
+اللي فيه بتسوي مين ال degree اللي اتش يبقى صرا ان
+
+253
+00:28:29,540 --> 00:28:33,220
+ال degree اللي فيه تسوي ال degree اللي جيه وهذا مش
+
+254
+00:28:33,220 --> 00:28:38,300
+صحيحلأنه يناقض ال lower degree او ال degree لم
+
+255
+00:28:38,300 --> 00:28:42,760
+يبقى يسوى ال degree لكشف وهذا كمان يناقض ال lower
+
+256
+00:28:42,760 --> 00:28:46,440
+degree وصار ال contradiction يبقى الفرض اللي فرضته
+
+257
+00:28:46,440 --> 00:28:50,360
+غلط وعكسه هو الصح يبقى صار ال P of X is
+
+258
+00:28:50,360 --> 00:28:56,600
+irreducible على نمشي العكس نفترض ان P of X is
+
+259
+00:28:56,600 --> 00:29:02,490
+irreducible عالمياعليك لنثبت ان ال principle ideal
+
+260
+00:29:02,490 --> 00:29:07,450
+generated by P of X is maximum لشان maximum قدامنا
+
+261
+00:29:07,450 --> 00:29:12,190
+طريقيا فاخترنا طريقة التعريف ولم نختار طريقة نظرية
+
+262
+00:29:12,190 --> 00:29:16,570
+فقلنا افترض ان عندي ideal I موجود في capital F of
+
+263
+00:29:16,570 --> 00:29:21,470
+X بحيث ال P of X من principle ideal subset من I
+
+264
+00:29:21,470 --> 00:29:26,920
+subset من ال field capital F of Xال F of X عبارة
+
+265
+00:29:26,920 --> 00:29:30,740
+عن فين؟ هو عبارة عن principle, ideal, domain يعني
+
+266
+00:29:30,740 --> 00:29:36,620
+كل ideal فيه is a principle تمام؟ مدام كل ideal
+
+267
+00:29:36,620 --> 00:29:40,900
+فيه is a principle يبقى هذه بدي أروح أكتبها على
+
+268
+00:29:40,900 --> 00:29:46,740
+الشكل اللي عندنا هذا بهذا الشكل طيب بالدليل الأول
+
+269
+00:29:46,740 --> 00:29:50,920
+ال P of X موجود في ال ideal هذا هذا subset من هذا
+
+270
+00:29:50,920 --> 00:29:55,730
+إذا ال P of X موجود هنامدان موجود هنا إذا بدأ أكتب
+
+271
+00:29:55,730 --> 00:30:01,250
+على حاصل ضرب P of X في كولونومي الأخرى صار حاصل
+
+272
+00:30:01,250 --> 00:30:04,850
+ضرب two كولونومي زي ما انتوا شايفينه لكن احنا
+
+273
+00:30:04,850 --> 00:30:10,990
+فرضنا الأساسي ان P of X is irreducible يبقى هذا
+
+274
+00:30:10,990 --> 00:30:15,950
+الكلام لا يمكن ان يكون صحيحا إلا إذا كان أحدهم
+
+275
+00:30:15,950 --> 00:30:21,180
+بمقدار ثالثيبقى يا إما الـG of X مقدار ثابت يا إما
+
+276
+00:30:21,180 --> 00:30:26,860
+الـH of X مقدار ثابت بدي أخد كل من الحالتين و نشوف
+
+277
+00:30:26,860 --> 00:30:31,580
+شو نستفيد منه فبعدين بقول لو كانت الـG constant
+
+278
+00:30:31,580 --> 00:30:39,700
+يبقى بدها صير unit يعني بدها جبل ال field كله
+
+279
+00:30:39,700 --> 00:30:44,980
+الحالة التانية لو كانت الـH constant بظل ال
+
+280
+00:30:44,980 --> 00:30:49,390
+polynomial فيههي ال polynomial .. هي ال polynomial
+
+281
+00:30:49,390 --> 00:30:54,850
+تبع ال G يبقى هذا و هذا ايش معناه؟ معناه ال P is
+
+282
+00:30:54,850 --> 00:31:00,750
+maximum I هذه هي النظرية، الآن على هذه النظرية في
+
+283
+00:31:00,750 --> 00:31:06,730
+two equilateralism واحدة بسيطة ع السريع و واحدة
+
+284
+00:31:06,730 --> 00:31:08,030
+أطول شوية
+
+285
+00:31:21,150 --> 00:31:26,870
+نجي الـ Crawler الأولى الـ Crawler بتقول معاكي أن
+
+286
+00:31:26,870 --> 00:31:34,670
+الـ FBA field and
+
+287
+00:31:34,670 --> 00:31:37,790
+P
+
+288
+00:31:37,790 --> 00:31:41,350
+of X is irreducible
+
+289
+00:31:44,600 --> 00:31:55,900
+is irreducible polynomial over
+
+290
+00:31:55,900 --> 00:32:00,620
+F.Then
+
+291
+00:32:00,620 --> 00:32:03,720
+F
+
+292
+00:32:03,720 --> 00:32:10,500
+of X modularly principal idea generated by P of X
+
+293
+00:32:11,020 --> 00:32:25,900
+is a field مرة
+
+294
+00:32:25,900 --> 00:32:31,920
+تانية ال F field أخدنا polynomial ال polynomial
+
+295
+00:32:31,920 --> 00:32:37,920
+irreducible على F يبقى ال factor ring او ال factor
+
+296
+00:32:37,920 --> 00:32:44,960
+field صار ان هذابندفت انه عبارة عن P X بسيطة جدا
+
+297
+00:32:44,960 --> 00:32:50,800
+البرهان بدي اخد من الفرض و ابدأ يبقى بداشي اقوله
+
+298
+00:32:50,800 --> 00:33:01,840
+assume افترض ان P of X is irreducible polynomial
+
+299
+00:33:01,840 --> 00:33:06,040
+polynomial
+
+300
+00:33:06,040 --> 00:33:07,780
+over
+
+301
+00:33:09,190 --> 00:33:17,330
+كامة ال F طبقا للنظرية ال maximum يبقى ماجي بقوله
+
+302
+00:33:17,330 --> 00:33:27,850
+by the above theorem بالنظرية اعلى ال P of X او ال
+
+303
+00:33:27,850 --> 00:33:35,330
+principle id generated by P of X is maximum خذنا
+
+304
+00:33:35,330 --> 00:33:42,160
+نظرية سابقة لو عندى feelوعندي maximal ideal يبقى
+
+305
+00:33:42,160 --> 00:33:49,180
+الفاكتور field الفاكتور بصير ايش؟ بصير field يبقى
+
+306
+00:33:49,180 --> 00:33:57,440
+هنا برضه by ايه؟ previous term الذاكرين هذا من هذا
+
+307
+00:33:57,440 --> 00:34:04,400
+ولا لا؟ لما كان prime لما كان prime بصير integral
+
+308
+00:34:04,400 --> 00:34:10,430
+domain لما كان maximal بصير fieldيبقى my previous
+
+309
+00:34:10,430 --> 00:34:18,490
+theorem F of X modular principle ID generated by X
+
+310
+00:34:18,490 --> 00:34:24,930
+is A3 خلّي
+
+311
+00:34:24,930 --> 00:34:31,770
+المعلومة عندك لازملي أرجعلها بعد قليل كرولر اتنين
+
+312
+00:34:31,770 --> 00:34:36,190
+النتيجة رقم اتنين
+
+313
+00:34:40,300 --> 00:34:48,080
+النص تبعها كانت تالية بيقول
+
+314
+00:34:48,080 --> 00:34:57,620
+let ال FB إيه فيهم let كانت ال FB إيه فيهم and let
+
+315
+00:34:57,620 --> 00:35:01,360
+ال
+
+316
+00:35:01,360 --> 00:35:10,510
+P of X و ال A of X و ال P of Xموجودة في capital F
+
+317
+00:35:10,510 --> 00:35:16,870
+of X F ال
+
+318
+00:35:16,870 --> 00:35:31,410
+P of X is irreducible is irreducible over F over
+
+319
+00:35:31,410 --> 00:35:43,900
+FN ال P of Xdivides ال a of x في ال b of x then ال
+
+320
+00:35:43,900 --> 00:35:54,300
+p of x divides ال a of x or ال p of x divides ال b
+
+321
+00:35:54,300 --> 00:35:55,840
+of x
+
+322
+00:36:29,960 --> 00:36:37,200
+نقرأه نرجع للنص مرة تانية if فيه أخدت three
+
+323
+00:36:37,200 --> 00:36:43,770
+polynomials موجوداتفي capital F of X عندي معلومتين
+
+324
+00:36:43,770 --> 00:36:48,330
+المعلومة الأولى ان P of X is reducible على F
+
+325
+00:36:48,330 --> 00:36:54,830
+المعلومة الثانية P of X تقسم حاصل ضاربهما ان حدث
+
+326
+00:36:54,830 --> 00:36:59,350
+ذلك اذا القولنومية الأولى بتقسم القولنومية التانية
+
+327
+00:36:59,350 --> 00:37:05,430
+او القولنومية الأولى بتقسمها P of X بتقسمها بدون
+
+328
+00:37:05,430 --> 00:37:12,630
+باقي يعنيلو قسمنا P of .. لو قسمنا A of X على P of
+
+329
+00:37:12,630 --> 00:37:18,450
+X تنتهي القسمة بدون باب طيب نيجي للبرهان اللي
+
+330
+00:37:18,450 --> 00:37:23,990
+عندنا يبقى بدي افترض ان ال P of X is irreducible
+
+331
+00:37:23,990 --> 00:37:34,310
+على F يبقى assume that ان ال P of X is
+
+332
+00:37:37,090 --> 00:37:47,010
+irreducible over if. من النظرية إيش بنستنتج؟ إن ال
+
+333
+00:37:47,010 --> 00:37:55,790
+P of X is maximal ID. إذا بقولوا هنا by the above
+
+334
+00:37:55,790 --> 00:38:01,610
+theorem ال
+
+335
+00:38:01,610 --> 00:38:09,590
+ID اللي عندنا هذاis maximal طيب
+
+336
+00:38:09,590 --> 00:38:20,730
+الكرولري اللي فوق يادى field يبقى بي كرولري one
+
+337
+00:38:20,730 --> 00:38:30,770
+capital F of X modular principle ID generated by P
+
+338
+00:38:30,770 --> 00:38:39,520
+is a fieldطب ينفع يكون integral domain؟ اه ينفع
+
+339
+00:38:39,520 --> 00:38:45,400
+يكون انتجرال دومين ينفع يكون انتجرال دومين ينفع
+
+340
+00:38:45,400 --> 00:38:51,520
+يكون انتجرال
+
+341
+00:38:51,520 --> 00:38:59,440
+دومين ينفع يكون انتجرال دومين ينفع يكون انتجرال
+
+342
+00:38:59,440 --> 00:39:06,360
+دومين ينفع يكون انتجرال دومينالشماكة بال natural
+
+343
+00:39:06,360 --> 00:39:14,100
+homomorphism ال homomorphism الطبيعي وهي من ال
+
+344
+00:39:14,100 --> 00:39:21,280
+ring ل ring موديلويدية صحيح ولا لأ يبقى هنا define
+
+345
+00:39:21,280 --> 00:39:30,420
+the natural homomorphism
+
+346
+00:39:34,440 --> 00:39:43,360
+Homomorphism Phi من اللي هو capital F of X إلى
+
+347
+00:39:43,360 --> 00:39:51,140
+capital F of X modulo لprinciple ideal generated
+
+348
+00:39:51,140 --> 00:40:01,340
+by P of X. Phi شو شكل المعادلة؟ Phiلما تأثر على ال
+
+349
+00:40:01,340 --> 00:40:06,760
+element F of X اللي موجودة في capital F of X بدي
+
+350
+00:40:06,760 --> 00:40:12,680
+يعطينا ال F of X itself زائد ال principle ideal
+
+351
+00:40:12,680 --> 00:40:20,040
+generated by P of X حتى الآن كل الشغل اشتغلناه
+
+352
+00:40:20,040 --> 00:40:26,080
+بمعلومة واحدة المعلومة التانية لسه مامسكناش مظبوط؟
+
+353
+00:40:26,080 --> 00:40:35,500
+طيب ده بيقول sinceبما ان ال P of X بتقسم ال A of X
+
+354
+00:40:35,500 --> 00:40:45,140
+في ال P of X We have ان ال A of X في ال P of X
+
+355
+00:40:45,140 --> 00:40:54,340
+يساوي ال P of X في فانكشن تانية والتكن P of X for
+
+356
+00:40:54,340 --> 00:41:02,450
+someG of X اللي موجودة في capital F of X نظرها لإن
+
+357
+00:41:02,450 --> 00:41:07,910
+ال P of X بتقسم حاصل الضرب إذا الحاصل الضرب بيساوي
+
+358
+00:41:07,910 --> 00:41:12,750
+P of X في ال polynomial التالي السؤال هو هذه أين
+
+359
+00:41:12,750 --> 00:41:17,930
+موجودة يا عزيزي؟ ال principle ID حسب التعريف
+
+360
+00:41:17,930 --> 00:41:24,450
+فمعناته هذه موجودة في ال principle ID مظبوط؟ يبقى
+
+361
+00:41:24,450 --> 00:41:33,220
+هناالآن ال A of X في ال B of X يساوي ال P of X في
+
+362
+00:41:33,220 --> 00:41:38,700
+ال G of X موجودة في ال principle ideal generated
+
+363
+00:41:38,700 --> 00:41:44,500
+by P of X ليش؟ لأن هذا تعريف ال principle ideal
+
+364
+00:41:44,500 --> 00:41:50,300
+معناته صار ال A في B موجود في ال principle يبقى
+
+365
+00:41:50,300 --> 00:41:56,820
+هذا معناته أن ال A of Xفي ال P of X موجود في ال
+
+366
+00:41:56,820 --> 00:42:03,800
+principle ideal generated by P of X طيب لو جتنا ال
+
+367
+00:42:03,800 --> 00:42:12,180
+homomorphism Phi of AX BX حسب ال definition اللي
+
+368
+00:42:12,180 --> 00:42:19,180
+احنا جايبينه فوق بده يساوي A of X في P of Xزائد
+
+369
+00:42:19,180 --> 00:42:25,380
+لـPrincipal Ideal Generated by Geographics. أكيد ؟
+
+370
+00:42:25,380 --> 00:42:30,700
+طيب هذا وين موجود ؟ ان هذا كله قد مش بديه ساوي.
+
+371
+00:42:31,080 --> 00:42:37,080
+بديه ساوي اللي هو الـPrincipal Ideal Generated by
+
+372
+00:42:37,080 --> 00:42:43,640
+Geographics. مش هذا هو الـzero element في الفكرة
+
+373
+00:42:43,640 --> 00:42:50,010
+اللي عندنا هنا صح ولا لا ؟P of X هو ال .. ال .. ال
+
+374
+00:42:50,010 --> 00:42:55,270
+zero element في ال factor field اللي عندناها طيب
+
+375
+00:42:55,270 --> 00:43:04,630
+لو جيت أخدت ال Phi of A of X فال Phi of ال P of X
+
+376
+00:43:04,630 --> 00:43:11,830
+حسب التعريف اللي فوق بده يساوي ال A of X زائد ال
+
+377
+00:43:11,830 --> 00:43:21,190
+principle ideal generatedby P of X في P of X زائد
+
+378
+00:43:21,190 --> 00:43:30,630
+ال principle ideal generated by P of X طبقا
+
+379
+00:43:30,630 --> 00:43:36,010
+اللي حصل ضرب ال lift cassettes هذا الكلام شو بده
+
+380
+00:43:36,010 --> 00:43:43,090
+يساوي ال A of X في P of Xزائد لـ Principle Ideal
+
+381
+00:43:43,090 --> 00:43:53,550
+Generated by P of X طيب هذه كم هتعطينا Principle
+
+382
+00:43:53,550 --> 00:44:01,310
+Ideal يبقى هذه بتعطينا Principle Ideal فقط لإن ال
+
+383
+00:44:01,310 --> 00:44:07,050
+AX والBX موجودة في ال Principle طيب تعالوا نشوف
+
+384
+00:44:07,050 --> 00:44:13,480
+إيش رأيكوا في الموضوع خلي بالكوا هناحاصر ضرر two
+
+385
+00:44:13,480 --> 00:44:18,960
+elements بديوا يساوي ال zero element في main في ال
+
+386
+00:44:18,960 --> 00:44:25,860
+factor ring اللي عندنا مظبوط يبقى ال factor ايش
+
+387
+00:44:25,860 --> 00:44:31,000
+قولنا عليه integral domain مادام integral domain
+
+388
+00:44:31,000 --> 00:44:35,920
+يا هذا بال zero يا التاني بال zero يبقى بالي بقول
+
+389
+00:44:35,920 --> 00:44:43,940
+since بما ان ال F of Xmoderate principle ideal
+
+390
+00:44:43,940 --> 00:44:56,880
+generated by is an integral domain we have بده
+
+391
+00:44:56,880 --> 00:45:02,520
+يصير عندنا ال a of x زائد ال principle ideal
+
+392
+00:45:02,520 --> 00:45:08,740
+generated by p of x بده يساوي ال zero elementاللي
+
+393
+00:45:08,740 --> 00:45:15,440
+هو ال principle ideal generated by P of X او او
+
+394
+00:45:15,440 --> 00:45:21,720
+التانية اللي هو P of X زائد ال principle ideal
+
+395
+00:45:21,720 --> 00:45:26,380
+generated by P of X بده يساوي ال principle ideal
+
+396
+00:45:26,380 --> 00:45:32,580
+generated by P of X اما هذه او غيرها طب ايش تفسيرك
+
+397
+00:45:32,580 --> 00:45:42,800
+لهذه ال P of X موجودة وين؟هذا معناته ان ال A of X
+
+398
+00:45:42,800 --> 00:45:51,100
+موجود في ال principle ideal generated by P of X او
+
+399
+00:45:51,100 --> 00:45:57,660
+ال P of X موجود في ال principle ideal generated by
+
+400
+00:45:57,660 --> 00:46:07,040
+P of X طب هذا ايش معناه؟بتساوي A of X بتساوي P of
+
+401
+00:46:07,040 --> 00:46:16,240
+X في Polynomial أخرى يفجر هذا معناته ان ال A of X
+
+402
+00:46:16,240 --> 00:46:28,340
+بتساوي P of X في G1 of X and ال P of X بتساوي P of
+
+403
+00:46:28,340 --> 00:46:39,810
+X في G2 of Xالكلام هذا صحيح for الصام G1 of X وجيه
+
+404
+00:46:39,810 --> 00:46:47,730
+اتنين of X اللي موجودة في capital F of X ايش
+
+405
+00:46:47,730 --> 00:46:52,990
+تفسيرك ليه هذا الجدار؟ ان ال P of X بتقسم ال A of
+
+406
+00:46:52,990 --> 00:47:03,220
+X لإن هذا معناته ان ال P of X بتقسم ال A of Xor P
+
+407
+00:47:03,220 --> 00:47:12,120
+of X تقسم P of X هذا المقال مطلوب؟ مقال مطلوب لو
+
+408
+00:47:12,120 --> 00:47:18,000
+كانت ال F is irreducible وبتقسم حصل ضرر two
+
+409
+00:47:18,000 --> 00:47:23,080
+polynomials P of X لازم تقسم ال polynomial الأولى
+
+410
+00:47:23,080 --> 00:47:29,490
+أو تقسم ال polynomial الثانيةبدنا نعطي إشارة عربية
+
+411
+00:47:29,490 --> 00:47:36,710
+بسيطة give
+
+412
+00:47:36,710 --> 00:47:49,030
+you example one example one construct a
+
+413
+00:47:49,030 --> 00:47:55,690
+field of order 8
+
+414
+00:47:57,560 --> 00:48:04,740
+مش يعني انشؤونا field ال order إله يسوى تماما
+
+415
+00:48:04,740 --> 00:48:08,960
+باستخدام الكرولاريز باستخدام النظرية اللي بدكوا
+
+416
+00:48:08,960 --> 00:48:14,500
+يعملها مشكلة القصة بسيطة جدا بدي أختار polynomial
+
+417
+00:48:14,500 --> 00:48:20,680
+و أختار field بحيث تبقى ال polynomial irreducible
+
+418
+00:48:20,680 --> 00:48:25,720
+على هذا ال field يبقى هنا solution
+
+419
+00:48:28,690 --> 00:48:37,290
+ودا يقولوا let f of x ده ساول x تكعيب مثلا زائد x
+
+420
+00:48:37,290 --> 00:48:48,430
+زائد واحد هاي polynomial وهنا let كمان let الفيه
+
+421
+00:48:48,430 --> 00:48:55,870
+let z اتنين بيه الفيه
+
+422
+00:48:59,980 --> 00:49:04,840
+بدى اشوف هذه الـreduce و لا على z2 ولا لا يبقى بدي
+
+423
+00:49:04,840 --> 00:49:13,460
+اخد f of 0 جداش تساوي واحد طب و ال f of واحد z2
+
+424
+00:49:13,460 --> 00:49:19,220
+مصبوط ولا لا يبقى معناته ليش ماعنديش zeros لهذه ال
+
+425
+00:49:19,220 --> 00:49:26,740
+function في z2 يبقى هذا معناته ان ال f of x has no
+
+426
+00:49:26,740 --> 00:49:37,260
+zerosNZ2 هذا معناته ايه N Radio 7 هذا معناته ان F
+
+427
+00:49:37,260 --> 00:49:51,360
+of X is Radio 7 over Z2 تمام يبقى ال ID للمكون
+
+428
+00:49:51,360 --> 00:49:59,110
+بيكون maximum صح بالنص النظريةيبقى بقى دي بقوله by
+
+429
+00:49:59,110 --> 00:50:09,690
+the above theorem the principle ideal generated by
+
+430
+00:50:09,690 --> 00:50:16,550
+the highest maximal مدام
+
+431
+00:50:16,550 --> 00:50:24,750
+maximal هذا الآل بده يعطينا ان z2 modulo هذا ال
+
+432
+00:50:24,750 --> 00:50:39,100
+idealماله؟ as a field يبقى as a field طبعا ايه شكل
+
+433
+00:50:39,100 --> 00:50:49,280
+هذا ال field؟ z to modulo x تكرير زائد x زائد واحد
+
+434
+00:50:49,280 --> 00:51:00,140
+بالديسام انا ازعمأنه على شكل تالت A X تربيع زائد B
+
+435
+00:51:00,140 --> 00:51:05,600
+X زائد C زائد ال principle ideal generated by X
+
+436
+00:51:05,600 --> 00:51:11,880
+تكييف زائد X زائد 1 بحيث ال A والB والC موجودة في
+
+437
+00:51:11,880 --> 00:51:20,480
+زيادة 2.معقول هيك يكون صحيح؟ طب هم البرنامج يكون
+
+438
+00:51:20,480 --> 00:51:25,100
+من ضلالي الرابع أو الخمسة أو السلسة أو ميلادبنضم
+
+439
+00:51:25,100 --> 00:51:32,000
+لهذه وضل أقل من الدرجات التي همين الدرجات التانية
+
+440
+00:51:32,000 --> 00:51:39,500
+أنا أزعم أن هذا لا يوجد فيه إلا ثمانية عناصر و ال
+
+441
+00:51:39,500 --> 00:51:43,720
+exercise اللي كنا المرة القادمة بس يجيبلي شكل
+
+442
+00:51:43,720 --> 00:51:48,080
+العناصر والله يعطيك العفو يجيب أول ما نيجي المرة
+
+443
+00:51:48,080 --> 00:51:54,850
+جاى بدنا ناقش شكل العناصركيف؟ ليش ايه؟ مين اللي
+
+444
+00:51:54,850 --> 00:52:00,790
+بتسأل؟ انا بسأل لسه معرفة ما هي مطلوبة انك تجيب
+
+445
+00:52:00,790 --> 00:52:07,230
+عليها من هنا؟ انا بسأل لسه من هنا؟ انا بسأل لسه من
+
+446
+00:52:07,230 --> 00:52:07,830
+هنا؟ انا بسأل لسه من هنا؟ انا بسأل لسه من هنا؟ انا
+
+447
+00:52:07,830 --> 00:52:07,830
+بسأل لسه من هنا؟ انا بسأل لسه من هنا؟ انا بسأل لسه
+
+448
+00:52:07,830 --> 00:52:07,830
+من هنا؟ انا بسأل لسه من هنا؟ انا بسأل لسه من هنا؟
+
+449
+00:52:07,830 --> 00:52:09,370
+انا بسأل لسه من هنا؟ انا بسأل لسه من هنا؟ انا بسأل
+
+450
+00:52:09,370 --> 00:52:14,130
+لسه من هنا؟ انا بسأل لسه من هنا؟ انا بسأل لسه من
+
+451
+00:52:14,130 --> 00:52:30,730
+هنا؟ انا بسأل لسالجبال يوجد فقط 8 علماء منهم المرة
+
+452
+00:52:30,730 --> 00:52:32,470
+القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..307cdafeeda46faeee18f99953dc397b7bb60f3f
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY.srt
@@ -0,0 +1,783 @@
+1
+00:00:20,890 --> 00:00:26,230
+بسم الله الرحمن الرحيم، أحنا المرة الماضية كتبنا
+
+2
+00:00:26,230 --> 00:00:31,690
+آخر نظرية، ونظرا لقصر الوقت لم نتمكن من إثباتها، وها
+
+3
+00:00:31,690 --> 00:00:37,010
+نحن سنبرهنها في هذا اليوم إن شاء الله، نظرية تقول
+
+4
+00:00:37,010 --> 00:00:43,330
+ما يلي: A non-empty subset S of a ring R is
+
+5
+00:00:43,330 --> 00:00:48,330
+a subring إذا كان الـ A والـ (-B) موجودين في الـ S
+
+6
+00:00:48,630 --> 00:00:54,850
+لكل A و B موجودين في S، وكذلك A - B  يجب أن يكون
+
+7
+00:00:54,850 --> 00:00:59,970
+موجوداً في subset S، إذا كان الـ A والـ B موجودين في
+
+8
+00:00:59,970 --> 00:01:07,270
+الـ S. طيب، يبقى إحنا عندنا ring A، أخذنا subset منها
+
+9
+00:01:07,270 --> 00:01:15,220
+S، عندي شرطين، هذين موجودين، تمام. والشرط الأول أن الـ
+
+10
+00:01:15,220 --> 00:01:20,080
+S non-empty، يبقى ثلاثة شروط في الحقيقة، تحت هذه
+
+11
+00:01:20,080 --> 00:01:25,680
+الشروط الثلاثة، لنثبت أنها subring. يبقى
+
+12
+00:01:25,680 --> 00:01:29,660
+بالنسبة للنقطة الأولى، يبقى بالبداية أقول له let
+
+13
+00:01:29,660 --> 00:01:40,540
+S be a non-empty subset of
+
+14
+00:01:40,540 --> 00:01:42,560
+a ring.
+
+15
+00:01:45,920 --> 00:01:51,500
+بعدين، الخطوات اللي عندي لكي أثبت أنها subring، الخطوات
+
+16
+00:01:51,500 --> 00:01:57,300
+الثلاثة اللي عندي، بدي أبين أنهم عبارة عن الست
+
+17
+00:01:57,300 --> 00:02:04,020
+نقاط اللي قلنا، هذول بيكونوا subring. الآن،  بدايتي
+
+18
+00:02:04,020 --> 00:02:08,600
+أخذ اللي هو خاصية الـ associativity بالنسبة لعملية
+
+19
+00:02:08,600 --> 00:02:14,720
+الجمع، وكذلك خاصية الإبدال. يبقى بدايتي أقول له: الـ
+
+20
+00:02:14,720 --> 00:02:23,830
+A و B موجودين في S، ثم A و B موجودة
+
+21
+00:02:23,830 --> 00:02:30,650
+في R أيضاً؟ لأن الـ S هي subset من من؟ من الـ R.
+
+22
+00:02:30,650 --> 00:02:38,050
+مدام هيك، يبقى A + B = B + A.
+
+23
+00:02:38,050 --> 00:02:41,690
+هل
+
+24
+00:02:41,690 --> 00:02:48,050
+الكل صحيح؟ لكل A و B الموجودة في S.
+
+25
+00:02:48,050 --> 00:02:55,510
+زيادة على ذلك، لو جئت قلت: خذ A، B، C
+
+26
+00:02:55,510 --> 00:03:03,190
+موجودة في S، then A، B، C موجودة في R.
+
+27
+00:03:03,190 --> 00:03:09,130
+يبقى هذا معناه أن الـ distributive law صحيح، هذا
+
+28
+00:03:09,130 --> 00:03:12,310
+يعني أن الـ distributive
+
+29
+00:03:17,540 --> 00:03:23,140
+law صحيح، وكذلك
+
+30
+00:03:23,140 --> 00:03:33,340
+خاصية الدمج أيضاً تعتبر صحيحة. distributive law
+
+31
+00:03:33,340 --> 00:03:42,360
+صحيح و الـ associativity صحيح.
+
+32
+00:03:43,880 --> 00:03:48,540
+يبقى قانون التوزيع وقانون الدمج، الاثنان صحيحان لأن
+
+33
+00:03:48,540 --> 00:03:56,760
+جميع العناصر اللي عندنا موجودة في R. طيب، نجيب نثبت
+
+34
+00:03:56,760 --> 00:04:04,580
+أن الـ zero موجود في S. يبقى باجي بقول له: since بما أن
+
+35
+00:04:04,580 --> 00:04:12,580
+A - B موجود في S لكل A و B  اللي
+
+36
+00:04:12,580 --> 00:04:19,240
+موجودة في S. لو أخذت
+
+37
+00:04:19,240 --> 00:04:29,020
+A = B، we have أن A - A موجود في S.
+
+38
+00:04:29,020 --> 00:04:35,480
+طبعاً، من الشرط الأول، we have هذا من الـ
+
+39
+00:04:35,480 --> 00:04:39,940
+first condition. طيب، A - A اللي هي بتعطينا من؟
+
+40
+00:04:39,940 --> 00:04:45,540
+الـ zero. يبقى الـ zero موجودة وين؟ في S. يبقى
+
+41
+00:04:45,540 --> 00:04:49,420
+معناها أن الـ S is non-empty، زي ما احنا
+
+42
+00:04:49,420 --> 00:04:56,480
+فرضنا قبل. وزيادة على ذلك، الـ zero موجود في S، يبقى
+
+43
+00:04:56,480 --> 00:05:00,720
+هذا الـ zero element موجود في S وبالتالي الـ S is
+
+44
+00:05:00,720 --> 00:05:06,490
+non-empty. طيب، نجي للنقطة الثانية، الشرط الثاني، مش هغيره،
+
+45
+00:05:06,490 --> 00:05:11,870
+الحين عندي الـ zero موجود في S والـ B موجود في S.
+
+46
+00:05:11,870 --> 00:05:24,490
+يبقى إذا بقول له: for any B اللي موجود في S. from
+
+47
+00:05:24,490 --> 00:05:28,290
+الشرط الأول،
+
+48
+00:05:28,290 --> 00:05:33,850
+من الشرط الأول،  الـ zero - B
+
+49
+00:05:34,210 --> 00:05:40,770
+موجود في S. أخذنا B في S، و zero أصلاً موجود في S، تبقى
+
+50
+00:05:40,770 --> 00:05:45,950
+أخذنا الفرق في ما بينهما، هذا إيش بده يعطيني؟ بده
+
+51
+00:05:45,950 --> 00:05:51,770
+يعطيني -B موجود في S. إذا، المعكوس
+
+52
+00:05:51,770 --> 00:05:58,370
+الجمعي لأي عنصر موجود في S بده يكون موجود في
+
+53
+00:05:58,370 --> 00:06:02,440
+S. يبقى -element موجود في S، هذا الـ
+
+54
+00:06:02,440 --> 00:06:09,080
+رابع شرط من شروط الـ
+
+55
+00:06:09,080 --> 00:06:14,020
+ring. ممتاز، يبقى الـ zero موجود في S، الـ -B موجود في S، هنا الخاصية الإبدال صحيحة بالنسبة
+
+56
+00:06:14,020 --> 00:06:19,820
+للجمع، وكذلك بالنسبة لـ associativity عملية الضرب،
+
+57
+00:06:19,820 --> 00:06:24,700
+وخاصية الـ distributive كذلك بالنسبة لعملية الجمع
+
+58
+00:06:24,700 --> 00:06:28,990
+والضرب. خاصية الـ distributive  بالنسبة لعملية الجمع
+
+59
+00:06:28,990 --> 00:06:34,050
+والضرب، الاثنتان معاً، مُحققة لأن جميع العناصر في R.
+
+60
+00:06:34,050 --> 00:06:40,850
+يبقى، بس نثبت حكاية الـ binary operation، تمام.
+
+61
+00:06:40,850 --> 00:06:49,530
+الآن، from condition، from
+
+62
+00:06:49,530 --> 00:06:59,010
+condition two، من الشرط الثاني، أن A × B موجودة في S لكل
+
+63
+00:06:59,010 --> 00:07:06,750
+A و B اللي موجودة في S. مدام هذا موجود في S،
+
+64
+00:07:06,750 --> 00:07:14,810
+حصل الضرب. لكل A الموجودة في S، we have أن الـ
+
+65
+00:07:14,810 --> 00:07:20,290
+multiplication، multiplication is
+
+66
+00:07:24,230 --> 00:07:29,470
+a binary operation.
+
+67
+00:07:29,470 --> 00:07:33,030
+on
+
+68
+00:07:33,030 --> 00:07:42,190
+S. بقى الباقي علينا حاجة واحدة،
+
+69
+00:07:42,190 --> 00:07:47,270
+ما هي هذه الحاجة؟ نثبت أن عملية الجمع كذلك هي
+
+70
+00:07:47,270 --> 00:07:59,990
+binary operation على S. يبقى finally، وأخيراً، الـ -B
+
+71
+00:07:59,990 --> 00:08:10,730
+موجود في S،  أيه تمام؟ يبقى بدايتي أقول له: أن from
+
+72
+00:08:10,730 --> 00:08:13,970
+condition
+
+73
+00:08:13,970 --> 00:08:17,450
+one،
+
+74
+00:08:17,450 --> 00:08:27,280
+يجب أن يكون عندي A - (-B). أخذنا العنصر A
+
+75
+00:08:27,280 --> 00:08:32,060
+والـ -B، وأخذنا الشرط... الشرط... لأ،
+
+76
+00:08:32,060 --> 00:08:36,160
+condition one، مش condition two. condition one يا
+
+77
+00:08:36,160 --> 00:08:41,680
+أستاذ، يبقى الـ condition one، يبقى الأول ناقص الثاني،
+
+78
+00:08:41,680 --> 00:08:47,440
+يبقى الأول ناقص الثاني، أخذناه من... يا شباب!
+
+79
+00:08:47,440 --> 00:08:55,680
+الشغل. يساوي A + B موجود في S. إيش يعني؟ يعني
+
+80
+00:08:55,680 --> 00:09:00,480
+closed under addition. يبقى هذه binary
+
+81
+00:09:00,480 --> 00:09:10,120
+operation. يبقى this means that
+
+82
+00:09:10,120 --> 00:09:15,320
+addition is
+
+83
+00:09:16,840 --> 00:09:21,360
+a binary operation.
+
+84
+00:09:21,360 --> 00:09:26,940
+on
+
+85
+00:09:26,940 --> 00:09:35,220
+set S. ممتاز.
+
+86
+00:09:35,220 --> 00:09:41,640
+يبقى بناء عليه، تحققت كل شروط الـ subring، ومن هنا
+
+87
+00:09:41,640 --> 00:09:51,500
+الـ S is a subring. يبقى هكذا، الـ S is a sub
+
+88
+00:09:51,500 --> 00:10:00,680
+ring of R. إذاً هذه النتيجة، أو اللي بتسميها subring،
+
+89
+00:10:00,680 --> 00:10:06,940
+اختصرت لي اللي هو شروط الـ ring الستة، والـ two
+
+90
+00:10:06,940 --> 00:10:09,880
+binary operations اللي عليها، يعني بيعتبر ثمانية،
+
+91
+00:10:09,880 --> 00:10:15,850
+اختصرتهم للثلاثة. الآن، لو عندي ring وأخذت منها
+
+92
+00:10:15,850 --> 00:10:21,810
+subset، إذا أثبت أن هذه الـ subset non-empty، واثبت
+
+93
+00:10:21,810 --> 00:10:25,910
+أخذت عنصرين منها، وإثبت الفرق بينهما موجود في نفس
+
+94
+00:10:25,910 --> 00:10:30,050
+الـ set S، أخذت عنصرين من S، وأثبت أن حاصل ضربهما موجود
+
+95
+00:10:30,050 --> 00:10:34,310
+في S، تبقى بناء عليه، automatically أحكم على S أنها sub
+
+96
+00:10:34,310 --> 00:10:39,990
+ring من الـ ring R. ممتاز. طيب، الآن بدنا نبدأ
+
+97
+00:10:39,990 --> 00:10:45,980
+نأخذ أمثلة مختلفة، عملية على الـ subring. بس جاب
+
+98
+00:10:45,980 --> 00:10:51,560
+المثال، لو جاب،  أخذ أمثلة، لو كانت الـ ring
+
+99
+00:10:51,560 --> 00:10:56,760
+فيها unity، هل ضروري الـ subring يكون فيها نفس الـ
+
+100
+00:10:56,760 --> 00:11:02,780
+unity؟ لأ، لأ، ممكن ما يكونش هناك بالمرة، وممكن يكون
+
+101
+00:11:02,780 --> 00:11:08,020
+فيها unity غير الـ unity تبع الـ ring، كما سنرى بعد
+
+102
+00:11:08,020 --> 00:11:13,130
+قليل إن شاء الله، من خلال بعض الأمثلة. يبقى بنا نيجي
+
+103
+00:11:13,130 --> 00:11:22,790
+لأول مثال، وبدي أبدأ بأبسط مثال. example الأول
+
+104
+00:11:22,790 --> 00:11:28,090
+مثال، خليني
+
+105
+00:11:28,090 --> 00:11:32,970
+أجعل الـ group قليلاً، ثم نتقل إلى الـ ring. في حاجة
+
+106
+00:11:32,970 --> 00:11:36,450
+بنسميها الـ trivial subgroup. من
+
+107
+00:11:36,450 --> 00:11:40,730
+الـ trivial subgroup؟ اللي فيها بس الـ subgroup اللي
+
+108
+00:11:40,730 --> 00:11:46,650
+فيها من؟ الـ identity element بس. تمام، يبقى الـ set
+
+109
+00:11:46,650 --> 00:11:50,930
+اللي فيها الـ zero، هي عبارة عن subgroup كمان.
+
+110
+00:11:50,930 --> 00:11:57,950
+سؤال من مبادئ الرياضيات، أخذنا: any set is a subset
+
+111
+00:11:57,950 --> 00:12:03,730
+of itself. تمام، كمان هنا: any ring is a subring of
+
+112
+00:12:03,730 --> 00:12:09,490
+itself، لأن كل الشروط مُتحققة عليها. يبقى هنا الـ zero
+
+113
+00:12:09,490 --> 00:12:23,450
+و R are subrings of the ring R.
+
+114
+00:12:32,200 --> 00:12:38,260
+the trivial ring, the trivial
+
+115
+00:12:38,260 --> 00:12:43,620
+يعني من العربي: تافه، بس إحنا ما بنقولش تافه، يعني أبسط
+
+116
+00:12:43,620 --> 00:12:49,920
+حاجة. the trivial، البديهي. يبقى هذه بنسميها
+
+117
+00:12:49,920 --> 00:12:55,360
+الحلقة الجزئية البديهية من الـ ring الأصلية، اللي هي
+
+118
+00:12:55,360 --> 00:13:09,060
+R. مثال اثنين، مثال اثنين، نقول Z6، Z6 اللي على الصراحة
+
+119
+00:13:09,060 --> 00:13:14,020
+هي:  الـ zero، وواحد، واثنين، وثلاثة، وأربعة،
+
+120
+00:13:14,020 --> 00:13:30,140
+وخمسة، كلهم هذول is a ring of integers modulo
+
+121
+00:13:30,140 --> 00:13:47,510
+6, modulo 6 with unity 1, with unity 1, that's it. لو
+
+122
+00:13:47,510 --> 00:13:56,530
+أخذنا الـ {0, 2, 4}، نرجع
+
+123
+00:13:56,530 --> 00:14:03,460
+مرة ثانية. أنا أخذت الـ ring Z6 على السريع، يعني
+
+124
+00:14:03,460 --> 00:14:07,640
+من zero لغاية خمسة. طبعاً، لو رحتوا لبعض كنتوا ممكن
+
+125
+00:14:07,640 --> 00:14:13,580
+تكتبوا زي ما إحنا كتبناها. لو تكتبوا: 0, 6, 1, 6,
+
+126
+00:14:13,580 --> 00:14:15,140
+2, 6, 2, 6, 2, 6, 2,
+
+127
+00:14:15,140 --> 00:14:15,360
+6, 2, 6, 2, 6, 2, 6,
+
+128
+00:14:15,360 --> 00:14:20,260
+2, 6, 2, 6, 2, 6, 2,
+
+129
+00:14:20,260 --> 00:14:24,280
+6, 2,
+
+130
+00:14:24,280 --> 00:14:29,440
+6, 2, 6, 2, 6, 2, 6,
+
+131
+00:14:29,440 --> 00:14:34,130
+2. طبعاً، هذه هي الـ unity، اللي هو الـ identity
+
+132
+00:14:34,130 --> 00:14:39,330
+element، أو الـ unity، بالنسبة لها. روحنا أخذنا منها
+
+133
+00:14:39,330 --> 00:14:46,850
+مجموعة جزئية: {0, 2, 4}. هل هذه الـ subring؟ بمعنى non-
+
+134
+00:14:46,850 --> 00:14:55,740
+empty. لو طرحت أي اثنين من بعض، موجود داخل الـ Z6. لو
+
+135
+00:14:55,740 --> 00:15:00,320
+ضربت أي اثنين في بعض، بده يكون موجود داخل الـ Z6.
+
+136
+00:15:00,320 --> 00:15:07,480
+مثال،  لو قلت لك: 4 + 2 =؟ 0.
+
+137
+00:15:07,480 --> 00:15:14,520
+لو قلت لك: 4 - 2 =؟ 2.  إذاً،
+
+138
+00:15:14,520 --> 00:15:22,240
+قلت لك: 2 - 4 = -2.  4 - 2 = 2.
+
+139
+00:15:22,240 --> 00:15:27,280
+2 - 4 = -2.  -2  هذه، ما عنديش -2، لكن -2 هو كم؟ أضيف
+
+140
+00:15:27,280 --> 00:15:31,320
+عليها 6، لما أضيف عليها 6،  بتصير 4. موجودة
+
+141
+00:15:31,320 --> 00:15:35,000
+ولا لا؟ إذاً، -2 موجودة، بمعنى 4 موجودة،
+
+142
+00:15:35,000 --> 00:15:39,160
+ولا لا؟ إذاً، -2 موجودة، بمعنى 4 موجودة،
+
+143
+00:15:39,160 --> 00:15:47,140
+موجودة. لما نقول يا شباب، هام جداً، أنه 2 - 4
+
+144
+00:15:47,140 --> 00:15:52,540
+تساوي -2، كله modulo 6. لو أضفت لها
+
+145
+00:15:52,540 --> 00:15:57,720
+6، يعني كأنه أضفت صفر بالنسبة لها، يبقى هذا بدي
+
+146
+00:15:57,720 --> 00:16:05,620
+يعطينا 4. موجودة داخل Z6. إذاً، الـ -2 هي
+
+147
+00:16:05,620 --> 00:16:15,390
+4. هذا كله موجود داخل Z6. هل هذه فيها
+
+148
+00:16:15,390 --> 00:16:20,390
+unity؟ لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+149
+00:16:20,390 --> 00:16:20,490
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+150
+00:16:20,490 --> 00:16:23,410
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+151
+00:16:23,410 --> 00:16:24,750
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+152
+00:16:24,750 --> 00:16:25,330
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+153
+00:16:25,330 --> 00:16:34,790
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+154
+00:16:34,790 --> 00:16:35,370
+لأ
+
+155
+00:16:44,520 --> 00:16:46,800
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+156
+00:16:46,800 --> 00:16:48,480
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+157
+00:16:48,480 --> 00:16:53,200
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+158
+00:16:53,200 --> 00:16:54,820
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+159
+00:16:54,820 --> 00:16:56,580
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+160
+00:16:56,580 --> 00:16:59,040
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+161
+00:16:59,040 --> 00:17:01,660
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+162
+00:17:01,660 --> 00:17:04,620
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر، هو
+
+163
+00:17:04,620 --> 00:17:07,900
+ما له علاقة بالـ unity تبع الـ ring الأصلية. هذه لها
+
+164
+00:17:07,900 --> 00:17:12,640
+unity، وهذه unity ثانية كما أشَرْنا إلى ذلك قبل أن
+
+165
+00:17:12,640 --> 00:17:19,320
+نبدأ في الأمثلة. يبقى the set هذه is a subring
+
+166
+00:17:19,320 --> 00:17:29,160
+with unity. 4،  4 هو unity للـ subring، لكن الـ
+
+167
+00:17:29,160 --> 00:17:33,080
+ring الأصلية، الـ unity لها بكم؟ 1، وهي
+
+168
+00:17:33,080 --> 00:17:38,000
+الواحد صحيح. وهذه الـ unity اللي هي 4. وهي الفرق
+
+169
+00:17:38,000 --> 00:17:42,380
+ما بين العنصرين، أو جداء أي عنصرين. عندك 4 × 0
+
+170
+00:17:42,380 --> 00:17:46,680
+= 0، 4 × 2 = 8 = 2. 4 × 4
+
+171
+00:17:46,680 --> 00:17:53,440
+= 16 = 4. يبقى هو كل هذا، مغلق تحت عملية الضرب.
+
+172
+00:17:53,440 --> 00:18:01,640
+يعني تحققت الشروط الثلاثة لل subring. النقطة الثالثة، أو
+
+173
+00:18:01,640 --> 00:18:16,100
+المثال الثالث: for each positive integer n, for each
+
+174
+00:18:16
+
+223
+00:23:26,700 --> 00:23:34,360
+موجود في الـ NZ يبقى تحقق الشرطان أو ثلاثة شروط تبعت
+
+224
+00:23:34,360 --> 00:23:39,240
+النظرية يبقى بناءً على أن Z is a subgroup
+
+225
+00:23:39,240 --> 00:23:58,460
+from Z يبقى هنا أن Z is a subgroup of Z  كويس
+
+226
+00:24:01,280 --> 00:24:08,600
+يبقى هذا هو المثال رقم 3، ننتقل للمثال رقم 4
+
+227
+00:24:41,810 --> 00:24:50,690
+مثال رقم 4: لو جئنا أخذنا Z of I، وهي ماذا؟ كل
+
+228
+00:24:50,690 --> 00:24:58,850
+العناصر على صلة A  مثل الـB في I، بحيث أن A و B
+
+229
+00:24:58,850 --> 00:25:09,770
+موجودة في؟ موجودة في Z as a subring
+
+230
+00:25:09,770 --> 00:25:10,730
+ 
+
+231
+00:25:17,650 --> 00:25:24,910
+بالـ X عندي، ألا أقدر؟  بـ صفر في Y، يبقى
+
+232
+00:25:24,910 --> 00:25:29,370
+صفر في Y يعطيني ماذا؟ الصفر هذا يجب
+
+233
+00:25:29,370 --> 00:25:37,890
+أن يعطيني أن X و Y موجودة في S، هنا لكل X و Y التي
+
+234
+00:25:37,890 --> 00:25:44,410
+موجودة في S، وهنا كذلك لكل X و Y التي موجودة
+
+235
+00:25:44,410 --> 00:25:55,890
+في S، وبالتالي S is a subring of A. وصلنا
+
+236
+00:25:55,890 --> 00:26:03,170
+إلى التمارين، يبقى تمارين  للطلاب
+
+237
+00:26:03,640 --> 00:26:07,960
+سنراجع المسائل في المرة القادمة
+
+238
+00:26:07,960 --> 00:26:13,600
+حلّ المسائل هنا، ونريدكم أن تكونوا قد  عملتموها
+
+239
+00:26:13,600 --> 00:26:27,460
+سؤال 8، 13، 19، 23، وأضيف أيضاً 22، 
+
+240
+00:26:27,460 --> 00:26:38,410
+23، ... 28، 30، 32،
+
+241
+00:26:38,410 --> 00:26:46,410
+33، 39، 41،
+
+242
+00:26:46,410 --> 00:26:53,850
+46، 50.  من أول التمرين،
+
+243
+00:26:53,850 --> 00:27:00,040
+من وسط التمرين، ومن آخر التمرين. في المرة القادمة
+
+244
+00:27:00,040 --> 00:27:03,620
+نرى ماذا سنختار منها
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c4b2f8d95ff0461978e91e642215cdd70bdd0919
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4833, "start": 20.89, "end": 48.33, "text": "بسم الله الرحمن الرحيم أحنا المرة الماضية كتبنا آخر نظرية ونظرا لقصر الوقت لم نتمكن من مرهانها وها نحن سنبرهنها في هذا اليوم إن شاء الله نظرية نص ماتتبعك وبيقول A non-empty subset S of A ring R is A sub ring إذا كان الـA ومينوس الـB موجود في الـS", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 5551, 5016, 8315, 9673, 25720, 9673, 46958, 10632, 9122, 2655, 3555, 8315, 19753, 34740, 8717, 19913, 2288, 10632, 4032, 1863, 19913, 23557, 5296, 4587, 9381, 2288, 2423, 30543, 2655, 32767, 8717, 39237, 19452, 9154, 3714, 2288, 3224, 7649, 11296, 4032, 11296, 8717, 5016, 1863, 8608, 1863, 26890, 3224, 1863, 11296, 8978, 23758, 45595, 20498, 36145, 13412, 16606, 21984, 8717, 19913, 2288, 10632, 8717, 9381, 3714, 9307, 2655, 3555, 3615, 4117, 4032, 21292, 39648, 316, 2107, 12, 4543, 88, 25993, 318, 295, 316, 4875, 497, 307, 316, 1422, 4875, 11933, 15730, 25961, 2423, 39184, 32, 4032, 2304, 9957, 41779, 2423, 39184, 33, 3714, 29245, 23328, 8978, 2423, 39184, 50], "avg_logprob": -0.2106726670921859, "compression_ratio": 1.6598360655737705, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 20.89, "end": 21.11, "word": "بسم", "probability": 0.890625}, {"start": 21.11, "end": 21.29, "word": " الله", "probability": 0.9658203125}, {"start": 21.29, "end": 21.71, "word": " الرحمن", "probability": 0.97509765625}, {"start": 21.71, "end": 22.33, "word": " الرحيم", "probability": 0.9949544270833334}, {"start": 22.33, "end": 24.41, "word": " أحنا", "probability": 0.730224609375}, {"start": 24.41, "end": 24.73, "word": " المرة", "probability": 0.9453125}, {"start": 24.73, "end": 25.39, "word": " الماضية", "probability": 0.9954427083333334}, {"start": 25.39, "end": 26.23, "word": " كتبنا", "probability": 0.9801025390625}, {"start": 26.23, "end": 26.73, "word": " آخر", "probability": 0.891357421875}, {"start": 26.73, "end": 27.39, "word": " نظرية", "probability": 0.9779052734375}, 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"text": "عالميا على ال sub ring بس جابي المثال لو جابي المبدأ أخد أمثلة لو كانت ال ring فيها unity هل ضروري ال sub ring يكون فيها نفس ال unity؟ لأ لأ ممكن مايكونش هناك بالمرة ويمكن يكون فيها unity غير ال unity تبع ال ring كما سنرى بعد قليل ان شاء الله من خلال بعض الأمثلة", "tokens": [3615, 45340, 25528, 15844, 2423, 1422, 4875, 4724, 3794, 10874, 16758, 1829, 9673, 12984, 6027, 45164, 10874, 16758, 1829, 9673, 44510, 10721, 5551, 9778, 3215, 5551, 2304, 12984, 37977, 45164, 25961, 2655, 2423, 4875, 8978, 11296, 18205, 8032, 1211, 48812, 2288, 13063, 1829, 2423, 1422, 4875, 7251, 30544, 8978, 11296, 8717, 36178, 2423, 18205, 22807, 5296, 10721, 5296, 10721, 3714, 43020, 19446, 1829, 30544, 8592, 34105, 4117, 20666, 2304, 25720, 4032, 32640, 19452, 7251, 30544, 8978, 11296, 18205, 32771, 13546, 2423, 18205, 6055, 3555, 3615, 2423, 4875, 9122, 15042, 8608, 1863, 2288, 7578, 39182, 12174, 20292, 1211, 16472, 13412, 16606, 21984, 9154, 16490, 1211, 6027, 45030, 11242, 16247, 2304, 12984, 37977], "avg_logprob": -0.1510881700419954, "compression_ratio": 1.8893805309734513, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 642.26, "end": 643.12, "word": "عالميا", "probability": 0.9720052083333334}, {"start": 643.12, "end": 643.84, "word": " على", "probability": 0.83349609375}, {"start": 643.84, "end": 644.46, "word": " ال", "probability": 0.79150390625}, {"start": 644.46, "end": 644.7, "word": " sub", "probability": 0.67431640625}, {"start": 644.7, "end": 645.0, "word": " ring", "probability": 0.349853515625}, {"start": 645.0, "end": 645.62, "word": " بس", "probability": 0.876953125}, {"start": 645.62, "end": 645.98, "word": " جابي", "probability": 0.6605631510416666}, {"start": 645.98, "end": 647.26, "word": " المثال", "probability": 0.87060546875}, {"start": 647.26, "end": 647.82, "word": " لو", "probability": 0.67431640625}, {"start": 647.82, "end": 648.26, "word": " جابي", "probability": 0.8033854166666666}, {"start": 648.26, "end": 648.74, "word": " المبدأ", "probability": 0.9801432291666666}, {"start": 648.74, "end": 649.16, "word": " أخد", "probability": 0.7919921875}, {"start": 649.16, "end": 649.74, "word": " أمثلة", "probability": 0.9735107421875}, {"start": 649.74, "end": 650.5, "word": " لو", "probability": 0.9189453125}, {"start": 650.5, "end": 651.1, "word": " كانت", "probability": 0.97900390625}, {"start": 651.1, "end": 651.28, "word": " ال", "probability": 0.99072265625}, {"start": 651.28, "end": 651.56, "word": " ring", "probability": 0.98193359375}, {"start": 651.56, "end": 652.06, "word": " فيها", "probability": 0.989013671875}, {"start": 652.06, "end": 652.82, "word": " unity", "probability": 0.88720703125}, {"start": 652.82, "end": 653.92, "word": " هل", "probability": 0.97314453125}, {"start": 653.92, "end": 654.66, "word": " ضروري", "probability": 0.97705078125}, {"start": 654.66, "end": 654.92, "word": " ال", "probability": 0.94580078125}, {"start": 654.92, "end": 655.26, "word": " sub", "probability": 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بعد", "probability": 0.951171875}, {"start": 668.02, "end": 668.5, "word": " قليل", "probability": 0.8515625}, {"start": 668.5, "end": 668.72, "word": " ان", "probability": 0.70849609375}, {"start": 668.72, "end": 669.0, "word": " شاء", "probability": 0.978515625}, {"start": 669.0, "end": 669.16, "word": " الله", "probability": 0.953125}, {"start": 669.16, "end": 669.46, "word": " من", "probability": 0.99462890625}, {"start": 669.46, "end": 670.32, "word": " خلال", "probability": 0.9923502604166666}, {"start": 670.32, "end": 670.88, "word": " بعض", "probability": 0.958740234375}, {"start": 670.88, "end": 671.7, "word": " الأمثلة", "probability": 0.9608154296875}], "temperature": 1.0}, {"id": 24, "seek": 69145, "start": 671.99, "end": 691.45, "text": "يبقى بنا نيجي لأول مثال و بدي أبدأ بأبسط مثال example أول مثال خليني أجعل ال group قليلا ثم نتقل إلى ال ring", "tokens": [1829, 3555, 4587, 7578, 4724, 8315, 8717, 1829, 7435, 1829, 5296, 10721, 12610, 50113, 6027, 4032, 4724, 16254, 5551, 44510, 10721, 4724, 10721, 3555, 3794, 9566, 50113, 6027, 1365, 5551, 12610, 50113, 6027, 16490, 1211, 9957, 1829, 5551, 7435, 30241, 2423, 1594, 12174, 20292, 15040, 38637, 2304, 8717, 2655, 4587, 1211, 30731, 2423, 4875], "avg_logprob": -0.29630682901902633, "compression_ratio": 1.390625, "no_speech_prob": 0.0, "words": [{"start": 671.99, "end": 672.49, "word": "يبقى", "probability": 0.8380126953125}, {"start": 672.49, "end": 672.75, "word": " بنا", "probability": 0.4935302734375}, {"start": 672.75, "end": 673.13, "word": " نيجي", "probability": 0.746826171875}, {"start": 673.13, "end": 673.67, "word": " لأول", "probability": 0.9275716145833334}, {"start": 673.67, "end": 674.33, "word": " مثال", "probability": 0.99267578125}, {"start": 674.33, "end": 674.77, "word": " و", "probability": 0.587890625}, {"start": 674.77, "end": 675.09, "word": " بدي", "probability": 0.55816650390625}, {"start": 675.09, "end": 675.81, "word": " أبدأ", "probability": 0.8494466145833334}, {"start": 675.81, "end": 676.89, "word": " بأبسط", "probability": 0.9685546875}, {"start": 676.89, "end": 677.73, "word": " مثال", "probability": 0.991455078125}, {"start": 677.73, "end": 679.17, "word": " example", "probability": 0.2376708984375}, {"start": 679.17, "end": 682.79, "word": " أول", "probability": 0.756591796875}, {"start": 682.79, "end": 683.77, "word": " مثال", "probability": 0.98486328125}, {"start": 683.77, "end": 688.09, "word": " خليني", "probability": 0.704345703125}, {"start": 688.09, "end": 688.45, "word": " أجعل", "probability": 0.5819498697916666}, {"start": 688.45, "end": 688.63, "word": " ال", "probability": 0.32763671875}, {"start": 688.63, "end": 688.91, "word": " group", "probability": 0.92626953125}, {"start": 688.91, "end": 689.53, "word": " قليلا", "probability": 0.9632161458333334}, {"start": 689.53, "end": 689.97, "word": " ثم", "probability": 0.943603515625}, {"start": 689.97, "end": 690.57, "word": " نتقل", "probability": 0.73858642578125}, {"start": 690.57, "end": 690.87, "word": " إلى", "probability": 0.59033203125}, {"start": 690.87, "end": 691.11, "word": " ال", "probability": 0.88232421875}, {"start": 691.11, "end": 691.45, "word": " ring", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 25, "seek": 72081, "start": 692.35, "end": 720.81, "text": "في حاجة بيبقى نسميها بنات الـtrivial subgroup مين الـtrivial subgroup؟ اللي فيها بس الـsubgroup اللي فيها مين؟ الـidentity element بس تمام يبقى ال set اللي فيش فيها ال zero هي عبارة عن subgroup كمان سؤال من مبادئ الرياضيات أخدنا any set is a subset of itself تمام كمان هنا", "tokens": [41185, 11331, 26108, 3660, 4724, 1829, 3555, 4587, 7578, 8717, 38251, 1829, 11296, 4724, 8315, 2655, 2423, 39184, 83, 470, 22640, 1422, 17377, 3714, 9957, 2423, 39184, 83, 470, 22640, 1422, 17377, 22807, 13672, 1829, 8978, 11296, 4724, 3794, 2423, 39184, 30131, 17377, 13672, 1829, 8978, 11296, 3714, 9957, 22807, 2423, 39184, 1078, 507, 4478, 4724, 3794, 46811, 10943, 7251, 3555, 4587, 7578, 2423, 992, 13672, 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"end": 1564.8, "word": " في", "probability": 0.908203125}, {"start": 1564.8, "end": 1565.54, "word": " المسائل", "probability": 0.8831787109375}, {"start": 1565.54, "end": 1566.08, "word": " المرة", "probability": 0.918701171875}, {"start": 1566.08, "end": 1566.68, "word": " القادمة", "probability": 0.9899088541666666}, {"start": 1566.68, "end": 1566.94, "word": " على", "probability": 0.226318359375}, {"start": 1566.94, "end": 1567.36, "word": " المرة", "probability": 0.968017578125}, {"start": 1567.36, "end": 1567.96, "word": " القادمة", "probability": 0.9934895833333334}, {"start": 1567.96, "end": 1568.44, "word": " حل", "probability": 0.86572265625}, {"start": 1568.44, "end": 1569.24, "word": " المسائل", "probability": 0.82110595703125}, {"start": 1569.24, "end": 1569.7, "word": " هنا", "probability": 0.97509765625}, {"start": 1569.7, "end": 1570.26, "word": " و", "probability": 0.70751953125}, {"start": 1570.26, "end": 1570.6, "word": " بدنا", "probability": 0.6866455078125}, {"start": 1570.6, "end": 1571.38, "word": " نشغلكم", "probability": 0.886328125}, {"start": 1571.38, "end": 1571.84, "word": " يكونوا", "probability": 0.8927408854166666}, {"start": 1571.84, "end": 1572.72, "word": " مشتغلين", "probability": 0.93623046875}, {"start": 1572.72, "end": 1573.6, "word": " آيو", "probability": 0.5607503255208334}, {"start": 1573.6, "end": 1574.9, "word": " سؤال", "probability": 0.8997395833333334}, {"start": 1574.9, "end": 1575.48, "word": " 8", "probability": 0.58251953125}, {"start": 1575.48, "end": 1576.26, "word": " و", "probability": 0.75}, {"start": 1576.26, "end": 1577.26, "word": " 13", "probability": 0.498779296875}, {"start": 1577.26, "end": 1578.42, "word": " و", "probability": 0.974609375}, {"start": 1578.42, "end": 1579.14, "word": " 19", "probability": 0.91552734375}, {"start": 1579.14, "end": 1580.14, "word": " و", "probability": 0.99658203125}, {"start": 1580.14, "end": 1581.3, "word": " 23", "probability": 0.74853515625}, {"start": 1581.3, "end": 1582.9, "word": " آه", "probability": 0.34332275390625}, {"start": 1582.9, "end": 1583.06, "word": " ثم", "probability": 0.6663818359375}, {"start": 1583.06, "end": 1583.58, "word": " أحط", "probability": 0.7789713541666666}, {"start": 1583.58, "end": 1584.06, "word": " كمان", "probability": 0.9375}, {"start": 1584.06, "end": 1585.02, "word": " 22", "probability": 0.9462890625}, {"start": 1585.02, "end": 1585.9, "word": " معاه", "probability": 0.778564453125}, {"start": 1585.9, "end": 1586.88, "word": " 22", "probability": 0.88818359375}, {"start": 1586.88, "end": 1587.46, "word": " و", "probability": 0.9921875}, {"start": 1587.46, "end": 1588.12, "word": " 23", "probability": 0.7021484375}], "temperature": 1.0}, {"id": 57, "seek": 161699, "start": 1589.93, "end": 1616.99, "text": "و .. و تمانية و عشرين و تلاتين و إتنين و تلاتين و تلاتة و تلاتين و تسعة و تلاتين و واحد و أربعين و ستة و أربعين و خمسين يا أبو عياسل من أول التمرين و من نص التمرين و من آخر التمرين", "tokens": [2407, 4386, 4032, 46811, 7649, 10632, 4032, 6225, 46309, 9957, 4032, 6055, 1211, 9307, 9957, 4032, 11933, 2655, 1863, 9957, 4032, 6055, 1211, 9307, 9957, 4032, 6055, 1211, 9307, 3660, 4032, 6055, 1211, 9307, 9957, 4032, 6055, 3794, 27884, 4032, 6055, 1211, 9307, 9957, 4032, 36764, 24401, 4032, 5551, 25513, 3615, 9957, 4032, 8608, 2655, 3660, 4032, 5551, 25513, 3615, 9957, 4032, 16490, 2304, 3794, 9957, 35186, 5551, 3555, 2407, 6225, 1829, 32277, 1211, 9154, 5551, 12610, 16712, 29973, 9957, 4032, 9154, 8717, 9381, 16712, 29973, 9957, 4032, 9154, 19753, 34740, 16712, 29973, 9957], "avg_logprob": -0.103618417915545, "compression_ratio": 2.404580152671756, "no_speech_prob": 0.0, "words": [{"start": 1589.93, "end": 1590.45, "word": "و", "probability": 0.93896484375}, {"start": 1590.45, "end": 1590.97, "word": " ..", "probability": 0.30712890625}, {"start": 1590.97, "end": 1591.27, "word": " و", "probability": 0.93017578125}, {"start": 1591.27, "end": 1592.29, "word": " تمانية", "probability": 0.9407552083333334}, {"start": 1592.29, "end": 1592.67, "word": " و", "probability": 0.9736328125}, {"start": 1592.67, "end": 1593.71, "word": " عشرين", "probability": 0.8714192708333334}, {"start": 1593.71, "end": 1593.93, "word": " و", "probability": 0.974609375}, {"start": 1593.93, "end": 1595.15, "word": " تلاتين", "probability": 0.97412109375}, {"start": 1595.15, "end": 1596.31, "word": " و", "probability": 0.9814453125}, {"start": 1596.31, "end": 1596.95, "word": " إتنين", "probability": 0.76202392578125}, {"start": 1596.95, "end": 1597.15, "word": " و", "probability": 0.99365234375}, {"start": 1597.15, "end": 1598.41, "word": " تلاتين", "probability": 0.983642578125}, {"start": 1598.41, "end": 1598.69, "word": " و", "probability": 0.99560546875}, {"start": 1598.69, "end": 1599.37, "word": " تلاتة", "probability": 0.9638671875}, {"start": 1599.37, "end": 1599.53, "word": " و", "probability": 0.82666015625}, {"start": 1599.53, "end": 1600.75, "word": " تلاتين", "probability": 0.981689453125}, {"start": 1600.75, "end": 1601.45, "word": " و", "probability": 0.984375}, {"start": 1601.45, "end": 1602.23, "word": " تسعة", "probability": 0.9930013020833334}, {"start": 1602.23, "end": 1602.57, "word": " و", "probability": 0.99755859375}, {"start": 1602.57, "end": 1603.55, "word": " تلاتين", "probability": 0.97998046875}, {"start": 1603.55, "end": 1603.73, "word": " و", "probability": 0.98583984375}, {"start": 1603.73, "end": 1604.27, "word": " واحد", "probability": 0.949462890625}, {"start": 1604.27, "end": 1604.51, "word": " و", "probability": 0.9765625}, {"start": 1604.51, "end": 1605.71, "word": " أربعين", "probability": 0.9271240234375}, {"start": 1605.71, "end": 1606.41, "word": " و", "probability": 0.99560546875}, {"start": 1606.41, "end": 1607.37, "word": " ستة", "probability": 0.9498697916666666}, {"start": 1607.37, "end": 1607.65, "word": " و", "probability": 0.966796875}, {"start": 1607.65, "end": 1608.59, "word": " أربعين", "probability": 0.9501953125}, {"start": 1608.59, "end": 1608.81, "word": " و", "probability": 0.99951171875}, {"start": 1608.81, "end": 1609.99, "word": " خمسين", "probability": 0.97021484375}, {"start": 1609.99, "end": 1611.55, "word": " يا", "probability": 0.85986328125}, {"start": 1611.55, "end": 1611.73, "word": " أبو", "probability": 0.6005859375}, {"start": 1611.73, "end": 1612.29, "word": " عياسل", "probability": 0.6729736328125}, {"start": 1612.29, "end": 1612.51, "word": " من", "probability": 0.91015625}, {"start": 1612.51, "end": 1612.97, "word": " أول", "probability": 0.97900390625}, {"start": 1612.97, "end": 1613.73, "word": " التمرين", "probability": 0.9811197916666666}, {"start": 1613.73, "end": 1613.85, "word": " و", "probability": 0.96240234375}, {"start": 1613.85, "end": 1614.05, "word": " من", "probability": 0.9677734375}, {"start": 1614.05, "end": 1614.39, "word": " نص", "probability": 0.9794921875}, {"start": 1614.39, "end": 1615.17, "word": " التمرين", "probability": 0.994140625}, {"start": 1615.17, "end": 1615.29, "word": " و", "probability": 0.9970703125}, {"start": 1615.29, "end": 1615.53, "word": " من", "probability": 0.982421875}, {"start": 1615.53, "end": 1616.01, "word": " آخر", "probability": 0.90576171875}, {"start": 1616.01, "end": 1616.99, "word": " التمرين", "probability": 0.99609375}], "temperature": 1.0}, {"id": 58, "seek": 162362, "start": 1617.8, "end": 1623.62, "text": "وفترة المرة القادمة نشوف إيش بدفس حلو منها", "tokens": [38688, 2655, 25720, 9673, 25720, 25062, 18513, 46007, 8717, 8592, 38688, 11933, 1829, 8592, 47525, 36178, 11331, 1211, 2407, 9154, 11296], "avg_logprob": -0.25710225918076257, "compression_ratio": 1.1323529411764706, "no_speech_prob": 0.0, "words": [{"start": 1617.8, "end": 1618.68, "word": "وفترة", "probability": 0.6185709635416666}, {"start": 1618.68, "end": 1619.36, "word": " المرة", "probability": 0.9501953125}, {"start": 1619.36, "end": 1620.04, "word": " القادمة", "probability": 0.99072265625}, {"start": 1620.04, "end": 1621.14, "word": " نشوف", "probability": 0.9856770833333334}, {"start": 1621.14, "end": 1621.8, "word": " إيش", "probability": 0.7037760416666666}, {"start": 1621.8, "end": 1622.28, "word": " بدفس", "probability": 0.363037109375}, {"start": 1622.28, "end": 1623.02, "word": " حلو", "probability": 0.9886067708333334}, {"start": 1623.02, "end": 1623.62, "word": " منها", "probability": 0.991943359375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1624.28225, "duration_after_vad": 1534.4193749999972}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9b28be3c21daae1e6d4ab2728c27f5a90f194766
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M.srt
@@ -0,0 +1,1387 @@
+1
+00:00:20,690 --> 00:00:25,730
+بسم الله الرحمن الرحيم ننتقل الآن إلى chapter 17
+
+2
+00:00:25,730 --> 00:00:32,410
+بعد أن أنهينا الـ chapter 16، chapter 17 يتكلم عن
+
+3
+00:00:32,410 --> 00:00:39,190
+الـ factorization of polynomial، تحليل كثيرات الحدود
+
+4
+00:00:39,190 --> 00:00:45,950
+أو تفكيك كثيرات الحدود إلى عوامل.  ممكن نقدر نفككها،
+
+5
+00:00:45,950 --> 00:00:52,550
+إلى عوامل، وممكن ما نقدرش. كيف ممكن نَقدر وكيف ممكن ما
+
+6
+00:00:52,550 --> 00:00:57,910
+نقدرش نفككها إلى عوامل؟ نبدأ بالتعريف الأول، يقول لي:
+
+7
+00:00:57,910 --> 00:01:03,010
+افترض أن D هو عبارة عن integral domain، وأخذنا
+
+8
+00:01:03,010 --> 00:01:08,850
+بولينوميال F(x) موجودة في F(x). من
+
+9
+00:01:08,850 --> 00:01:14,330
+هو F(x) هذا؟ ماذا العناصر التي فيه؟
+
+10
+00:01:14,330 --> 00:01:18,250
+ما هو شكل العنصر الموجود في F(x)؟
+
+11
+00:01:20,330 --> 00:01:25,330
+Polynomial، العناصر التي اتفقتها من أين؟ من الأعلى.
+
+12
+00:01:25,330 --> 00:01:33,370
+آه، لا لا لا، هذه خطأ، فهذه D[x]، يعني هذه D، نحن
+
+13
+00:01:33,370 --> 00:01:38,550
+نشتغل في integral domain في D[x] وليس في F[x].
+
+14
+00:01:38,550 --> 00:01:44,790
+ماذا هي D[x]؟ هي الـ polynomials التي عناصرها
+
+15
+00:01:44,790 --> 00:01:49,940
+من الـ...  المعَاملات التابعة
+
+16
+00:01:49,940 --> 00:01:54,580
+مأخوذة من الـ integral domain D، تمام؟ إذاً الـ
+
+17
+00:01:54,580 --> 00:01:59,920
+element F(x) هو كثيرات حدود، معاملات كثيرات
+
+18
+00:01:59,920 --> 00:02:03,940
+الحدود أو كثيرة الحدود هذه مأخوذة من أين؟ من الـ
+
+19
+00:02:03,940 --> 00:02:09,460
+integral domain D. طيب، الـ F(x) هذه ليست
+
+20
+00:02:09,460 --> 00:02:16,200
+Zero polynomial، يعني الـ F(x) لا
+
+21
+00:02:16,200 --> 00:02:22,300
+تساوي صفر،  و ليست a unit في D[x].
+
+22
+00:02:22,300 --> 00:02:27,480
+يعني هذا الـ F(x) ليس له معكوس، أنه has no
+
+23
+00:02:27,480 --> 00:02:33,040
+invertible element في D[x]. يبقى الـ F(x) عليها
+
+24
+00:02:33,040 --> 00:02:39,000
+شرطان: ليست كثيرة الحدود الصفرية، وليست لها معكوس. طيب، ماذا هذه؟ هذه الـ polynomial  أقول
+
+25
+00:02:39,000 --> 00:02:44,030
+عنها irreducible، يعني لا يمكن تفكيكها أو لا يمكن
+
+26
+00:02:44,030 --> 00:02:50,810
+تحليلها إلى حاصل ضرب two polynomials، three
+
+27
+00:02:50,810 --> 00:02:56,510
+polynomials، أكثر من ذلك. يبقى it's called
+
+28
+00:02:56,510 --> 00:03:00,310
+irreducible over the... if whenever أن حدث أن الـ F(
+
+29
+00:03:00,310 --> 00:03:06,610
+x) قدرنا نعبر عنها على حاصل ضرب two polynomials
+
+30
+00:03:06,610 --> 00:03:12,020
+موجودات في D[x]، يبقى واحدة من الاثنين: إما تبقى a
+
+31
+00:03:12,020 --> 00:03:18,400
+unit في D[x]. مرة ثانية أقول: أنا integral domain
+
+32
+00:03:18,400 --> 00:03:26,040
+D، أخذنا F(x) هو عنصر غير صفري وليس له معكوس، وهذا
+
+33
+00:03:26,040 --> 00:03:35,320
+العنصر موجود في D[x]، تمام. الـ D[x] هذا، العنصر الـ
+
+34
+00:03:35,320 --> 00:03:41,600
+F(x) الذي أخذته عندنا، هذا لو قدرنا نعبر عنه كحاصل
+
+35
+00:03:41,600 --> 00:03:49,200
+ضرب two polynomials موجودات في الـ D[x]، يبقى واحد
+
+36
+00:03:49,200 --> 00:03:54,960
+فيهم بدي يكون... ما هو واحد فيهم بدي يكون is a unit.
+
+37
+00:03:54,960 --> 00:04:00,220
+يبقى يا إما الـ G(x) يكون unit يا إما الـ H(x)
+
+38
+00:04:00,220 --> 00:04:08,620
+بدها تكون واحدة من الاثنين. إن قدرنا نعمل هذه
+
+39
+00:04:08,620 --> 00:04:13,820
+الشغلة، ما قدرناش، خلاص، يبقى irreducible، معناته لا
+
+40
+00:04:13,820 --> 00:04:18,900
+يمكن تفكيكها أو لا يمكن تحليلها. إذا كان بقدر الله
+
+41
+00:04:18,900 --> 00:04:24,820
+قدرنا نحللها أو قدرنا نفككها إلى حاصل ضرب Polynomials،
+
+42
+00:04:24,820 --> 00:04:31,720
+موجودة في D[x]، لازم واحد فيهم يكون unit. هذا
+
+43
+00:04:31,720 --> 00:04:37,090
+التعريف الأول. التعريف الثاني المرتبط به يقول:
+
+44
+00:04:37,090 --> 00:04:41,470
+عندي Polynomial ليست صفر وليست unit، لا unit ولا
+
+45
+00:04:41,470 --> 00:04:48,110
+صفر، اللي هو نفس الـ condition اللي في الأول فوق.
+
+46
+00:04:48,110 --> 00:04:50,890
+إذاً F(x) موجود في D[x]، الذي يكون irreducible،
+
+47
+00:04:50,890 --> 00:04:58,090
+أقول عنه ماذا؟ reducible. يبقى هذا العنصر الذي يكون غير
+
+48
+00:04:58,090 --> 00:05:04,320
+irreducible، يعني نفي الـ irreducible يعطيني من؟
+
+49
+00:05:04,320 --> 00:05:10,460
+reducible. يبقى نفي نفي الـ irreducible إثبات، يبقى
+
+50
+00:05:10,460 --> 00:05:15,360
+reducible. بنفي irreducible، ها not reducible،
+
+51
+00:05:15,360 --> 00:05:21,680
+يبقى نفي النفي إثبات، يبقى يصبح irreducible، يبقى
+
+52
+00:05:21,680 --> 00:05:27,120
+بقول عن الـ F(x) هذا irreducible، إذا كان not a
+
+53
+00:05:27,120 --> 00:05:34,680
+unit. طيب... طيب، السؤال الذي أريد أن أسأله، هذا الذي
+
+54
+00:05:34,680 --> 00:05:39,480
+محيرني قليلاً. إذا شفنا فاهمين زي ما أنا فاهم، والله
+
+55
+00:05:39,480 --> 00:05:43,900
+مش فاهمين، والله أفهمكم، وغير فاهمين، طالع. فأولاً،
+
+56
+00:05:43,900 --> 00:05:48,280
+إحنا قلنا خذ هذا integral domain، ورحنا حطينا
+
+57
+00:05:48,280 --> 00:05:52,600
+التعريف وما إلى ذلك، وأخذنا... يا أخي، سؤالي هو: هل
+
+58
+00:05:52,600 --> 00:05:58,000
+كل Polynomial بدها تبقى صحيحة هنا؟ يعني لو كانت
+
+59
+00:05:58,000 --> 00:06:04,360
+irreducible على integral domain، بدها تبقى
+
+60
+00:06:04,360 --> 00:06:08,940
+irreducible على كل integral domain؟ مجال الشيء،
+
+61
+00:06:08,940 --> 00:06:14,560
+مجال الشيء، ومش كل element كمان ينطبق عليه هذا
+
+62
+00:06:14,560 --> 00:06:19,500
+التعريف.  جاء الـ element الذي تأخذه، ينطبق عليه
+
+63
+00:06:19,500 --> 00:06:23,800
+هذا التعريف ويقول عنه irreducible، ما ينطبقش، خلاص،
+
+64
+00:06:23,800 --> 00:06:27,320
+ما أقدرش أقول irreducible. يبقى هذا الكلام الـ الـ
+
+65
+00:06:27,320 --> 00:06:31,770
+polynomial قد تكون irreducible على integral domain
+
+66
+00:06:31,770 --> 00:06:36,470
+وقد تكون reducible على integral domain آخر، صح؟
+
+67
+00:06:36,470 --> 00:06:42,210
+يبقى هذه هي التي نقولها، والآن سنوضح هذا الكلام.
+
+68
+00:06:42,210 --> 00:06:46,030
+بس قبل التوضيح، نُذَكّر بالـ two definitions مرة ثانية.
+
+69
+00:06:46,030 --> 00:06:49,750
+نثبت المعلومة، مشان نبدأ نبني عليها. هذه
+
+70
+00:06:49,750 --> 00:06:55,250
+integral domain. أخذت عنصر F(x) في D[x].
+
+71
+00:06:55,250 --> 00:06:59,890
+ماذا هذا العنصر؟ غير الصفري، يعني F(x) لا تساوي
+
+72
+00:06:59,890 --> 00:07:05,210
+صفر. اثنين، فالـ F(x) ليس unit، ماهو
+
+73
+00:07:05,210 --> 00:07:11,330
+معكوس. تمام. يبقى هذا أقول عنه Irreducible. إذا
+
+74
+00:07:11,330 --> 00:07:17,450
+بقدر الله قدرنا نكتب F(x) على حاصل ضرب two
+
+75
+00:07:17,450 --> 00:07:22,790
+polynomials موجودات في D[x]، يبقى واحدة منهم تكون unit.
+
+76
+00:07:22,790 --> 00:07:27,780
+غير هيك، يبعتلنا الله. طيب، التعريف الثاني الذي تكون
+
+77
+00:07:27,780 --> 00:07:34,200
+ليست صفر وليست unit وليست irreducible، يبقى
+
+78
+00:07:34,200 --> 00:07:40,640
+reducible. فلأ، يبقى نفي فوق irreducible. طيب،
+
+79
+00:07:40,640 --> 00:07:46,360
+الملاحظة الأولى: قلت لك perhaps، ربما، ماذا ربما؟ الـ F(
+
+80
+00:07:46,360 --> 00:07:52,610
+x) تبقى Irreducible على Integral Domain لكنها
+
+81
+00:07:52,610 --> 00:07:57,230
+Reducible على Integral Domain آخر. لم أقل For All
+
+82
+00:07:57,230 --> 00:08:02,850
+Integral Domains. أخذت Integral Domain واحد، وأخذت
+
+83
+00:08:02,850 --> 00:08:07,430
+عنصر موجود فيه، تبقى هذا لا ينطبق على كل Integral
+
+84
+00:08:07,430 --> 00:08:11,750
+Domain. يعني العنصر الذي أريد أن آخذه، F(x)، ممكن يكون
+
+85
+00:08:11,750 --> 00:08:17,680
+irreducible على integral domain و reducible على
+
+86
+00:08:17,680 --> 00:08:21,640
+integral domain آخر، كما سنراه من الأمثلة بعد
+
+87
+00:08:21,640 --> 00:08:26,260
+قليل. الملاحظة الثانية: طالما نتكلم على الـ F على الـ
+
+88
+00:08:26,260 --> 00:08:31,140
+integral domain، لنحكي على من؟ على الـ F. يبقى لو كان
+
+89
+00:08:31,140 --> 00:08:36,760
+الـ F فيه، أخذنا non-constant polynomial زي ما قلنا
+
+90
+00:08:36,760 --> 00:08:42,040
+فوق، non-constant polynomial، مش قادر أقول non-unit،
+
+91
+00:08:42,040 --> 00:08:46,430
+لأن الـ field في كل عنصر غير صفري هو unit، تمام؟ بطل
+
+92
+00:08:46,430 --> 00:08:52,750
+نتكلم عن الـ unit. يبقى non-constant polynomial F(
+
+93
+00:08:52,750 --> 00:08:57,630
+x) الموجود في الـ F[x]، اسميها الـ
+
+94
+00:08:57,630 --> 00:09:01,070
+reducible على F. الـ F ما قدرتُش أكتبها written as
+
+95
+00:09:01,070 --> 00:09:07,950
+the product of two non-constant polynomials of
+
+96
+00:09:07,950 --> 00:09:11,130
+lower degree. ماذا يعني؟ يعني الذي أقول عنها
+
+97
+00:09:11,130 --> 00:09:17,180
+irreducible، إن كانت عنصر غير صفري، اثنين، ما قدرش
+
+98
+00:09:17,180 --> 00:09:24,140
+أكتبها كحاصل ضرب two polynomials، درجة كل واحدة
+
+99
+00:09:24,140 --> 00:09:30,040
+فيهم أقل من درجة الـ polynomial الأصلية. هذا المقصود
+
+100
+00:09:30,040 --> 00:09:36,020
+هنا. of lower degree في F[x]. نوضح الصورة قليلاً. لو
+
+101
+00:09:36,020 --> 00:09:42,270
+قلت أني عندي polynomial F(x) تساوي x⁵
+
+102
+00:09:42,270 --> 00:09:49,330
+زائد ٣x² زائد ٢x زائد ١،
+
+103
+00:09:49,330 --> 00:09:53,570
+موجودة في field F[x]. تمام. الـ lower
+
+104
+00:09:53,570 --> 00:09:59,490
+degree له ٤ و ٣ و ٢ و ١ و صفر، كمان.
+
+105
+00:09:59,490 --> 00:10:04,990
+الصفر ما أقدرش أكتب polynomial مع الدرجة الصفرية، لأن
+
+106
+00:10:04,990 --> 00:10:08,610
+بصي، درجة الـ polynomial الثانية هي درجة الـ polynomial
+
+107
+00:10:08,610 --> 00:10:12,970
+الأصلية. هذا المقصود بـ of lower degree. الدرجة بتكون أي
+
+108
+00:10:12,970 --> 00:10:17,430
+شكل. ممكن إن قدرنا نحللها، واحدة من الدرجة الأولى،
+
+109
+00:10:17,430 --> 00:10:23,210
+واحدة من الدرجة الرابعة، واحدة من الدرجة الثانية،
+
+110
+00:10:23,210 --> 00:10:27,330
+واحدة من الدرجة الثالثة، وهكذا. يبقى هذا اسم التحليل
+
+111
+00:10:27,330 --> 00:10:32,890
+of lower degree. طيب، الـ F(x) أقول عنها is
+
+112
+00:10:32,890 --> 00:10:37,590
+irreducible إذا ما قدرناش نكتبها على صورة حاصل ضرب
+
+113
+00:10:37,590 --> 00:10:43,540
+two polynomials، درجة كل واحدة فيهم أقل من درجة الـ
+
+114
+00:10:43,540 --> 00:10:49,000
+polynomial الأصلية. هذه هي التي يقولونها. لما انتقلنا من
+
+115
+00:10:49,000 --> 00:10:54,380
+integral domain إلى field، صار التعريف اللي فوق
+
+116
+00:10:54,380 --> 00:11:00,120
+غيرناه إلى التعريف التالي: F(x) تُكتب على
+
+117
+00:11:00,120 --> 00:11:05,900
+حاصل ضرب two polynomials، لازم يكون درجة كل واحدة
+
+118
+00:11:05,900 --> 00:11:10,430
+من الاثنين أقل من درجة الـ polynomial الأصلية. إذا
+
+119
+00:11:10,430 --> 00:11:15,410
+ما قدرناش، يبقى هي irreducible. طيب قدرنا؟
+
+120
+00:11:15,410 --> 00:11:20,470
+reducible. على طول، القدرة، يبقى إذا ما قدرناش نكتب
+
+121
+00:11:20,470 --> 00:11:25,570
+الـ polynomial الأصلية على صورة حاصل ضرب two
+
+122
+00:11:25,570 --> 00:11:30,050
+polynomials of lower degree، يبقى الأصلية
+
+123
+00:11:30,050 --> 00:11:34,490
+irreducible. طيب قدرنا؟ يبقى تصبح reducible. هي التي
+
+124
+00:11:34,490 --> 00:11:39,420
+تقولها الملاحظة الثانية. قبل أن ندخل إلى الأمثلة،
+
+125
+00:11:39,420 --> 00:11:43,340
+في تساؤل عندكم؟ ندخل في الأمثلة؟ طيب، نبدأ في
+
+126
+00:11:43,340 --> 00:11:50,480
+المثال الأول. المثال الأول يقول ما يأتي: هذا
+
+127
+00:11:50,480 --> 00:11:56,520
+polynomial، هذا polynomial.
+
+128
+00:11:56,520 --> 00:12:01,080
+F(x) التي تساوي ٢x² زائد ٤ is
+
+129
+00:12:01,080 --> 00:12:12,230
+irreducible
+
+130
+00:12:12,230 --> 00:12:15,670
+over الـ... but irreducible over
+
+131
+00:12:15,670 --> 00:12:28,050
+الـ...  أنا أخذت Polynomial F(x) تساوي ٢x² زائد
+
+132
+00:12:46,060 --> 00:12:52,420
+أنا أخذت Polynomial F(x) تساوي ٢x² زائد
+
+133
+00:12:52,420 --> 00:12:58,480
+أربعة. أنا أزعم أن هذا الـ polynomial is irreducible على
+
+134
+00:12:58,480 --> 00:13:05,680
+الـ Q لكنها reducible على Z. طيب، السؤال هو: الـ Q
+
+135
+00:13:05,680 --> 00:13:12,580
+integral domain؟ هو integral domain. و Z integral domain؟
+
+136
+00:13:15,110 --> 00:13:19,910
+يبقى اثنين integral domains. يبقى هذول اثنين are
+
+137
+00:13:19,910 --> 00:13:27,730
+integral domains because الـ Q and الـ Z are
+
+138
+00:13:27,730 --> 00:13:38,330
+integral domains.
+
+139
+00:13:38,330 --> 00:13:47,750
+F(x) = ٢x² + ٤. هي بقدر
+
+140
+00:13:47,750 --> 00:13:54,690
+الله حللتُ الـ F(x) إلى حاصل ضرب، حاصل ضرب two
+
+141
+00:13:54,690 --> 00:14:00,570
+elements أو two factors. عاملين، هي العامل الأول، وهي
+
+142
+00:14:00,570 --> 00:14:07,930
+العامل الثاني. حللته هكذا. أقول: هذه irreducible over
+
+143
+00:14:07,930 --> 00:14:15,590
+Q. طيب، حللناها إلى عاملين. تمام. بيقول: لو طلع واحد فيهم
+
+144
+00:14:15,590 --> 00:14:21,070
+unit، تبقى irreducible. يبقى أنا قلت irreducible
+
+145
+00:14:21,070 --> 00:14:27,070
+لماذا؟ على من؟ على الـ Q، لأنه 2 is a unit في الـ
+
+146
+00:14:27,070 --> 00:14:35,730
+Q. من المعقول، سبعَة، اثنين؟ نصف موجود في الـ Q؟ نعم،
+
+147
+00:14:35,730 --> 00:14:40,160
+موجود في الـ Q. يبقى هذا because they are integral
+
+148
+00:14:40,160 --> 00:14:45,620
+domains and الـ F(x) = ٢
+
+149
+00:14:45,620 --> 00:14:57,580
+and الـ x² زائد ٢ موجودة في الـ Q. والاثنين
+
+150
+00:14:57,580 --> 00:15:05,340
+is a unit. but الـ
+
+151
+00:15:05,340 --> 00:15:13,030
+F(x) = ٢ في x² زائد ٢ is
+
+152
+00:15:13,030 --> 00:15:23,810
+reducible in Z[x]. هل
+
+153
+00:15:23,810 --> 00:15:32,230
+هذا unit في Z؟ ٢ unit في Z؟ لأن معكوسها يبقى نصف،
+
+154
+00:15:32,230 --> 00:15:38,110
+ونصف ليس موجود. يبقى هذا أقول عنها reducible. يبقى
+
+155
+00:15:38,110 --> 00:15:43,610
+قدرنا نحللها إلى two factors ولا واحد فيهم unit،
+
+156
+00:15:43,610 --> 00:15:49,230
+لكن في الأول في Q وطلع واحد فيهم unit، ومن هنا قلنا
+
+157
+00:15:49,230 --> 00:15:55,730
+irreducible. يعني قدرنا نحلل الـ polynomial لأن على
+
+158
+00:15:55,730 --> 00:16:01,510
+حاصل ضرب، حاصل ضرب two polynomials، بس واحدة
+
+159
+00:16:01,510 --> 00:16:06,130
+فيهم... والثانية ما عندناش مشكلة بها، ما عليها الشرط،
+
+160
+00:16:06,130 --> 00:16:08,950
+المهم واحدة فيهم يكون unit. وواحدة فيهم unit، يبقى
+
+161
+00:16:08,950 --> 00:16:15,950
+irreducible. طيب، قدرنا نحللها بدون مشاكل، يبقى هذا
+
+162
+00:16:15,950 --> 00:16:19,850
+reducible على Z و irreducible على الـ Q.  نعطي
+
+163
+00:16:19,850 --> 00:16:26,370
+مثالاً آخر.
+
+164
+00:16:26,370 --> 00:16:27,510
+مثلاً
+
+165
+00:16:50,580 --> 00:16:57,860
+مثلاً... مثلاً...
+
+169
+00:16:59,300 --> 00:17:09,920
+over the set of real numbers، but reducible
+
+170
+00:17:09,920 --> 00:17:19,200
+over the set of complex numbers، التي
+
+171
+00:17:19,200 --> 00:17:24,120
+هي main، التي هي C. السبب because
+
+172
+00:17:33,940 --> 00:17:38,460
+يبقى نفس الـ polynomial، غيرت الـ integral domains
+
+173
+00:17:38,460 --> 00:17:42,800
+الذي عندي، وانتقلت من الـ integral domains إلى main
+
+174
+00:17:42,800 --> 00:17:50,680
+إلى field. بقول: لو كان الـ F field، وعندك non
+
+175
+00:17:50,680 --> 00:17:54,360
+constant polynomial، يبقى هذه non-constant
+
+176
+00:17:54,360 --> 00:17:59,160
+polynomial. يبقى هذه أقول عنها reducible إذا
+
+177
+00:17:59,160 --> 00:18:04,350
+ما قدرتش أكتبها على شكل product of two non-constant
+
+178
+00:18:04,350 --> 00:18:10,450
+polynomials of lower degree. بقوله:  كويس، يبقى الـ
+
+179
+00:18:10,450 --> 00:18:15,430
+polynomial هذه irreducible على R، but reducible
+
+180
+0
+
+223
+00:23:02,810 --> 00:23:11,290
+ضرب two polynomials of lower degree and the X  الاطس
+
+224
+00:23:11,290 --> 00:23:21,830
+جذري اتنين I وال X ذاتي جذري اتنين I are of lower
+
+225
+00:23:21,830 --> 00:23:30,800
+degree degree ده هو degree than F يبقى الدرجة
+
+226
+00:23:30,800 --> 00:23:38,640
+سبعتهم أقل من مين أقل من درجة اللي هو ال ال
+
+227
+00:23:38,640 --> 00:23:44,540
+polynomial الأصلية اللي هي F of A ناخد كمان مثال
+
+228
+00:23:44,540 --> 00:23:50,280
+يبقى هذا مثال رقم 2 مثال رقم 3
+
+229
+00:23:53,800 --> 00:23:58,600
+The polynomial f
+
+230
+00:23:58,600 --> 00:24:10,320
+of x يساوى x تربيعه ناقص اتنين is irreducible
+
+231
+00:24:10,320 --> 00:24:13,380
+over
+
+232
+00:24:13,380 --> 00:24:20,240
+a cube but irreducible over R
+
+233
+00:24:27,920 --> 00:24:35,780
+معقول؟ طب من هنا نشوف ما هو السبب بيقول إيه؟
+
+234
+00:24:35,780 --> 00:24:41,280
+Irreducible على ليكيوم لكنها irreducible على ..
+
+235
+00:24:41,280 --> 00:24:47,680
+السؤال هو ليكيوم are are fields، مظهر؟ يفجر هنا
+
+236
+00:24:47,680 --> 00:24:58,610
+because أن ليكيوم عندك ال are are fieldsهذه
+
+237
+00:24:58,610 --> 00:25:05,490
+الناحية الأولى الناحية الثانية f of x هي x تربيع
+
+238
+00:25:05,490 --> 00:25:13,230
+ناقص اتنين بقدر أحلل x ناقص جذري اتنين في x زائد
+
+239
+00:25:13,230 --> 00:25:18,270
+جذري اتنين إذا قدرت أكتبها على حاصل ضرب two
+
+240
+00:25:18,270 --> 00:25:23,580
+polynomial الدرجة التي اتبعتهم أقل من 100أقل من
+
+241
+00:25:23,580 --> 00:25:26,480
+ضرر القلعون الملاصية، القلعون الملاصية من الدرجة
+
+242
+00:25:26,480 --> 00:25:29,800
+الثانية هتقول كل واحدة أقل من الدرجة الأولى اللي
+
+243
+00:25:29,800 --> 00:25:35,340
+هي أقل من اتنين طيب هل هذا ال element موجود في ال
+
+244
+00:25:35,340 --> 00:25:42,360
+IQ؟ لأ و هذا و شرط أساسي لازم يكونوا في ال IQ،
+
+245
+00:25:42,360 --> 00:25:47,740
+مظلوم؟ يعني هذا التحليل لا يمكن أن يتم داخل ال IQ
+
+246
+00:25:47,740 --> 00:25:53,570
+لأن جذر اتنين is an irrational numberما هو عدد
+
+247
+00:25:53,570 --> 00:26:01,850
+نسبي مش موجود في ال Q يبقى هنا F of X هذا بدي
+
+248
+00:26:01,850 --> 00:26:12,970
+أقين أن ال F of X is irreducible over ال Q السبب
+
+249
+00:26:12,970 --> 00:26:21,590
+because أن ال X ناقص جدر اتنين وال X زائد جدر
+
+250
+00:26:21,590 --> 00:26:30,780
+اتنين does not belong to Q بقى موجودة في R بينما
+
+251
+00:26:30,780 --> 00:26:38,860
+و اللي هو ال X ناقص جذر اتنين وال X زائد جذر اتنين
+
+252
+00:26:38,860 --> 00:26:46,400
+belongs to mean في R موجودة في R and each of them
+
+253
+00:26:46,400 --> 00:26:50,600
+each of them
+
+254
+00:26:53,300 --> 00:27:07,820
+Each of them is of lower degree than the F of X كل
+
+255
+00:27:07,820 --> 00:27:13,560
+واحد فيهم درجته أقل من درجة ال F of X العصرية ال F
+
+256
+00:27:13,560 --> 00:27:19,020
+of X العصرية من الدرجة الثانية كل واحد فيهم من
+
+257
+00:27:19,020 --> 00:27:25,860
+الدرجة الأولى والـ R is a field بهذا كلامنا صحيح طب
+
+258
+00:27:25,860 --> 00:27:30,680
+إحنا اللي هنعطينا بدل المثال تلاتة على integral
+
+259
+00:27:30,680 --> 00:27:37,460
+domain field مشهورة عندنا نتقل شوية مثال رقم أربع
+
+260
+00:27:37,460 --> 00:27:41,500
+مثال
+
+261
+00:27:41,500 --> 00:27:44,200
+رقم أربع بيقول ما تدا polynomial
+
+262
+00:27:49,510 --> 00:27:57,150
+f of x اللي بده يساوي x تكعيب زائد واحد is
+
+263
+00:27:57,150 --> 00:28:00,590
+irreducible
+
+264
+00:28:00,590 --> 00:28:10,610
+over Z تلاتة but irreducible
+
+265
+00:28:10,610 --> 00:28:15,510
+over
+
+266
+00:28:15,510 --> 00:28:18,330
+Z خمسة
+
+267
+00:28:22,770 --> 00:28:32,050
+معقول؟ فبس أنا بسأل هل Z تلاتة فيلد؟ أو Z خمسة؟
+
+268
+00:28:32,050 --> 00:28:37,730
+يبقى Z فيلد لأن Z P is A فيلد where ال P is a prime.
+
+269
+00:28:38,190 --> 00:28:44,730
+يبقى Z تلاتة هو فيلد و Z خمسة هو فيلد. يبقى إيه؟
+
+270
+00:28:44,730 --> 00:28:58,970
+Because Z تلاتة and Z خمسة are fields and
+
+271
+00:28:58,970 --> 00:29:01,990
+ال
+
+272
+00:29:01,990 --> 00:29:09,330
+F of X بده يساوي X تكعيب زائد واحد من وين صار
+
+273
+00:29:09,330 --> 00:29:13,690
+السؤال هذا أصعب من اللي جابه من التحليل اللي بدنا
+
+274
+00:29:13,690 --> 00:29:20,930
+نعمل لو جيت أحلل هذاممكن أقول لك اتنين X زائد واحد
+
+275
+00:29:20,930 --> 00:29:27,570
+في تلاتة X زائد واحد معقول التحليل هذا صحيح؟ تعال
+
+276
+00:29:27,570 --> 00:29:36,730
+نشوف اتنين في تلاتة ستة X تربيع تمام في Z تلاتة
+
+277
+00:29:36,730 --> 00:29:41,910
+صفر بطل يصير من الدرجة الثانية الباقي كله من
+
+278
+00:29:41,910 --> 00:29:48,090
+الدرجة الأولى يبقى هذا بالشكل هذا غير موجود في Z3
+
+279
+00:29:48,090 --> 00:29:56,750
+هل موجود في Z5 تعال نشوف يبقى 2 في 3 ب 6 X تربيع
+
+280
+00:29:56,750 --> 00:30:03,050
+في Z5 X تربيع واحدة مظبوط لأن ما نشيل الخمسة يبقى
+
+281
+00:30:03,050 --> 00:30:08,450
+من ال 6 واحد يبقى X تربيع واحدة هي هو يجعلنا X
+
+282
+00:30:08,450 --> 00:30:17,100
+تربيع نيجي لبعدهنا 2x و 3x و 5x في Z خمسة صفر
+
+283
+00:30:17,100 --> 00:30:21,380
+طاري ثرمان طلعنا بس واحد في واحد في واحد في واحد
+
+284
+00:30:21,380 --> 00:30:23,700
+في واحد في واحد في واحد في واحد
+
+285
+00:30:23,700 --> 00:30:24,860
+في واحد في واحد في واحد في واحد
+
+286
+00:30:24,860 --> 00:30:25,440
+في واحد في واحد في واحد في واحد
+
+287
+00:30:25,440 --> 00:30:26,020
+في واحد في واحد في واحد في واحد
+
+288
+00:30:26,020 --> 00:30:26,300
+في واحد في واحد في واحد في واحد
+
+289
+00:30:26,300 --> 00:30:27,120
+في واحد في واحد في واحد في واحد
+
+290
+00:30:27,120 --> 00:30:27,540
+في واحد في واحد في واحد في واحد
+
+291
+00:30:27,540 --> 00:30:28,700
+في واحد في واحد في واحد في واحد
+
+292
+00:30:28,700 --> 00:30:34,520
+في واحد في واحد في واحد في واحد
+
+293
+00:30:34,520 --> 00:30:44,430
+في واحد في واحدأنا بدي أسوأ X تربيع زائد واحد و اتنين
+
+294
+00:30:44,430 --> 00:30:54,350
+X زائد واحد و تلاتة X زائد واحد اتنين هذول موجودات
+
+295
+00:30:54,350 --> 00:31:00,070
+وين في Z خمسة و كذلك موجودات في Z تلاتة موجودات في
+
+296
+00:31:00,070 --> 00:31:05,630
+الاتنين لكن المهم بدنا مين بقى بس هذا لأ هذا لأ
+
+297
+00:31:05,630 --> 00:31:09,880
+ينفعشيبقى فتح مش موجود في زد تلاتة، زد تلاتة صفر
+
+298
+00:31:09,880 --> 00:31:18,320
+واحد واتنين، هذول اتنين موجودات في زد خمسة and
+
+299
+00:31:18,320 --> 00:31:32,080
+each of them is of lower degree than
+
+300
+00:31:36,560 --> 00:31:42,420
+اللي هو main than ال F ال F من الدرجة الثانية وكل
+
+301
+00:31:42,420 --> 00:31:46,540
+واحد من ال اتنين هدول من ال main من الدرجة الأولى
+
+302
+00:31:46,540 --> 00:31:51,560
+تبقى صلة ال F of X reducible في Z خمسة
+
+303
+00:31:51,560 --> 00:31:55,500
+وirreducible في Z تلاتة
+
+304
+00:32:11,970 --> 00:32:19,030
+نطرح أول نظرية على هذا الموضوع النظرية بتقول ما
+
+305
+00:32:19,030 --> 00:32:28,950
+بيذكر تاريخ ال
+
+306
+00:32:28,950 --> 00:32:35,810
+FDAC لكبت ال FDAC
+
+307
+00:32:42,760 --> 00:32:54,500
+F of X موجودة في كارتة F of X عند ال degree لل F
+
+308
+00:32:54,500 --> 00:33:04,560
+بدأت تساوي اتنين أو تلاتة say M then ال F then ال F
+
+309
+00:33:04,560 --> 00:33:09,200
+is reducible
+
+310
+00:33:10,690 --> 00:33:19,210
+radius of one لأن ال F is irreducible over capital
+
+311
+00:33:19,210 --> 00:33:32,690
+F F and only F F and only F and F of X has a zero
+
+312
+00:33:32,690 --> 00:33:38,670
+has a zero and no capital F
+
+313
+00:33:53,130 --> 00:34:00,830
+نقرا النظريه ثاني وقبل البرهنة نحاول نطرح سؤال ربما
+
+314
+00:34:00,830 --> 00:34:07,150
+هذا السؤال طرق على أذهانكم جال ال A phase أخدت
+
+315
+00:34:07,150 --> 00:34:12,870
+عنصر F of X موجود في capital F of X ضربت ال F of X
+
+316
+00:34:12,870 --> 00:34:17,370
+اتنين ما عندها مشكلة تلاتة ما عندها مشكلة اتنين أو
+
+317
+00:34:17,370 --> 00:34:23,940
+تلاتة سيارة بقول أن ال F is reducible على F if and
+
+318
+00:34:23,940 --> 00:34:30,260
+only if ال F of X هي Zero in capital F السؤال اللي
+
+319
+00:34:30,260 --> 00:34:35,580
+بدي أطرحه طب لو كان ال degree ل F هي اتنين ولا
+
+320
+00:34:35,580 --> 00:34:42,100
+تلاتة أربعة مثلاً خمسة ستة هذه نظرية صحيحة؟ لا ليست
+
+321
+00:34:42,100 --> 00:34:47,740
+صحيحة وسنثبت هذا الكلام عملياً بمثال إن شاء الله
+
+322
+00:34:47,740 --> 00:34:53,800
+بعد إيه؟ بعد أن أثبت هذه النظرية يبقى الـ O يبقى
+
+323
+00:34:53,800 --> 00:35:02,400
+أنا بدي أطلب أنها that ال F of X موجودة في capital
+
+324
+00:35:02,400 --> 00:35:15,300
+F of X with degree لل F هذا تساوي 2 أو 3 النظرية كل
+
+325
+00:35:15,300 --> 00:35:20,600
+F عندهم F يبقى الكلام بدي يصير وينالاتجاهية ناخد
+
+326
+00:35:20,600 --> 00:35:25,620
+الاتجاهية لما نوص مذات ثاني ثم العكس يبقى هنا
+
+327
+00:35:25,620 --> 00:35:36,140
+بالداخل أقول أسوم ذات افترض أن ال F is reducible
+
+328
+00:35:36,140 --> 00:35:39,540
+over
+
+329
+00:35:39,540 --> 00:35:47,160
+F then F
+
+330
+00:35:47,160 --> 00:35:54,970
+of Xهتصير حاصل ضرب ده اللي ده تبقى حاصل ضرب في
+
+331
+00:35:54,970 --> 00:36:06,070
+البرنامج يبقى g of x في h of x حيث ال g of x
+
+332
+00:36:06,070 --> 00:36:16,370
+و ال h of x هذه موجودة وين؟ في capital F of X and
+
+333
+00:36:16,370 --> 00:36:18,730
+h
+
+334
+00:36:19,560 --> 00:36:30,660
+of ال F و ال H of X أو ال G of X and اللي هو ال H
+
+335
+00:36:30,660 --> 00:36:40,300
+of X is of lower degree then
+
+336
+00:36:56,890 --> 00:37:02,670
+يبقى كل من الجيولتش بيكون من الدرجة الأولى لو قلنا
+
+337
+00:37:02,670 --> 00:37:07,250
+تلاتة يبقى على الأقل واحدة فيهم بيكون من وين
+
+338
+00:37:07,250 --> 00:37:12,530
+الدرجة اللي بيبقى على كل الأمرين الواحدة منهم
+
+339
+00:37:12,530 --> 00:37:19,250
+بيكون of the first degree مظبوط؟ يبقى that is
+
+340
+00:37:22,110 --> 00:37:38,150
+at least one of الـG of X or الـH of X has degree one
+
+341
+00:37:38,150 --> 00:37:44,270
+إذا واحدة من التنتين بدأت تكون من الدرجة الأولى لو
+
+342
+00:37:44,270 --> 00:37:48,430
+افترضنا إن الـG هذه من الدرجة الأولى
+
+343
+00:37:51,410 --> 00:38:02,950
+A degree تبع الـG of X أو B1 درجة هذه هي من الدرجة
+
+344
+00:38:02,950 --> 00:38:09,230
+الأولى لا يمكنك تدفع شكلها بالأعلى ثم الـG of X
+
+345
+00:38:09,230 --> 00:38:18,830
+بدأ تساوي AX زائد B A ممكن تساوي  صفر والـ B ممكن
+
+346
+00:38:18,830 --> 00:38:23,550
+تساوي صفر ما عندنا مشكلة لكن الـ A ممنوع تساوي صفر
+
+347
+00:38:23,550 --> 00:38:30,550
+فبحط فاصلة و الـ A does not equal to Zero فلو ساوت
+
+348
+00:38:30,550 --> 00:38:34,790
+صفر بتبطل يصير من الدرجة الأولى بيصير constant
+
+349
+00:38:34,790 --> 00:38:46,400
+polynomial طيب كويس ال F of X بنحصل ضرب تنتين يبقى
+
+350
+00:38:46,400 --> 00:38:54,700
+واحدة فيهم قلنا ax زائد b التانية h of x ال h of
+
+351
+00:38:54,700 --> 00:38:59,360
+x قد تكون من الدرجة الأولى وقد تكون من الدرجة
+
+352
+00:38:59,360 --> 00:39:03,260
+الثانية إحنا بنشتغل في integral domain  وفي
+
+353
+00:39:03,260 --> 00:39:10,940
+field في field يبقى كل عنصر له معكوس طبعاً طبعاً شو
+
+354
+00:39:10,940 --> 00:39:18,560
+رأيك لو جيت أنا قلت لك letالـ X يساوي ثابت A
+
+355
+00:39:18,560 --> 00:39:25,760
+inverse B مثلاً خذي الـ X يساوي N مثلاً بدي أشوف شو
+
+356
+00:39:25,760 --> 00:39:35,380
+بده تساوي يعني يبقى N بدنا ناخد ال F of ثابت A
+
+357
+00:39:35,380 --> 00:39:42,790
+inverse B تمام؟ بده تساوي يا شباب إنو يبقى A الـ A
+
+358
+00:39:42,790 --> 00:39:51,130
+inverse B بس بشارت سالب هاي سالب A inverse B
+
+359
+00:39:51,130 --> 00:39:59,090
+تمام؟ وهذه كلها .. كلها .. آه .. آه طبعاً فاهمين؟
+
+360
+00:39:59,090 --> 00:40:07,470
+في زائد B التاني هذه كلها في الـ H of X الـ F
+
+361
+00:40:07,470 --> 00:40:13,630
+inverse of B شلت ال X وحطيت قيمتها وهذه بدي
+
+362
+00:40:13,630 --> 00:40:22,470
+أحسبها كمان جدار ال H of سالب A inverse B هذه
+
+363
+00:40:22,470 --> 00:40:31,930
+بدي اياها تساوي سالب B زائد B مضروبة مين في ال H of سالب
+
+364
+00:40:31,930 --> 00:40:40,960
+A inverse B يعني جدار صفر يبقى هذه الـ 0 في ماذا؟
+
+365
+00:40:40,960 --> 00:40:47,400
+الـ H of سالب A inverse B يبقى يساوي 0 بمعنى هذا
+
+366
+00:40:47,400 --> 00:40:52,280
+الكلام، هذا الـ element أيش يمثل بالنسبة للدالة F؟
+
+367
+00:40:52,280 --> 00:41:00,300
+هو الـ 0  للدالة يبقى الـ X يساوي سالب A inverse B
+
+368
+00:41:00,300 --> 00:41:11,010
+هو A 0 for the function of the polynomial of the
+
+369
+00:41:11,010 --> 00:41:16,150
+polynomial of
+
+370
+00:41:16,150 --> 00:41:24,370
+f of x  عظمها المطلوب لفوفيكس هيزيرو انف يبقى اللي
+
+371
+00:41:24,370 --> 00:41:28,850
+هي zero هي أو جمالها اللي هو ال element اللي هو
+
+372
+00:41:28,850 --> 00:41:35,540
+صفر الآن بدنا نمشي معاكس للتجاه المعاكس يجب دلّا
+
+373
+00:41:35,540 --> 00:41:50,260
+conversion conversion
+
+374
+00:41:50,260 --> 00:41:58,060
+assume
+
+375
+00:41:58,060 --> 00:42:16,360
+that ال F has a zero in capital F  الآن
+
+376
+00:42:16,360 --> 00:42:25,540
+بدي أفترض أن ال F has a zero in capital F that is
+
+377
+00:42:25,540 --> 00:42:31,160
+that
+
+378
+00:42:31,160 --> 00:42:45,120
+is قايلة assume أن ال a is a zero of ال f then ال f
+
+379
+00:42:45,120 --> 00:42:51,800
+of a بدو يساوي قداش بدو يساوي zero مدام هذا zero
+
+380
+00:42:51,800 --> 00:42:57,680
+أخذنا تمارين في الشابتر الماضي أنه لو كان في عندي
+
+381
+00:42:57,680 --> 00:43:02,800
+zero لل function f يبقى ال x ناقص هذا العنصر هو
+
+382
+00:43:02,800 --> 00:43:10,700
+factor للدالة يبقى هنا هذا بدو يعطينا أن ال X
+
+383
+00:43:10,700 --> 00:43:24,340
+ناقص ال A is a factor for the polynomial F
+
+384
+00:43:24,340 --> 00:43:38,220
+of X that is  أن ال F of X يساوي ال X ناقص ال A في
+
+385
+00:43:38,220 --> 00:43:46,900
+ال Q of X or some
+
+386
+00:43:46,900 --> 00:43:56,520
+Q of X اللي موجودة في مين؟ في capital F of X إيش
+
+387
+00:43:56,520 --> 00:44:02,940
+تفسيرك لهذا الكلام؟ كتبته خلصت، يبقى إذن
+
+388
+00:44:03,350 --> 00:44:09,650
+reducible قدرت أحللها إلى حاصل ضرب two polynomials
+
+389
+00:44:09,650 --> 00:44:21,110
+هذا يعني this means this means
+
+390
+00:44:21,110 --> 00:44:32,270
+that أن ال F is reducible أو
+
+391
+00:44:32,270 --> 00:44:32,870
+حاصل ضرب
+
+392
+00:44:42,260 --> 00:44:50,420
+أعطيكم العافية نكمل إن شاء الله المحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3cfa65e4e752e573fa000d9ecb7d76997e10de34
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_postprocess.srt
@@ -0,0 +1,1568 @@
+1
+00:00:20,690 --> 00:00:25,730
+بسم الله الرحمن الرحيم ننتقل الان الى chapter 17
+
+2
+00:00:25,730 --> 00:00:32,410
+بعد انهينا اللى هو chapter 16 chapter 17 بتتكلم عن
+
+3
+00:00:32,410 --> 00:00:39,190
+ال factorization of polynomial تحليل كثيرات الحدود
+
+4
+00:00:39,190 --> 00:00:45,950
+او تفكيك كثيرات الحدود الى عوامل ممكن نقدر نفككم
+
+5
+00:00:45,950 --> 00:00:52,550
+الى عوامل وممكن مانقدرشكيف ممكن نقدر وكيف ممكن ما
+
+6
+00:00:52,550 --> 00:00:57,910
+نقدرش نفككهم إلى عامل نبدأ بالتعريف الأول يقول لي
+
+7
+00:00:57,910 --> 00:01:03,010
+افترض ان دوي هو عبارة عن integral domain واخدنا
+
+8
+00:01:03,010 --> 00:01:08,850
+كولونوميا ال F of X موجودة في capital F of X مين
+
+9
+00:01:08,850 --> 00:01:14,330
+هو capital F of X هذا بنا؟ ايش العناصر اللي فيه؟
+
+10
+00:01:14,330 --> 00:01:18,250
+ما هو الشكل العنصر اللي موجود في capital F of X
+
+11
+00:01:20,330 --> 00:01:25,330
+Polynomial العواب اللي اتفقتها من وين؟ من الاعلى
+
+12
+00:01:25,330 --> 00:01:33,370
+اه لأ لأ لأ هذه خطأ فهذه D of X يعني هذي دي احنا
+
+13
+00:01:33,370 --> 00:01:38,550
+بنشتغل في Integral لون في D of X وليس في F of X
+
+14
+00:01:38,550 --> 00:01:44,790
+يفجر مين هي D of X؟ هي ال polynomial اللي عناصرها
+
+15
+00:01:44,790 --> 00:01:49,940
+من ال .. مش اللي عناصرهاإن المعاملات تبعاتها
+
+16
+00:01:49,940 --> 00:01:54,580
+ماخودة من الـ integral domain D تمام؟ إذا ال
+
+17
+00:01:54,580 --> 00:01:59,920
+element F of X هو كثيرات حدود معاملات كثيرات
+
+18
+00:01:59,920 --> 00:02:03,940
+الحدود أو كثيرة الحدود هذه ماخودة من مين؟ من ال
+
+19
+00:02:03,940 --> 00:02:09,460
+integral domain D طيب ال F of X هذه بقالها مش
+
+20
+00:02:09,460 --> 00:02:16,200
+Google اللي ليست Zero polynomialيعني ال F of X لا
+
+21
+00:02:16,200 --> 00:02:22,300
+تساوي Zero أي واحدة اتنين nor a unit in D of X
+
+22
+00:02:22,300 --> 00:02:27,480
+يعني هذا ال F of X مالهاش معكوس انه has no
+
+23
+00:02:27,480 --> 00:02:33,040
+invertible element in D of X يبقى ال F of X عليها
+
+24
+00:02:33,040 --> 00:02:39,000
+شرطين ليست كثيرة الحدود الصفرية وليست Polynomial
+
+25
+00:02:39,000 --> 00:02:44,030
+لها معكوس طيب مالها هذه؟هذه ال polynomial بقول
+
+26
+00:02:44,030 --> 00:02:50,810
+عنها irreducible يعني لا يمكن تفكيكها او لا يمكن
+
+27
+00:02:50,810 --> 00:02:56,510
+تحليلها الى حاصل ضرب two polynomials three
+
+28
+00:02:56,510 --> 00:03:00,310
+polynomials اكتر من ذلك يبقى it's called
+
+29
+00:03:00,310 --> 00:03:06,610
+irreducible over the if whenever ان حدث ان ال f of
+
+30
+00:03:06,610 --> 00:03:12,020
+x قدرنا نعكر عنها على حاصل ضربtwo polynomials
+
+31
+00:03:12,020 --> 00:03:18,400
+موجودات في D of X يبقى واحدة من اتنتين بدأت تبقى a
+
+32
+00:03:18,400 --> 00:03:26,040
+unit in D of X مرة تانية بقول انا integral domain
+
+33
+00:03:26,040 --> 00:03:35,320
+D أخدنا F of X هو عنصر غير صفري وليس له معكوس وهذا
+
+34
+00:03:35,320 --> 00:03:41,600
+العنصر موجود في D of X تمامال D of X هذا العنصر ال
+
+35
+00:03:41,600 --> 00:03:49,200
+F of X اللي أخدته عندنا هذا لو جدرت أعبر عنه كحاصل
+
+36
+00:03:49,200 --> 00:03:54,960
+ضرب two chronomials موجودات في ال D of X يبقى واحد
+
+37
+00:03:54,960 --> 00:04:00,220
+فيهم بدي يكون ما هو واحد فيهم بدي يكون is a unit
+
+38
+00:04:00,220 --> 00:04:08,620
+يبقى يا إما ال D of X بيكون unitيا إما ال H of X
+
+39
+00:04:08,620 --> 00:04:13,820
+بدها تكون واحد من الاتنين إن جدرنا نعمل هذه
+
+40
+00:04:13,820 --> 00:04:18,900
+الشغلة، ماجدرناش خلاص، يبقى irreducible، معناته لا
+
+41
+00:04:18,900 --> 00:04:24,820
+يمكن تفكيكها أو لا يمكن تحليلها، إذا كان بقدر الله
+
+42
+00:04:24,820 --> 00:04:31,720
+جدرنا نحللها أو جدرنا نفككها إلى حصل ضربهم صغير،
+
+43
+00:04:31,720 --> 00:04:37,090
+موجود في D of X لازم واحد فيهم يكونionate هذا
+
+44
+00:04:37,090 --> 00:04:41,470
+التعريف الأولى التعريف التاني المرتبط فيه بيقول
+
+45
+00:04:41,470 --> 00:04:48,110
+عندي بلونوميا ليست zero وليست unit لا unit ولا
+
+46
+00:04:48,110 --> 00:04:50,890
+zero اللي هو نفس ال condition اللي في الأول فوق
+
+47
+00:04:50,890 --> 00:04:58,090
+answer f of x موجود في DOS اللي بيكون irreducible
+
+48
+00:04:58,090 --> 00:05:04,320
+بقول عنه ايش? reducibleيبجى هذا العنصر اللى بيكونش
+
+49
+00:05:04,320 --> 00:05:10,460
+irreducible يعني نفي ال irreducible بيعطيني مين؟
+
+50
+00:05:10,460 --> 00:05:15,360
+irreducible يبجى نفي نفي النفي اثبات يبجى
+
+51
+00:05:15,360 --> 00:05:21,680
+irreducible بننفي irreducible ها not reducible
+
+52
+00:05:21,680 --> 00:05:27,120
+يبجى نفي النفي اثبات يبجى بصير irreducible يبجى
+
+53
+00:05:27,120 --> 00:05:34,680
+بقول عن ال F of X هدا irreducibleإذا كان not a
+
+54
+00:05:34,680 --> 00:05:39,480
+radius طب .. طب السؤال اللي بدي أسأله هذا اللي
+
+55
+00:05:39,480 --> 00:05:43,900
+محيرني شوية إذا شوفوا فاهمين زي ما انا فاهم و الله
+
+56
+00:05:43,900 --> 00:05:48,280
+مش فاهمين و الله فاهمكم و غير فاهمين طالع فأول
+
+57
+00:05:48,280 --> 00:05:52,600
+احنا قولنا خد دي integral domain و روحنا حطينا
+
+58
+00:05:52,600 --> 00:05:58,000
+التعريف و ما إلى ذلك و أخدنا يا أخوك سؤالي هو هل
+
+59
+00:05:58,000 --> 00:06:04,360
+كل polynomialبدها تبقى صحيحة هنا؟ يعني لو كانت
+
+60
+00:06:04,360 --> 00:06:08,940
+irreducible على integral domain، بدها تبقى
+
+61
+00:06:08,940 --> 00:06:14,560
+irreducible على كل integral domain؟ مجال الشيء،
+
+62
+00:06:14,560 --> 00:06:19,500
+مجال الشيء، ومش كل element كمان ينطبق عليه هذا
+
+63
+00:06:19,500 --> 00:06:23,800
+التعريف، جال ال element اللي بتاخده، ينطبق عليه
+
+64
+00:06:23,800 --> 00:06:27,320
+هذا التعريف ويقول عنه irreducible، ماينطبقش خلاص،
+
+65
+00:06:27,320 --> 00:06:31,770
+ماقدرش أقول irreducibleيبقى هذا الكلام ال ال
+
+66
+00:06:31,770 --> 00:06:36,470
+polynomial قد تكون irreducible على integral domain
+
+67
+00:06:36,470 --> 00:06:42,210
+وقد تكون reducible على integral domain آخر صح؟
+
+68
+00:06:42,210 --> 00:06:46,030
+يبقى هاي اللي احنا بنقوله والان هنوضح لكذا الكلام
+
+69
+00:06:46,030 --> 00:06:49,750
+بس قبل التوضيح بذاري على two definitions مرة تانية
+
+70
+00:06:49,750 --> 00:06:55,250
+نثبت المعلومة مشان نبدأ نبدأ نبني عليها دي
+
+71
+00:06:55,250 --> 00:06:59,890
+integral domainأخدت عنصر F of X في D of E of X
+
+72
+00:06:59,890 --> 00:07:05,210
+ماله هذا العنصر غير الصفري يعني F of X لا تساوي
+
+73
+00:07:05,210 --> 00:07:11,330
+Zero اتنين فال F of X ليس Unit ماهواش عنصر ماهو
+
+74
+00:07:11,330 --> 00:07:17,450
+معكس تمام يبقى هذا بقول عنه Irreducible فيديو إذا
+
+75
+00:07:17,450 --> 00:07:22,790
+بقدر الله جدرنا نكتب F of X على حاصل ضرب two
+
+76
+00:07:22,790 --> 00:07:27,780
+polynomials موجوداتفى دى يبقى واحدة منهم يبقى unit
+
+77
+00:07:27,780 --> 00:07:34,200
+غير هيك يبعتلنا الله طيب التعريف التانى اللى بتكون
+
+78
+00:07:34,200 --> 00:07:40,640
+ليست zero وليست unit وليست irreducible يبقى
+
+79
+00:07:40,640 --> 00:07:46,360
+irreducible فلأ يبقى نافلة فوق irreducible طيب
+
+80
+00:07:46,360 --> 00:07:52,610
+الملاحظة الأولى قلت لك perhaps ربما ايش ربماالـ F
+
+81
+00:07:52,610 --> 00:07:57,230
+of X تبقى Irreducible على Integral Domain لكنها
+
+82
+00:07:57,230 --> 00:08:02,850
+Reducible على Integral Domain أخر لما قلتش For All
+
+83
+00:08:02,850 --> 00:08:07,430
+Integral Domains أخدت Integral Domain واحد واخدت
+
+84
+00:08:07,430 --> 00:08:11,750
+عنصر موجود فيه تبقى هذا لا ينفذق على كل Integral
+
+85
+00:08:11,750 --> 00:08:17,680
+Domain يعني العنصر اللي بدي أخده F of Xممكن يكون
+
+86
+00:08:17,680 --> 00:08:21,640
+irreducible على integral domain وreducible على
+
+87
+00:08:21,640 --> 00:08:26,260
+integral domain أخر كما ستراهنا من الأمثلة بعد
+
+88
+00:08:26,260 --> 00:08:31,140
+قليل الملاحظة التانية فاطلنا نتكلم على ال F على ال
+
+89
+00:08:31,140 --> 00:08:36,760
+integral domain لنحكي على مين على ال F يبقى لو كان
+
+90
+00:08:36,760 --> 00:08:42,040
+ال F فيه أخدنا non constant polynomial زي ما قلنا
+
+91
+00:08:42,040 --> 00:08:46,430
+فوق non constant polynomialمش قادر اقول non-unit
+
+92
+00:08:46,430 --> 00:08:52,750
+لإن الفيل في كل عمصر غير صفري هو unit تمام؟ بطل
+
+93
+00:08:52,750 --> 00:08:57,630
+نتكلم عن ال unit يبقى non-constant polynomial F of
+
+94
+00:08:57,630 --> 00:09:01,070
+X اللي موجود في ال capital F of X بسميها ال
+
+95
+00:09:01,070 --> 00:09:07,950
+reduceable على F F ال F ماقدرتش اكتبها written as
+
+96
+00:09:07,950 --> 00:09:11,130
+the product of two non-constant polynomials of
+
+97
+00:09:11,130 --> 00:09:17,180
+lower degree ايش يعني؟يعني اللي بقول عنها
+
+98
+00:09:17,180 --> 00:09:24,140
+irreducible إن كانت عنصر غير صفري إتنين ماقدرش
+
+99
+00:09:24,140 --> 00:09:30,040
+أكتبها كحاصل ضرب two polynomials درجة كل واحدة
+
+100
+00:09:30,040 --> 00:09:36,020
+فيهم أقل من درجة ال polynomial الأصلية هي المقصود
+
+101
+00:09:36,020 --> 00:09:42,270
+هنا of lower degree in F of X نوضح الصورة شويةلو
+
+102
+00:09:42,270 --> 00:09:49,330
+قلت اني عندي polynomial f of x تساوي اكسوس خمسة
+
+103
+00:09:49,330 --> 00:09:53,570
+زائد تلاتة اكس تربية زائد اتنين اكس زائد واحد
+
+104
+00:09:53,570 --> 00:09:59,490
+موجودة في field capital F of X تمام ال lower
+
+105
+00:09:59,490 --> 00:10:04,990
+degree ليه اربعة و تلاتة و اتنين و واحد و صفر كمان
+
+106
+00:10:04,990 --> 00:10:08,610
+الصفر ماقدرش اكتب polynomial مع الدرجة الصفرية لان
+
+107
+00:10:08,610 --> 00:10:12,970
+بصي درجة ال polynomial التانيةهي درجة الكلوميا
+
+108
+00:10:12,970 --> 00:10:17,430
+الأصلية هذا قلق لأ of lower degree الدرجة بتكون اي
+
+109
+00:10:17,430 --> 00:10:23,210
+شكل ممكن إن جدرت أحلله واحدة من الدرجة الأولى
+
+110
+00:10:23,210 --> 00:10:27,330
+واحدة من الدرجة الرابعة واحدة من الدرجة التانية
+
+111
+00:10:27,330 --> 00:10:32,890
+واحدة من الدرجة التالتة وهكذا يبقى هذا اسم التحليل
+
+112
+00:10:32,890 --> 00:10:37,590
+of lower degree طيب ال F of X بقول عنها is
+
+113
+00:10:37,590 --> 00:10:43,540
+irreducible إذا ما جدرتشأكتبها على صورة Haselberg
+
+114
+00:10:43,540 --> 00:10:49,000
+two polynomials درجة كل واحدة فيهم أقل من درجة ال
+
+115
+00:10:49,000 --> 00:10:54,380
+polynomial الأصلية هاي اللي بيقولوا لما انتقلنا من
+
+116
+00:10:54,380 --> 00:11:00,120
+integral domain إلى field صار التعريف اللي فوق
+
+117
+00:11:00,120 --> 00:11:05,900
+غيرناه إلى التعريف التالي f of x بتكتب على
+
+118
+00:11:05,900 --> 00:11:10,430
+Haselberg two polynomialsلازم يكون درجة كل واحدة
+
+119
+00:11:10,430 --> 00:11:15,410
+من التنتين اقل من درجة ال polynomial الأصلية، إذا
+
+120
+00:11:15,410 --> 00:11:20,470
+ماقدرناش، يبقى هي irreducible، طب قدرنا؟
+
+121
+00:11:20,470 --> 00:11:25,570
+Irreducible، على طول القدر، يبقى إذا ماقدرناش نكتب
+
+122
+00:11:25,570 --> 00:11:30,050
+ال polynomial الأصلية على صيرة لحاصل ضرب to
+
+123
+00:11:30,050 --> 00:11:34,490
+polynomials of lower degree، يبقى الأصلية
+
+124
+00:11:34,490 --> 00:11:39,420
+irreducible، طب قدرنا؟يبقى بصير رديو سفر. هي اللي
+
+125
+00:11:39,420 --> 00:11:43,340
+بتقوله الملاحظة التانية. قبل أن ندخل إلى الأمثلة،
+
+126
+00:11:43,340 --> 00:11:50,480
+في تساؤل عندكم؟ ندخل في الأمثلة؟ طيب، نبدأ في
+
+127
+00:11:50,480 --> 00:11:56,520
+المثال الأول. المثال الأول بيقول ما يأتي ده
+
+128
+00:11:56,520 --> 00:12:01,080
+polynomial، ده polynomial.
+
+129
+00:12:03,560 --> 00:12:12,230
+F of Xاللي تساوي اتنين X عربية زائد أربعة is
+
+130
+00:12:12,230 --> 00:12:15,670
+irreducible
+
+131
+00:12:15,670 --> 00:12:28,050
+over لكي و but irreducible over
+
+132
+00:12:46,060 --> 00:12:52,420
+أنا أخدت برنامج F of X مزاوية اتنين X تربية زائد
+
+133
+00:12:52,420 --> 00:12:58,480
+أربعة أنا أزعم أن هذه البرنامج is irreducible على
+
+134
+00:12:58,480 --> 00:13:05,680
+الـQ لكنها irreducible على Z طب السؤال هو الـQ
+
+135
+00:13:05,680 --> 00:13:12,580
+انتجرال دومان؟ فهو انتجرال دومان وZ انتجرال دومان؟
+
+136
+00:13:15,110 --> 00:13:19,910
+يبقى اتنين integral domains يبقى هذول اتنتين are
+
+137
+00:13:19,910 --> 00:13:27,730
+integral domains because ال Q and ال Z are
+
+138
+00:13:27,730 --> 00:13:38,330
+integral domains and
+
+139
+00:13:38,330 --> 00:13:47,750
+F of Xبقدر اقول اتنين X تربية زائد اتنين هي بقدر
+
+140
+00:13:47,750 --> 00:13:54,690
+الله حللت ال F of X إلى حاصل ضرمين حاصل ضرم two
+
+141
+00:13:54,690 --> 00:14:00,570
+elements او two factors عاملين هي العامل الأول وهي
+
+142
+00:14:00,570 --> 00:14:07,930
+العامل الثاني حللته عنيش بقول هذه irreducible over
+
+143
+00:14:07,930 --> 00:14:15,590
+Qطب حللتها إلى عاملين تمام بيقول لو طلع واحد فيهم
+
+144
+00:14:15,590 --> 00:14:21,070
+unit تبقى irreducible يبقى انا قلت irreducible
+
+145
+00:14:21,070 --> 00:14:27,070
+ليش؟ على مين؟ على ال EQ لإنه اتنين is a unit في ال
+
+146
+00:14:27,070 --> 00:14:35,730
+EQ مين المعقود سبعة اتنين؟ نص موجود في ال EQ؟ اه
+
+147
+00:14:35,730 --> 00:14:40,160
+موجود في ال EQيبقى هادى because are integral
+
+148
+00:14:40,160 --> 00:14:45,620
+domains and ال F والاتنين
+
+149
+00:14:45,620 --> 00:14:57,580
+and ال X تربية زائد اتنين موجودة في ال Q والاتنين
+
+150
+00:14:57,580 --> 00:15:05,340
+is a unit but ال
+
+151
+00:15:05,340 --> 00:15:13,030
+F of Xتساوي اتنين في X تربيع زائد اتنين is
+
+152
+00:15:13,030 --> 00:15:23,810
+reducible in Z of X هل
+
+153
+00:15:23,810 --> 00:15:32,230
+هذا unit في Z؟ اتنين unit في Z؟ لأن معكوس تبقى و
+
+154
+00:15:32,230 --> 00:15:38,110
+نص، و نص مش موجوديبقى هذا بقول عنها Reducible يبقى
+
+155
+00:15:38,110 --> 00:15:43,610
+جدرنا نحللها إلى two factors وولا واحد فيهم unit
+
+156
+00:15:43,610 --> 00:15:49,230
+لكن في الأول فلكي وطلع واحد فيهم unit ومن هنا قلنا
+
+157
+00:15:49,230 --> 00:15:55,730
+Irreducible يعني جدرنا نحط ال polynomial لأن على
+
+158
+00:15:55,730 --> 00:16:01,510
+حاصل بلاصيرة حاصل ضارب two polynomial بس واحدة
+
+159
+00:16:01,510 --> 00:16:06,130
+فيهموالتانية مانعاش مشكلة بيها ما عليها الشرط
+
+160
+00:16:06,130 --> 00:16:08,950
+المهم واحدة فيهم يكون unit وواحدة فيهم unit يبقى
+
+161
+00:16:08,950 --> 00:16:15,950
+irreducible طيب جدرنا انحللهم بدون مشاكل يبقى هذا
+
+162
+00:16:15,950 --> 00:16:19,850
+strategy اتنين في x تربيه زائد اتنين يبقى
+
+163
+00:16:19,850 --> 00:16:26,370
+reducible على z وirreducible عالميا على ال Q نعطي
+
+164
+00:16:26,370 --> 00:16:27,510
+مثلا اخر
+
+165
+00:16:50,580 --> 00:16:53,160
+يبقى مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+166
+00:16:53,160 --> 00:16:53,360
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+167
+00:16:53,360 --> 00:16:53,760
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+168
+00:16:53,760 --> 00:16:57,860
+مثلًا مثلًا مثلًا مثلًا
+
+169
+00:16:59,300 --> 00:17:09,920
+over a على ال six real numbers but ولكن reducible
+
+170
+00:17:09,920 --> 00:17:19,200
+ولكن reducible over ال six of complex numbers اللي
+
+171
+00:17:19,200 --> 00:17:24,120
+هي main اللي هي C السبب because
+
+172
+00:17:33,940 --> 00:17:38,460
+يبقى نفس ال paranormal غيرت ال integral domains
+
+173
+00:17:38,460 --> 00:17:42,800
+اللي عندى وانتقل من ال integral domains الى main
+
+174
+00:17:42,800 --> 00:17:50,680
+الى field بقول لو كان ال F field هو عندك non
+
+175
+00:17:50,680 --> 00:17:54,360
+constant paranormal يبقى هيها non constant
+
+176
+00:17:54,360 --> 00:17:59,160
+paranormal يبقى هذه بقول عنها ال reduce اذا
+
+177
+00:17:59,160 --> 00:18:04,350
+ماقدرتش اكتبها على شكل productالـ two non constant
+
+178
+00:18:04,350 --> 00:18:10,450
+polynomials of lower degree بقوله كويس يبقى ال
+
+179
+00:18:10,450 --> 00:18:15,430
+polynomial هذه irreducible على R both reducible
+
+180
+00:18:15,430 --> 00:18:27,570
+على C ليه؟ لأن الـ R and الـ C are integral R
+
+181
+00:18:27,570 --> 00:18:28,510
+fields
+
+182
+00:18:33,400 --> 00:18:41,540
+طيب في ال 6th real number بقدر احلل هذه الى حاصر
+
+183
+00:18:41,540 --> 00:18:49,180
+ضرب تعالى نشوف الان بيدادي لل F of X يساوي 2 X
+
+184
+00:18:49,180 --> 00:18:57,340
+تربيع زائد 2 يقولى على الفيل إذا عندك non constant
+
+185
+00:18:57,340 --> 00:19:01,900
+polynomial هيها non constant polynomialis called
+
+186
+00:19:01,900 --> 00:19:07,240
+irreducible if ال if cannot be written as a
+
+187
+00:19:07,240 --> 00:19:13,700
+product of two non-conustant polynomials تقدروا
+
+188
+00:19:13,700 --> 00:19:19,600
+تكتبوا هذه ك product of non-conustant polynomials؟
+
+189
+00:19:19,600 --> 00:19:25,800
+مقدرش يعني مقدرش اتنين هذه أستبدلها ب polynomial
+
+190
+00:19:25,800 --> 00:19:31,600
+تانية ماهياش conustant يبقى هذه إيش؟irreducible
+
+191
+00:19:31,600 --> 00:19:39,200
+يبقى فيه ال F of X هذه is irreducible
+
+192
+00:19:39,200 --> 00:19:49,880
+over R زي ما قلنا irreducible over R لإنها since
+
+193
+00:19:49,880 --> 00:19:55,300
+الإتنين is a constant
+
+194
+00:20:05,840 --> 00:20:13,000
+فولونوميا طيب الآن أنا بقول irreducible على R لكن
+
+195
+00:20:13,000 --> 00:20:21,460
+أزعم أنها irreducible على ال IQ يبقى هنا بعض ولكن
+
+196
+00:20:21,460 --> 00:20:31,480
+ال F of X يساوي 2 في X تربيه زائد 2 الradiusable
+
+197
+00:20:31,480 --> 00:20:43,920
+over set of complex numbers since لإن ال F of X
+
+198
+00:20:43,920 --> 00:20:50,940
+بقدر أكتبها على الشكل تاني نين بدي أكتبها على صيرة
+
+199
+00:20:50,940 --> 00:20:58,900
+حاصل ضرج ل two complex numbers ودرجتهمأقل من درجة
+
+200
+00:20:58,900 --> 00:21:03,740
+القولونوميا الأصلية القولونوميا الأصلية من الدرجة
+
+201
+00:21:03,740 --> 00:21:10,320
+الثانية يبقى بدي أكتب التنتين هذول كحاصل ضرب من
+
+202
+00:21:10,320 --> 00:21:14,820
+الدرجة الأولى ليه أقل من الدرجة الثانية مش هقول
+
+203
+00:21:14,820 --> 00:21:18,740
+واحدة من الدرجة الصفرية وواحدة من الدرجة التانية
+
+204
+00:21:18,740 --> 00:21:21,720
+يبقى لو قلت واحدة من الدرجة التانية صار زي الأصلية
+
+205
+00:21:21,720 --> 00:21:26,500
+يبقى هذا يتناقض مع الكلام اللي احنا قلناه اتنين
+
+206
+00:21:26,780 --> 00:21:31,780
+يتنخذ ان الاتنين constant و هنا قلنا non constant
+
+207
+00:21:31,780 --> 00:21:37,480
+polynomial product of two non constant صارت واحدة
+
+208
+00:21:37,480 --> 00:21:42,580
+constant يبقى هنا في عيبين لو قلنا اللي هو
+
+209
+00:21:42,580 --> 00:21:47,340
+irreducible انه اتنين اللي هو ماهياش non constant
+
+210
+00:21:47,340 --> 00:21:52,480
+صارت constant اتنين الاتنين ماهماش of lower degree
+
+211
+00:21:52,480 --> 00:21:57,690
+صحيح ال constant polynomialال degree تبعها أقل من
+
+212
+00:21:57,690 --> 00:22:01,590
+اتنين لكن التانية لأ ال degree تبعها يسوى اتنين
+
+213
+00:22:01,590 --> 00:22:06,570
+يبقى عيبين موجودين في وين في السواق يبقى هذا بدي
+
+214
+00:22:06,570 --> 00:22:12,090
+أحللها طبعا انتوا أخدتوا complex number بقدر أحلل
+
+215
+00:22:12,090 --> 00:22:19,950
+هذه و أقول ناقص جدر اتنين في I وهذه ال X زائد جدر
+
+216
+00:22:19,950 --> 00:22:28,590
+اتنين في Iصحيه كده؟ تعالى نشوف هذا تحرير الفرق بين
+
+217
+00:22:28,590 --> 00:22:35,710
+المرابعين مظبوط؟ مربع الأولى في X ترابية هيه و هي
+
+218
+00:22:35,710 --> 00:22:41,070
+اتنين اللي برا هي اضاينا برا ناقص مربع التانية جذر
+
+219
+00:22:41,070 --> 00:22:48,130
+اتنين I لكل ترابية باتنين في سالب I وعندي سالب
+
+220
+00:22:48,130 --> 00:22:53,330
+يبقى بصير زائد اتنين يبقى زائد اتنين هيهيبقى
+
+221
+00:22:53,330 --> 00:22:57,510
+تحليلنا سليم مائة بالمائة يبقى هذا ال element
+
+222
+00:22:57,510 --> 00:23:02,810
+irreducible عالى C since ال F of X حلناه إلى حاصل
+
+223
+00:23:02,810 --> 00:23:11,290
+ضرب two polynomials of lower degree and ال X لاطس
+
+224
+00:23:11,290 --> 00:23:21,830
+جذري اتنين I وال X ذاتي جذري اتنين I are of lower
+
+225
+00:23:21,830 --> 00:23:30,800
+degreedegree ده هو degree than F يبقى الدرجة
+
+226
+00:23:30,800 --> 00:23:38,640
+سبعتهم أقل من مين أقل من درجة اللي هو ال ال
+
+227
+00:23:38,640 --> 00:23:44,540
+polynomial الأصلية اللي هي F of A ناخد كمان مثال
+
+228
+00:23:44,540 --> 00:23:50,280
+يبقى هذا مثال رقم 2 مثال رقم 3
+
+229
+00:23:53,800 --> 00:23:58,600
+The polynomial f
+
+230
+00:23:58,600 --> 00:24:10,320
+of x يساوى x ترابيعه ناقص اتنين is irreducible
+
+231
+00:24:10,320 --> 00:24:13,380
+over
+
+232
+00:24:13,380 --> 00:24:20,240
+a cube but irreducible over R
+
+233
+00:24:27,920 --> 00:24:35,780
+معقول؟ طب من هنا نشوف ما هو السبب بيقول إيه؟
+
+234
+00:24:35,780 --> 00:24:41,280
+Irreducible على ليكيوم لكنها irreducible على ..
+
+235
+00:24:41,280 --> 00:24:47,680
+السؤال هو ليكيوم are are fields، مظهر؟ يفجر هنا
+
+236
+00:24:47,680 --> 00:24:58,610
+because ان ليكيوم عندك ال are are fieldsهذه
+
+237
+00:24:58,610 --> 00:25:05,490
+الناحية الأولى الناحية الثانية f of x هي x ترابيع
+
+238
+00:25:05,490 --> 00:25:13,230
+ناقص اتنين بقدر احلل اكس ناقص جدري اتنين في x زائد
+
+239
+00:25:13,230 --> 00:25:18,270
+جدري اتنين اذا قدرت اكتبها على حاصل درج two
+
+240
+00:25:18,270 --> 00:25:23,580
+polynomial الدرجة التي اتبعتهم اقل من 100أقل من
+
+241
+00:25:23,580 --> 00:25:26,480
+ضرر القلعون الملاصية، القلعون الملاصية من الدرجة
+
+242
+00:25:26,480 --> 00:25:29,800
+الثانية هتقول كل واحدة أقل من الدرجة الأولى اللي
+
+243
+00:25:29,800 --> 00:25:35,340
+هي أقل من اتنين طيب هل هذا ال element موجود في ال
+
+244
+00:25:35,340 --> 00:25:42,360
+IQ؟ لأ و هذا و شرط أساسي لازم يكونوا في ال IQ،
+
+245
+00:25:42,360 --> 00:25:47,740
+مظلوم؟ يعني هذا التحليل لا يمكن أن يتم داخل ال IQ
+
+246
+00:25:47,740 --> 00:25:53,570
+لأن جذر اتنين is irrational numberما هو اش عدد
+
+247
+00:25:53,570 --> 00:26:01,850
+نسبي مش موجود في ال EQ يبقى هنا F of X هذا بدي
+
+248
+00:26:01,850 --> 00:26:12,970
+يقين ان ال F of X is irreducible over ال EQ السبب
+
+249
+00:26:12,970 --> 00:26:21,590
+because ان ال X ناقص جدر اتنين وال X زائد جدر
+
+250
+00:26:21,590 --> 00:26:30,780
+اتنينdoes not belong to Q بقى موجودة في R Y بينما
+
+251
+00:26:30,780 --> 00:26:38,860
+Y اللي هو ال X ناقص جذر اتنين وال X زائد جذر اتنين
+
+252
+00:26:38,860 --> 00:26:46,400
+belongs to mean في R موجودة في R and each of them
+
+253
+00:26:46,400 --> 00:26:50,600
+each of them
+
+254
+00:26:53,300 --> 00:27:07,820
+Each of them is of lower degree than the F of X كل
+
+255
+00:27:07,820 --> 00:27:13,560
+واحد فيهم درجته أقل من درجة ال F of X العصرية ال F
+
+256
+00:27:13,560 --> 00:27:19,020
+of X العصرية من الدرجة الثانية كل واحد فيهم من
+
+257
+00:27:19,020 --> 00:27:25,860
+الدرجة الأولىوالـ R is a field بهذا كلامنا صحيح طب
+
+258
+00:27:25,860 --> 00:27:30,680
+احنا اللي هنعطينا بدل المثال تلاتة على integral
+
+259
+00:27:30,680 --> 00:27:37,460
+domino field مشهورة عندنا نتقل شوية مثال رقم أربع
+
+260
+00:27:37,460 --> 00:27:41,500
+مثال
+
+261
+00:27:41,500 --> 00:27:44,200
+رقم أربع بيقول ما تدا polynomial
+
+262
+00:27:49,510 --> 00:27:57,150
+f of x اللي بده يساوي x ترمية زائد واحد is
+
+263
+00:27:57,150 --> 00:28:00,590
+irreducible
+
+264
+00:28:00,590 --> 00:28:10,610
+over z تلاتة but irreducible
+
+265
+00:28:10,610 --> 00:28:15,510
+over
+
+266
+00:28:15,510 --> 00:28:18,330
+z خمسة
+
+267
+00:28:22,770 --> 00:28:32,050
+عقول؟ فبس انا بنسأل هل Z تلاتة فيد؟ او Z خمسة؟
+
+268
+00:28:32,050 --> 00:28:37,730
+يبقى 2 فيد لإن Z P is A فيد where ال P is a prime.
+
+269
+00:28:38,190 --> 00:28:44,730
+يبقى Z تلاتة هو فيد و Z خمسة هو فيد. يبقى ايه؟
+
+270
+00:28:44,730 --> 00:28:58,970
+Because Z تلاتةand Z خمسة are fields and
+
+271
+00:28:58,970 --> 00:29:01,990
+ال
+
+272
+00:29:01,990 --> 00:29:09,330
+F of X بده يساوي X ترابية زي إدوة من وين صار
+
+273
+00:29:09,330 --> 00:29:13,690
+السؤال هذا أصعب من اللي جابله من التحليل اللي بدنا
+
+274
+00:29:13,690 --> 00:29:20,930
+نعمل لو جيت أحلل هذهممكن أقولك اتنين X زائد واحد
+
+275
+00:29:20,930 --> 00:29:27,570
+في تلاتة X زائد واحد معقول التحليل هذا صحيح؟ تعالى
+
+276
+00:29:27,570 --> 00:29:36,730
+نشوف اتنين في تلاتة ستة X ترابيع تمام في Z تلاتة
+
+277
+00:29:36,730 --> 00:29:41,910
+زيرو بطل يصير من الدرجة التانية بالباقي كله من
+
+278
+00:29:41,910 --> 00:29:48,090
+الدرجة الأولىيبقى هذا بالشكل هذا غير موجود في Z3
+
+279
+00:29:48,090 --> 00:29:56,750
+هل موجود في Z5 تعالى نشوف يبقى 2 في 3 ب 6 X تربيع
+
+280
+00:29:56,750 --> 00:30:03,050
+في Z5 X تربيع واحدة مظبوط لإن ما نشيل الخمسة يبقى
+
+281
+00:30:03,050 --> 00:30:08,450
+من ال 6 واحد يبقى X تربيع واحدة هي هو يجعلنا X
+
+282
+00:30:08,450 --> 00:30:17,100
+تربيع نيجي لبعدهنا 2x و 3x و 5x في z خمسة Zero
+
+283
+00:30:17,100 --> 00:30:21,380
+طاري ثرمان طلعنا بس واحد في واحد في واحد في واحد
+
+284
+00:30:21,380 --> 00:30:23,700
+في واحد في واحد في واحد في واحد في واحد في واحد في
+
+285
+00:30:23,700 --> 00:30:24,860
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+286
+00:30:24,860 --> 00:30:25,440
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+287
+00:30:25,440 --> 00:30:26,020
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+288
+00:30:26,020 --> 00:30:26,300
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+289
+00:30:26,300 --> 00:30:27,120
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+290
+00:30:27,120 --> 00:30:27,540
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+291
+00:30:27,540 --> 00:30:28,700
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+292
+00:30:28,700 --> 00:30:34,520
+واحد في واحد في واحد في واحد في واحد في
+
+293
+00:30:34,520 --> 00:30:44,430
+واحد في واحدأنا بدي أسوأ X تربية زائد واحد و اتنين
+
+294
+00:30:44,430 --> 00:30:54,350
+X زائد واحد و تلاتة X زائد واحد اتنين هذول موجودات
+
+295
+00:30:54,350 --> 00:31:00,070
+وين في Z خمسة و كذلك موجودات في Z تلاتة موجودات في
+
+296
+00:31:00,070 --> 00:31:05,630
+الاتنين لكن المهم بدنا مين بقى بس هذا لأ هذا لأ
+
+297
+00:31:05,630 --> 00:31:09,880
+انفعشيبقى فتح مش موجود في زد تلاتة، زد تلاتة Zero
+
+298
+00:31:09,880 --> 00:31:18,320
+واحد واتنين، هذول اتنين موجودات في زد خمسة and
+
+299
+00:31:18,320 --> 00:31:32,080
+each of them is of lower degree than
+
+300
+00:31:36,560 --> 00:31:42,420
+اللي هو main than ال F ال F من الدرجة الثانية وكل
+
+301
+00:31:42,420 --> 00:31:46,540
+واحد من ال اتنين هدول من ال main من الدرجة الو
+
+302
+00:31:46,540 --> 00:31:51,560
+تبقى صلة ال F of X reducible في Z خمسة
+
+303
+00:31:51,560 --> 00:31:55,500
+وirreducible في Z تلت
+
+304
+00:32:11,970 --> 00:32:19,030
+نعطل أول نظرية على هذا الموضوع النظرية بتقول ما
+
+305
+00:32:19,030 --> 00:32:28,950
+يكتر تاريخ ال
+
+306
+00:32:28,950 --> 00:32:35,810
+FDAC لكبت ال FDAC
+
+307
+00:32:42,760 --> 00:32:54,500
+F of X موجودة في كارتة F of X عند ال degree لل F
+
+308
+00:32:54,500 --> 00:33:04,560
+بدأت سوى اتنين او تلاتة say M then ال F then ال F
+
+309
+00:33:04,560 --> 00:33:09,200
+is reducible
+
+310
+00:33:10,690 --> 00:33:19,210
+radius of one لإن ال F is irreducible over capital
+
+311
+00:33:19,210 --> 00:33:32,690
+F F and only F F and only F and F of X has a zero
+
+312
+00:33:32,690 --> 00:33:38,670
+has a zero and no capital F
+
+313
+00:33:53,130 --> 00:34:00,830
+نقرأ النصب ثاني وقبل البرهنة حاول نطرح سؤال ربما
+
+314
+00:34:00,830 --> 00:34:07,150
+هذا السؤال طرق على أذهانكم جال ال A phase أخدت
+
+315
+00:34:07,150 --> 00:34:12,870
+عنصر F of X موجود في capital F of X ضريت ال F of X
+
+316
+00:34:12,870 --> 00:34:17,370
+اتنين ماعندها مشكلة تلاتة ماعندها مشكلة اتنين او
+
+317
+00:34:17,370 --> 00:34:23,940
+تلاتة سيارةبقول ان ال F is reducible على F if and
+
+318
+00:34:23,940 --> 00:34:30,260
+only if ال F of X هي Zero in capital F السؤال اللي
+
+319
+00:34:30,260 --> 00:34:35,580
+بده أطرحه طب لو كان ال degree ل F ل هي اتنين ولا
+
+320
+00:34:35,580 --> 00:34:42,100
+تلت اربعة مثلا خمس ستة ده نظرية صحيحة؟ لا ليس
+
+321
+00:34:42,100 --> 00:34:47,740
+صحيحة وسنثبت هذا الكلام عامليا بمثال ان شاء الله
+
+322
+00:34:47,740 --> 00:34:53,800
+بعد ايه؟بعد أن أثبت هذه النظرية يبقى الـ O يبقى
+
+323
+00:34:53,800 --> 00:35:02,400
+أنا بدي أطلب أنها that ال F of X موجودة في capital
+
+324
+00:35:02,400 --> 00:35:15,300
+F of X with degree لل F هذا سوى 2 أو 3 النظرية كل
+
+325
+00:35:15,300 --> 00:35:20,600
+F عندهم F يبقى القرآن بدي أصير وينالاتجاهية ناخد
+
+326
+00:35:20,600 --> 00:35:25,620
+الاتجاهية لما نوص مذات ثاني ثم العكس يبقى هنا
+
+327
+00:35:25,620 --> 00:35:36,140
+بالداخل اقول اسيوم ذات افترض ان ال F is reducible
+
+328
+00:35:36,140 --> 00:35:39,540
+over
+
+329
+00:35:39,540 --> 00:35:47,160
+F then F
+
+330
+00:35:47,160 --> 00:35:54,970
+of Xهتصير حاصل ضارب ده اللي ده تبقى حاصل ضارب في
+
+331
+00:35:54,970 --> 00:36:06,070
+البرنامج يبقى g of x في h of x where حيث ال g of x
+
+332
+00:36:06,070 --> 00:36:16,370
+و ال h of x هذه موجودة وين؟ في capital F of X and
+
+333
+00:36:16,370 --> 00:36:18,730
+h
+
+334
+00:36:19,560 --> 00:36:30,660
+of ال F و ال H of X او ال G of X and اللي هو ال H
+
+335
+00:36:30,660 --> 00:36:40,300
+of X is of lower degree then
+
+336
+00:36:56,890 --> 00:37:02,670
+يبقى كل من الجيولتش بيكون من الدرجة الأولى لو قلنا
+
+337
+00:37:02,670 --> 00:37:07,250
+تلاتة يبقى على الأقل واحدة فيهم بيكون من وين
+
+338
+00:37:07,250 --> 00:37:12,530
+الدرجة اللي بيبقى على كل الأمرين الواحدة منهم
+
+339
+00:37:12,530 --> 00:37:19,250
+بيكون of the first degree مظبوط؟ يبقى that is
+
+340
+00:37:22,110 --> 00:37:38,150
+I am one of الـG of X or الـH of X has degree one
+
+341
+00:37:38,150 --> 00:37:44,270
+إذا واحدة من التنتين بدأت تكون من الدرجة الأولى لو
+
+342
+00:37:44,270 --> 00:37:48,430
+افترضنا إن الـG هذه من الدرجة الأولى
+
+343
+00:37:51,410 --> 00:38:02,950
+A degree تبع الـG of X او B1 درجة هذه هي من الدرجة
+
+344
+00:38:02,950 --> 00:38:09,230
+الأولى لا يمكنك تدفع شكلها بالأعلى ثم الـG of X
+
+345
+00:38:09,230 --> 00:38:18,830
+بدأ تساوي AX زي B A ممكن تساوي زي ذوالـ B ممكن
+
+346
+00:38:18,830 --> 00:38:23,550
+تسوى Zero فاناش مشكلة لكن الـ A ممنوع تسوى Zero
+
+347
+00:38:23,550 --> 00:38:30,550
+فبحط فاصلة و الـ A does not equal to Zero فلو سوى
+
+348
+00:38:30,550 --> 00:38:34,790
+Zero بتبطل يصير من الدرجة الأولى بيصير constant
+
+349
+00:38:34,790 --> 00:38:46,400
+polynomial طيب كويس ال F of X بنحاصر ضرب تنتينيبقى
+
+350
+00:38:46,400 --> 00:38:54,700
+واحدة فيهم قولنا ax زائد b التانية h of x ال h of
+
+351
+00:38:54,700 --> 00:38:59,360
+x قد تكون من الدرجة الأولى وقد تكون من الدرجة
+
+352
+00:38:59,360 --> 00:39:03,260
+الثانية احنا بنشتغل في integral domain و الله في
+
+353
+00:39:03,260 --> 00:39:10,940
+field في field يبقى كل عمصر له معكوس طبعا طبعا شو
+
+354
+00:39:10,940 --> 00:39:18,560
+رايك لو جيت انا قلت لك letالـ X يساوي ثابت A
+
+355
+00:39:18,560 --> 00:39:25,760
+inverse B مثلا خدي الـ X يساوي N مثلا بدي أشوف شو
+
+356
+00:39:25,760 --> 00:39:35,380
+بده تساوي يعني يبقى N بدنا أخد ال F أُر ثابت A
+
+357
+00:39:35,380 --> 00:39:42,790
+inverse B تمام؟ بده تساوي يا شبنان؟ يبقى Aالـ A
+
+358
+00:39:42,790 --> 00:39:51,130
+inverse B بس بيشارت سالب هاي سالب A inverse B
+
+359
+00:39:51,130 --> 00:39:59,090
+تمام؟ وهذه كلها .. كلها .. أه .. أه طبعا فاهمين؟
+
+360
+00:39:59,090 --> 00:40:07,470
+في زائد B التاني هذه كلها في الـ H of X الـ F
+
+361
+00:40:07,470 --> 00:40:13,630
+inverse of Bشيلت ال X و حطيت قيمتها وهذه بدي
+
+362
+00:40:13,630 --> 00:40:22,470
+احسبها كمان جدار ال H of سالب A inverse B هذه
+
+363
+00:40:22,470 --> 00:40:31,930
+بديها تسوى سالب B زائد B مضربه مين في ال H of سالب
+
+364
+00:40:31,930 --> 00:40:40,960
+A inverse B يعني جدار Zeroيبقى هذه الـ 0 في ماذا؟
+
+365
+00:40:40,960 --> 00:40:47,400
+الـ H أُسالف A inverse B يبقى يساوي 0 بمعنى هذا
+
+366
+00:40:47,400 --> 00:40:52,280
+الكلام، هذا الـ element أيش يمثل بالنسبة للدلة F؟
+
+367
+00:40:52,280 --> 00:41:00,300
+هو الـ 0 الألم يبقى الـ X يساوي أسالف A inverse B
+
+368
+00:41:00,300 --> 00:41:11,010
+هو A 0 forthe function of the polynomial of the
+
+369
+00:41:11,010 --> 00:41:16,150
+polynomial of
+
+370
+00:41:16,150 --> 00:41:24,370
+f of x عظمها المطلوب لفوفيكس هيزيرو انف يبقى اللي
+
+371
+00:41:24,370 --> 00:41:28,850
+هي zero هي أو جمالها اللي هو ال element اللي هو
+
+372
+00:41:28,850 --> 00:41:35,540
+زيرو الان بدنا نمشي معاكس للتجاه المعاكسيجب دلّا
+
+373
+00:41:35,540 --> 00:41:50,260
+conversion conversion
+
+374
+00:41:50,260 --> 00:41:58,060
+assume
+
+375
+00:41:58,060 --> 00:42:16,360
+that ال Earthhas a zero in capital F دلوقت
+
+376
+00:42:16,360 --> 00:42:25,540
+بدي افترض ان ال F has a zero in capital F that is
+
+377
+00:42:25,540 --> 00:42:31,160
+that
+
+378
+00:42:31,160 --> 00:42:45,120
+is قايلة assumeإن ال a is a zero of ال f then ال f
+
+379
+00:42:45,120 --> 00:42:51,800
+of a بدى يسوى قداش بدى يسوى zero مدام هذا zero
+
+380
+00:42:51,800 --> 00:42:57,680
+أخدنا تمين في الشكتر الماضي أنه لو كان في عندي
+
+381
+00:42:57,680 --> 00:43:02,800
+zero لل function f يبقى ال x ناقص هذا الامت هو ال
+
+382
+00:43:02,800 --> 00:43:10,700
+factor لمينلدالة يبقى هنا هذا بدي يعطينا ان ال X
+
+383
+00:43:10,700 --> 00:43:24,340
+ناقص ال A is a factor for the polynomial F
+
+384
+00:43:24,340 --> 00:43:38,220
+of X that is I N ال F of Xيساوي ال X نقص ال A في
+
+385
+00:43:38,220 --> 00:43:46,900
+ال Q of X or sum a
+
+386
+00:43:46,900 --> 00:43:56,520
+Q of X اللي موجودة في مين؟ في كارتن F of X إيش
+
+387
+00:43:56,520 --> 00:44:02,940
+تفسيرك لهذا الكلام؟ كتبته خلصت، يبقى سارتين
+
+388
+00:44:03,350 --> 00:44:09,650
+reducible جدرت أحللها إلى حاصل ضرب two polynomials
+
+389
+00:44:09,650 --> 00:44:21,110
+يرجى this means this means
+
+390
+00:44:21,110 --> 00:44:32,270
+that أن ال F is reducible أو
+
+391
+00:44:32,270 --> 00:44:32,870
+ضرب
+
+392
+00:44:42,260 --> 00:44:50,420
+عطيكم العافية نكمل ان شاء الله المحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8e0338dda234050812b6a4ac19705bed2582b77a
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_raw.json
@@ -0,0 +1 @@
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0.61279296875}, {"start": 381.28, "end": 381.94, "word": " element", "probability": 0.8857421875}, {"start": 381.94, "end": 382.42, "word": " اللي", "probability": 0.923828125}, {"start": 382.42, "end": 383.04, "word": " بتاخده،", "probability": 0.8720703125}, {"start": 383.04, "end": 383.56, "word": " ينطبق", "probability": 0.84453125}, {"start": 383.56, "end": 383.8, "word": " عليه", "probability": 0.5458984375}, {"start": 383.8, "end": 384.0, "word": " هذا", "probability": 0.93994140625}, {"start": 384.0, "end": 384.38, "word": " التعريف", "probability": 0.9940185546875}, {"start": 384.38, "end": 384.68, "word": " ويقول", "probability": 0.7277018229166666}, {"start": 384.68, "end": 385.04, "word": " عنه", "probability": 0.65673828125}, {"start": 385.04, "end": 386.04, "word": " irreducible،", "probability": 0.9622802734375}, {"start": 386.04, "end": 386.82, "word": " ماينطبقش", "probability": 0.78515625}, {"start": 386.82, "end": 387.32, "word": " خلاص،", "probability": 0.96142578125}, {"start": 387.32, "end": 387.72, "word": " ماقدرش", "probability": 0.8316650390625}, {"start": 387.72, "end": 387.96, "word": " أقول", "probability": 0.77880859375}, {"start": 387.96, "end": 388.76, "word": " irreducible", "probability": 0.7784016927083334}], "temperature": 1.0}, {"id": 14, "seek": 41623, "start": 389.29, "end": 416.23, "text": "يبقى هذا الكلام ال ال polynomial قد تكون irreducible على integral domain وقد تكون reducible على integral domain آخر صح؟ يبقى هاي اللي احنا بنقوله والان هنوضح لكذا الكلام بس قبل التوضيح بذاري على two definitions مرة تانية نثبت المعلومة مشان نبدأ نبدأ نبني عليها دي integral domain", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 2423, 2423, 26110, 12174, 3215, 6055, 30544, 16014, 769, 32128, 15844, 11573, 9274, 4032, 28543, 6055, 30544, 2783, 32128, 15844, 11573, 9274, 19753, 34740, 20328, 5016, 22807, 7251, 3555, 4587, 7578, 8032, 47302, 13672, 1829, 1975, 5016, 8315, 44945, 39648, 3224, 4032, 6027, 7649, 8032, 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23, "seek": 66782, "start": 641.06, "end": 667.82, "text": "أكتبها على صورة Haselberg two polynomials درجة كل واحدة فيهم أقل من درجة ال polynomial الأصلية هاي اللي بيقولوا لما انتقلنا من integral domain إلى field صار التعريف اللي فوق غيرناه إلى التعريف التالي f of x بتكتب على Haselberg two polynomials", "tokens": [10721, 4117, 2655, 3555, 11296, 15844, 20328, 13063, 3660, 8646, 338, 6873, 732, 22560, 12356, 11778, 47341, 3660, 28242, 36764, 24401, 3660, 8978, 16095, 5551, 4587, 1211, 9154, 11778, 47341, 3660, 2423, 26110, 16247, 9381, 20292, 3660, 8032, 47302, 13672, 1829, 4724, 1829, 39648, 14407, 5296, 15042, 16472, 2655, 4587, 1211, 8315, 9154, 11573, 9274, 30731, 2519, 20328, 9640, 16712, 3615, 16572, 5172, 13672, 1829, 6156, 30543, 32771, 13546, 8315, 3224, 30731, 16712, 3615, 16572, 5172, 16712, 6027, 1829, 283, 295, 2031, 39894, 4117, 2655, 3555, 15844, 8646, 338, 6873, 732, 22560, 12356], "avg_logprob": -0.20129654223614551, "compression_ratio": 1.6774193548387097, 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735.67, "word": " irreducible", "probability": 0.8092447916666666}, {"start": 735.67, "end": 738.41, "word": " over", "probability": 0.85595703125}, {"start": 738.41, "end": 740.73, "word": " لكي", "probability": 0.568115234375}, {"start": 740.73, "end": 741.01, "word": " و", "probability": 0.324462890625}, {"start": 741.01, "end": 742.59, "word": " but", "probability": 0.1751708984375}, {"start": 742.59, "end": 745.55, "word": " irreducible", "probability": 0.8541666666666666}, {"start": 745.55, "end": 748.05, "word": " over", "probability": 0.90869140625}], "temperature": 1.0}, {"id": 27, "seek": 79258, "start": 766.06, "end": 792.58, "text": "أنا أخدت برنامج F of X مزاوية اتنين X تربية زائد أربعة أنا أزعم أن هذه البرنامج is irreducible على الـQ لكنها irreducible على Z طب السؤال هو الـQ انتجرال دومان؟ فهو انتجرال دومان وZ انتجرال دومان؟", "tokens": [10721, 8315, 5551, 9778, 3215, 2655, 4724, 2288, 8315, 2304, 7435, 479, 295, 1783, 3714, 11622, 995, 2407, 10632, 1975, 2655, 1863, 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835.99, "end": 837.07, "word": " factors", "probability": 0.9638671875}, {"start": 837.07, "end": 838.25, "word": " عاملين", "probability": 0.986083984375}, {"start": 838.25, "end": 838.47, "word": " هي", "probability": 0.56201171875}, {"start": 838.47, "end": 839.11, "word": " العامل", "probability": 0.974609375}, {"start": 839.11, "end": 839.67, "word": " الأول", "probability": 0.843505859375}, {"start": 839.67, "end": 840.57, "word": " وهي", "probability": 0.8017578125}, {"start": 840.57, "end": 841.21, "word": " العامل", "probability": 0.9866536458333334}, {"start": 841.21, "end": 841.95, "word": " الثاني", "probability": 0.8841552734375}, {"start": 841.95, "end": 843.35, "word": " حللته", "probability": 0.83603515625}, {"start": 843.35, "end": 843.89, "word": " عنيش", "probability": 0.4585367838541667}, {"start": 843.89, "end": 844.45, "word": " بقول", "probability": 0.979736328125}, {"start": 844.45, "end": 845.55, "word": " هذه", "probability": 0.470947265625}, {"start": 845.55, "end": 847.01, "word": " irreducible", "probability": 0.8924153645833334}, {"start": 847.01, "end": 847.93, "word": " over", "probability": 0.8662109375}, {"start": 847.93, "end": 848.61, "word": " Q", "probability": 0.58154296875}], "temperature": 1.0}, {"id": 30, "seek": 87671, "start": 849.27, "end": 876.71, "text": "طب حللتها إلى عاملين تمام بيقول لو طلع واحد فيهم unit تبقى irreducible يبقى انا قلت irreducible ليش؟ على مين؟ على ال EQ لإنه اتنين is a unit في ال EQ مين المعقود سبعة اتنين؟ نص موجود في ال EQ؟ اه موجود في ال EQ", "tokens": [9566, 3555, 11331, 1211, 1211, 2655, 11296, 30731, 6225, 10943, 1211, 9957, 46811, 10943, 4724, 1829, 39648, 45164, 23032, 1211, 3615, 36764, 24401, 8978, 16095, 4985, 6055, 3555, 4587, 7578, 16014, 769, 32128, 7251, 3555, 4587, 7578, 1975, 8315, 12174, 1211, 2655, 16014, 769, 32128, 32239, 8592, 22807, 15844, 3714, 9957, 22807, 15844, 2423, 33580, 5296, 28814, 1863, 3224, 1975, 2655, 1863, 9957, 307, 257, 4985, 8978, 2423, 33580, 3714, 9957, 9673, 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"seek": 90670, "start": 877.18, "end": 906.7, "text": "يبقى هادى because are integral domains and ال F والاتنين and ال X تربية زائد اتنين موجودة في ال Q والاتنين is a unit but ال F of X", "tokens": [1829, 3555, 4587, 7578, 8032, 18513, 7578, 570, 366, 11573, 25514, 293, 2423, 479, 16070, 9307, 1863, 9957, 293, 2423, 1783, 6055, 25513, 10632, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 3714, 29245, 23328, 3660, 8978, 2423, 1249, 16070, 9307, 1863, 9957, 307, 257, 4985, 457, 2423, 479, 295, 1783], "avg_logprob": -0.32536764355266795, "compression_ratio": 1.3529411764705883, "no_speech_prob": 0.0, "words": [{"start": 877.18, "end": 878.02, "word": "يبقى", "probability": 0.94482421875}, {"start": 878.02, "end": 878.62, "word": " هادى", "probability": 0.5542805989583334}, {"start": 878.62, "end": 879.18, "word": " because", "probability": 0.6591796875}, {"start": 879.18, "end": 879.54, "word": " are", "probability": 0.1021728515625}, {"start": 879.54, "end": 880.16, "word": " integral", 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933.57, "text": "تساوي اتنين في X تربيع زائد اتنين is reducible in Z of X هل هذا unit في Z؟ اتنين unit في Z؟ لأن معكوس تبقى و نص، و نص مش موجود", "tokens": [2655, 3794, 995, 45865, 1975, 2655, 1863, 9957, 8978, 1783, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 307, 2783, 32128, 294, 1176, 295, 1783, 8032, 1211, 23758, 4985, 8978, 1176, 22807, 1975, 2655, 1863, 9957, 4985, 8978, 1176, 22807, 5296, 33456, 20449, 4117, 41779, 6055, 3555, 4587, 7578, 4032, 8717, 9381, 12399, 4032, 8717, 9381, 37893, 3714, 29245, 23328], "avg_logprob": -0.24462891183793545, "compression_ratio": 1.3661971830985915, "no_speech_prob": 0.0, "words": [{"start": 907.27, "end": 908.01, "word": "تساوي", "probability": 0.7425537109375}, {"start": 908.01, "end": 908.61, "word": " اتنين", "probability": 0.8251953125}, {"start": 908.61, "end": 908.97, "word": " في", "probability": 0.8125}, {"start": 908.97, "end": 909.31, "word": " X", "probability": 0.6591796875}, {"start": 909.31, "end": 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two", "probability": 0.662109375}, {"start": 940.89, "end": 941.61, "word": " factors", "probability": 0.91943359375}, {"start": 941.61, "end": 942.19, "word": " وولا", "probability": 0.71435546875}, {"start": 942.19, "end": 942.65, "word": " واحد", "probability": 0.99072265625}, {"start": 942.65, "end": 943.13, "word": " فيهم", "probability": 0.960693359375}, {"start": 943.13, "end": 943.61, "word": " unit", "probability": 0.92578125}, {"start": 943.61, "end": 944.37, "word": " لكن", "probability": 0.85107421875}, {"start": 944.37, "end": 944.59, "word": " في", "probability": 0.9013671875}, {"start": 944.59, "end": 945.03, "word": " الأول", "probability": 0.94970703125}, {"start": 945.03, "end": 945.63, "word": " فلكي", "probability": 0.5567220052083334}, {"start": 945.63, "end": 946.09, "word": " وطلع", "probability": 0.9425048828125}, {"start": 946.09, "end": 946.41, "word": " واحد", "probability": 0.99365234375}, {"start": 946.41, "end": 946.71, "word": " فيهم", "probability": 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{"start": 955.73, "end": 956.51, "word": " حاصل", "probability": 0.798828125}, {"start": 956.51, "end": 957.55, "word": " بلاصيرة", "probability": 0.60614013671875}, {"start": 957.55, "end": 958.75, "word": " حاصل", "probability": 0.9695638020833334}, {"start": 958.75, "end": 959.45, "word": " ضارب", "probability": 0.9169921875}, {"start": 959.45, "end": 959.81, "word": " two", "probability": 0.861328125}, {"start": 959.81, "end": 960.49, "word": " polynomial", "probability": 0.54296875}, {"start": 960.49, "end": 961.15, "word": " بس", "probability": 0.921142578125}, {"start": 961.15, "end": 961.51, "word": " واحدة", "probability": 0.9825846354166666}, {"start": 961.51, "end": 962.01, "word": " فيهم", "probability": 0.984375}], "temperature": 1.0}, {"id": 34, "seek": 98751, "start": 963.01, "end": 987.51, "text": "والتانية مانعاش مشكلة بيها ما عليها الشرط المهم واحدة فيهم يكون unit وواحدة فيهم unit يبقى irreducible طيب جدرنا انحللهم بدون مشاكل يبقى هذا strategy اتنين في x تربيه زائد اتنين يبقى reducible على z وirreducible عالميا على ال Q نعطي مثلا اخر", "tokens": [2407, 6027, 2655, 7649, 10632, 3714, 7649, 3615, 33599, 37893, 28820, 3660, 4724, 1829, 11296, 19446, 25894, 11296, 25124, 2288, 9566, 9673, 16095, 36764, 24401, 3660, 8978, 16095, 7251, 30544, 4985, 4032, 14407, 24401, 3660, 8978, 16095, 4985, 7251, 3555, 4587, 7578, 16014, 769, 32128, 23032, 1829, 3555, 10874, 3215, 2288, 8315, 16472, 5016, 1211, 1211, 16095, 47525, 11536, 37893, 995, 28820, 7251, 3555, 4587, 7578, 23758, 5206, 1975, 2655, 1863, 9957, 8978, 2031, 6055, 2288, 21292, 3224, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 2783, 32128, 15844, 710, 4032, 347, 265, 769, 32128, 6225, 45340, 25528, 15844, 2423, 1249, 8717, 3615, 9566, 1829, 50113, 15040, 1975, 34740], "avg_logprob": -0.2617533059246772, "compression_ratio": 1.7647058823529411, "no_speech_prob": 0.0, "words": [{"start": 963.01, "end": 963.97, "word": "والتانية", "probability": 0.6375732421875}, {"start": 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1123.34, "end": 1124.74, "word": " الان", "probability": 0.6815185546875}, {"start": 1124.74, "end": 1125.38, "word": " بيدادي", "probability": 0.39990234375}, {"start": 1125.38, "end": 1125.58, "word": " لل", "probability": 0.67529296875}, {"start": 1125.58, "end": 1126.06, "word": " F", "probability": 0.62451171875}, {"start": 1126.06, "end": 1126.52, "word": " of", "probability": 0.79931640625}, {"start": 1126.52, "end": 1127.04, "word": " X", "probability": 0.9306640625}, {"start": 1127.04, "end": 1128.1, "word": " يساوي", "probability": 0.7204132080078125}, {"start": 1128.1, "end": 1128.64, "word": " 2", "probability": 0.93701171875}, {"start": 1128.64, "end": 1129.18, "word": " X", "probability": 0.373046875}, {"start": 1129.18, "end": 1130.38, "word": " تربيع", "probability": 0.56390380859375}, {"start": 1130.38, "end": 1131.12, "word": " زائد", "probability": 0.8098958333333334}, {"start": 1131.12, "end": 1131.64, "word": " 2", "probability": 0.87841796875}, {"start": 1131.64, 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"temperature": 1.0}, {"id": 40, "seek": 116946, "start": 1141.0, "end": 1169.46, "text": "is called irreducible if ال if cannot be written as a product of two non-conustant polynomials تقدروا تكتبوا هذه ك product of non-conustant polynomials؟ مقدرش يعني مقدرش اتنين هذه أستبدلها ب polynomial تانية ماهياش conustant يبقى هذه إيش؟", "tokens": [271, 1219, 16014, 769, 32128, 498, 2423, 498, 2644, 312, 3720, 382, 257, 1674, 295, 732, 2107, 12, 1671, 381, 394, 22560, 12356, 6055, 28543, 2288, 14407, 6055, 4117, 2655, 3555, 14407, 29538, 9122, 1674, 295, 2107, 12, 1671, 381, 394, 22560, 12356, 22807, 3714, 28543, 2288, 8592, 37495, 22653, 3714, 28543, 2288, 8592, 1975, 2655, 1863, 9957, 29538, 5551, 14851, 44510, 1211, 11296, 4724, 26110, 6055, 7649, 10632, 19446, 3224, 1829, 33599, 416, 381, 394, 7251, 3555, 4587, 7578, 29538, 11933, 1829, 8592, 22807], "avg_logprob": -0.25744911716427915, "compression_ratio": 1.5897435897435896, "no_speech_prob": 0.0, "words": [{"start": 1141.0, "end": 1141.34, "word": "is", "probability": 0.360595703125}, {"start": 1141.34, "end": 1141.9, "word": " called", "probability": 0.92041015625}, {"start": 1141.9, "end": 1143.68, "word": " irreducible", "probability": 0.8815104166666666}, {"start": 1143.68, "end": 1144.46, "word": " if", "probability": 0.904296875}, {"start": 1144.46, "end": 1144.74, "word": " ال", "probability": 0.7080078125}, {"start": 1144.74, "end": 1145.04, "word": " if", "probability": 0.408447265625}, {"start": 1145.04, "end": 1145.42, "word": " cannot", "probability": 0.556640625}, {"start": 1145.42, "end": 1145.84, "word": " be", "probability": 0.94775390625}, {"start": 1145.84, "end": 1146.32, "word": " written", "probability": 0.908203125}, {"start": 1146.32, "end": 1146.8, "word": " as", "probability": 0.94970703125}, {"start": 1146.8, "end": 1147.24, "word": " a", "probability": 0.90869140625}, {"start": 1147.24, "end": 1147.88, "word": " product", "probability": 0.953125}, {"start": 1147.88, "end": 1148.5, "word": " of", "probability": 0.97021484375}, {"start": 1148.5, "end": 1149.18, "word": " two", "probability": 0.8466796875}, {"start": 1149.18, "end": 1150.22, "word": " non", "probability": 0.8798828125}, {"start": 1150.22, "end": 1151.38, "word": "-conustant", "probability": 0.61138916015625}, {"start": 1151.38, "end": 1152.34, "word": " polynomials", "probability": 0.7069091796875}, {"start": 1152.34, "end": 1153.7, "word": " تقدروا", "probability": 0.7386474609375}, {"start": 1153.7, "end": 1154.46, "word": " تكتبوا", "probability": 0.9806640625}, {"start": 1154.46, "end": 1154.92, "word": " هذه", "probability": 0.69873046875}, {"start": 1154.92, "end": 1155.48, "word": " ك", "probability": 0.91796875}, {"start": 1155.48, "end": 1156.18, "word": " product", "probability": 0.55810546875}, {"start": 1156.18, "end": 1156.72, "word": " of", "probability": 0.9462890625}, {"start": 1156.72, "end": 1157.04, "word": " non", "probability": 0.89208984375}, {"start": 1157.04, "end": 1157.82, "word": "-conustant", "probability": 0.9039306640625}, {"start": 1157.82, "end": 1159.6, "word": " polynomials؟", "probability": 0.6451822916666666}, {"start": 1159.6, "end": 1160.26, "word": " مقدرش", "probability": 0.7933349609375}, {"start": 1160.26, "end": 1161.06, "word": " يعني", "probability": 0.739013671875}, {"start": 1161.06, "end": 1161.8, "word": " مقدرش", "probability": 0.9007568359375}, {"start": 1161.8, "end": 1162.38, "word": " اتنين", "probability": 0.90234375}, {"start": 1162.38, "end": 1162.8, "word": " هذه", "probability": 0.806640625}, {"start": 1162.8, "end": 1164.58, "word": " أستبدلها", "probability": 0.807861328125}, {"start": 1164.58, "end": 1165.08, "word": " ب", "probability": 0.97119140625}, {"start": 1165.08, "end": 1165.8, "word": " polynomial", "probability": 0.197509765625}, {"start": 1165.8, "end": 1166.54, "word": " تانية", "probability": 0.9833984375}, {"start": 1166.54, "end": 1167.1, "word": " ماهياش", "probability": 0.9183349609375}, {"start": 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0.863525390625}, {"start": 1183.5, "end": 1183.68, "word": " ما", "probability": 0.9638671875}, {"start": 1183.68, "end": 1184.24, "word": " قلنا", "probability": 0.939453125}, {"start": 1184.24, "end": 1185.74, "word": " irreducible", "probability": 0.7318572998046875}, {"start": 1185.74, "end": 1186.64, "word": " over", "probability": 0.92822265625}, {"start": 1186.64, "end": 1187.2, "word": " R", "probability": 0.9794921875}, {"start": 1187.2, "end": 1188.74, "word": " لإنها", "probability": 0.7608642578125}, {"start": 1188.74, "end": 1189.88, "word": " since", "probability": 0.75732421875}, {"start": 1189.88, "end": 1192.54, "word": " الإتنين", "probability": 0.8048095703125}, {"start": 1192.54, "end": 1193.2, "word": " is", "probability": 0.93408203125}, {"start": 1193.2, "end": 1194.04, "word": " a", "probability": 0.9833984375}, {"start": 1194.04, "end": 1195.3, "word": " constant", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 42, "seek": 122868, "start": 1205.84, "end": 1228.68, "text": "فولونوميا طيب الآن أنا بقول irreducible على R لكن أزعم أنها irreducible على ال IQ يبقى هنا بعض ولكن ال F of X يساوي 2 في X تربيه زائد 2 ال", "tokens": [5172, 12610, 11536, 20498, 25528, 23032, 1829, 3555, 6024, 48506, 41850, 4724, 39648, 16014, 769, 32128, 15844, 497, 44381, 5551, 11622, 25957, 14739, 11296, 16014, 769, 32128, 15844, 2423, 28921, 7251, 3555, 4587, 7578, 34105, 45030, 11242, 35525, 19452, 2423, 479, 295, 1783, 7251, 3794, 995, 45865, 568, 8978, 1783, 6055, 2288, 21292, 3224, 30767, 16373, 3215, 568, 2423], "avg_logprob": -0.34531251043081285, "compression_ratio": 1.3896103896103895, "no_speech_prob": 0.0, "words": [{"start": 1205.84, "end": 1207.04, "word": "فولونوميا", "probability": 0.49007568359375}, {"start": 1207.04, "end": 1208.24, "word": " طيب", "probability": 0.7344563802083334}, {"start": 1208.24, "end": 1209.7, "word": " الآن", "probability": 0.6007080078125}, {"start": 1209.7, "end": 1209.94, "word": " أنا", "probability": 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1226.14, "end": 1226.74, "word": " زائد", "probability": 0.80908203125}, {"start": 1226.74, "end": 1227.36, "word": " 2", "probability": 0.91357421875}, {"start": 1227.36, "end": 1228.68, "word": " ال", "probability": 0.51220703125}], "temperature": 1.0}, {"id": 43, "seek": 125696, "start": 1229.22, "end": 1256.96, "text": "radiusable over set of complex numbers since لإن ال F of X بقدر أكتبها على الشكل تاني نين بدي أكتبها على صيرة حاصل ضرج ل two complex numbers ودرجتهم", "tokens": [6206, 4872, 712, 670, 992, 295, 3997, 3547, 1670, 5296, 28814, 1863, 2423, 479, 295, 1783, 4724, 28543, 2288, 5551, 4117, 2655, 3555, 11296, 15844, 25124, 28820, 6055, 7649, 1829, 8717, 9957, 4724, 16254, 5551, 4117, 2655, 3555, 11296, 15844, 20328, 48923, 11331, 33546, 1211, 48812, 47341, 5296, 732, 3997, 3547, 4032, 3215, 47341, 2655, 16095], "avg_logprob": -0.25918310985230564, "compression_ratio": 1.3483870967741935, "no_speech_prob": 0.0, "words": [{"start": 1229.22, "end": 1231.48, "word": 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2466.35, "end": 2467.27, "word": " function", "probability": 0.85498046875}, {"start": 2467.27, "end": 2468.29, "word": " of", "probability": 0.43798828125}, {"start": 2468.29, "end": 2468.53, "word": " the", "probability": 0.68798828125}, {"start": 2468.53, "end": 2469.29, "word": " polynomial", "probability": 0.845703125}, {"start": 2469.29, "end": 2470.83, "word": " of", "probability": 0.25146484375}, {"start": 2470.83, "end": 2471.01, "word": " the", "probability": 0.174072265625}, {"start": 2471.01, "end": 2472.67, "word": " polynomial", "probability": 0.8779296875}, {"start": 2472.67, "end": 2476.15, "word": " of", "probability": 0.64404296875}, {"start": 2476.15, "end": 2476.61, "word": " f", "probability": 0.35205078125}, {"start": 2476.61, "end": 2477.49, "word": " of", "probability": 0.119873046875}, {"start": 2477.49, "end": 2478.11, "word": " x", "probability": 0.6630859375}, {"start": 2478.11, "end": 2479.07, "word": " عظمها", "probability": 0.50146484375}, {"start": 2479.07, "end": 2479.83, "word": " المطلوب", "probability": 0.89453125}, {"start": 2479.83, "end": 2481.67, "word": " لفوفيكس", "probability": 0.6278483072916666}, {"start": 2481.67, "end": 2482.87, "word": " هيزيرو", "probability": 0.461395263671875}, {"start": 2482.87, "end": 2483.29, "word": " انف", "probability": 0.48089599609375}, {"start": 2483.29, "end": 2484.07, "word": " يبقى", "probability": 0.9033203125}, {"start": 2484.07, "end": 2484.37, "word": " اللي", "probability": 0.5498046875}, {"start": 2484.37, "end": 2484.63, "word": " هي", "probability": 0.859375}, {"start": 2484.63, "end": 2485.01, "word": " zero", "probability": 0.5126953125}, {"start": 2485.01, "end": 2485.37, "word": " هي", "probability": 0.385498046875}, {"start": 2485.37, "end": 2486.07, "word": " أو", "probability": 0.4931640625}, {"start": 2486.07, "end": 2487.13, "word": " جمالها", "probability": 0.76806640625}, {"start": 2487.13, "end": 2487.61, "word": " اللي", "probability": 0.979248046875}, {"start": 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0.92578125}], "temperature": 1.0}, {"id": 86, "seek": 252271, "start": 2494.16, "end": 2522.72, "text": "يجب دلّا conversion conversion assume that ال Earth", "tokens": [1829, 7435, 3555, 11778, 1211, 11703, 995, 14298, 14298, 6552, 300, 2423, 4755], "avg_logprob": -0.5689174362591335, "compression_ratio": 1.0169491525423728, "no_speech_prob": 0.0, "words": [{"start": 2494.16, "end": 2494.68, "word": "يجب", "probability": 0.6129557291666666}, {"start": 2494.68, "end": 2495.54, "word": " دلّا", "probability": 0.580718994140625}, {"start": 2495.54, "end": 2496.46, "word": " conversion", "probability": 0.29443359375}, {"start": 2496.46, "end": 2510.26, "word": " conversion", "probability": 0.650390625}, {"start": 2510.26, "end": 2518.06, "word": " assume", "probability": 0.76611328125}, {"start": 2518.06, "end": 2520.42, "word": " that", "probability": 0.931640625}, {"start": 2520.42, "end": 2522.2, "word": " ال", "probability": 0.9091796875}, {"start": 2522.2, "end": 2522.72, "word": " Earth", "probability": 0.230224609375}], "temperature": 1.0}, {"id": 87, "seek": 255332, "start": 2524.82, "end": 2553.32, "text": "has a zero in capital F دلوقت بدي افترض ان ال F has a zero in capital F that is that is قايلة assume", "tokens": [12438, 257, 4018, 294, 4238, 479, 11778, 1211, 30543, 2655, 47525, 1829, 1975, 5172, 2655, 43042, 16472, 2423, 479, 575, 257, 4018, 294, 4238, 479, 300, 307, 300, 307, 12174, 995, 26895, 3660, 6552], "avg_logprob": -0.4020089319774083, "compression_ratio": 1.2577319587628866, "no_speech_prob": 0.0, "words": [{"start": 2524.8199999999997, "end": 2526.22, "word": "has", "probability": 0.12744140625}, {"start": 2526.22, "end": 2527.62, "word": " a", "probability": 0.732421875}, {"start": 2527.62, "end": 2528.94, "word": " zero", "probability": 0.47265625}, {"start": 2528.94, "end": 2530.44, "word": " in", "probability": 0.9189453125}, {"start": 2530.44, "end": 2532.0, "word": " capital", "probability": 0.65380859375}, {"start": 2532.0, "end": 2532.86, "word": " F", "probability": 0.87109375}, {"start": 2532.86, "end": 2536.36, "word": " دلوقت", "probability": 0.52557373046875}, {"start": 2536.36, "end": 2536.66, "word": " بدي", "probability": 0.53759765625}, {"start": 2536.66, "end": 2537.24, "word": " افترض", "probability": 0.715576171875}, {"start": 2537.24, "end": 2538.1, "word": " ان", "probability": 0.908203125}, {"start": 2538.1, "end": 2538.36, "word": " ال", "probability": 0.71240234375}, {"start": 2538.36, "end": 2538.72, "word": " F", "probability": 0.814453125}, {"start": 2538.72, "end": 2539.3, "word": " has", "probability": 0.8212890625}, {"start": 2539.3, "end": 2539.74, "word": " a", "probability": 0.966796875}, {"start": 2539.74, "end": 2540.2, "word": " zero", "probability": 0.86572265625}, {"start": 2540.2, "end": 2541.1, "word": " in", "probability": 0.966796875}, {"start": 2541.1, "end": 2541.6, "word": " capital", "probability": 0.8876953125}, {"start": 2541.6, "end": 2542.02, "word": " F", "probability": 0.990234375}, {"start": 2542.02, "end": 2542.84, "word": " that", "probability": 0.70947265625}, {"start": 2542.84, "end": 2545.54, "word": " is", "probability": 0.96728515625}, {"start": 2545.54, "end": 2551.16, "word": " that", "probability": 0.3623046875}, {"start": 2551.16, "end": 2551.64, "word": " is", "probability": 0.9697265625}, {"start": 2551.64, "end": 2552.52, "word": " قايلة", "probability": 0.7264404296875}, {"start": 2552.52, "end": 2553.32, "word": " assume", "probability": 0.7880859375}], "temperature": 1.0}, {"id": 88, "seek": 258416, "start": 2554.7, "end": 2584.16, "text": "إن ال a is a zero of ال f then ال f of a بدى يسوى قداش بدى يسوى zero مدام هذا zero أخدنا تمين في الشكتر الماضي أنه لو كان في عندي zero لل function f يبقى ال x ناقص هذا الامت هو ال factor لمين", "tokens": [28814, 1863, 2423, 257, 307, 257, 4018, 295, 2423, 283, 550, 2423, 283, 295, 257, 47525, 7578, 7251, 3794, 2407, 7578, 12174, 3215, 33599, 47525, 7578, 7251, 3794, 2407, 7578, 4018, 3714, 3215, 10943, 23758, 4018, 5551, 9778, 3215, 8315, 46811, 9957, 8978, 25124, 4117, 2655, 2288, 9673, 46958, 1829, 14739, 3224, 45164, 25961, 8978, 18871, 16254, 4018, 24976, 2445, 283, 7251, 3555, 4587, 7578, 2423, 2031, 8717, 995, 4587, 9381, 23758, 2423, 10943, 2655, 31439, 2423, 5952, 32767, 9957], "avg_logprob": -0.3761574074074074, "compression_ratio": 1.5792349726775956, "no_speech_prob": 0.0, "words": [{"start": 2554.7, "end": 2555.16, "word": "إن", "probability": 0.635986328125}, {"start": 2555.16, "end": 2555.56, "word": " ال", "probability": 0.6982421875}, {"start": 2555.56, "end": 2556.02, "word": " a", "probability": 0.25}, {"start": 2556.02, "end": 2556.76, "word": " is", "probability": 0.335693359375}, {"start": 2556.76, "end": 2557.44, "word": " a", "probability": 0.9130859375}, {"start": 2557.44, "end": 2558.54, "word": " zero", "probability": 0.150146484375}, {"start": 2558.54, "end": 2560.08, "word": " of", "probability": 0.8828125}, {"start": 2560.08, 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" zero", "probability": 0.68359375}, {"start": 2569.38, "end": 2570.76, "word": " مدام", "probability": 0.7140299479166666}, {"start": 2570.76, "end": 2571.18, "word": " هذا", "probability": 0.489990234375}, {"start": 2571.18, "end": 2571.8, "word": " zero", "probability": 0.47119140625}, {"start": 2571.8, "end": 2573.16, "word": " أخدنا", "probability": 0.8443603515625}, {"start": 2573.16, "end": 2574.2, "word": " تمين", "probability": 0.5970458984375}, {"start": 2574.2, "end": 2574.36, "word": " في", "probability": 0.9111328125}, {"start": 2574.36, "end": 2575.0, "word": " الشكتر", "probability": 0.71331787109375}, {"start": 2575.0, "end": 2575.72, "word": " الماضي", "probability": 0.8720703125}, {"start": 2575.72, "end": 2576.36, "word": " أنه", "probability": 0.62744140625}, {"start": 2576.36, "end": 2576.54, "word": " لو", "probability": 0.986328125}, {"start": 2576.54, "end": 2576.92, "word": " كان", "probability": 0.9873046875}, {"start": 2576.92, "end": 2577.16, "word": " في", 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0.93359375}, {"start": 2582.5, "end": 2582.8, "word": " ال", "probability": 0.30517578125}, {"start": 2582.8, "end": 2583.36, "word": " factor", "probability": 0.9228515625}, {"start": 2583.36, "end": 2584.16, "word": " لمين", "probability": 0.904296875}], "temperature": 1.0}, {"id": 89, "seek": 261317, "start": 2584.46, "end": 2613.18, "text": "لدالة يبقى هنا هذا بدي يعطينا ان ال X ناقص ال A is a factor for the polynomial F of X that is I N ال F of X", "tokens": [1211, 3215, 6027, 3660, 7251, 3555, 4587, 7578, 34105, 23758, 4724, 16254, 37495, 9566, 1829, 8315, 16472, 2423, 1783, 8717, 995, 4587, 9381, 2423, 316, 307, 257, 5952, 337, 264, 26110, 479, 295, 1783, 300, 307, 286, 426, 2423, 479, 295, 1783], "avg_logprob": -0.28779070599134576, "compression_ratio": 1.1626016260162602, "no_speech_prob": 0.0, "words": [{"start": 2584.46, "end": 2585.68, "word": "لدالة", "probability": 0.6822509765625}, {"start": 2585.68, "end": 2586.82, "word": " يبقى", "probability": 0.94580078125}, {"start": 2586.82, "end": 2587.34, "word": " هنا", "probability": 0.97705078125}, {"start": 2587.34, "end": 2588.24, "word": " هذا", "probability": 0.71923828125}, {"start": 2588.24, "end": 2588.74, "word": " بدي", "probability": 0.43157958984375}, {"start": 2588.74, "end": 2589.62, "word": " يعطينا", "probability": 0.9173583984375}, {"start": 2589.62, "end": 2590.0, "word": " ان", "probability": 0.79248046875}, {"start": 2590.0, "end": 2590.3, "word": " ال", "probability": 0.7353515625}, {"start": 2590.3, "end": 2590.7, "word": " X", "probability": 0.69140625}, {"start": 2590.7, "end": 2591.84, "word": " ناقص", "probability": 0.71209716796875}, {"start": 2591.84, "end": 2592.12, "word": " ال", "probability": 0.83154296875}, {"start": 2592.12, "end": 2592.42, "word": " A", "probability": 0.720703125}, {"start": 2592.42, "end": 2593.16, "word": " is", "probability": 0.619140625}, {"start": 2593.16, "end": 2594.04, "word": " a", "probability": 0.70458984375}, {"start": 2594.04, "end": 2595.4, "word": " factor", "probability": 0.8388671875}, {"start": 2595.4, "end": 2596.96, "word": " for", "probability": 0.84033203125}, {"start": 2596.96, "end": 2599.0, "word": " the", "probability": 0.65087890625}, {"start": 2599.0, "end": 2600.74, "word": " polynomial", "probability": 0.88818359375}, {"start": 2600.74, "end": 2604.34, "word": " F", "probability": 0.50927734375}, {"start": 2604.34, "end": 2604.76, "word": " of", "probability": 0.744140625}, {"start": 2604.76, "end": 2605.32, "word": " X", "probability": 0.984375}, {"start": 2605.32, "end": 2607.22, "word": " that", "probability": 0.78125}, {"start": 2607.22, "end": 2608.22, "word": " is", "probability": 0.9638671875}, {"start": 2608.22, "end": 2609.6, "word": " I", "probability": 0.62158203125}, {"start": 2609.6, "end": 2610.24, "word": " N", "probability": 0.61181640625}, {"start": 2610.24, "end": 2611.56, "word": " ال", "probability": 0.65234375}, {"start": 2611.56, "end": 2612.08, "word": " F", "probability": 0.97119140625}, {"start": 2612.08, "end": 2612.62, "word": " of", "probability": 0.91845703125}, {"start": 2612.62, "end": 2613.18, "word": " X", "probability": 0.99658203125}], "temperature": 1.0}, {"id": 90, "seek": 264294, "start": 2613.48, "end": 2642.94, "text": "يساوي ال X نقص ال A في ال Q of X or sum a Q of X اللي موجودة في مين؟ في كارتن F of X إيش تفسيرك لهذا الكلام؟ كتبته خلصت، يبقى سارتين", "tokens": [1829, 3794, 995, 45865, 2423, 1783, 8717, 4587, 9381, 2423, 316, 8978, 2423, 1249, 295, 1783, 420, 2408, 257, 1249, 295, 1783, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 3714, 9957, 22807, 8978, 9122, 9640, 2655, 1863, 479, 295, 1783, 11933, 1829, 8592, 6055, 36178, 13546, 4117, 46740, 15730, 2423, 28820, 10943, 22807, 9122, 2655, 3555, 2655, 3224, 16490, 1211, 9381, 2655, 12399, 7251, 3555, 4587, 7578, 8608, 9640, 2655, 9957], "avg_logprob": -0.273871539781491, "compression_ratio": 1.4256756756756757, "no_speech_prob": 0.0, "words": [{"start": 2613.48, "end": 2614.66, "word": "يساوي", "probability": 0.7821044921875}, {"start": 2614.66, "end": 2615.16, "word": " ال", "probability": 0.8271484375}, {"start": 2615.16, "end": 2615.6, "word": " X", "probability": 0.431640625}, {"start": 2615.6, "end": 2616.7, "word": " نقص", "probability": 0.78955078125}, {"start": 2616.7, "end": 2617.02, "word": " ال", "probability": 0.8857421875}, {"start": 2617.02, "end": 2617.5, "word": " A", "probability": 0.75146484375}, {"start": 2617.5, "end": 2618.22, "word": " في", "probability": 0.8828125}, {"start": 2618.22, "end": 2618.42, "word": " ال", "probability": 0.9326171875}, {"start": 2618.42, "end": 2619.06, "word": " Q", "probability": 0.8583984375}, {"start": 2619.06, "end": 2619.68, "word": " of", "probability": 0.802734375}, {"start": 2619.68, "end": 2620.2, "word": " X", "probability": 0.99365234375}, {"start": 2620.2, "end": 2621.96, "word": " or", "probability": 0.352294921875}, {"start": 2621.96, "end": 2623.78, "word": " sum", "probability": 0.259033203125}, {"start": 2623.78, "end": 2626.9, "word": " a", "probability": 0.55322265625}, {"start": 2626.9, "end": 2627.34, "word": " Q", "probability": 0.91455078125}, {"start": 2627.34, "end": 2627.94, "word": " of", "probability": 0.966796875}, {"start": 2627.94, "end": 2628.48, "word": " X", "probability": 0.9921875}, {"start": 2628.48, "end": 2629.36, "word": " اللي", "probability": 0.823486328125}, {"start": 2629.36, "end": 2630.1, "word": " موجودة", "probability": 0.9825439453125}, {"start": 2630.1, "end": 2630.24, "word": " في", "probability": 0.89208984375}, {"start": 2630.24, "end": 2631.1, "word": " مين؟", "probability": 0.6544596354166666}, {"start": 2631.1, "end": 2631.38, "word": " في", "probability": 0.82666015625}, {"start": 2631.38, "end": 2632.34, "word": " كارتن", "probability": 0.599334716796875}, {"start": 2632.34, "end": 2632.92, "word": " F", "probability": 0.93359375}, {"start": 2632.92, "end": 2633.4, "word": " of", "probability": 0.97509765625}, {"start": 2633.4, "end": 2633.9, "word": " X", "probability": 0.9970703125}, {"start": 2633.9, "end": 2636.52, "word": " إيش", "probability": 0.7447916666666666}, {"start": 2636.52, "end": 2637.18, "word": " تفسيرك", "probability": 0.9912109375}, {"start": 2637.18, "end": 2637.56, "word": " لهذا", "probability": 0.9287109375}, {"start": 2637.56, "end": 2638.8, "word": " الكلام؟", "probability": 0.864013671875}, {"start": 2638.8, "end": 2640.62, "word": " كتبته", "probability": 0.77626953125}, {"start": 2640.62, "end": 2641.54, "word": " خلصت،", "probability": 0.70595703125}, {"start": 2641.54, "end": 2642.18, "word": " يبقى", "probability": 0.8524169921875}, {"start": 2642.18, "end": 2642.94, "word": " سارتين", "probability": 0.699462890625}], "temperature": 1.0}, {"id": 91, "seek": 267287, "start": 2643.35, "end": 2672.87, "text": "reducible جدرت أحللها إلى حاصل ضرب two polynomials يرجى this means this means that أن ال F is reducible أو ضرب", "tokens": [265, 769, 32128, 10874, 3215, 43500, 5551, 5016, 1211, 1211, 11296, 30731, 11331, 33546, 1211, 48812, 25513, 732, 22560, 12356, 7251, 47341, 7578, 341, 1355, 341, 1355, 300, 14739, 2423, 479, 307, 2783, 32128, 34051, 48812, 25513], "avg_logprob": -0.5185032941793141, "compression_ratio": 1.1916666666666667, "no_speech_prob": 0.0, "words": [{"start": 2643.35, "end": 2644.75, "word": "reducible", "probability": 0.63812255859375}, {"start": 2644.75, "end": 2645.57, "word": " جدرت", "probability": 0.6888427734375}, {"start": 2645.57, "end": 2646.23, "word": " أحللها", "probability": 0.805517578125}, {"start": 2646.23, "end": 2646.47, "word": " إلى", "probability": 0.896484375}, {"start": 2646.47, "end": 2647.19, "word": " حاصل", "probability": 0.83544921875}, {"start": 2647.19, "end": 2647.65, "word": " ضرب", "probability": 0.938232421875}, {"start": 2647.65, "end": 2648.37, "word": " two", "probability": 0.4462890625}, {"start": 2648.37, "end": 2649.65, "word": " polynomials", "probability": 0.58001708984375}, {"start": 2649.65, "end": 2650.95, "word": " يرجى", "probability": 0.5253092447916666}, {"start": 2650.95, "end": 2651.47, "word": " this", "probability": 0.319091796875}, {"start": 2651.47, "end": 2653.55, "word": " means", "probability": 0.76220703125}, {"start": 2653.55, "end": 2656.23, "word": " this", "probability": 0.207763671875}, {"start": 2656.23, "end": 2661.11, "word": " means", "probability": 0.61474609375}, {"start": 2661.11, "end": 2663.17, "word": " that", "probability": 0.89990234375}, {"start": 2663.17, "end": 2664.47, "word": " أن", "probability": 0.259033203125}, {"start": 2664.47, "end": 2664.73, "word": " ال", "probability": 0.736328125}, {"start": 2664.73, "end": 2665.23, "word": " F", "probability": 0.61572265625}, {"start": 2665.23, "end": 2666.71, "word": " is", "probability": 0.75244140625}, {"start": 2666.71, "end": 2668.77, "word": " reducible", "probability": 0.8388671875}, {"start": 2668.77, "end": 2672.27, "word": " أو", "probability": 0.392822265625}, {"start": 2672.27, "end": 2672.87, "word": " ضرب", "probability": 0.80859375}], "temperature": 1.0}, {"id": 92, "seek": 269042, "start": 2682.26, "end": 2690.42, "text": "عطيكم العافية نكمل ان شاء الله المحاضرة القادمة", "tokens": [3615, 9566, 1829, 24793, 18863, 31845, 10632, 8717, 24793, 1211, 16472, 13412, 16606, 21984, 9673, 5016, 46958, 25720, 25062, 18513, 46007], "avg_logprob": -0.28746448728171264, "compression_ratio": 1.16, "no_speech_prob": 0.0, "words": [{"start": 2682.2599999999998, "end": 2683.66, "word": "عطيكم", "probability": 0.4440727233886719}, {"start": 2683.66, "end": 2684.56, "word": " العافية", "probability": 0.9728190104166666}, {"start": 2684.56, "end": 2687.3, "word": " نكمل", "probability": 0.923828125}, {"start": 2687.3, "end": 2687.78, "word": " ان", "probability": 0.78173828125}, {"start": 2687.78, "end": 2688.12, "word": " شاء", "probability": 0.96728515625}, {"start": 2688.12, "end": 2688.3, "word": " الله", "probability": 0.96728515625}, {"start": 2688.3, "end": 2689.36, "word": " المحاضرة", "probability": 0.9735107421875}, {"start": 2689.36, "end": 2690.42, "word": " القادمة", "probability": 0.9397786458333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2690.9373125, "duration_after_vad": 2552.4899999999925}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GScGwkt4KIA_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GScGwkt4KIA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..72f87fb80fd8a2eeaeda5eede784cd89cce36e3b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GScGwkt4KIA_postprocess.srt
@@ -0,0 +1,1768 @@
+1
+00:00:20,700 --> 00:00:25,320
+بالله الرحمن الرحيم نكمل ما ابتدأنا فيه المرة
+
+2
+00:00:25,320 --> 00:00:30,980
+الماضية و آخر مرة مكتوب معاكم هو definition تعريف
+
+3
+00:00:30,980 --> 00:00:36,480
+ال principle ideal domain وقلنا في هذا التعريف ان
+
+4
+00:00:36,480 --> 00:00:42,380
+ال integral domain لو كان كل ideal في ال integral
+
+5
+00:00:42,380 --> 00:00:47,340
+domain هو principle ideal بسميه principle ideal
+
+6
+00:00:47,340 --> 00:00:53,880
+domainهذا آخر تعريف مكتوب معاكم طيب، الآن النظرية
+
+7
+00:00:53,880 --> 00:00:58,140
+على هذه النقطة، على هذا التعريف النظرية بتقول ليه؟
+
+8
+00:00:58,140 --> 00:01:03,780
+ود ال F عبارة عن فيه؟ يبقى ال capital F of X is a
+
+9
+00:01:03,780 --> 00:01:09,520
+principal ideal domain بمعنى كل ideal في capital F
+
+10
+00:01:09,520 --> 00:01:16,490
+of X هو عبارة عن ال principal idealإن أثبتنا هذا
+
+11
+00:01:16,490 --> 00:01:20,670
+الكلام فعلاً يكون capital F of X هو عبارة عن ال
+
+12
+00:01:20,670 --> 00:01:26,710
+principle ideal domain طيب الآن ال F field يبقى
+
+13
+00:01:26,710 --> 00:01:34,450
+هنا فاجب أقول له let ال F دي اي field بنفع يكون
+
+14
+00:01:34,450 --> 00:01:41,190
+integral domain؟ بنفع لأن أي field هو عبارة عن
+
+15
+00:01:41,190 --> 00:01:46,430
+integral domain لكن العكس ليس صحيحايبقى هنا little
+
+16
+00:01:46,430 --> 00:01:59,150
+f با field then ال F is an integral domain لو
+
+17
+00:01:59,150 --> 00:02:04,930
+رجعنا إلى أول نظرية أخذناها في هذا ال chapter قلنا
+
+18
+00:02:04,930 --> 00:02:09,670
+لو كان ال F integral domain يبقى ال capital F of X
+
+19
+00:02:09,670 --> 00:02:16,100
+هو عبارة عن integral domainيبقى باجي بقول by a
+
+20
+00:02:16,100 --> 00:02:28,380
+previous theorem نظرية سابقة capital F of X is an
+
+21
+00:02:28,380 --> 00:02:35,600
+integral domain تمام
+
+22
+00:02:35,600 --> 00:02:45,490
+بتروح أخد ideal في capital F of X يبقى letالـ I be
+
+23
+00:02:45,490 --> 00:02:58,070
+an ideal في اله capital F of X ان هو لا طريقة ال
+
+24
+00:02:58,070 --> 00:03:04,230
+ideal هذا principle ideal بصير capital F of X is a
+
+25
+00:03:04,230 --> 00:03:09,710
+principle ideal domain ال ideal اللي أخدته احتمال
+
+26
+00:03:10,890 --> 00:03:16,330
+الـ ideal هذا يكون بـ zero واحتمال ان لا يكون بـ
+
+27
+00:03:16,330 --> 00:03:22,670
+zero صحيح؟ طيب if ال ideal I بده يساوي zero then
+
+28
+00:03:22,670 --> 00:03:27,670
+ال ideal هو ال principle ال ideal generated by
+
+29
+00:03:27,670 --> 00:03:32,470
+zero مافيش فيه الا العنصر الصفري ال principle ولا
+
+30
+00:03:32,470 --> 00:03:41,730
+لا صح؟ يبقى هذا بده يعطينا ان ال I isa principal
+
+31
+00:03:41,730 --> 00:03:51,750
+ideal لو ماكنش بالزيرو يبقى بداجي اقوله if ال
+
+32
+00:03:51,750 --> 00:04:02,530
+ideal I كان لا يساوي زيرو انتقل في طريقة اني اخد
+
+33
+00:04:02,530 --> 00:04:12,230
+polynomial Geo of X موجودة في I such thatبحيث ان
+
+34
+00:04:12,230 --> 00:04:21,730
+الـG of X is of minimum degree
+
+35
+00:04:21,730 --> 00:04:25,570
+in
+
+36
+00:04:25,570 --> 00:04:31,710
+I ايش قصدك تقولي عنه بالظبط؟ نفهم العبارة يعني
+
+37
+00:04:31,710 --> 00:04:39,590
+يبقى أنا أخدت polynomial موجودة في الـID الـIطبعا
+
+38
+00:04:39,590 --> 00:04:44,750
+في polynomial كتير لإنه لا يسوى ال zero تمام؟ يبقى
+
+39
+00:04:44,750 --> 00:04:50,390
+أخدت واحدة منهم بشرط ان يكون درجة هذه ال
+
+40
+00:04:50,390 --> 00:04:56,010
+polynomial هي أقل درجة ل polynomial موجودة في ال
+
+41
+00:04:56,010 --> 00:05:02,730
+ID ال I يعني لو ال I أقل درجة فيهي الدرجة التالتة
+
+42
+00:05:02,730 --> 00:05:08,130
+مثلا يبقى ال Ge of X من الدرجة التالتةلو كان أقل
+
+43
+00:05:08,130 --> 00:05:14,950
+هي الدرجة التانية يبقى ال polynomial هذي من الدرجة
+
+44
+00:05:14,950 --> 00:05:20,310
+الثانية و هكذا هي المقصود فيها يبقى أخدنها GeoVec
+
+45
+00:05:20,310 --> 00:05:26,590
+هو عنصر موجود في ال I بحيث ال GeoVec of minimum
+
+46
+00:05:26,590 --> 00:05:32,970
+degree in I أقل درجة موجودة ليه؟ موجودة ليه
+
+47
+00:05:32,970 --> 00:05:40,870
+polynomial في ال ideal I؟الحين دي كل .. كل .. كل
+
+48
+00:05:40,870 --> 00:05:47,550
+حاجة بشغلها ، كل شغلة بشغلها. الان أنا أدعي ان ال
+
+49
+00:05:47,550 --> 00:05:52,450
+ideal اللي أخدتها هى هو ال principle، ال ideal
+
+50
+00:05:52,450 --> 00:05:54,430
+generated by Geovics.
+
+51
+00:05:56,550 --> 00:06:02,200
+انا أدعيإن ال ideal I هو ال principle ideal
+
+52
+00:06:02,200 --> 00:06:06,260
+generated by اللي أخدتها minimum degree اللي بتسأل
+
+53
+00:06:06,260 --> 00:06:11,260
+عنها يبقى مش أخدتها بالبلاش لأ أخدتها لهدف بالديام
+
+54
+00:06:11,260 --> 00:06:23,440
+تمام؟ we shall show that بدنا نبين إن ال ideal I
+
+55
+00:06:23,440 --> 00:06:27,840
+هو ال principle ideal generated by ال Geographic
+
+56
+00:06:28,970 --> 00:06:35,350
+إذا قدرنا نثبت صحة هذا الكلام بيكون تمام تماما طيب
+
+57
+00:06:35,350 --> 00:06:42,030
+كويس بدي أجي أقوله let ال F of X موجودة في ال
+
+58
+00:06:42,030 --> 00:06:49,090
+ideal I إذا قدرت أثبت أن ال F of X موجودة هنا بصير
+
+59
+00:06:49,090 --> 00:06:53,410
+ال I subset من ال principle ideal generated by G
+
+60
+00:06:53,410 --> 00:06:59,560
+of X عملت العكس بيحدثي التساوي اللي أنا قاعدبدور
+
+61
+00:06:59,560 --> 00:07:05,460
+عليه وبالتالي ان حدث ذلك بيصير اي Ideal عبارة عن
+
+62
+00:07:05,460 --> 00:07:10,560
+ال principle لأن يساوي zero طالع موجود في I تمام؟
+
+63
+00:07:10,560 --> 00:07:13,440
+لا يساوي zero بدنا نشوف وين بدنا نتوجه معاها
+
+64
+00:07:13,440 --> 00:07:19,480
+الدنيا تمام؟ يبقى بدي احاول اثبت ان ال ideal I هو
+
+65
+00:07:19,480 --> 00:07:24,060
+ال principle ideal generated by geofix حيث ال
+
+66
+00:07:24,060 --> 00:07:30,970
+geofix هيأصغر درجة لقلنوميل او اصغر درجة موجودة في
+
+67
+00:07:30,970 --> 00:07:36,170
+ال I دي ال I بقولك وين خد ال F of X موجودة في ال I
+
+68
+00:07:36,170 --> 00:07:42,850
+اذا بقدر بال division algorithm اكتب F of X بدلالة
+
+69
+00:07:42,850 --> 00:07:53,290
+100 T of X يبقى هنا then by division algorithm
+
+70
+00:07:57,610 --> 00:08:02,470
+we have ان
+
+71
+00:08:02,470 --> 00:08:14,150
+ال F of X بدها تسمى جي جي of X فالي Q of X زائد ال
+
+72
+00:08:14,150 --> 00:08:26,370
+R of X و حيث ال R of X ممكن تكون ب Zero اوالدرجة
+
+73
+00:08:26,370 --> 00:08:34,490
+تبع ال R of X أقل من الدرجة تبع ال G of X بس هو
+
+74
+00:08:34,490 --> 00:08:41,030
+أقل إيش؟ صحيح بس G of X أقل إيش؟ كيف؟ G of X أقل
+
+75
+00:08:41,030 --> 00:08:46,450
+درجة محروفش يقول Minimum degree؟ أقل شرقين من
+
+76
+00:08:46,450 --> 00:08:51,210
+الأول يعني ال F of X أعلى في الدرجة من مين؟من G of
+
+77
+00:08:51,210 --> 00:08:56,130
+X لأنه أنا ماخد G of X of minimum degree in I
+
+78
+00:08:56,130 --> 00:09:01,710
+واخدت ال F of X موجودة في I يبقى أقل ما فينا تكون
+
+79
+00:09:01,710 --> 00:09:05,770
+جدها في الدرجة صح ولا لأ؟ يبقى لو كانت جدها في
+
+80
+00:09:05,770 --> 00:09:09,650
+الدرجة يبقى صير ال remainder ب zero و بصير حاصر
+
+81
+00:09:09,650 --> 00:09:15,810
+الدرجة فده هو اللي بتسوي ال F of X ما علينا يبقى
+
+82
+00:09:15,810 --> 00:09:19,930
+انا كتبتها بال division algorithmحيث R of X يسوي
+
+83
+00:09:19,930 --> 00:09:28,070
+Zero أو درجة R of X أقل من درجة G of X تمام؟ طيب،
+
+84
+00:09:28,070 --> 00:09:33,210
+ماشي الحال، تعالوا نشوف بتخلي الـR of X في ناحية و
+
+85
+00:09:33,210 --> 00:09:38,610
+باقى المعادلة في ناحية ثانية يبقى بناء عليه الـR
+
+86
+00:09:38,610 --> 00:09:46,120
+of X بدي ساوي الـF of X ماقص الـG of Xمضروبة في ال
+
+87
+00:09:46,120 --> 00:09:51,440
+Geo-Vecs السؤال هو كل واحد بيقدر يسوي الشغل هذه
+
+88
+00:09:51,440 --> 00:09:59,460
+هذه موجودة في ال ideal I على فرض ايه هذه موجودة في
+
+89
+00:09:59,460 --> 00:10:05,960
+ال ideal I لإن ال Geo-Vecs موجودة في I و ال I is
+
+90
+00:10:05,960 --> 00:10:10,220
+an idealيبقى الـG of X مضروبة في أي Paranomial
+
+91
+00:10:10,220 --> 00:10:14,480
+أخرى إذا كانت موجودة في الـI دي الـI يبقى هذا
+
+92
+00:10:14,480 --> 00:10:23,500
+موجود في الـI دي الـI السبب because إن الـF of X
+
+93
+00:10:23,500 --> 00:10:34,160
+موجودة في I والـG of X موجودة في I and الـI is an
+
+94
+00:10:34,160 --> 00:10:49,920
+idealالنفجة صار اللي هو R of X موجودة في I طيب
+
+95
+00:10:49,920 --> 00:10:57,580
+احنا اقل درجة في I كانت قدش الـG الهذا درجته اقل
+
+96
+00:10:57,580 --> 00:11:02,040
+من الـG يا اما R of X بدى يساوي Zero ايش
+
+97
+00:11:02,040 --> 00:11:03,180
+بتستنتجوا؟
+
+98
+00:11:05,310 --> 00:11:11,310
+الـ R of X تساوي Zero لأن الـ G of X هي أقل درجة
+
+99
+00:11:11,310 --> 00:11:18,170
+موجودة في I يبقى هذا بدّي يعطينا ان الـ R of X
+
+100
+00:11:18,170 --> 00:11:28,370
+بتساوي Zero السبب because ان الـ G of X is of
+
+101
+00:11:28,370 --> 00:11:38,830
+minimum degree in Iطبعا يبقى ال R of X سوى Zero.
+
+102
+00:11:39,130 --> 00:11:47,610
+إيه صار عندك؟ فال F of X بتسوى ال G of X مضروبة في
+
+103
+00:11:47,610 --> 00:11:53,170
+ال Q of X. هذا العنصر موجود في ال principle؟
+
+104
+00:11:53,170 --> 00:12:00,170
+Generated by Q of X صح؟ يبقى هذا موجود في ال
+
+105
+00:12:00,170 --> 00:12:06,960
+principle ideal generated by G of X.هذا معناته
+
+106
+00:12:06,960 --> 00:12:13,020
+يبقى أنا أخدت ال F of X موجود في I طلع عندي ال F
+
+107
+00:12:13,020 --> 00:12:17,900
+of X موجود في ال principle يبقى هذا يعطينا ان ال
+
+108
+00:12:17,900 --> 00:12:23,820
+ID ال I صابست من مين من ال principle ID generated
+
+109
+00:12:23,820 --> 00:12:31,760
+by X وخليلي هذه المعادلة رقم واحد الآن بدأ امشي
+
+110
+00:12:31,760 --> 00:12:40,050
+للاتجاه الثانيthe other hand من الناحية الأخرى
+
+111
+00:12:40,050 --> 00:12:47,170
+خوديلي ال F of X موجودة في ال principle ideal
+
+112
+00:12:47,170 --> 00:12:57,850
+generated by G of X then ال F of X بدها تساوي ال G
+
+113
+00:12:57,850 --> 00:13:04,810
+of X في function تانية و ليكن مثلا ال Eq of Xfor
+
+114
+00:13:04,810 --> 00:13:16,050
+some Q of X اللي موجودة في مين؟ في capital F of X
+
+115
+00:13:16,050 --> 00:13:19,370
+تمام
+
+116
+00:13:19,370 --> 00:13:27,990
+طيب هذا معناته ال G of X موجود في I ال G of X وهذه
+
+117
+00:13:27,990 --> 00:13:34,890
+Q of X تماميبقى ال F of X مضروبة في G of X في ال Q
+
+118
+00:13:34,890 --> 00:13:39,730
+ال Q of X موجودة وين؟ في I يبقى هذه كلها حصلت ضرب
+
+119
+00:13:39,730 --> 00:13:48,190
+وين موجودة؟ موجودة في I يبقى هنا فال F of X موجود
+
+120
+00:13:48,190 --> 00:13:57,450
+في ال I اسسبب because ان ال G of X موجودة في I and
+
+121
+00:13:57,450 --> 00:14:07,020
+ال I isan ideal is an ideal يبقى بناءً عليه so
+
+122
+00:14:07,020 --> 00:14:12,000
+بدأنا بماذا؟ بدأنا بالprinciple اللي وجدته موجود
+
+123
+00:14:12,000 --> 00:14:17,480
+في I يبقى ال principle ideal generated by g of x
+
+124
+00:14:17,480 --> 00:14:23,800
+صابست من مين؟ من ال I وهذه العلاقة رقم اتنين يبقى
+
+125
+00:14:23,800 --> 00:14:33,120
+بالي بقوله from واحد and اتنينwe have ان ال I هذا
+
+126
+00:14:33,120 --> 00:14:38,900
+هو ال principle ideal generated by g of x يبقاش
+
+127
+00:14:38,900 --> 00:14:46,000
+استنتجنة استنتجنة ان any ideal في capital F of X
+
+128
+00:14:46,000 --> 00:14:53,500
+is a principle ideal صحيح ولا لأ يبقى this means
+
+129
+00:14:53,500 --> 00:15:09,190
+that هذا يعني انAny ideal I in capital F of X is
+
+130
+00:15:09,190 --> 00:15:14,410
+principal يبقى
+
+131
+00:15:14,410 --> 00:15:24,290
+ساعة capital F of X is a principal ideal
+
+132
+00:15:24,290 --> 00:15:24,890
+domain
+
+133
+00:15:30,760 --> 00:15:35,940
+هو المفروض اقول الفكرة مرة تانية لامهالكم مع بعض
+
+134
+00:15:35,940 --> 00:15:40,780
+عشان ترسخ المعلومة عادي عندنا if field بيقول ليه
+
+135
+00:15:40,780 --> 00:15:44,980
+capital F of X هو principal ideal domain يعني كل
+
+136
+00:15:44,980 --> 00:15:49,620
+ideal فيه بيكون principal ideal بيقول لك واحد
+
+137
+00:15:49,620 --> 00:15:54,620
+اخدنا if field يبقى هنا integral domain بأول نظرية
+
+138
+00:15:54,620 --> 00:15:58,220
+في هذا ال chapter capital F of X is an integral
+
+139
+00:15:58,220 --> 00:16:02,410
+domainهذه النقطة الأولى، نقطة تانية أخدنا ID
+
+140
+00:16:02,410 --> 00:16:07,390
+الموجود في capital F of X والله إذا كان هذا هو
+
+141
+00:16:07,390 --> 00:16:13,230
+Zero مافي إلا Zero element يبقى هذا يتولد بواسطة
+
+142
+00:16:13,230 --> 00:16:17,990
+ال Zero يبقى ال ID ال principle ID إذا والله لا
+
+143
+00:16:17,990 --> 00:16:22,570
+يساوي Zero روحت على ال ID ال I اللي مليان Pronomic
+
+144
+00:16:22,570 --> 00:16:27,770
+الخان أصغر واحدة من ال functions من ناحية ال
+
+145
+00:16:27,770 --> 00:16:31,750
+degreeالـ polynomial اللي ال degree تبعتها أصغر
+
+146
+00:16:31,750 --> 00:16:36,730
+واحدة في كل ال polynomials اللي موجودة في I و روحت
+
+147
+00:16:36,730 --> 00:16:41,550
+زعمت ان ال I هذا بدي يسوي ال principle ideal
+
+148
+00:16:41,550 --> 00:16:47,210
+generated by Jehovah أمشي خطوات أثبت هذا الكلام
+
+149
+00:16:47,210 --> 00:16:55,270
+فعلا إذا صار ال non zero ideal هو عبارة عن
+
+150
+00:16:55,270 --> 00:16:59,770
+principle ideal يعني اي non zeroواللي جابله حتى لو
+
+151
+00:16:59,770 --> 00:17:04,310
+كان Zero كمان Principle يبقى أي Ideal في capital F
+
+152
+00:17:04,310 --> 00:17:09,770
+of X هو عبارة عن Principle Ideal Domain يبقى
+
+153
+00:17:09,770 --> 00:17:14,510
+Principle Ideal يبقى Capital F of X is a Principle
+
+154
+00:17:14,510 --> 00:17:20,910
+Ideal Domain تمام؟ طيب، في عنا كمان نظرية تانية
+
+155
+00:17:20,910 --> 00:17:26,920
+متعلقة بيها ومرتبطة بيها تمام؟ حد بتسأل؟مش ممكن
+
+156
+00:17:26,920 --> 00:17:31,620
+أنه أقل درجة لـ GeoVex؟ أه GeoVex كيف GeoVex
+
+157
+00:17:31,620 --> 00:17:37,420
+موجودة في ال ID؟ كيف؟ كيف GeoVex موجودة في ال ID؟
+
+158
+00:17:37,420 --> 00:17:42,400
+ال GeoVex كنت قولت هي ال remainder، وصلنا إلى
+
+159
+00:17:42,400 --> 00:17:48,040
+المعادلة هذه، شايفها؟ هذا فرق بين تولوز، ال ID
+
+160
+00:17:48,040 --> 00:17:52,770
+أصلا subringلو أخدت two elements في ال sub ring و
+
+161
+00:17:52,770 --> 00:17:56,270
+جبت الفرق بينهم موجود في ال sub ring يعني موجود في
+
+162
+00:17:56,270 --> 00:18:02,430
+ال ideal صح أو لا لأ يبقى هذا هذا هذي فرضه في I
+
+163
+00:18:02,430 --> 00:18:09,450
+اتنين ال Geo fix موجود في I و ال I ideal other بأي
+
+164
+00:18:09,450 --> 00:18:13,490
+element من ال ideal لأي element من ال ring موجود
+
+165
+00:18:13,490 --> 00:18:16,950
+في ال ideal مش هذا هو الشرط الأخير من شروط ال
+
+166
+00:18:16,950 --> 00:18:21,050
+idealأه طيب لو ما نجلتش أنا على طرف التاني لو إيش؟
+
+167
+00:18:21,050 --> 00:18:25,970
+يعني لو مااخدتش RX فى طرف الحال مش ال GX لو إيش
+
+168
+00:18:25,970 --> 00:18:31,050
+عيدي تاني؟ لو مااخدتش ال RX فى طرف الحال طيب مش ال
+
+169
+00:18:31,050 --> 00:18:35,690
+GX هي أقل الدرجة؟ ممتاز يعني مافيش أقل منها طيب
+
+170
+00:18:35,690 --> 00:18:40,670
+ماشي شو المشكلة؟ طب حنا سوينا غير هي كان؟ لأ كيف
+
+171
+00:18:40,670 --> 00:18:48,230
+موجودة فى ال I؟هذه polynomial في ال I الفرق بينهم
+
+172
+00:18:48,230 --> 00:18:51,990
+موجود في ال I ولا لا؟ لو مش موجود في ال I، عمره ما
+
+173
+00:18:51,990 --> 00:19:00,810
+كان لا Ideal ولا Subring، مظبوط؟ يا أختي إيه يا
+
+174
+00:19:00,810 --> 00:19:03,950
+حميدة، بتقولي كيف؟ موجود في ال I، صح ولا لا؟ هي
+
+175
+00:19:03,950 --> 00:19:08,350
+سؤالك، إحنا بنقول لما عرفنا ال Subring، ثم روحنا
+
+176
+00:19:08,350 --> 00:19:13,670
+عرفنا اللي هو ال Idealإحدى الشروط إنه لو أخدت two
+
+177
+00:19:13,670 --> 00:19:17,270
+elements من ال ID اللي يبقى الفرق بينهما موجود في
+
+178
+00:19:17,270 --> 00:19:22,550
+ال ID، صحيح ولا لأ؟ طيب، روحنا عند المعادلات،
+
+179
+00:19:22,550 --> 00:19:26,270
+خلّينا ال aerobics في شكل والباقي في ناحيتان،
+
+180
+00:19:26,270 --> 00:19:32,070
+مظبوط؟ هذه ال aerobics هي موجودة في I، وهذه موجودة
+
+181
+00:19:32,070 --> 00:19:35,930
+في I، إذا الفرق بينهما موجود في I، صحيح؟ هو لو
+
+182
+00:19:35,930 --> 00:19:41,020
+فسرت لك ليه؟الـ F of X في I والـ G في I والـ I اي
+
+183
+00:19:41,020 --> 00:19:44,440
+دي يعني لما نقضر الـ G of X في اي Polynomial أخرى،
+
+184
+00:19:44,440 --> 00:19:48,900
+فهو موجود في الـ I، صحيح ولا لا؟ يبقى صار تلقى الـ
+
+185
+00:19:48,900 --> 00:19:53,700
+R of X في الـ I ولا لا؟ طيب، نجي الـ R of X، مشان
+
+186
+00:19:53,700 --> 00:19:57,140
+تبقى في I، بد ال degree تبعها تكون أقل من ال
+
+187
+00:19:57,140 --> 00:20:00,880
+degree of G، إن لم يحدث فالـ R of X بـ Zero
+
+188
+00:20:04,000 --> 00:20:08,020
+أو ال degree لل R أقل من ال degree لل G، صحيح ولا
+
+189
+00:20:08,020 --> 00:20:12,600
+لأ؟ طيب ال degree لل R ليست أقل من ال degree لأن
+
+190
+00:20:12,600 --> 00:20:17,640
+ال G هي ال minimum، تبقى إيش ضال عندي؟ R of X بده
+
+191
+00:20:17,640 --> 00:20:21,580
+يساوي 0، صح ولا لأ؟ مالهاش درجة ال R بيقوم وصحيح؟
+
+192
+00:20:21,580 --> 00:20:24,320
+مالهاش درجة، مش الاقتران الصفر؟ اللي هو مين؟ ال R
+
+193
+00:20:24,320 --> 00:20:28,480
+X بيساوي صفر؟ ماشي، صحيح، معاكي، لكن إحنا بنقول
+
+194
+00:20:28,480 --> 00:20:33,160
+أحد يحتمل أن هي إما هذا أو هذا،هذا سقط لأن Geomext
+
+195
+00:20:33,160 --> 00:20:41,300
+أقل درجة موجودة ايه المشروط اللي عندي Geomext أقل
+
+196
+00:20:41,300 --> 00:20:47,360
+درجة موجودة ايه المشروط اللي عندي Geomext أقل درجة
+
+197
+00:20:47,360 --> 00:20:51,080
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+198
+00:20:51,080 --> 00:20:54,260
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+199
+00:20:54,260 --> 00:20:56,160
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+200
+00:20:56,160 --> 00:20:57,900
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+201
+00:20:57,900 --> 00:20:58,880
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+202
+00:20:58,880 --> 00:21:02,490
+موجودة Geإذا أصبح ال F of X موجود في الprinciple
+
+203
+00:21:02,490 --> 00:21:08,930
+يبدأ يبقى subset of I subset of B طيب النضرية
+
+204
+00:21:08,930 --> 00:21:16,870
+الثانية بتقول ما يأتي تغيرها بيقول
+
+205
+00:21:16,870 --> 00:21:22,210
+ان انت ال FBA field زي النضرية اللي قبلها FBA
+
+206
+00:21:22,210 --> 00:21:41,370
+field وال Ian ideal of capital F of X and
+
+207
+00:21:41,370 --> 00:21:53,050
+g of x an element of
+
+208
+00:21:53,050 --> 00:22:05,090
+capital F of Xthen ال I هي ال principle ideal
+
+209
+00:22:05,090 --> 00:22:13,750
+generated by G of X if and only if ال G of X is a
+
+210
+00:22:13,750 --> 00:22:23,910
+non-zero polynomial is a non-zero polynomial
+
+211
+00:22:27,080 --> 00:22:38,920
+non-zero polynomial of minimum degree
+
+212
+00:22:38,920 --> 00:22:50,120
+minimum degree in R of اللي
+
+213
+00:22:50,120 --> 00:22:54,100
+هو دفعه
+
+214
+00:22:56,490 --> 00:23:03,110
+as similar to
+
+215
+00:23:03,110 --> 00:23:08,530
+the role
+
+216
+00:23:08,530 --> 00:23:16,690
+of the above hero
+
+217
+00:23:30,820 --> 00:23:36,700
+نفس البرنامج أخدنا G أنه one zero element of
+
+218
+00:23:36,700 --> 00:23:40,960
+minimum degree يبقى من النظرية اللي قبلها أثبتنا
+
+219
+00:23:40,960 --> 00:23:48,800
+أنه يساوي I إلى نفس القصة برضه بده يساوي I إذا كرق
+
+220
+00:23:48,800 --> 00:23:54,140
+ال G of minimum نعطي سؤال أو مثال تنضيحي على ذلك
+
+221
+00:23:54,140 --> 00:23:54,780
+example
+
+222
+00:23:59,940 --> 00:24:11,060
+بقول let Phi من الـ A of X onto a set of complex
+
+223
+00:24:11,060 --> 00:24:17,140
+numbers C given
+
+224
+00:24:17,140 --> 00:24:31,080
+by .. given by اللي هو Phi من الـ F of Xبدا تساوي
+
+225
+00:24:31,080 --> 00:24:42,500
+F of I بـ Homomorphism هذا يعطيني Homomorphism
+
+226
+00:24:42,500 --> 00:24:55,220
+المطلوب الأول شهو ذات بيجيلي شهو ذات ان ال X تربيع
+
+227
+00:24:55,220 --> 00:25:02,740
+زائد الواحدموجود للكيرنال للـ Phi الامر يبين show
+
+228
+00:25:02,740 --> 00:25:15,780
+that .. show that بيّن كذلك إن ال R of X موديلو لـ
+
+229
+00:25:15,780 --> 00:25:20,960
+principle ideal generated by X ترمية زاد واحد
+
+230
+00:25:20,960 --> 00:25:29,750
+isomorphic لل set of complex numbers اللي هو Cمرة
+
+231
+00:25:29,750 --> 00:25:36,970
+تانية عندنا في هموموفيزم من ال R of X إلى ال 6 of
+
+232
+00:25:36,970 --> 00:25:41,410
+complex number مُعطَى بالفي لما تأثر عليه ال
+
+233
+00:25:41,410 --> 00:25:46,370
+polynomial اللي موجودة في R of X بدي يعطينا F of I
+
+234
+00:25:46,370 --> 00:25:52,190
+يعني complex number عدد موجود في C المطموب الأول
+
+235
+00:25:52,190 --> 00:25:56,860
+جاني اثبت ان ال functionأو البرنامج ال X تربية
+
+236
+00:25:56,860 --> 00:26:01,780
+زائد واحد موجودة في ال kernel يقول والله إذا
+
+237
+00:26:01,780 --> 00:26:06,220
+صورتها طلعت ب zero يبقى موجودة في ال kernel ما
+
+238
+00:26:06,220 --> 00:26:10,060
+طلعت ب zero يبقى مش موجودة في ال kernel يبقى عين
+
+239
+00:26:10,060 --> 00:26:17,380
+مقتلولة طيب بشأن هيك بداجة أقوله افترض ان ال F of
+
+240
+00:26:17,380 --> 00:26:21,580
+X بدي سوى ال X تربية زائد واحد then
+
+241
+00:26:23,670 --> 00:26:30,410
+بدي أخد ال F of I كده بده ثالث I ترمية زايد واحد
+
+242
+00:26:30,410 --> 00:26:37,790
+كده I ترمية ثالث واحد يبقى ثالث واحد زايد واحد
+
+243
+00:26:37,790 --> 00:26:46,470
+يسوى كده؟ Zero طب ال F of I مش هي صورة F of X يبقى
+
+244
+00:26:46,470 --> 00:26:55,890
+هنا ال F of I هي Phi لل F of Xيبدو يساوي Zero هذا
+
+245
+00:26:55,890 --> 00:27:02,850
+معناه ان ال F of X يعني X تربيه زائد واحد موجودة
+
+246
+00:27:02,850 --> 00:27:08,370
+للكامل للفاتر خلصنا
+
+247
+00:27:08,370 --> 00:27:14,870
+المطبوخ الأول فهذا المطبوخ التالي نمر هذه بدنا
+
+248
+00:27:14,870 --> 00:27:22,070
+نثبت ان ال R of X Modulo ال X تربيه زائد واحد
+
+249
+00:27:22,370 --> 00:27:29,730
+Isomorphic لمن؟ لـ set of complex numbers تمام طيب
+
+250
+00:27:29,730 --> 00:27:34,710
+مش هنطول كتير مش هروح أعرف function one to one و
+
+251
+00:27:34,710 --> 00:27:40,450
+one to one لأ لأ بدي أاخد جاهز تمام طيب كيف ناخد
+
+252
+00:27:40,450 --> 00:27:45,950
+جاهز؟ اللي بيبين ليه انه هات ال first isomorphism
+
+253
+00:27:45,950 --> 00:27:51,070
+theorem بيقول الارو بيرس موديولون كيرنيت طيب سؤال
+
+254
+00:27:51,600 --> 00:28:00,180
+هذا ال X تربيه زائد واحد موجود في ال kernel موجودة
+
+255
+00:28:00,180 --> 00:28:07,340
+في ال kernel تمام انا ادعي ان ال kernel لل FI هو
+
+256
+00:28:07,340 --> 00:28:11,320
+عبارة عن ال X principal ID generated by X تربيه
+
+257
+00:28:11,320 --> 00:28:16,500
+زائد واحد هم بيقولك هذا الكلام تعالوا نشوفه نجيبه
+
+258
+00:28:16,500 --> 00:28:20,610
+لنا خليني أقولكوا هنا بقىأحنا عندنا الآن ال X
+
+259
+00:28:20,610 --> 00:28:27,290
+تربيها زي الواحد موجودة في الكيرنر طيب سؤال هل
+
+260
+00:28:27,290 --> 00:28:32,610
+هناك polynomial أصغر من ال polynomial هذه في
+
+261
+00:28:32,610 --> 00:28:39,450
+الدرجة الموجودة في الكيرنر؟ تقدر تجيبولي بس واحدة؟
+
+262
+00:28:39,450 --> 00:28:45,330
+مش إمكانية لأنه لما تيجي تعوض ب F of I ليمكن أن
+
+263
+00:28:45,330 --> 00:28:52,210
+تطلع Zero تمام؟يبقى لو جيت قلت له الامر لو أخدت ال
+
+264
+00:28:52,210 --> 00:29:02,450
+G of X يساوي ال A X زائد B وروحت قلت خذي ال G of I
+
+265
+00:29:02,450 --> 00:29:10,830
+يبقى بده يساوي A I زائد B هذه ممكن تساوي Zero؟ لأ
+
+266
+00:29:11,100 --> 00:29:16,020
+لكن لو قلت a و b ب0 يصير 0 يبقى انت مااخدتش ولا
+
+267
+00:29:16,020 --> 00:29:19,500
+حاجة اخدت معناه في الصفر وجهة تضحك علينا لا احنا
+
+268
+00:29:19,500 --> 00:29:25,180
+بدنا polynomial in general يبقى هذه does not
+
+269
+00:29:25,180 --> 00:29:30,180
+belong لprinciple ideal generated by X تربية زائد
+
+270
+00:29:30,180 --> 00:29:35,640
+واحد بمعناته ال X تربية هي ال polynomial of
+
+271
+00:29:35,640 --> 00:29:43,750
+minimum degree in I يبقى هنا ساعةالـ F of X يساوي
+
+272
+00:29:43,750 --> 00:29:57,910
+X تربية زائد واحد is .. is a polynomial of
+
+273
+00:29:57,910 --> 00:30:07,710
+minimum degree in the principle ideal generated by
+
+274
+00:30:07,710 --> 00:30:13,980
+X تربية زائد واحد، هذه أصغر واحدةطب اطلعيلي طب
+
+275
+00:30:13,980 --> 00:30:20,960
+اطلعيلي على نص النظرية رقم اتنين بيقولش اذا g of x
+
+276
+00:30:20,960 --> 00:30:26,400
+non zero polynomial of minimum degree يبدو ال I
+
+277
+00:30:26,400 --> 00:30:34,460
+بدو يساوي مين؟ بدو يساوي ال g of x يبقى by the
+
+278
+00:30:34,460 --> 00:30:36,160
+above
+
+279
+00:30:39,880 --> 00:30:49,100
+Any Ideal I Any Ideal I بده يساوي ال principle
+
+280
+00:30:49,100 --> 00:30:58,260
+Ideal generated by X³±1 طيب
+
+281
+00:30:58,260 --> 00:31:05,760
+السؤال هل الكيرنل الفي هو Ideal؟ صح ولا لا؟ يبقى
+
+282
+00:31:05,760 --> 00:31:10,030
+الكيرنل بديه يساوي مين؟ بديه يساوي هذهيبقى باري
+
+283
+00:31:10,030 --> 00:31:20,370
+بيقوله since بما أن ال kernel للفاي is an ideal R
+
+284
+00:31:20,370 --> 00:31:31,630
+اللي هو capital R of X we have من الاتنين هدول
+
+285
+00:31:31,630 --> 00:31:36,760
+يبقى ال kernel للفايبدي يساوي ال principle ideal
+
+286
+00:31:36,760 --> 00:31:43,120
+generated by X تربية زايد واحد صح؟ سكتش يا عزيزي
+
+287
+00:31:43,120 --> 00:31:52,420
+أي ideal على الشكل هذا مظبوط؟ يبقى أي ideal موجود
+
+288
+00:31:52,420 --> 00:31:57,420
+على الشكل هذا ال kernel لل Phi أثبتناه قبل ذلك أنه
+
+289
+00:31:57,420 --> 00:32:01,820
+ideal صح ولا لا؟ إذا ال kernel على الشكل اللي
+
+290
+00:32:01,820 --> 00:32:06,490
+عندنا هذا بدي يساوي هذاطب ماذا أستفيد من ذلك؟
+
+291
+00:32:06,490 --> 00:32:12,350
+بقوله R by the
+
+292
+00:32:12,350 --> 00:32:18,070
+first isomorphism
+
+293
+00:32:18,070 --> 00:32:29,870
+theorem we have ان ال R of X modulo ال L كيرنل لل
+
+294
+00:32:29,870 --> 00:32:40,410
+Phi isomorphicللـ Phi of R of X يداشى الـ Phi للـ
+
+295
+00:32:40,410 --> 00:32:47,950
+R of X؟ C لإنها on two تمام يبقى هذه بدها ساوي C
+
+296
+00:32:47,950 --> 00:32:58,090
+since Phi is on two فهي هذه صارت مين؟ الـ R of X
+
+297
+00:32:58,790 --> 00:33:03,550
+موديله ال kernel هو ال principle ID ال generated
+
+298
+00:33:03,550 --> 00:33:09,830
+by one يبقى هذا isomorphic لمين؟ لـC عظيم هو
+
+299
+00:33:09,830 --> 00:33:15,590
+المطلوب؟ و هو المطلوب خلاصه حد فيكوا بتسأل أي سؤال
+
+300
+00:33:15,590 --> 00:33:20,990
+هنا؟ ايوة احنا اتفكنا انه مش درجة اقل من اكتر برد
+
+301
+00:33:20,990 --> 00:33:26,690
+واحد ممكن تساوي سفر صح؟ تكون في ال IDيعني الـ X
+
+302
+00:33:26,690 --> 00:33:29,710
+تربية زاد واحد، الدرجة التانية هي أقل الـ
+
+303
+00:33:29,710 --> 00:33:34,970
+polynomial موجودة في هذا الـ ID الـ I دي الـ I
+
+304
+00:33:34,970 --> 00:33:37,590
+اللي هو بدنا نثبت إنه بساوي الكيرنات
+
+305
+00:33:45,200 --> 00:33:50,620
+لأيش؟ لأن ال X تربية زاد واحد أقل degree حققت F of
+
+306
+00:33:50,620 --> 00:33:53,700
+Y سوى Zero بس مش موجودة في ال ID ولا مش موجودة في
+
+307
+00:33:53,700 --> 00:33:59,560
+ال Kernel؟ مش موجودة في ال Kernel طيب ما احنا ال
+
+308
+00:33:59,560 --> 00:34:03,080
+Kernel هتتفنى .. بس احنا بالأسل أول يعني بس ..
+
+309
+00:34:03,080 --> 00:34:08,580
+احنا قلنا هذا هاي اللي أخد G of X سوى هذا G of Y
+
+310
+00:34:08,580 --> 00:34:14,880
+سوى كذا مش موجود في ال X يعني لا يحقق هذه المعادلة
+
+311
+00:34:15,580 --> 00:34:20,480
+وبعد شوية بصير هذا مش موجود في ال I لإن ال I هي ال
+
+312
+00:34:20,480 --> 00:34:24,900
+kernel هي ال principle ideal generated by X تربية
+
+313
+00:34:24,900 --> 00:34:30,160
+زاد واحد هي هي يعني هذه كمان ولا يهمك تقول it does
+
+314
+00:34:30,160 --> 00:34:36,200
+not belong to I برضه موافق هذه و هذه التنتين صح
+
+315
+00:34:36,200 --> 00:34:40,700
+لإن بعد شوية أثبت لك أن هذا هو هذا سواء هذا والله
+
+316
+00:34:40,700 --> 00:34:47,670
+هذا سيئة في أي استفسار أخرطيب، لأت الآن لحل بعض
+
+317
+00:34:47,670 --> 00:34:56,110
+الأسئلة خلاص
+
+318
+00:34:56,110 --> 00:35:01,770
+الشفتة فسي
+
+319
+00:35:01,770 --> 00:35:07,860
+الجبر تلاقي النظر يحبي معروفانوالأسئلة فيها
+
+320
+00:35:07,860 --> 00:35:15,160
+معلومات برضه كتيرة وكأنها جديدة أحيانا. يبقى بنيدي
+
+321
+00:35:15,160 --> 00:35:24,560
+على شبتر ستاشر. فشبتر ستاشر بلد اللي هو الأسئلة
+
+322
+00:35:24,560 --> 00:35:30,640
+بتبعه. يبقى exercises على شبتر ستاشر.
+
+323
+00:35:40,760 --> 00:35:45,280
+السؤال الأول حلناه زيه السؤال التالت عرض مباشر
+
+324
+00:35:45,280 --> 00:35:51,140
+السؤال التالت حلناه شخصيا حلناه السؤال هذا بدنا
+
+325
+00:35:51,140 --> 00:35:59,020
+نروح للسؤال الغرق الغرق بيقول لي if ال a is
+
+326
+00:35:59,020 --> 00:36:09,200
+commutative commutative ring شو
+
+327
+00:36:09,200 --> 00:36:19,050
+دهshow that إن ال characteristics لل R of X بدأت
+
+328
+00:36:19,050 --> 00:36:35,530
+ساوى ال characteristics لمين لل R بحل
+
+329
+00:36:35,530 --> 00:36:41,420
+هذا السؤال نكون حلينا سؤال أربعةو السؤال تمانية و
+
+330
+00:36:41,420 --> 00:36:47,220
+احنا مش ذارين هم بنوريكم كيف نحلهم اتنين مرة واحدة
+
+331
+00:36:47,220 --> 00:36:54,140
+بسؤال اربع بيقول لي لو فات ال R commutative يبقى
+
+332
+00:36:54,140 --> 00:36:59,060
+ال characteristic ل ال R هي نفس ال characteristic
+
+333
+00:36:59,060 --> 00:37:06,620
+لمين؟ R of X بنقول له تماني بدي اروح اجيب صوت ب
+
+334
+00:37:06,620 --> 00:37:11,640
+ring من مين؟من ال ring A من ال polynomial ring A
+
+335
+00:37:11,640 --> 00:37:22,300
+تمام ابادي بقوله ما يأتي led ال S بي the set of
+
+336
+00:37:22,300 --> 00:37:33,540
+all constant polynomials polynomials
+
+337
+00:37:33,540 --> 00:37:47,840
+ofR of X ذات X هذا كلام غريب ده أحطه في صيغة يهضيه
+
+338
+00:37:47,840 --> 00:37:54,540
+لما أحطه في صيغة يهضيه يتجلس كل ال polynomials
+
+339
+00:37:54,540 --> 00:38:03,280
+اللي هو F of X اللي موجودة في capital R of X بحيث
+
+340
+00:38:03,280 --> 00:38:14,390
+أنf of x بده يساوي a و ال a is constant عزيزي
+
+341
+00:38:14,390 --> 00:38:21,970
+شوفنا هذه السيطرة قبل هيك في الأسئلة قبل شترين و
+
+342
+00:38:21,970 --> 00:38:29,290
+أثبتنا إنها صابرين تمام؟ يبقى هذا بده يخلي هذي ي
+
+343
+00:38:29,290 --> 00:38:32,090
+check that
+
+344
+00:38:33,610 --> 00:38:42,530
+الـ S is a subring of
+
+345
+00:38:42,530 --> 00:38:55,530
+X تأكديلي أن هذه هي subring من الـ S تمام الآن سوف
+
+346
+00:38:55,530 --> 00:38:59,190
+أعرف الـ function Define
+
+347
+00:39:01,070 --> 00:39:06,950
+A function على A mapping Phi
+
+348
+00:39:06,950 --> 00:39:19,190
+من الـR للـS by Phi of ال element R يجب أن أضعه في
+
+349
+00:39:19,190 --> 00:39:26,750
+S يعني constant لأن كلهم constant و ليكن R لكل
+
+350
+00:39:26,750 --> 00:39:29,010
+الـR اللي موجودة في الـR
+
+351
+00:39:34,020 --> 00:39:40,640
+متعرف فانكشن فاي من R إلى S By Phi of R بيبقى ساوي
+
+352
+00:39:40,640 --> 00:39:46,380
+R ليش؟ لإن ال S العناصر اللي بيبقى F of X كلها
+
+353
+00:39:46,380 --> 00:39:52,580
+بيبقى ساوي constant مقدار ثابت يبقى المقدار ثابت
+
+354
+00:39:52,580 --> 00:39:57,720
+اللي هو R إلي عندنا إذا أثبت أن Phi هو
+
+355
+00:39:57,720 --> 00:40:02,830
+homomorphism هو one to oneوانتوا تصير في
+
+356
+00:40:02,830 --> 00:40:09,950
+isomorphism ما بين الاتنين سؤال هو واش استفدناه؟
+
+357
+00:40:09,950 --> 00:40:13,910
+يبقى نفس الخواصة الرياضية يعني ال characteristic
+
+358
+00:40:13,910 --> 00:40:20,610
+لل R بصير هو ال characteristic لمين؟ لل S اتنين زي
+
+359
+00:40:20,610 --> 00:40:25,370
+بعض و بعدين بيظل علينا خطوة بنعملها مش مشكلة طيب
+
+360
+00:40:25,810 --> 00:40:33,690
+يبقى بداخل اقول الـ Phi is homomorphic يبقى بداخل
+
+361
+00:40:33,690 --> 00:40:43,710
+Phi of R1 زائد R2 حسب التعريف R1 زائد R2 R1 هي Phi
+
+362
+00:40:43,710 --> 00:40:55,370
+of R1 والتانية Phi of R2 اللي بعدها and Phi of R1
+
+363
+00:40:55,830 --> 00:41:03,930
+R2 هذا الكلام يتساوي R1 R2 طبقا للـ definition الـ
+
+364
+00:41:03,930 --> 00:41:12,650
+R1 هي Phi of R1 و Phi of R2 هذا الكلام صحيح لكل
+
+365
+00:41:12,650 --> 00:41:19,330
+الـ R1 وR2 اللي موجود في الـ R وهذا صحيح لكل الـ
+
+366
+00:41:19,330 --> 00:41:24,770
+R1وR2 اللي موجود في الـR لذلك Phi is a
+
+367
+00:41:24,770 --> 00:41:32,670
+homomorphism Phi is one to one يمكن بالدرجة أقوله
+
+368
+00:41:32,670 --> 00:41:41,390
+افترض ان Phi of R1 بتساوي Phi of R2 عسب ال
+
+369
+00:41:41,390 --> 00:41:48,230
+definition Phi of R1 هي في R1 Phi of R2 هي في R2
+
+370
+00:41:48,470 --> 00:41:54,690
+يبقى أخد صوتين متساويتين لقيت أن أصلهم متساوي لذلك
+
+371
+00:41:54,690 --> 00:42:04,010
+five is one to one بعدين five is on يقعد ياخد
+
+372
+00:42:04,010 --> 00:42:15,210
+element وليكن وي موجود في اسم وي موجود في اسم يبقى
+
+373
+00:42:15,210 --> 00:42:24,190
+هذا بالدنيا قيمةإن Y تساوي مين؟ تساوي F of X اللي
+
+374
+00:42:24,190 --> 00:42:33,130
+هو constant وليكن A لأن عناصر S كله اللي هو دوال
+
+375
+00:42:33,130 --> 00:42:40,310
+ثوابت تمام أليس هذا هو I of A حسب ال definition
+
+376
+00:42:40,310 --> 00:42:48,690
+تمام يبقى Y اللي أخدته في S لجيتله أصلفي من؟ في ال
+
+377
+00:42:48,690 --> 00:42:54,730
+.. في R اللي هو من اللي هو إيه؟ يبقى Phi is under
+
+378
+00:42:54,730 --> 00:43:05,650
+يبقى هنا ف Phi is an isomorphism طيب إيش استفدنا
+
+379
+00:43:05,650 --> 00:43:15,080
+من ذلك؟ استفدنا إن ال characteristic لل-Rيساوي
+
+380
+00:43:15,080 --> 00:43:23,200
+characteristic لمن؟ لل S فبستنى شوية هل في منها
+
+381
+00:43:23,200 --> 00:43:30,500
+فائدة؟ أه في منها فائدة شو الفائدة المرجوة منها؟
+
+382
+00:43:30,500 --> 00:43:34,020
+السؤال
+
+383
+00:43:34,020 --> 00:43:38,980
+هو إيش علاقة ال S ب capital R
+
+384
+00:43:44,390 --> 00:43:55,870
+بما أن ال S صبست من R of X نحن لدينا ان ال
+
+385
+00:43:55,870 --> 00:44:03,190
+characteristic لل S أقل من أو يساوي ال
+
+386
+00:44:03,190 --> 00:44:09,790
+characteristic لمن؟ لل A طب ال characteristic لل S
+
+387
+00:44:09,790 --> 00:44:16,110
+من هو؟هو لو شفت اكتر استك لل R بدي اشيله و اكتب
+
+388
+00:44:16,110 --> 00:44:24,010
+بداله ال characteristic ال characteristic لل R of
+
+389
+00:44:24,010 --> 00:44:29,590
+X هذا بدي اعطيكي ال characteristic لل S هشيلها و
+
+390
+00:44:29,590 --> 00:44:38,210
+اكتب بدالها ال characteristic لل R اقل من او يساوي
+
+391
+00:44:38,210 --> 00:44:44,050
+ال characteristicللـ R of X واتبريلي هذه المعادلة
+
+392
+00:44:44,050 --> 00:44:50,850
+لرقم واحد إذا قدرت أثبت إن ال characteristics للـ
+
+393
+00:44:50,850 --> 00:44:55,710
+R of X أقل من أو يسوء ال characteristics لـ R يبقى
+
+394
+00:44:55,710 --> 00:45:04,790
+بيحدث التساوي تمام؟ يبقى بدالي أقولك للـ
+
+395
+00:45:04,790 --> 00:45:08,730
+R has بي
+
+396
+00:45:11,400 --> 00:45:19,260
+of characteristic k طب ال R ال characteristic L هي
+
+397
+00:45:19,260 --> 00:45:33,380
+يسوى k and let f of x بتسوى a n x n a n minus ال 1
+
+398
+00:45:33,380 --> 00:45:42,330
+x n minus ال 1 زائد a 1 x زائد ال a نوتموجودة وين؟
+
+399
+00:45:42,330 --> 00:45:48,230
+في ال R of X مرة
+
+400
+00:45:48,230 --> 00:45:54,630
+تانية فردت ان ال characteristic ل R يسوي K وفردت
+
+401
+00:45:54,630 --> 00:45:59,590
+ان ال F of X موجودة وين؟ في ال R of X اللي عندنا
+
+402
+00:45:59,590 --> 00:46:07,730
+ايش رأيكم؟ بدي اضرب K في ال F of X و بدي اضرب K في
+
+403
+00:46:07,730 --> 00:46:14,700
+الناحية التانية كلهاهذا سيعطينا k في مين؟ في a in
+
+404
+00:46:14,700 --> 00:46:23,340
+x in a in minus one x in minus one زائد a one x
+
+405
+00:46:23,340 --> 00:46:30,660
+زائد a naught هذا الكلام يساوي k في a in x to the
+
+406
+00:46:30,660 --> 00:46:38,580
+power n k في a in minus one x to the power n minus
+
+407
+00:46:38,580 --> 00:46:47,840
+oneزائد الـK في الـA1X زائد الـK في الـA0 سؤال هو
+
+408
+00:46:47,840 --> 00:46:55,280
+كده هذا؟ Zero لأن الـANPR والـcharacteristic L هي
+
+409
+00:46:55,280 --> 00:47:03,300
+سوى K كده هذا؟ Zero وهذا Zero وهذا Zero وهذا Zero
+
+410
+00:47:03,300 --> 00:47:09,920
+لأن الإيهات كلهم عناصر من عناصر الـRing A تماممدام
+
+411
+00:47:09,920 --> 00:47:17,280
+زيرو يسوى زيرو زائد زيرو زائد زيرو بتسوى زيرو
+
+412
+00:47:17,280 --> 00:47:26,700
+تمام؟ إذا الكابلات ضربته في أحد عناصر اللي هو ال R
+
+413
+00:47:26,700 --> 00:47:31,580
+of X طالع الناتد يسوى زيرو يبقى يا هذا هو ال
+
+414
+00:47:31,580 --> 00:47:37,440
+characteristic يا رقم أصغر منه صح ولا لا؟يعني لما
+
+415
+00:47:37,440 --> 00:47:41,480
+أقول K هو الـ Characteristic اتنين K بيجيب ليه
+
+416
+00:47:41,480 --> 00:47:44,920
+أصفار و تلاتة K بيجيب و مية K بيجيب ليها أصفار
+
+417
+00:47:44,920 --> 00:47:51,040
+كلهم يبقى الـ Characteristic يا K يا إما أقل من K،
+
+418
+00:47:51,040 --> 00:47:58,980
+تمام؟ هاي ضربت الـ K في element من ال R of X يبقى
+
+419
+00:47:58,980 --> 00:48:08,600
+هنا سواء الـ Characteristic للـ R of Xأقل من وقد
+
+420
+00:48:08,600 --> 00:48:17,040
+يساوي K طيب من هو ال K characteristic لها؟ يبقى
+
+421
+00:48:17,040 --> 00:48:25,540
+هذا بده يعطينا ان ال characteristic لل R of X أقل
+
+422
+00:48:25,540 --> 00:48:32,500
+من أو يساوي ال characteristic لمن؟ لل R هو يساوي K
+
+423
+00:48:32,500 --> 00:48:38,730
+هذه العلاقة رقم اتنينطالعيلي في واحد و اثنين في
+
+424
+00:48:38,730 --> 00:48:47,370
+واحد و اثنين اتنين R equal يبقى هنا from واحد and
+
+425
+00:48:47,370 --> 00:48:54,130
+اتنين ال characteristic لcapital
+
+426
+00:48:54,130 --> 00:49:03,210
+R of X هو بالضبط تماما ال characteristic لمين بالR
+
+427
+00:49:04,080 --> 00:49:08,260
+فيها انا طرحت كلمة لكن مش شايفين هو هنا في الشغل
+
+428
+00:49:08,260 --> 00:49:13,260
+شغل كلمة قولناها ده حل سؤال تمانية سؤال تمانية
+
+429
+00:49:13,260 --> 00:49:17,540
+بيقولي خد ال R commutative ring بيجيلي ان ال R of
+
+430
+00:49:17,540 --> 00:49:25,120
+X has a sub ring isomorphic لمين؟ isomorphic ل R،
+
+431
+00:49:25,120 --> 00:49:29,520
+مين هي؟ ال S اللي أخدناها هذه وهي أتبعناها
+
+432
+00:49:29,520 --> 00:49:33,900
+isomorphic ل Rيبقى حلينا سؤال تمانية واحدة مش
+
+433
+00:49:33,900 --> 00:49:42,960
+دارية تمام؟ خديني .. خديني المسائل التالية يبقى
+
+434
+00:49:42,960 --> 00:49:51,080
+هذا ال exercises قلول سؤال أتناشر تجيبوا حلينه
+
+435
+00:49:51,080 --> 00:49:55,080
+إزاي سؤال إحدى عشر اللي جابله طبعا زي إحدى عشر
+
+436
+00:49:55,080 --> 00:49:59,260
+والإحدى عشر جواب عنكوا بالكتابة هذا مش حلول بنا
+
+437
+00:49:59,260 --> 00:50:09,330
+نحلله زيهوغير الـ 12، بدنا سؤال 17، نظرة لأهميته
+
+438
+00:50:09,330 --> 00:50:18,050
+لزملة في ال chapters القادمة، وسؤال 18،
+
+439
+00:50:18,050 --> 00:50:22,550
+سؤال 24،
+
+440
+00:50:22,550 --> 00:50:29,090
+وسؤال 30، وسؤال 36،
+
+441
+00:50:32,600 --> 00:50:41,640
+وسؤال اتنين واربعين. يالا. طيب إذا هنا انتهت هذه
+
+442
+00:50:41,640 --> 00:50:45,360
+المحاضرة و القادة المحاضرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aa62fba5155d6ef2c36d5b27923419ca828f787c
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk.srt
@@ -0,0 +1,1350 @@
+1
+00:00:20,740 --> 00:00:25,440
+بسم الله الرحمن الرحيم. اليوم، إن شاء الله، سنكمل حل
+
+2
+00:00:25,440 --> 00:00:29,220
+المسائل التابعة لهذا الـ section، المرة القادمة ستكون
+
+3
+00:00:29,220 --> 00:00:35,580
+حلنا بعض المسائل، ووقفنا عند سؤال أربعين. طيب، سؤال
+
+4
+00:00:35,580 --> 00:00:42,400
+أربعين يقول لي: النقطة الأولى، اثبت لي أن Z سبعة أو
+
+5
+00:00:42,400 --> 00:00:48,400
+جذر ثلاثة هي عبارة عن ماذا؟ فسؤال أربعين هو عبارة
+
+6
+00:00:48,400 --> 00:00:58,880
+عن مطلوبين. المطلوب الأول (نمرة a): show that Z7 of
+
+7
+00:00:58,880 --> 00:01:06,800
+square root لثلاثة is. ولو بحط التعريف التابع له، دفع
+
+8
+00:01:06,800 --> 00:01:15,020
+التعريف التابع لهذا هو عبارة عن a + b جذر
+
+9
+00:01:15,020 --> 00:01:24,190
+ثلاثة، بحيث أن a و b موجودة في Z سبعة. is a field.
+
+10
+00:01:24,190 --> 00:01:31,850
+هذا ما بدنا نقوله. الحل كان كالآتي: solution. الحل
+
+11
+00:01:31,850 --> 00:01:36,570
+بسيط جداً، موجود بين أيديكم. ولو أنكم مش ماخذين
+
+12
+00:01:36,570 --> 00:01:43,590
+بالكوينز كيف موجود بين أيدينا. السؤال هو: Z سبعة هو
+
+13
+00:01:43,590 --> 00:01:48,310
+square root لثلاثة، commutative ring with unity؟ أم لا؟
+
+14
+00:01:48,310 --> 00:01:59,950
+لا، الـ ZN عموماً يبقى هذا commutative ring with
+
+15
+00:01:59,950 --> 00:02:05,690
+unity. تمام.
+
+16
+00:02:05,690 --> 00:02:13,790
+طيب، الآن، لو رجعنا إلى المثال رقم أربعة الذي شرحناه
+
+17
+00:02:13,790 --> 00:02:19,440
+في المحاضرة الأولى. مثال رقم أربعة، يبقى بقول هنا:
+
+18
+00:02:19,440 --> 00:02:31,080
+from example four، شرحناها سابقاً. We have we have
+
+19
+00:02:31,080 --> 00:02:40,200
+أن Zp جذر ثلاثة، ولا Z سبعة لأن p هنا عندنا
+
+20
+00:02:40,200 --> 00:02:49,090
+هنا يعني سبعة، يبقى Z سبعة جذر ثلاثة is an
+
+21
+00:02:49,090 --> 00:02:56,530
+integral domain. تمام؟
+
+22
+00:02:56,530 --> 00:03:01,090
+يبقى هذه integral domain. السؤال هو: هل هذه الـ ring
+
+23
+00:03:01,090 --> 00:03:04,810
+finite أم infinite؟ والـ integral domain finite
+
+24
+00:03:04,810 --> 00:03:08,770
+أم infinite؟ finite. واحنا خدنا نظرية: every
+
+25
+00:03:08,770 --> 00:03:16,490
+finite integral domain is a field. يبقى بطبيعة الحال، Z
+
+26
+00:03:16,490 --> 00:03:29,350
+سبعة جذر ثلاثة is finite. مادام finite و integral
+
+27
+00:03:29,350 --> 00:03:40,410
+domain finite and integral domain، يبقى هذا يعطينا
+
+28
+00:03:40,410 --> 00:03:50,290
+أن Z سبعة جذر ثلاثة is a... فيه ال... ده يبقى
+
+29
+00:03:50,290 --> 00:03:54,110
+هذا عبارة عن ماذا؟ عبارة عن field. يبقى هذا المطلوب
+
+30
+00:03:54,110 --> 00:03:58,150
+الأول من السؤال، وهو المطلوب السهل الذي ما فيه
+
+31
+00:03:58,150 --> 00:04:05,290
+فيه مشكلة. نمرة ب: المشكلة في نمرة ب. نمرة ب يقول
+
+32
+00:04:05,290 --> 00:04:18,490
+لي: ما يأتي. يقول لي: بدنا find the necessary and
+
+33
+00:04:18,490 --> 00:04:23,110
+sufficient
+
+34
+00:04:23,110 --> 00:04:32,650
+condition
+
+35
+00:04:32,650 --> 00:04:41,870
+for Zp
+
+36
+00:04:42,870 --> 00:04:53,470
+جذر الـ k. جذر الـ k، ثم يقفل
+
+37
+00:04:53,470 --> 00:05:01,670
+ثم يقفل.
+
+38
+00:05:01,670 --> 00:05:07,230
+راح
+
+39
+00:05:07,230 --> 00:05:14,290
+يأخذ k  عدد صحيح، ويأخذ p عدد أولي. قال: هات لي الـ necessary
+
+40
+00:05:14,290 --> 00:05:21,990
+and sufficient condition بحيث يكون Zp جذر الـ k
+
+41
+00:05:21,990 --> 00:05:28,350
+is a field. أنا أَدّعي أن الـ necessary and sufficient
+
+42
+00:05:28,350 --> 00:05:36,770
+condition for Zp جذر k to be a field is: x تربيع
+
+43
+00:05:36,770 --> 00:05:54,150
+تساوي k has no solution in Zp. that is in الـ
+
+44
+00:05:54,150 --> 00:06:07,490
+x تربيع تساوي k has no solution in Zp if and only
+
+45
+00:06:07,490 --> 00:06:22,300
+if Zp جذر الـ k is a field. تمام؟
+
+46
+00:06:22,300 --> 00:06:30,020
+طيب، نوضح هذا الكلام. نمضي
+
+47
+00:06:30,020 --> 00:06:37,490
+من السؤال: ما هو الشرط الضروري والكافي الذي
+
+48
+00:06:37,490 --> 00:06:44,790
+يتحقق في كل من p و k بحيث أنّه يطلع Zp جذر k هو
+
+49
+00:06:44,790 --> 00:06:50,730
+عبارة عن field. تصبح هذه السيارة رياضية. أنا
+
+50
+00:06:50,730 --> 00:06:57,770
+أَدّعي أن الشرط هو: x تربيع تساوي k has no solution
+
+51
+00:06:57,770 --> 00:07:04,570
+in Zp if and only if Zp جذر الـ k is a field.
+
+52
+00:07:05,110 --> 00:07:11,950
+الادعاء هذا لا يكون صحيحاً إلا إذا أثبتناه. يبقى
+
+53
+00:07:11,950 --> 00:07:18,870
+بقول: الحلقة التالية. كلمة field. field تعني أن المسار
+
+54
+00:07:18,870 --> 00:07:25,890
+يسير باتجاهين. يبقى بالاختصار أقول: افترض أن الـ x
+
+55
+00:07:25,890 --> 00:07:38,670
+تربيع تساوي k has no solution. no solution in Zp. ماذا
+
+56
+00:07:38,670 --> 00:07:45,110
+أريد أن أثبت؟ أريد أن أثبت أن Zp جذر k is a field.
+
+57
+00:07:45,110 --> 00:07:54,370
+يعني كل عنصر غير صفري يكون له معكوس ضربي في الـ field.
+
+58
+00:07:54,370 --> 00:08:00,830
+ما معنى field؟ كل عنصر غير صفري له معكوس
+
+59
+00:08:00,830 --> 00:08:06,300
+multiplicative inverse. يبقى كل عنصر غير صفري له
+
+60
+00:08:06,300 --> 00:08:10,560
+معكوس. يبقى نقول: افترض أن x تربيع تساوي k
+
+61
+00:08:10,560 --> 00:08:16,040
+has no solution in Zp. مالهاش حل، الذي هو الادعاء
+
+62
+00:08:16,040 --> 00:08:21,160
+الذي نحن متَّدعِينه. بدنا نثبت أن هذا الكلام is a
+
+63
+00:08:21,160 --> 00:08:29,220
+field. لذلك، أذهب وأقول: خذ لي عنصر a + b
+
+64
+00:08:29,220 --> 00:08:40,980
+جذر الـ k موجود في Zp جذر الـ k such that بحيث أن
+
+65
+00:08:40,980 --> 00:08:51,120
+a + b جذر الـ k  ≠ 0. هذا الكلام لا
+
+66
+00:08:51,120 --> 00:08:59,820
+يساوي صفراً. نذهب ونثبت أن هذا العنصر معكوس
+
+67
+00:08:59,820 --> 00:09:04,470
+له. (English). إذا كنتَ تثبت أن له معكوس، العنصر
+
+68
+00:09:04,470 --> 00:09:09,270
+العشوائي، معناته فعلاً... زي نقول: نجي للحالة
+
+69
+00:09:09,270 --> 00:09:13,530
+الثانية، التي b لا تساوي صفر. بعد ما انتهينا من
+
+70
+00:09:13,530 --> 00:09:18,970
+الحالة b تساوي صفر. فلو كانت الـ b لا تساوي صفر،
+
+71
+00:09:18,970 --> 00:09:23,970
+أفترض أنا من عندي أن هذه القيمة لا تساوي صفر، و
+
+72
+00:09:23,970 --> 00:09:28,150
+أريد أن أُروحها بالبرهان. يعني مش أَدّعي ادعاء دون برهان.
+
+73
+00:09:28,150 --> 00:09:33,230
+أريد أن أبرهنها. فجئت وقلت: لو كان يساوي صفر،
+
+74
+00:09:33,230 --> 00:09:37,090
+ماذا أريد أن يحدث؟ أُمْشي بالشكل الذي أنا لقيته: k
+
+75
+00:09:37,090 --> 00:09:43,070
+يساوي a + b تربيع. يعني هذه المعادلة: x تربيع يساوي k
+
+76
+00:09:43,070 --> 00:09:48,130
+صار لها حلٌّ، وأنا فرضت أنها مالهاش حلّ، يبقى هذا
+
+77
+00:09:48,130 --> 00:09:53,150
+الادعاء غير صحيح، وعكسه هو الصحيح. إذا الـ
+
+78
+00:09:53,150 --> 00:09:58,870
+a تربيع ناقص b تربيع k لا يمكن أن يساوي... لا يمكن أن
+
+79
+00:09:58,870 --> 00:10:04,450
+يساوي صفر. مادام لا يمكن أن يساوي صفر، يبقى واحد
+
+80
+00:10:04,450 --> 00:10:09,310
+على هذا المقدار يصير معرف، لأن لو كان المقام يساوي
+
+81
+00:10:09,310 --> 00:10:13,870
+صفر، يصير ∞ غير معرف. لكن المقام لا يساوي
+
+82
+00:10:13,870 --> 00:10:17,410
+صفراً، يبقى واحد على هذا المقدار يصير معرف. أذهب
+
+83
+00:10:17,410 --> 00:10:23,270
+(Symmetry) أو a تربيع ناقص b تربيع k، كلّه مرفوع للأس
+
+84
+00:10:23,270 --> 00:10:28,560
+سالِب واحد. المهم، هذا يأخذ حاصل ضرب القوسين هذين.
+
+85
+00:10:28,560 --> 00:10:34,040
+نَظراً لضربنا القسمة، صار ضرب. المقدار الذي عندنا هذا، أريد
+
+86
+00:10:34,040 --> 00:10:40,260
+أن أرى لماذا وصل إلى هذا. مع السلامة. يبقى هذا يريد
+
+87
+00:10:40,260 --> 00:10:52,630
+أن يُساوي a تربيع ناقص... ناقص b تربيع k. كلّه قوس. هذا
+
+88
+00:10:52,630 --> 00:11:01,030
+الكلام يريد أن يُساوي a تربيع ناقص b تربيع k. b تربيع k
+
+89
+00:11:01,030 --> 00:11:08,730
+كله مضروب في c. c هيها فوق. يبقى فيه a تربيع ناقص
+
+90
+00:11:08,730 --> 00:11:14,950
+b تربيع k أس سالب واحد. هذا القوس، هذا القوس نفسه.
+
+91
+00:11:14,950 --> 00:11:21,200
+يبقى هذا عبارة عن الأس صفر. يبقى كلّه في... قداش؟ واحد.
+
+92
+00:11:21,200 --> 00:11:26,680
+يبقى هذا العنصر له معكوس. من هو معكوسه؟ الذي هو الـ term
+
+93
+00:11:26,680 --> 00:11:35,040
+الذي عندنا هذا. يبقى this means that هذا يعني every
+
+94
+00:11:35,040 --> 00:11:47,960
+non-zero element، الذي هو الـ a + b جذر الـ k in Z
+
+95
+00:11:47,960 --> 00:11:57,070
+p جذر k has an inverse. يبقى معنى هذا الكلام
+
+96
+00:11:57,070 --> 00:12:06,290
+أن هذا is a field. يبقى صراحةً Zp
+
+97
+00:12:06,290 --> 00:12:15,350
+جذر k is a field. اهو المفهوم، نمشي من اتجاه
+
+98
+00:12:15,350 --> 00:12:24,840
+المعاكس. يبقى أبدأ أقول: conversely. Assume that
+
+99
+00:12:24,840 --> 00:12:36,020
+Assume that Zp جذر k is a field.
+
+100
+00:12:36,020 --> 00:12:47,030
+one to show. one to show. بما أذهب، أُبين أن x
+
+101
+00:12:47,030 --> 00:12:57,970
+تربيع تساوي k has no solution. no
+
+102
+00:12:57,970 --> 00:13:05,190
+solution in Zp. أظن أخذنا البرهان بالـ
+
+103
+00:13:05,190 --> 00:13:12,330
+Contrapositive. مطلوب هذه. أريد أن أفترض عكسها، إذا وصلتُ
+
+104
+00:13:12,330 --> 00:13:18,980
+إلى تناقض، يبقى فرضي خاطئ، وعكسه هو الصحيح. طبعاً، يعني
+
+105
+00:13:18,980 --> 00:13:28,320
+يبقى أقول: الآن، let x تربيع تساوي k has a
+
+106
+00:13:28,320 --> 00:13:39,640
+solution in Zp. هذا يريد أن يعطينا أن a تربيع تساوي
+
+107
+00:13:39,640 --> 00:13:49,870
+k، و a موجودة في Zp. طبعاً، مرة ثانية أقول: نحن لا
+
+108
+00:13:49,870 --> 00:13:55,130
+نمشي لاتجاه الآخر، لاتجاه المعاكس. يبقى فرضي هذا
+
+109
+00:13:55,130 --> 00:13:59,650
+عبارة عن field، وأريد أن أحاول أثبت أن المعادلة x تساوي
+
+110
+00:13:59,650 --> 00:14:04,890
+و x تربيع تساوي k هذه، مالهاش حلٌّ، لأنّ أذهب وأفترض أنّها
+
+111
+00:14:04,890 --> 00:14:13,930
+لها حلٌّ. لها حلٌّ. معناته كل عنصر في Zp
+
+112
+00:14:14,380 --> 00:14:19,840
+أريد... ممكن أقول: a تربيع يريد أن يُساوي من؟ يريد أن يُساوي k.
+
+113
+00:14:19,840 --> 00:14:26,780
+هذا الكلام صحيح، أريد أن أفترضه. تمام. خذ لي هذين العنصرين، و
+
+114
+00:14:26,780 --> 00:14:33,740
+تعالَ نرى إلى أين يريدون أن يصلوا. فَأَجِبُ وأقول: let x
+
+115
+00:14:33,740 --> 00:14:45,110
+يساوي a  zp - 1 جذر k  موجود في Zp.
+
+116
+00:14:45,110 --> 00:14:54,030
+وفي جذر k أم لا؟ لأن هذا رقم، صح؟ والـ y بدل
+
+117
+00:14:54,030 --> 00:15:03,750
+أن يُساوي a + جذر k. ذلك. أريد أن آخذ x في y،
+
+118
+00:15:03,750 --> 00:15:10,310
+أرى ماذا يعطيني. إلى أين أريد أن أصل؟ أخذت عنصرين، أستطيع
+
+119
+00:15:10,310 --> 00:15:18,180
+الله أعلم. سمّيت الأول a zp - 1 جذر k، وسمّيت
+
+120
+00:15:18,180 --> 00:15:25,340
+الثاني a + جذر k، وبدأت أضربهم في بعضهم. a في a بـ
+
+121
+00:15:25,340 --> 00:15:38,490
+a تربيع. a في جذر k بـ a جذر k. نضرب a في
+
+122
+00:15:38,490 --> 00:15:46,990
+كل الطرف الأيمن. أضربه هنا. p k في a. تمام. يبقى
+
+123
+00:15:46,990 --> 00:16:00,350
+زائد p p a جذر k. نضرب p جذر k في a.
+
+124
+00:16:00,350 --> 00:16:10,150
+الذي قُدامه ناقص a جذر k. ناقص a جذر k.
+
+125
+00:16:10,150 --> 00:16:20,750
+باقي عندنا آخر حاجة. يبقى باقي p في k. يبقى زائد p
+
+126
+00:16:20,750 --> 00:16:29,290
+في k. باقي عندنا ناقص الذي هو جذر k في جذر
+
+127
+00:16:29,290 --> 00:16:37,690
+k. يبقى ناقص k. يبقى نتيجة الـ xy... يبقى يصبح عندنا الـ x
+
+128
+00:16:37,690 --> 00:16:46,290
+y يساوي كذا. a تربيعها يا بنات؟ k. يبقى أستطيع
+
+129
+00:16:46,290 --> 00:16:51,270
+أن أشيلها وأضع مكانها k. يبقى هذا الكلام يساوي
+
+130
+00:16:51,270 --> 00:17:00,990
+k. طيب، زائد ak وناقص ak، مع السلامة. طيب، هذا الـ p
+
+131
+00:17:00,990 --> 00:17:03,810
+ak كذا؟
+
+132
+00:17:06,070 --> 00:17:13,230
+مضاعفات... التي هي العناصر في Zp. قد ايش؟ مضاعفات
+
+133
+00:17:13,230 --> 00:17:17,530
+إذاً هي p، بصفر. صح أم لا؟ صفر تضربه في أي حاجة بصفر.
+
+134
+00:17:17,530 --> 00:17:25,270
+صفر. نضرب هذا بصفر وهذا أيضاً يذهب بصفر. صح؟
+
+135
+00:17:25,270 --> 00:17:33,870
+مظبوط؟ ماذا بقي عندنا؟ بقي عندنا سالب k. نضرب هذا بسالب
+
+136
+00:17:33,870 --> 00:17:45,260
+k يساوي صفر. مظبوط. يبقى أصبح عندنا الـ x و y أو الـ
+
+137
+00:17:45,260 --> 00:17:56,020
+x و الـ y are zero divisors. مظبوط. يبقى لا يمكن أن يكون
+
+138
+00:17:56,020 --> 00:18:02,700
+integral domain. وبالتالي لا يمكن أن يكون field. لأ. يبقى هذا
+
+139
+00:18:02,700 --> 00:18:12,100
+معناه... هذا يريد أن يعطينا أن Zp جذر k
+
+140
+00:18:12,100 --> 00:18:25,400
+جذر k is not an integral domain. لأنه ما هوش
+
+141
+00:18:25,400 --> 00:18:31,440
+integral domain. هذا أيضاً يريد أن يعطينا أنّه ليس field.
+
+142
+00:18:34,250 --> 00:18:40,090
+طيب، وصلنا للتناقض. لماذا افترضنا من الأساس فيه؟ يبقى
+
+143
+00:18:40,090 --> 00:18:48,850
+هذا يريد أن يعطينا ماذا؟ contradiction. يبقى
+
+144
+00:18:48,850 --> 00:18:54,850
+هذا تناقض. يبقى الفرض الذي أنا فرضته has a solution.
+
+145
+00:18:54,850 --> 00:19:00,830
+خاطئ، وعكسه هو الصحيح. يبقى أذهب وأقول:
+
+146
+00:19:17,150 --> 00:19:23,070
+يبقى this is a contradiction. يبقى shown. x تربيع تساوي
+
+147
+00:19:23,070 --> 00:19:34,610
+k has no solution in Zp. يبقى بناءً عليه، أصبح
+
+148
+00:19:34,610 --> 00:19:38,950
+الشرط الضروري والكافي لـ Zp جذر k، الـ condition
+
+149
+00:19:38,950 --> 00:19:43,790
+field هو: مربع أي عنصر من عناصرها لا يمكن أن يُساوي
+
+150
+00:19:43,790 --> 00:19:48,630
+صفراً. لا يمكن أن يساوي صفراً. الشطر الثاني يُعتبر صعباً
+
+151
+00:19:48,630 --> 00:19:53,810
+جداً بالنسبة لكم، لكن الشطر الأول يُعتبر مباشراً من
+
+152
+00:19:53,810 --> 00:20:00,570
+سؤال أربعين. نجي لسؤال اثنين وأربعين. يقول: افترض الـ
+
+153
+00:20:00,570 --> 00:20:07,350
+a و b موجودتان في ring، commutative ring R، وكان الـ a
+
+154
+00:20:07,350 --> 00:20:12,490
+b zero divisor. يبقى نبين أنّه إمّا الـ a zero
+
+155
+00:20:12,490 --> 00:20:20,510
+divisor، إمّا الـ b هو عبارة عن zero divisor. يبقى
+
+156
+00:20:20,510 --> 00:20:24,970
+السؤال 42 يقول:
+
+157
+00:20:24,970 --> 00:20:33,990
+ليكن ab هو zero divisor
+
+158
+00:20:40,090 --> 00:20:46,330
+in a commutative
+
+159
+00:20:46,330 --> 00:20:51,830
+ring. تمام؟
+
+160
+00:20:51,830 --> 00:21:03,350
+بدنا نثبت أن هذا يريد أن يعطينا إما a أو b zero
+
+161
+00:21:03,350 --> 00:21:14,710
+divisor. القصة بسيطة جداً. solution. a, b is a zero
+
+162
+00:21:14,710 --> 00:21:23,130
+divisor. هذا ماذا يعني؟ يعني أن there exist
+
+163
+00:21:23,130 --> 00:21:31,750
+element c موجود في R، بحيث أن c لا يساوي صفر،
+
+164
+00:21:31,750 --> 00:21:33,310
+such that
+
+165
+00:21:35,850 --> 00:21:46,670
+ab في c يريد أن يُساوي 0. تمام. الـ ring
+
+166
+00:21:46,670 --> 00:21:50,950
+عندنا commutative. قال لي: بدك تثبت لي إمّا الـ a
+
+167
+00:21:50,950 --> 00:21:56,870
+zero divisor، إمّا الـ b zero divisor. أقول: تمام.
+
+168
+00:21:56,870 --> 00:22:04,430
+من خاصية الـ associativity أستطيع أن أقول: هذا عبارة عن a
+
+169
+00:22:05,610 --> 00:22:14,470
+في c في b يريد أن يُساوي صفر. صح؟ ماذا يعني هذا الكلام؟
+
+170
+00:22:14,470 --> 00:22:20,95
+
+223
+00:28:25,050 --> 00:28:32,130
+صح ولا لأ؟ أنا بدي A لحالها، أنا بدي A أو B
+
+224
+00:28:32,930 --> 00:28:35,830
+بيطلعناها من المعادلة الأولى، صح؟ طيب، أنا قاعدة
+
+225
+00:28:35,830 --> 00:28:39,310
+أفهمها بدي أطلع A من المعادلة الثانية طب أنا
+
+226
+00:28:39,310 --> 00:28:42,210
+مستفدتش من أنه نرميها، حكيت إن A, C تساوي صفر
+
+227
+00:28:42,210 --> 00:28:45,470
+إيه؟ مستفدناش من إيه؟ من أنه A, C تساوي صفر، ما
+
+228
+00:28:45,470 --> 00:28:49,090
+استخدمناهاش، يعني إحنا بس استخدمنا خاصية التجميع،
+
+229
+00:28:49,090 --> 00:28:52,130
+في الحلقة الثانية بس، يعني لو رفعنا A, C تساوي
+
+230
+00:28:52,130 --> 00:28:56,610
+صفر، مش حاسس، مش حاجة يا ست مش مشكلة، بنقول أرسل،
+
+231
+00:28:56,610 --> 00:29:01,990
+بدل هذه، بنرجع منها، وبنقول لك أرسل. طيب يا دكتور
+
+232
+00:29:01,990 --> 00:29:05,570
+طيب لو ما تساوي، لو ساوات صفر طيب؟ كيف لو A؟
+
+233
+00:29:05,570 --> 00:29:06,930
+استنى شوية واحدة واحدة استنى شوية واحدة واحدة
+
+234
+00:29:06,930 --> 00:29:07,150
+واحدة استنى شوية واحدة استنى شوية واحدة استنى
+
+235
+00:29:07,150 --> 00:29:14,370
+شوية واحدة استنى شوية واحدة استنى شوية
+
+236
+00:29:14,370 --> 00:29:18,150
+واحدة استنى شوية واحدة استنى شوية واحدة استنى
+
+237
+00:29:18,150 --> 00:29:20,590
+شوية واحدة استنى شوية واحدة استنى شوية واحدة
+
+238
+00:29:20,590 --> 00:29:25,370
+استنى شوية واحدة استنى ش
+
+239
+00:29:31,200 --> 00:29:38,120
+في B في C أو هي A في B في C يساوي صفر هو الأصل
+
+240
+00:29:38,120 --> 00:29:45,400
+مظبوط قدرت أطلع منه A لحالها في B في C هذا الكلام
+
+241
+00:29:45,400 --> 00:29:49,000
+بده يساوي صفر بده يساوي صفر ليش؟ لأن الـ A في الـ
+
+242
+00:29:49,000 --> 00:29:54,100
+B أصلاً أنا فرضتها في صفر صح ولا لا؟ يبقى هنا صارت
+
+243
+00:29:54,100 --> 00:29:57,860
+هذه النتيجة تساوي صفر يبقى الـ A زي صفر دلوقتي
+
+244
+00:29:57,860 --> 00:30:03,740
+أسهل،  A C في B بتساوي صفر، لو ما كانش A C بتساوي
+
+245
+00:30:03,740 --> 00:30:06,960
+صفر، هنجد  B .. حط في دماغك في الأول .. بس
+
+246
+00:30:06,960 --> 00:30:11,120
+اسمع .. إنت خليك تكمل .. حط في دماغك في الأول إن
+
+247
+00:30:11,120 --> 00:30:15,120
+الـ A في B بده يساوي صفر، وبدنا نشتغل عليها، يبقى
+
+248
+00:30:15,120 --> 00:30:21,000
+بنروح نجيب Element من الـ Ring ونضربه فيها، لأنها
+
+249
+00:30:21,000 --> 00:30:25,020
+Zero Divisor، يبقى بدنا نلاقي عنصر لا يساوي الصفر
+
+250
+00:30:25,020 --> 00:30:30,310
+مثل C، حصل ضرب فيهم، بده يساوي صفر، صح؟ يبقى هذه
+
+251
+00:30:30,310 --> 00:30:33,590
+هي المعادلة الأساسية مرة بدي أطلع منها A ومرة
+
+252
+00:30:33,590 --> 00:30:39,630
+بدي أطلع منها B  بالبلدي هيه ماشي A طلعنا منها
+
+253
+00:30:39,630 --> 00:30:43,770
+مرة A طلعنا منها B صار وهو المطلوب يجيب أحدهم
+
+254
+00:30:43,770 --> 00:30:48,890
+بدي يكون هو zero divisor يا إما الـ A يا إما الـ B
+
+255
+00:30:48,890 --> 00:30:54,570
+يا إما الـ A يا إما الـ B طيب نجي للسؤال اللي عندنا
+
+256
+00:30:54,570 --> 00:30:58,590
+هذا  سؤال 45 قبل أن ندخل إلى
+
+257
+00:30:58,590 --> 00:31:25,460
+السؤال 640 طيب
+
+258
+00:31:25,460 --> 00:31:27,640
+بدنا النقطة الأولى
+
+259
+00:31:33,130 --> 00:31:37,170
+علمًا بأن الـ X زائد Y to the power of P يسمى X to
+
+260
+00:31:37,170 --> 00:31:42,230
+the power of P زائد Y to the power of P علمًا بأن
+
+261
+00:31:42,230 --> 00:31:46,810
+الـ characteristic للـ ring اللي عندنا هو P هو ring
+
+262
+00:31:46,810 --> 00:31:51,450
+commutative بروح وبقولوا معناتها إحنا عندنا X
+
+263
+00:31:51,450 --> 00:31:58,040
+زائد Y كله to the power of P هذه خطوة نظرية ذات
+
+264
+00:31:58,040 --> 00:32:04,480
+الحدين في الاحتمالات وكذلك في الثانوية  برحبتها في
+
+265
+00:32:04,480 --> 00:32:11,500
+الكلمة فبقول هذه X to the power P زائد توافيق P من
+
+266
+00:32:11,500 --> 00:32:18,520
+الأشياء مأخوذة واحد واحد X أس P ناقص واحد Y زائد
+
+267
+00:32:18,520 --> 00:32:25,960
+توافيق P من الأشياء مأخوذة  P من P  X أس P ناقص إثنين
+
+268
+00:32:25,960 --> 00:32:32,620
+في الـ Y تربيع ونظل مستمرين لغاية ما نوصل للـ Y أس
+
+269
+00:32:32,620 --> 00:32:41,480
+P هذا الكلام يساوي X<sup>P</sup> هذا الآن يحتوي على P ولا لا؟
+
+270
+00:32:41,480 --> 00:32:50,100
+خليني أذكركم الآن  بجينا نقول توافيق R من الأشياء
+
+271
+00:32:50,100 --> 00:32:57,780
+مأخوذة R بجينا نقول N! على R!
+
+272
+00:32:57,780 --> 00:33:06,780
+N-R! تذكر هذه العلاقة في
+
+273
+00:33:06,780 --> 00:33:13,960
+التوافيق والتباديل تمام أو في توزيع ذات الحدين الآن
+
+274
+00:33:13,960 --> 00:33:19,580
+هذا العدد دائماً وأبداً يحتوي على العدد N
+
+275
+00:33:19,580 --> 00:33:25,570
+وبالتالي هذا عندنا دائماً يعتمد على عدد موجود في
+
+276
+00:33:25,570 --> 00:33:33,330
+عنصر P P مضروب في شغلة تمام؟ وهذا P مضروب في شغلة
+
+277
+00:33:33,330 --> 00:33:39,650
+وهذا P مضروب في شغلة فالسؤال هو هذا مش عنصر موجود
+
+278
+00:33:39,650 --> 00:33:44,330
+في الـ Ring ومضروب في P والـ characteristic اللي
+
+279
+00:33:44,330 --> 00:33:50,500
+هيساوي P يبقى كده نتيجة المقدار؟ صفر يبقى هذا هو 1
+
+280
+00:33:50,500 --> 00:33:56,620
+زائد صفر والثاني زائد صفر والثالث زائد صفر زائد
+
+281
+00:33:56,620 --> 00:34:01,480
+Y فيه كل العناصر  عدا العنصر الأول والعنصر الأخير
+
+282
+00:34:01,480 --> 00:34:06,380
+كلها موجودة فيها الرقم P الـ P هو الـ characteristic
+
+283
+00:34:06,380 --> 00:34:10,920
+للـ ring بتقدروا في جميع عناصر الـ ring يعطيني صفر
+
+284
+00:34:10,920 --> 00:34:16,170
+يبقى كل العناصر في النص بتروح بصفر يبقى يصير هذا
+
+285
+00:34:16,170 --> 00:34:23,810
+X<sup>P</sup> زائد Y<sup>P</sup> وهو المطلوب الأول المطلوب
+
+286
+00:34:23,810 --> 00:34:30,490
+الثاني نمر بها نمر بها بأنه نثبت أن X زائد Y مرفوع
+
+287
+00:34:30,490 --> 00:34:39,910
+للأس P<sup>N</sup> يساوي X<sup>PN</sup> و Y<sup>PN</sup> هذا الكلام by
+
+288
+00:34:39,910 --> 00:34:42,390
+induction
+
+289
+00:34:45,730 --> 00:34:50,390
+يبقى هذا بالاستنتاج الرياضي أو الاستقراء الرياضي
+
+290
+00:34:50,390 --> 00:34:55,590
+لو حطيت N بواحد عشان تطلع الحالة الأولى يبقى
+
+291
+00:34:55,590 --> 00:35:00,290
+الحالة الأولى يبقى  أفترض أن هذه صحيحة عند N
+
+292
+00:35:00,290 --> 00:35:07,690
+تساوي M وأثبت صحتها عند N تساوي M زائد 1 أظن سهلة
+
+293
+00:35:07,690 --> 00:35:11,750
+ويوم سويته زيها في مبادئ الرياضيات يبقى هذه سهلة
+
+294
+00:35:11,750 --> 00:35:19,040
+طيب نمر C  نمر C بيقول لي لـ Ring وفيها
+
+295
+00:35:19,040 --> 00:35:24,320
+عنصرين والـ characteristic لها بيساوي أربعة وهذه
+
+296
+00:35:24,320 --> 00:35:32,040
+العلاقة ماهياش صحيحة  ندور على Ring الـ
+
+297
+00:35:32,040 --> 00:35:38,400
+characteristic لها أربعة والعلاقة هذه مش صحيحة
+
+298
+00:35:38,400 --> 00:35:44,040
+إحنا أثبتنا صحتها لما كان الـ P prime لكن هل
+
+299
+00:35:44,040 --> 00:35:48,400
+الـ أربعة Prime؟ لأ مش صح يبقى بدي أدور على Ring الـ
+
+300
+00:35:48,400 --> 00:35:54,360
+characteristic اللي هي يساوي أربعة مين؟ Z<sub>4</sub>
+
+301
+00:35:54,360 --> 00:36:04,340
+ماشي يبقى بدي أخد الـ Ring اللي هي Z<sub>4</sub> هذا كـ
+
+302
+00:36:04,340 --> 00:36:12,100
+characteristic أربعة تمام يبقى هذه لها الـ
+
+303
+00:36:12,100 --> 00:36:17,400
+characteristic اللي هو يساوي مين؟ يساوي أربعة ندور
+
+304
+00:36:17,400 --> 00:36:23,620
+على عنصرين فيها لا يحققان هذه العلاقة عناصر Z<sub>4</sub>
+
+305
+00:36:23,620 --> 00:36:27,800
+صفر واحد وإثنين وثلاثة أربعة عناصر بس مش
+
+306
+00:36:27,800 --> 00:36:33,460
+غيرهم خليني نجرب أي رقمين فيهم وليكن مثلاً واحد
+
+307
+00:36:33,460 --> 00:36:40,580
+وثلاثة لو أخد X بواحد وY تساوي ثلاثة بهذا الشكل
+
+308
+00:36:40,580 --> 00:36:49,250
+تمام؟ وبالتالي أقول هذا يريد أن يعطينا أن الـ X زائد
+
+309
+00:36:49,250 --> 00:36:59,090
+Y<sup>4</sup> يساوي 1 زائد 3<sup>4</sup>
+
+310
+00:36:59,090 --> 00:37:09,310
+فبتشوف كده يساوي هذا كده 1 زائد 3  في Z<sub>4</sub> صفر صفر
+
+311
+00:37:09,310 --> 00:37:17,140
+هذا ب Z<sub>4</sub> بدي أخد واحد<sup>4</sup> ثلاثة<sup>4</sup>
+
+312
+00:37:17,140 --> 00:37:29,700
+واحد<sup>4</sup>  بواحد ثلاثة<sup>4</sup> بواحد أكيد
+
+313
+00:37:29,700 --> 00:37:35,380
+ثلاثة تربيع تسعة  بنشيل منها أربعة بظل واحد
+
+314
+00:37:35,380 --> 00:37:40,860
+والتاني بظل واحد في واحد بواحد أو تسعة في تسعة
+
+315
+00:37:40,860 --> 00:37:45,480
+بواحد وثمانين الثمانين بنقسمها لأربعة بنشيلها
+
+316
+00:37:45,480 --> 00:37:50,440
+بيظل الواحد هذه والله هذه سهل واحد يبقى النتيجة
+
+317
+00:37:50,440 --> 00:37:56,640
+تساوي إيش؟ إثنين هذا بدي أكد إن واحد زائد ثلاثة أس
+
+318
+00:37:56,640 --> 00:38:02,720
+أربعة لا يساوي واحد<sup>4</sup> زائد ثلاثة<sup>4</sup>
+
+319
+00:38:02,720 --> 00:38:08,910
+وهو المطلوب هذا سؤال 45 بروح الآن للسؤال
+
+320
+00:38:08,910 --> 00:38:15,430
+640 بيقول الـ R commutative ring with unity و
+
+321
+00:38:15,430 --> 00:38:24,030
+prime characteristic يبقى السؤال 640 الـ R
+
+322
+00:38:24,030 --> 00:38:36,130
+commutative ring with unity اللي هو الواحد و prime
+
+323
+00:38:36,130 --> 00:38:47,370
+characteristic will be prime as the characteristic
+
+324
+00:38:47,370 --> 00:38:58,650
+of R تمام أخذ الـ A موجودة في R nilpotent الـ A اللي
+
+325
+00:38:58,650 --> 00:39:06,750
+موجودة في R is nilpotent ما هو المطلوب بعد هذه
+
+326
+00:39:06,750 --> 00:39:12,790
+المعلومات بيقول إن الـ nilpotent prove there is a
+
+327
+00:39:12,790 --> 00:39:21,030
+positive integer k such that أثبت أن في عندك
+
+328
+00:39:21,030 --> 00:39:27,410
+positive integer k بحيث واحد زائد A<sup>k</sup>
+
+329
+00:39:27,410 --> 00:39:30,830
+يساوي واحد صحيح
+
+330
+00:39:51,250 --> 00:39:56,670
+إحنا الآن عندنا R commutative with unity واحد والـ
+
+331
+00:39:56,670 --> 00:40:01,170
+P prime هو الـ characteristic للـ ring اللي عندنا R
+
+332
+00:40:01,170 --> 00:40:09,270
+الـ A هو nilpotent بداية من واحد زائد A  رفعته  لـ
+
+333
+00:40:09,270 --> 00:40:13,810
+positive integer P منه المهم يجيب لي positive
+
+334
+00:40:13,810 --> 00:40:17,830
+integer أيش ما يكون شكله يكون بدي يا يطلع هذا
+
+335
+00:40:17,830 --> 00:40:23,210
+الكلام يساوي قدر واحد صحيح بنقول الحلقة التالية
+
+336
+00:40:23,210 --> 00:40:34,390
+solution الآن الـ nilpotent إيش يتطلب؟ هذا يتطلب أن الـ A
+
+337
+00:40:34,390 --> 00:40:43,230
+<sup>n</sup> تساوي صفر for some positive integer
+
+338
+00:40:51,120 --> 00:40:58,740
+إحنا الآن لو أخذنا الـ P prime مثلاً ثلاثة والـ K يساوي
+
+339
+00:40:58,740 --> 00:41:05,780
+عشرة مثلاً على سبيل المثال يبقى P<sup>2</sup>  P<sup>2</sup>
+
+340
+00:41:05,780 --> 00:41:10,500
+يعني ثلاثة تربيع أقل من عشرة لكن لو أخذنا K تكعيب
+
+341
+00:41:10,500 --> 00:41:15,160
+يعني ثلاثة تكعيب بيصير إيه؟ بيصير أكبر من عشرة صحيح
+
+342
+00:41:15,160 --> 00:41:20,660
+ولا لأ؟ يبقى أنا بدي أخد P prime لو رفعتها لأس
+
+343
+00:41:20,660 --> 00:41:28,120
+يكون أكبر من مين؟ أكبر من K اللي عندنا، تمام؟ يبقى
+
+344
+00:41:28,120 --> 00:41:39,080
+هنا let P<sup>i</sup> > N أكبر من N
+
+345
+00:41:39,080 --> 00:41:44,740
+then بتاخد
+
+346
+00:41:44,740 --> 00:41:54,380
+على مين؟ واحد زائد A<sup>P<sup>i</sup></sup> من سؤال
+
+347
+00:41:54,380 --> 00:42:00,840
+خمسة وأربعين يجب أن أقول واحد<sup>P<sup>i</sup></sup>
+
+348
+00:42:00,840 --> 00:42:10,990
+زائد A<sup>P<sup>i</sup></sup> طبعاً؟ طيب هذا الكلام
+
+349
+00:42:10,990 --> 00:42:15,990
+بقدر أكتبه على صيغة هذا كله  جدا شبهه يبقى هذا
+
+350
+00:42:15,990 --> 00:42:23,250
+الكلام from exercises خمسة وأربعين مش عشوائي يعني
+
+351
+00:42:23,250 --> 00:42:30,790
+هذا الكلام يساوي واحد زائد هذا A<sup>infinity of A<sup>P<sup>i</sup></sup> - m</sup> بقدر أكتب هذا
+
+352
+00:42:30,790 --> 00:42:37,700
+أكثر صح ليش؟ لأن الـ P و P<sup>i</sup> أكبر من الـ N وبالتالي
+
+353
+00:42:37,700 --> 00:42:45,020
+بقدر أخذ هذه منها طيب هذه كلها بقدر إيش؟ نشيل صفر
+
+354
+00:42:45,020 --> 00:42:50,740
+من الـ Quotient هيبقى لنا بصفر يبقى صارت النتيجة
+
+355
+00:42:50,740 --> 00:42:55,840
+واحد زائد صفر يساوي كده يعني يساوي واحد  يبقى يعني
+
+356
+00:42:55,840 --> 00:43:00,180
+قدرت أجيب له رقم K رفعته للأس هذا طلع الناتج يساوي
+
+357
+00:43:00,180 --> 00:43:07,690
+قدر واحد يبقى  عند الـ K تساوي P<sup>i</sup> قال جيب لي
+
+358
+00:43:07,690 --> 00:43:15,910
+أي positive integer K يحقق مين؟ يحقق هذه المعادلة
+
+359
+00:43:15,910 --> 00:43:22,590
+إذا كنا هنا من ستة وأربعين وصلنا لإثنين وخمسين
+
+360
+00:43:22,590 --> 00:43:29,130
+ولسه فاضل أربعة أسئلة طيب لأن لو جينا لسؤال 52 جالي
+
+361
+00:43:29,130 --> 00:43:36,420
+find all solutions سؤال
+
+362
+00:43:36,420 --> 00:43:42,460
+52 جالي هات لي الـ solutions للمعادلة X تربيع ناقص X
+
+363
+00:43:42,460 --> 00:43:50,340
+زائد 2 يساوي 0  في هذا
+
+364
+00:43:50,340 --> 00:43:58,780
+الـ Z<sub>3</sub>[i]  في Z<sub>3</sub>[i]  يبقى
+
+365
+00:43:59,570 --> 00:44:12,350
+إحنا عندنا معادلة والمعادلة هذه طلب الحلول لها
+
+366
+00:44:12,350 --> 00:44:16,950
+في Z<sub>3</sub>[i]  في Z<sub>3</sub>[i] كتبنا عناصرها
+
+367
+00:44:16,950 --> 00:44:22,930
+قبل هيك كم عنصر فيها؟ تسعة عناصر لو جيت للعناصر هذه
+
+368
+00:44:22,930 --> 00:44:29,800
+الـ تسعة كل عنصر نعوضه في المعادلة تمام؟ طبعاً زي
+
+369
+00:44:29,800 --> 00:44:35,120
+الثلاثة عوضنا بـ صفر واحد وإثنين ولا واحد فيهم
+
+370
+00:44:35,120 --> 00:44:39,220
+بيحقق المعادلة لكن لو جيتي إثنين زائد i و إثنين
+
+371
+00:44:39,220 --> 00:44:47,300
+زائد إثنين i هذول satisfy the above equation
+
+372
+00:44:47,300 --> 00:44:57,220
+أخذي واحدة فيهم نأخذ هذه تربيع يبقى i<sup>4</sup> زائد
+
+373
+00:44:58,880 --> 00:45:07,960
+أربعة i ناقص واحد ناقص x يبقى ناقص إثنين ناقص i
+
+374
+00:45:07,960 --> 00:45:17,740
+زائد إثنين وبيصير هذول قد إيش؟ ناقص ثلاثة زائد إثنين
+
+375
+00:45:17,740 --> 00:45:26,900
+بظل ناقص واحد وعندك أربعة بظل ثلاثة ثلاثة في Z<sub>3</sub>
+
+376
+00:45:27,250 --> 00:45:33,430
+بصفر يبقى الأرقام كلها بصفر تمام الأربعة i
+
+377
+00:45:33,430 --> 00:45:40,190
+بدي أشيل منها ثلاثة بظل i واحدة i واحدة و سالب i
+
+378
+00:45:40,190 --> 00:45:46,910
+كله راح بصفر يبقى هذه حققتها طويلة والتالي نفسه
+
+379
+00:45:46,910 --> 00:45:53,330
+بالصبابة نفس الرقم اللي هو عند هذا الـ complex number
+
+380
+00:45:53,330 --> 00:45:58,620
+سالب زي الإثنين بتلاقي بصفر يبقى هذول فقط هم اللي
+
+381
+00:45:58,620 --> 00:46:03,820
+بيحلوا المعادلة السؤال اللي بعده إزاي؟ بس اللي بعده
+
+382
+00:46:03,820 --> 00:46:08,760
+أربعة مطالب لأن كل واحدة فيهم شكل يعطيك معادلة
+
+383
+00:46:08,760 --> 00:46:13,600
+ويعطيك Ring ثانية نلحقها نحط عناصرها ونجيب عوضها
+
+384
+00:46:13,600 --> 00:46:23,180
+وحدة منهم هتلاقي فيها حلّين وحدة بتلاقي فيها ثلاثة حلول
+
+385
+00:46:23,180 --> 00:46:27,760
+وحدة مثلاً أربعة حلول إلى آخره فمثلاً فمثلاً لو جيتي
+
+386
+00:46:27,760 --> 00:46:34,940
+لسؤال 53 سؤال 53 سؤال 53 بتلاقي عندك نمرة A نمرة A
+
+387
+00:46:34,940 --> 00:46:47,660
+الحل تبعه اللي هو عبارة عن الـ X يساوي 2 و3 ونمرة
+
+388
+00:46:47,660 --> 00:46:56,380
+B الحل تبعه نمرة B الحل تبعه كمان 2 و3 ونمرة C
+
+389
+00:46:56,380 --> 00:47:09,100
+ونمرة C الحل تبعه 2 و3 و6 و11 ونمرة D الحل تبعه
+
+390
+00:47:09,100 --> 00:47:21,140
+إ
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..34f2ac8a101d4d6d35f92a9c2a01ff66393c42a4
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_postprocess.srt
@@ -0,0 +1,1576 @@
+1
+00:00:20,740 --> 00:00:25,440
+بسم الله الرحمن الرحيم اليوم إن شاء الله بنكمل حل
+
+2
+00:00:25,440 --> 00:00:29,220
+المسائل تبع هذا ال section المرة اللي بقى تكون
+
+3
+00:00:29,220 --> 00:00:35,580
+حلنا بعض المسائل ووقفنا عند سؤال أربعين طيب سؤال
+
+4
+00:00:35,580 --> 00:00:42,400
+أربعين بيقول لي النقطة الأولى اثبتلي إن زد سبعة أو
+
+5
+00:00:42,400 --> 00:00:48,400
+جذر تلاتة هي عبارة عن فين؟ فسؤال أربعين هو عبارة
+
+6
+00:00:48,400 --> 00:00:58,880
+عن مطلوبينالمطلوب الأول نمره a show that z7 of
+
+7
+00:00:58,880 --> 00:01:06,800
+square root لثلاثة is و لو بحط التعريف تبعه دفع
+
+8
+00:01:06,800 --> 00:01:15,020
+التعريف تبع هذا هو عبارة عن ال a زائد ال g جدر
+
+9
+00:01:15,020 --> 00:01:24,190
+تلاتةبحيث ال a و ال b موجودة في z سبعة is a field
+
+10
+00:01:24,190 --> 00:01:31,850
+هذا اللي بدنا نقوله الحل كانت تالي solution الحل
+
+11
+00:01:31,850 --> 00:01:36,570
+بسيط جدا موجود بين إيداكوا و لو انكم مش ماخدين
+
+12
+00:01:36,570 --> 00:01:43,590
+بالكوينز كيف موجود بين إيدانا السؤال هو z سبعة هو
+
+13
+00:01:43,590 --> 00:01:48,310
+square root ل 3communitative ring with unity و لا
+
+14
+00:01:48,310 --> 00:01:59,950
+لأ ال ZN عموما يبقى هذي communicative ring with
+
+15
+00:01:59,950 --> 00:02:05,690
+unity تمام
+
+16
+00:02:05,690 --> 00:02:13,790
+طيب الآن لو رجعنا إلى المثال رقم أربع اللي شرحناه
+
+17
+00:02:13,790 --> 00:02:19,440
+في المحاضرة الأولىمثال رقم أربع يبقى بقوله هنا
+
+18
+00:02:19,440 --> 00:02:31,080
+from example four بشرحناها سابقا we have we have
+
+19
+00:02:31,080 --> 00:02:40,200
+ان زد P قد جدر تلاتة ولا زد سبعة لإن P احنا عندنا
+
+20
+00:02:40,200 --> 00:02:49,090
+هنا يعني سبعة يبقى زد سبعة و جدر تلاتةis an
+
+21
+00:02:49,090 --> 00:02:56,530
+integral domain تمام؟
+
+22
+00:02:56,530 --> 00:03:01,090
+يبقى هذه integral domain السؤال هو هل هذه ال ring
+
+23
+00:03:01,090 --> 00:03:04,810
+finite ولا infinite؟ و ال integral domain finite
+
+24
+00:03:04,810 --> 00:03:08,770
+ولا infinite؟ finite و احنا خدنا نظرية every
+
+25
+00:03:08,770 --> 00:03:16,490
+finite integral domain is a field يبقى بطء ولكنزد
+
+26
+00:03:16,490 --> 00:03:29,350
+سبعة of جذر تلاتة is finite مادام finite وintegral
+
+27
+00:03:29,350 --> 00:03:40,410
+domain finite and integral domain يبقى هذا بيعطينا
+
+28
+00:03:40,410 --> 00:03:50,290
+ان زد سبعة ofجذر تلاتة is a .. فيه ال .. ده يبقى
+
+29
+00:03:50,290 --> 00:03:54,110
+هذا عبارة عن ايه؟ عبارة عن فيه يبقى هذا المطلوب
+
+30
+00:03:54,110 --> 00:03:58,150
+الأول من السؤال اللي هو المطلوب السهل اللي مافيش
+
+31
+00:03:58,150 --> 00:04:05,290
+فيه مشكلة نمر بيه المشكلة في نمر بيه نمر بيه بيقول
+
+32
+00:04:05,290 --> 00:04:18,490
+لي ما يأتي بيقول لي بدنا find thenecessary and
+
+33
+00:04:18,490 --> 00:04:23,110
+sufficient
+
+34
+00:04:23,110 --> 00:04:32,650
+condition
+
+35
+00:04:32,650 --> 00:04:41,870
+for zp
+
+36
+00:04:42,870 --> 00:04:53,470
+جذر الـ K جذر الـ K ثم بيقفل
+
+37
+00:04:53,470 --> 00:05:01,670
+ثم بيقفل
+
+38
+00:05:01,670 --> 00:05:07,230
+راح
+
+39
+00:05:07,230 --> 00:05:14,290
+أخد K انتجة و أخد P Primeقال هاتلي ال necessary
+
+40
+00:05:14,290 --> 00:05:21,990
+and sufficient condition بحيث يكون ZP of جذر ال K
+
+41
+00:05:21,990 --> 00:05:28,350
+is a field أنا أدعى أن ال necessary and sufficient
+
+42
+00:05:28,350 --> 00:05:36,770
+condition for ZP of K to be a field is ال X تربية
+
+43
+00:05:36,770 --> 00:05:54,150
+تساوي K hasno solution in zp that is in ال
+
+44
+00:05:54,150 --> 00:06:07,490
+x تربيع تساوي k has no solution in zp if and only
+
+45
+00:06:07,490 --> 00:06:22,300
+if zP of January الـ K is A field تمام؟
+
+46
+00:06:22,300 --> 00:06:30,020
+طيب بروح نوضح هذا الكلام نمربي
+
+47
+00:06:30,020 --> 00:06:37,490
+من السؤال بيقول ما هو الشرط الضروري والكافياللي
+
+48
+00:06:37,490 --> 00:06:44,790
+بتتحقق في كل من P وK بحيث انه يطلع ZP of K هو
+
+49
+00:06:44,790 --> 00:06:50,730
+عبارة عن field تصير هذا الكلام سيارة رياضية أنا
+
+50
+00:06:50,730 --> 00:06:57,770
+أدعي أن الشرط هو X تربيع تساوي K has no solution
+
+51
+00:06:57,770 --> 00:07:04,570
+in ZP if and only if ZP of جدر ال K is a field
+
+52
+00:07:05,110 --> 00:07:11,950
+الادعاء هذا لا يكون صحيحا إلا إذا أثبتناه يبقى
+
+53
+00:07:11,950 --> 00:07:18,870
+بقول الحلقة التالية كلمة F انحلي F تعني ان المسار
+
+54
+00:07:18,870 --> 00:07:25,890
+بيسير باتجاهين يبقى بالداجة اقوله افترض ان ال X
+
+55
+00:07:25,890 --> 00:07:38,670
+تربيه تساوي T has no solutionno solution in ZP ايش
+
+56
+00:07:38,670 --> 00:07:45,110
+بدي اثبت بدي اثبت ان ZP of general K is A field
+
+57
+00:07:45,110 --> 00:07:54,370
+يعني كل عنصر غير صفري يكون له ايش بكله في ال field
+
+58
+00:07:54,370 --> 00:08:00,830
+ايش معنى field كل عنصر غير صفري له معكوس
+
+59
+00:08:00,830 --> 00:08:06,300
+multiplicative inverseيبقى كل عنصر غير صفري لهو
+
+60
+00:08:06,300 --> 00:08:10,560
+معكوز يبقى مرتان يبقى قول افترض انكستر بيه تساوي K
+
+61
+00:08:10,560 --> 00:08:16,040
+has no solution in ZP مالهاش حل اللي هو الادعي
+
+62
+00:08:16,040 --> 00:08:21,160
+اللي احنا متدعينه بدنا نثبت ان هذا الكلام is a
+
+63
+00:08:21,160 --> 00:08:29,220
+fail لذلك بروح اقول ماهيأدي خديلي عنصر A زائد B
+
+64
+00:08:29,220 --> 00:08:40,980
+جدر ال Kموجود في ZP of جذر ال K such that بحيث أن
+
+65
+00:08:40,980 --> 00:08:51,120
+ال A زائد B جذر ال K not equal 0 هذا الكلام ما
+
+66
+00:08:51,120 --> 00:08:59,820
+يسوي السفر بالمرة نذهب و نثبت أن هذا العنصر عكوس
+
+67
+00:08:59,820 --> 00:09:04,470
+له Englishإذا كنت تثبت إنه إلو إن بصلاً العنصر
+
+68
+00:09:04,470 --> 00:09:09,270
+عشوائي معناته فعلاً زي نقول لها بدا نيجي للحالة
+
+69
+00:09:09,270 --> 00:09:13,530
+الثانية اللي بي لا تساوي زيرو بعد ما انتهينا من
+
+70
+00:09:13,530 --> 00:09:18,970
+الحالة بي تساوي زيرو فلو كانت ال بي لا تساوي زيرو
+
+71
+00:09:18,970 --> 00:09:23,970
+بفترض أنا من عندي إن هذه القيمة لا تساوي زيرو و
+
+72
+00:09:23,970 --> 00:09:28,150
+بدي أروحها بالصحيتة يعني مش تدعي ادعاء دون نسبة لأ
+
+73
+00:09:28,150 --> 00:09:33,230
+بدي أنفقهفبقى جيب الدئاتة وقلت لو كان يساوي zero
+
+74
+00:09:33,230 --> 00:09:37,090
+إيش اللي بدي يحصل؟ امشي بالشكل اللي انا لقيت K
+
+75
+00:09:37,090 --> 00:09:43,070
+ساوي A ل B تربيع يعني هذه المعادلة X تربيع يساوي K
+
+76
+00:09:43,070 --> 00:09:48,130
+صار لها حل وانا فرض انها مالهاش حل يبقى هذا
+
+77
+00:09:48,130 --> 00:09:53,150
+الإدعاء مش صحيح وعكس اللي هو هذا هو الصحيح إذا ال
+
+78
+00:09:53,150 --> 00:09:58,870
+A تربيع ناقص B تربيع K لا يمكن أن يساويلا يمكن أن
+
+79
+00:09:58,870 --> 00:10:04,450
+يساوي Zero مدام لا يمكن أن يساوي Zero يبقى واحد
+
+80
+00:10:04,450 --> 00:10:09,310
+على هذا المقدار بيصير معرف لأن لو كان المقام يساوي
+
+81
+00:10:09,310 --> 00:10:13,870
+Zero بيصير Infinity مش معرف لكن المقام لا يساوي
+
+82
+00:10:13,870 --> 00:10:17,410
+Zero يبقى واحد على هذا المقدار بيصير معرف روح
+
+83
+00:10:17,410 --> 00:10:23,270
+Symmetry أو A تربيه ناقص B تربيه K كله مرفوع للأس
+
+84
+00:10:23,270 --> 00:10:28,560
+سالك واحدالمهم ده دي ياخد حاصل ضرب القوسين هدول
+
+85
+00:10:28,560 --> 00:10:34,040
+نظره ضربنا القسم صار ضرب المقدار اللي عندنا ده بدي
+
+86
+00:10:34,040 --> 00:10:40,260
+اشوف ليش وصل هدى مع هدى مع السلامة يبقى هدى بدها
+
+87
+00:10:40,260 --> 00:10:52,630
+الساوي ايه تربيع ناقص ناقص بتربيع ككل قسيهذا
+
+88
+00:10:52,630 --> 00:11:01,030
+الكلام بده يساوي A تربيع ناقص B تربيع K B تربيع K
+
+89
+00:11:01,030 --> 00:11:08,730
+كله مضروف في C من C هيها فوق يبقى في A تربيع ناقص
+
+90
+00:11:08,730 --> 00:11:14,950
+B تربيع K أسالي واحد هذا القص مش هذا القص نفسه
+
+91
+00:11:14,950 --> 00:11:21,200
+يبقى هذا عبارة عن الأس Zero يبقى كله في قداشواحد
+
+92
+00:11:21,200 --> 00:11:26,680
+يبقى هذا العمصر له معكس مين معكسه اللي هو ال term
+
+93
+00:11:26,680 --> 00:11:35,040
+اللي عندنا هذا يبقى this means that هذا يعني every
+
+94
+00:11:35,040 --> 00:11:47,960
+none zero element اللي هو ال a زائد b جدر ال k n z
+
+95
+00:11:47,960 --> 00:11:57,070
+pof general K has an inverse يبقاش معنى هذا الكلام
+
+96
+00:11:57,070 --> 00:12:06,290
+ان هذا is a field يبقى صراحة ZP
+
+97
+00:12:06,290 --> 00:12:15,350
+of general K is a field اهو المفهوم نمشي من اتجاه
+
+98
+00:12:15,350 --> 00:12:24,840
+المعاكسيبقى بدأ أقوله conversely Assume that
+
+99
+00:12:24,840 --> 00:12:36,020
+Assume that the theme of gathering cake is a theme
+
+100
+00:12:36,020 --> 00:12:47,030
+one to show one to show بما أروح نبينإن الـ X
+
+101
+00:12:47,030 --> 00:12:57,970
+ترابيع تساوي K، has no solution No
+
+102
+00:12:57,970 --> 00:13:05,190
+solution in ZP أظن أخدته البرهين بالـ
+
+103
+00:13:05,190 --> 00:13:12,330
+Contrapositive مطلوب هذه بدي أفترض عكسها إذا وصلني
+
+104
+00:13:12,330 --> 00:13:18,980
+إلى تناقض يبقى فرضي غلطوعكسه هيوغو الصحي طبعا يعني
+
+105
+00:13:18,980 --> 00:13:28,320
+بيبقى بدي أقوله الآن لك ال X ترابيع تساوي K has a
+
+106
+00:13:28,320 --> 00:13:39,640
+solution in ZP هذا بده يعطينا ان ال A ترابيع تساوي
+
+107
+00:13:39,640 --> 00:13:49,870
+K وال A موجودة في ZPطبعا مرة تانية بقول احنا ما
+
+108
+00:13:49,870 --> 00:13:55,130
+نمشي لاتجاه الاخر، لاتجاه المعاكس، يبقى فرط هذا
+
+109
+00:13:55,130 --> 00:13:59,650
+عبارة عن field، وبدي أحاول أثبت أن المعادل X تساوي
+
+110
+00:13:59,650 --> 00:14:04,890
+و X تربع تساوي كده، مالهاش حل، لإن بروحت فترط إنه
+
+111
+00:14:04,890 --> 00:14:13,930
+إلها حل، هي إلها حل، معناته كل عنصر في Z P
+
+112
+00:14:14,380 --> 00:14:19,840
+بدي ممكن اقول ايه تربيع بدي يسوي مين بدي يسوي كي
+
+113
+00:14:19,840 --> 00:14:26,780
+هذا كلام صحيح بدي افترضه تمام وخديلي هال عنصرين و
+
+114
+00:14:26,780 --> 00:14:33,740
+تعالى يشوف لوين بدهم يوصلوا فبقى اجيب و بقوله F LX
+
+115
+00:14:33,740 --> 00:14:45,110
+يسوي A زي P ناقص واحد في جدر الكيك موجودفي الـ Z P
+
+116
+00:14:45,110 --> 00:14:54,030
+وفي جذر ال K ولا لا؟ لأن هذا رقم صح؟ والـ Y بدل
+
+117
+00:14:54,030 --> 00:15:03,750
+سوى A زائد جذر ال K، ذلك. بدي أخد ال X في ال Y،
+
+118
+00:15:03,750 --> 00:15:10,310
+هشوف إيش تعطيك. لوين بدي أتواصل؟ أخدت عنصرين بقدر
+
+119
+00:15:10,310 --> 00:15:18,180
+اللهسميت الأول a زي ال P نقص واحد في K وسميت
+
+120
+00:15:18,180 --> 00:15:25,340
+التاني A زي جذر ال K وبدأت أضغطهم في بعض A في A ب
+
+121
+00:15:25,340 --> 00:15:38,490
+A ترابيع ايه في جذر ال K ب A في جذر ال Kهيضربنا ال
+
+122
+00:15:38,490 --> 00:15:46,990
+a في كل الطرف المضاجي اضربه هنا P K في A تمام يبقى
+
+123
+00:15:46,990 --> 00:16:00,350
+زائد P P A في جزر ال P هيضربنا P في جزر ال K في A
+
+124
+00:16:00,350 --> 00:16:10,150
+اللي قاعدة ناقص A في جزر ال Kناقص A في جذر ال K
+
+125
+00:16:10,150 --> 00:16:20,750
+ضايل عندنا اخر حاجة يبقى ضايل P في K يبقى زائد P
+
+126
+00:16:20,750 --> 00:16:29,290
+في K ضايل عندنا بس ناقص اللي هو جذر ال K في جذر ال
+
+127
+00:16:29,290 --> 00:16:37,690
+K يبقى ناقص K يبقى تكيت ال XYيبقى بصير عندنا ال X
+
+128
+00:16:37,690 --> 00:16:46,290
+Y يساوي كداش ال A تربيها يا بنات؟ كيه؟ يبقى بقدر
+
+129
+00:16:46,290 --> 00:16:51,270
+أشيلها و أحط مكانها كيه؟ يبقى هذا الكلام يساوي
+
+130
+00:16:51,270 --> 00:17:00,990
+كيه؟ طيب زائد AK و ناقص AK مع السلامة طيب هذا ال P
+
+131
+00:17:00,990 --> 00:17:03,810
+AK كداش؟
+
+132
+00:17:06,070 --> 00:17:13,230
+مضاعفات اللي هو العناصر في Z ب P قد إيش؟ مضاعفات
+
+133
+00:17:13,230 --> 00:17:17,530
+إذا هي P ب Zero صح ولا لا؟ Zero تضربي في أي حاجة ب
+
+134
+00:17:17,530 --> 00:17:25,270
+Zero نفق الطار هذا ب Zero وهذا كمان راح ب Zero صح؟
+
+135
+00:17:25,270 --> 00:17:33,870
+مظبوط؟ إيش ضل عندنا؟ ضل عندنا سالب K نفق هذا سالب
+
+136
+00:17:33,870 --> 00:17:45,260
+Kيساوي Zero مظبوط يبقى صار عندنا ال X ه and او ال
+
+137
+00:17:45,260 --> 00:17:56,020
+X and ال Y are Zero divisors مظبوط يبقى بنفع يكون
+
+138
+00:17:56,020 --> 00:18:02,700
+Integral domain وبالتالي بنفع يكون فيل لأ يبقى هذا
+
+139
+00:18:02,700 --> 00:18:12,100
+معناههذا بدي يعطينا ان الـ Z P of general K of
+
+140
+00:18:12,100 --> 00:18:25,400
+general K is not an integral domain لأنه ما هوش
+
+141
+00:18:25,400 --> 00:18:31,440
+integral domain هذا كمان بدي يعطينا ان النقط فيه
+
+142
+00:18:34,250 --> 00:18:40,090
+طيب وصلنا للتناقض ليش هنفرض من الأساس فيه؟ يبقى
+
+143
+00:18:40,090 --> 00:18:48,850
+هذا بده يعطينا مين؟ contradiction يبقى
+
+144
+00:18:48,850 --> 00:18:54,850
+هذا تناقض يبقى الفرض اللي أنا فرضته has a solution
+
+145
+00:18:54,850 --> 00:19:00,830
+غلط وعكسه هو مين الصح يبقى بروح بقوله
+
+146
+00:19:17,150 --> 00:19:23,070
+يبقى this is contradiction يبقى shown X تربيه تسوي
+
+147
+00:19:23,070 --> 00:19:34,610
+K has no solution in Z بقى يبقى بناء عليه صار
+
+148
+00:19:34,610 --> 00:19:38,950
+الشرط الضروري والكافي ل Z P of جدري ال Kالـ cone
+
+149
+00:19:38,950 --> 00:19:43,790
+field هو مربع أي عنصر من عناصرها لا يمكن أن يساوي
+
+150
+00:19:43,790 --> 00:19:48,630
+100 لا يمكن أن يساوي 50 الشطرة الثانية يعتبر صعبة
+
+151
+00:19:48,630 --> 00:19:53,810
+جدا بالنسبة لكم لكن الشطرة الأولية يعتبر مباشرة من
+
+152
+00:19:53,810 --> 00:20:00,570
+سؤال أربعين نجي لسؤال أتنين وأربعين بقول افترض ال
+
+153
+00:20:00,570 --> 00:20:07,350
+A و B موجودات في ring commutative ring Rوكان ال A
+
+154
+00:20:07,350 --> 00:20:12,490
+B Zero Divisor يبقى نبين أنه يا إما ال A Zero
+
+155
+00:20:12,490 --> 00:20:20,510
+Divisor يا إما ال B هو عبارة عن Zero Divisor يبقى
+
+156
+00:20:20,510 --> 00:20:24,970
+السؤال 42 بيقول
+
+157
+00:20:24,970 --> 00:20:33,990
+ما يدى أن ال A B is A Zero Divisor
+
+158
+00:20:40,090 --> 00:20:46,330
+in a commutative
+
+159
+00:20:46,330 --> 00:20:51,830
+ring تمام؟
+
+160
+00:20:51,830 --> 00:21:03,350
+بدنا نثبت ان هذا بده يعطينا يا MLARBSA0
+
+161
+00:21:03,350 --> 00:21:14,710
+divisorالقصة بسيطة جدا solution ال a,b is a zero
+
+162
+00:21:14,710 --> 00:21:23,130
+divisor هذا ايش معناه؟ معناته ان there exist
+
+163
+00:21:23,130 --> 00:21:31,750
+element c موجود في الارض وحيث ال c لا يساوي zero
+
+164
+00:21:31,750 --> 00:21:33,310
+such that
+
+165
+00:21:35,850 --> 00:21:46,670
+ساعدش ذات ال A B في C بده يساوي Z تمام ال ring
+
+166
+00:21:46,670 --> 00:21:50,950
+عندنا commutative قاللي بدك تثبتلي يا إما ال A
+
+167
+00:21:50,950 --> 00:21:56,870
+Zero divisor يا إما ال B Zero divisor بقوله تمام
+
+168
+00:21:56,870 --> 00:22:04,430
+من خاصية ال associativity بقدر أقول هذا عبارة عن A
+
+169
+00:22:05,610 --> 00:22:14,470
+C8 في الـ B بده يساوي 0 صح؟ إيش معنى هذا الكلام؟
+
+170
+00:22:14,470 --> 00:22:20,950
+إن الـ B is zero divisible يبقى هذا بده يعطينا إن
+
+171
+00:22:20,950 --> 00:22:28,810
+الـ B is A zero divisible طيب
+
+172
+00:22:28,810 --> 00:22:41,100
+في حتمة أخر يبقى هنا أخدناإن ال F ال A C بده يساوي
+
+173
+00:22:41,100 --> 00:22:47,680
+Zero عشان مايصيرش شكك ولا حاجة F A C بده يساوي
+
+174
+00:22:47,680 --> 00:22:53,220
+Zero وهذا بده يساوي Zero يبقى ال B is A Zero
+
+175
+00:22:53,220 --> 00:22:59,300
+Divisor لايمكن أن تساوي Zero يبقى A Zero Divisor
+
+176
+00:22:59,300 --> 00:23:05,990
+طب لو كانتال AC لا يساوي زيرو لأ اللي فوق AC لا
+
+177
+00:23:05,990 --> 00:23:11,810
+يساوي زيرو لو كان ال AC بده يساوي زيرو زيرو في بيه
+
+178
+00:23:11,810 --> 00:23:13,250
+زيرو في بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+179
+00:23:13,250 --> 00:23:13,650
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+180
+00:23:13,650 --> 00:23:14,310
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+181
+00:23:14,310 --> 00:23:18,250
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+182
+00:23:18,250 --> 00:23:25,250
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه ب
+
+183
+00:23:30,850 --> 00:23:35,350
+هذه لو كان ال A C لا تساوي زيرو فجبه B يكون زيرو
+
+184
+00:23:35,350 --> 00:23:46,990
+تمام بدنا نيجي ناخد الحالة التالتة if ال A C تساوي
+
+185
+00:23:46,990 --> 00:23:58,470
+زيرو then احنا هنا مين A B C A B C بتساوي زيرو
+
+186
+00:23:58,470 --> 00:24:07,480
+impliesبقدر اقول هذه مين بقدر اقول a في b في c
+
+187
+00:24:07,480 --> 00:24:18,640
+مظبوط تساوي بقدر اعملها على الشكل التالي تساوي a b
+
+188
+00:24:18,640 --> 00:24:27,180
+في c ال a بيبقى داشر ب zero يبقى هذا بتعطيك zero
+
+189
+00:24:27,180 --> 00:24:32,200
+في c يساوي كده؟ Zeroيبقى معناه هذا الكلام انه ايش
+
+190
+00:24:32,200 --> 00:24:40,220
+ال a is a zero divisor يبقى هذا بيعطيك ان ال a is
+
+191
+00:24:40,220 --> 00:24:50,420
+a zero divisor تمام طيب يبقى هنا يا اما ال a zero
+
+192
+00:24:50,420 --> 00:24:55,840
+divisor يا اما ال b zero divisor هذه واحدة منهم
+
+193
+00:24:55,840 --> 00:25:02,800
+فقط طيب هذا سؤال جداسؤال اللي هو اتنين واربعين
+
+194
+00:25:02,800 --> 00:25:08,020
+الان سؤال ستة واربعين لا يمكن حله إذا حلنا سؤال
+
+195
+00:25:08,020 --> 00:25:12,960
+خمسة واربعين لأن سؤال ستة واربعين يعتمد على سؤال
+
+196
+00:25:12,960 --> 00:25:19,000
+خمسة واربعين إذا بدنا نروح لسؤال خمسة واربعين في
+
+197
+00:25:19,000 --> 00:25:27,550
+الأول وإذا حلنا بصير خمسة واربعين تحصيل حاصلخمسة
+
+198
+00:25:27,550 --> 00:25:32,610
+واربعين بيقول ما يعطي بيقول X وY موجودة في
+
+199
+00:25:32,610 --> 00:25:37,930
+commutative ring with prime characteristic X وY
+
+200
+00:25:37,930 --> 00:25:44,750
+موجودة في الأرض كمام
+
+201
+00:25:44,750 --> 00:25:51,290
+ليه في commutative ring with prime characteristic
+
+202
+00:25:51,910 --> 00:26:01,270
+وال characteristic إلها prime وليكن P. خلصنا؟ طيب،
+
+203
+00:26:01,270 --> 00:26:09,950
+الآن المطلوب الأول Show that بيّلي إن ال X زائد ال
+
+204
+00:26:09,950 --> 00:26:18,490
+Y to the power P يساوي X أوس P زائد Y أوس P. نمرى
+
+205
+00:26:18,490 --> 00:26:25,520
+بيه.بقول لمرة بيقول show that for all positive
+
+206
+00:26:25,520 --> 00:26:36,400
+integer n ال X زائد Y مرفوعة لمين لل P أُس N يزاوى
+
+207
+00:26:36,400 --> 00:26:47,140
+ال X أُس P N زائد ال Y أُس P N لمرة C لمرة C بيقول
+
+208
+00:26:47,140 --> 00:27:02,840
+هتلف عينعنصرين x و y find عنصرين x و y in R و ال
+
+209
+00:27:02,840 --> 00:27:09,640
+characteristic ل R بده يساوي أربعة و ال
+
+210
+00:27:09,640 --> 00:27:15,900
+characteristic ل R بده يساوي أربعة بحيث انه such
+
+211
+00:27:15,900 --> 00:27:16,560
+that
+
+212
+00:27:20,770 --> 00:27:29,950
+ال X زائد ال Y قص أربعة لا يساوي ال X قص أربعة
+
+213
+00:27:29,950 --> 00:27:38,430
+زائد ال Y قص أربعة بسبب ال prime طيب في السؤال
+
+214
+00:27:38,430 --> 00:27:42,750
+اللي جابني ايش دخل A C تساوي ستر؟ السؤال اللي
+
+215
+00:27:42,750 --> 00:27:45,470
+جابني انا مستفدتش في الحلقة التانية من الفرض ان A
+
+216
+00:27:45,470 --> 00:27:52,050
+C تساوي ستر هذا؟ اه وين هو؟أنا ما استخدمته مش هذا؟
+
+217
+00:27:52,050 --> 00:27:55,750
+اه طب احنا دخلنا A C لا يساوي Zero إذا استخدمي B
+
+218
+00:27:55,750 --> 00:28:00,490
+Zero دي بجر طبعا اللي بعد لو كان A C يساوي Zero
+
+219
+00:28:00,490 --> 00:28:06,310
+طلعت ال A لحال شايفة طلعت ال A لحال اللي أنا بديها
+
+220
+00:28:06,310 --> 00:28:13,390
+طبعا يبقى ما هو السبب اللي خل هذا Zero ال B ال ..
+
+221
+00:28:13,390 --> 00:28:20,270
+ال .. ال .. ال ..طلعت ال a و ال b لحالة اللي أصلاً
+
+222
+00:28:20,270 --> 00:28:25,050
+zero يبقى جدير الأستثمار أن ال a في هذا هو ال zero
+
+223
+00:28:25,050 --> 00:28:32,130
+صح ولا لأ؟ أنا بدي a لحالها، أنا بدي a أو b
+
+224
+00:28:32,930 --> 00:28:35,830
+بيطلعناها من المعادلة الأولى، صح؟ طيب، أنا قاعدة
+
+225
+00:28:35,830 --> 00:28:39,310
+يفهمها بدج يطلع أيه من المعادلة التانية طب انا
+
+226
+00:28:39,310 --> 00:28:42,210
+مستفدتش من انه نرمى، حكيت ان انت A, C تساوي صفر
+
+227
+00:28:42,210 --> 00:28:45,470
+ايه؟ مستفدناش من ايه اش؟ من انه A, C تساوي صفر، ما
+
+228
+00:28:45,470 --> 00:28:49,090
+استخدمنهاش، يعني احنا بس استخدمنا خاصية التجميع،
+
+229
+00:28:49,090 --> 00:28:52,130
+في الحلقة التانية بس، يعني لو رفعنا A, C تساوي
+
+230
+00:28:52,130 --> 00:28:56,610
+صفر، مش حاسس، مش حاجة يا ست مش مشكلة، بنقول أرسل،
+
+231
+00:28:56,610 --> 00:29:01,990
+بدل هذه، بنرايحك منها، و بنقولك أرسلطيب يا دكتور
+
+232
+00:29:01,990 --> 00:29:05,570
+طيب لو ماتساوي لو ساوات صفر طيب؟ كيف لو ايه؟
+
+233
+00:29:05,570 --> 00:29:06,930
+اتسانى شوية واحدة واحدة اتسانى شوية واحدة واحدة
+
+234
+00:29:06,930 --> 00:29:07,150
+واحدة اتسانى شوية واحدة اتسانى شوية واحدة اتسانى
+
+235
+00:29:07,150 --> 00:29:14,370
+شوية واحدة اتسانى شوية واحدة اتسانى شوية
+
+236
+00:29:14,370 --> 00:29:18,150
+واحدة اتسانى شوية واحدة اتسانى شوية واحدة اتسانى
+
+237
+00:29:18,150 --> 00:29:20,590
+شوية واحدة اتسانى شوية واحدة اتسانى شوية واحدة
+
+238
+00:29:20,590 --> 00:29:25,370
+اتسانى شوية واحدة اتسانى ش
+
+239
+00:29:31,200 --> 00:29:38,120
+فى B فى C او هي A فى B فى C يساوي Zero هو الأصل
+
+240
+00:29:38,120 --> 00:29:45,400
+مظبوط قدرت أطلع منه A لحاله فى B فى C هذا الكلام
+
+241
+00:29:45,400 --> 00:29:49,000
+بده يساوي Zero بده يساوي Zero ليش؟ لأن ال A فى ال
+
+242
+00:29:49,000 --> 00:29:54,100
+B أصلا أنا فرضها في Zero صح ولا لا؟ يبقى هنا صارت
+
+243
+00:29:54,100 --> 00:29:57,860
+هذه النتيجة تساوي Zero يبقى ال A زي Zero دلوقتي
+
+244
+00:29:57,860 --> 00:30:03,740
+أسهلعنا A C في B بتساوي Zero، لو ماكانش A C بتساوي
+
+245
+00:30:03,740 --> 00:30:06,960
+Zero، هاجدوا عنا B .. حط في دماغك في الأول .. بس
+
+246
+00:30:06,960 --> 00:30:11,120
+اسمع .. انت خليك تكمل .. حط في دماغي في الأول ان
+
+247
+00:30:11,120 --> 00:30:15,120
+ال A في B بدو ساوي Zero، و بدنا نشتغل عليها، يبقى
+
+248
+00:30:15,120 --> 00:30:21,000
+بنروح نجيب Element من ال Ring و نضربه فيها، لإنها
+
+249
+00:30:21,000 --> 00:30:25,020
+Zero Divisor، يبقى بدنا ناجي عنصر لا يساوي الصغر
+
+250
+00:30:25,020 --> 00:30:30,310
+مثل C، حصل ضربه فيهم، بدو ساوي Zero، صح؟يبقى هذه
+
+251
+00:30:30,310 --> 00:30:33,590
+هي المعادلة الأساسية مرة بدي أطلع منها ايه و مرة
+
+252
+00:30:33,590 --> 00:30:39,630
+بدي أطلع منها بيه بالبلد هيه ماشي ايه طلعنا منها
+
+253
+00:30:39,630 --> 00:30:43,770
+مرة ايه طلعنا منها بيه صار و هو المطلوب يجيب أحدهم
+
+254
+00:30:43,770 --> 00:30:48,890
+بدي يكون هو zero divisor يا إما الـA يا إما الـB
+
+255
+00:30:48,890 --> 00:30:54,570
+يا إما الـA يا إما الـB طيب نجي للسؤال اللي عنا
+
+256
+00:30:54,570 --> 00:30:58,590
+هذا غناط اللي وصار خمسة واربعين قبل أن ندخل إلى
+
+257
+00:30:58,590 --> 00:31:25,460
+السؤال640 طيب
+
+258
+00:31:25,460 --> 00:31:27,640
+بدنا النقطة الأولى
+
+259
+00:31:33,130 --> 00:31:37,170
+علمًا بأن الـ X زائد Y to the power of P يسمى X to
+
+260
+00:31:37,170 --> 00:31:42,230
+the power of P زائد Y to the power of P علمًا بأن
+
+261
+00:31:42,230 --> 00:31:46,810
+الـ characteristic لا الرنج اللي عندنا هو P هو رنج
+
+262
+00:31:46,810 --> 00:31:51,450
+commutative فبروح و بقولوا معناتي احنا عندنا X
+
+263
+00:31:51,450 --> 00:31:58,040
+زائد Y كله to the power of Pهذا خطوة نظرية ذات
+
+264
+00:31:58,040 --> 00:32:04,480
+الحدين في الاحتمالات وكذلك في الثانوية برحبتها في
+
+265
+00:32:04,480 --> 00:32:11,500
+الكلمة فبقول هذه X to the power P زائد توافق P من
+
+266
+00:32:11,500 --> 00:32:18,520
+الأشياء مأخوذة واحد واحد X أُس P ناقص واحد Y زائد
+
+267
+00:32:18,520 --> 00:32:25,960
+توافق P من الأشياء مأخوذة متنا متناXP ناقص اتنين
+
+268
+00:32:25,960 --> 00:32:32,620
+في الـY تربيع ونظل مستمرين لغاية ما نوصل للـY أُس
+
+269
+00:32:32,620 --> 00:32:41,480
+P هذا الكلام يساوي XP هذا الآن يحتوي على P ولا لا؟
+
+270
+00:32:41,480 --> 00:32:50,100
+خلّيني أذكركم الآن بجينا نقول توفي قنون من الأشياء
+
+271
+00:32:50,100 --> 00:32:57,780
+مأخوذة راء راءبجينا نقول N factorial على R
+
+272
+00:32:57,780 --> 00:33:06,780
+factorial N ناقص R factorial تذكرين العلاقة هذه في
+
+273
+00:33:06,780 --> 00:33:13,960
+التوافق والتباديل تمام أو في توزيع ذات الحدد الآن
+
+274
+00:33:13,960 --> 00:33:19,580
+هذا العمصر دائما و أبدا يحتوي على العمصر N
+
+275
+00:33:19,580 --> 00:33:25,570
+وبالتاليهذا عندنا دائما يعتمد على علم موجود في
+
+276
+00:33:25,570 --> 00:33:33,330
+عنصر P P مضروب في شغلة تمام؟ وهذا P مضروب في شغلة
+
+277
+00:33:33,330 --> 00:33:39,650
+وهذا P مضروب في شغلة فبالسؤال هو هذا مش عنصر موجود
+
+278
+00:33:39,650 --> 00:33:44,330
+في الريم ومضروب في P وال characteristic اللي
+
+279
+00:33:44,330 --> 00:33:50,500
+هيساوي P يبقى كده شهدة المقدار؟ Zeroيبقى هذا هو 1
+
+280
+00:33:50,500 --> 00:33:56,620
+زائد Zero والثاني زائد Zero والتالت زائد Zero زائد
+
+281
+00:33:56,620 --> 00:34:01,480
+Y فيه كل العناصر معدل الأنصر الأول والأنصر الأخير
+
+282
+00:34:01,480 --> 00:34:06,380
+كلها موجودة فيها الرقم P ال P هو ال characteristic
+
+283
+00:34:06,380 --> 00:34:10,920
+لل ring بتقدروا في جميع عناصر ال ring يعطيني Zero
+
+284
+00:34:10,920 --> 00:34:16,170
+يبقى كل العناصر في النص بتروح ب Zeroيبقى يصير هذا
+
+285
+00:34:16,170 --> 00:34:23,810
+X أُس P زائد Y أُس P وهو المطموب الأول المطموب
+
+286
+00:34:23,810 --> 00:34:30,490
+التام نمرأ به نمرأ به بإنه نثبت ان X زايد Y مرفوع
+
+287
+00:34:30,490 --> 00:34:39,910
+للأس P أُس N يساوي X أُس P N وY أُس P N هذا إلك by
+
+288
+00:34:39,910 --> 00:34:42,390
+induction
+
+289
+00:34:45,730 --> 00:34:50,390
+يبقى هذا بالاستنتاج الرياضي أو الاستقرار الرياضي
+
+290
+00:34:50,390 --> 00:34:55,590
+لو حطيت N بواحد عشان تطلع الحالة الأولى يبقى
+
+291
+00:34:55,590 --> 00:35:00,290
+الحالة الأولى يبقى بدأ أفترض أن هذه صحيحة عند N
+
+292
+00:35:00,290 --> 00:35:07,690
+تساوي M و أثبت صحتها عند N تساوي M زي 1 أظن سهلة
+
+293
+00:35:07,690 --> 00:35:11,750
+ويوم سويته زيها في مبادئ الرياضية يبقى هذه سهلة
+
+294
+00:35:11,750 --> 00:35:19,040
+طيب نمر ال C نمر ال Cبيقول لها لـ ring و فيها
+
+295
+00:35:19,040 --> 00:35:24,320
+عنصرين و ال characteristic إلها بيسوي أربعة و هذه
+
+296
+00:35:24,320 --> 00:35:32,040
+العلاقة ماهياش صحيحة طلع ندور على ring ال
+
+297
+00:35:32,040 --> 00:35:38,400
+characteristic إلها أربعة و العلاقة هذه مش صحيحة
+
+298
+00:35:38,400 --> 00:35:44,040
+احنا أثبتنا صحتها لما كان ال P prime لكن هل
+
+299
+00:35:44,040 --> 00:35:48,400
+الأربعة تانيةلأ مش صح يبقى بدي أدور على ring ال
+
+300
+00:35:48,400 --> 00:35:54,360
+characteristic اللي هي يساوي أربعة مين؟ زد أربعة
+
+301
+00:35:54,360 --> 00:36:04,340
+ماشي يبقى بدي أخد ال ring اللي هي زد أربعة هذا ك
+
+302
+00:36:04,340 --> 00:36:12,100
+characteristic أربعة تمام يبقى هذه إلها ال
+
+303
+00:36:12,100 --> 00:36:17,400
+characteristic اللي هو يساوي مين؟يساوي أربعة تدور
+
+304
+00:36:17,400 --> 00:36:23,620
+على عنصرين فيها لا يحققني هذه العلاقة عناصر زد
+
+305
+00:36:23,620 --> 00:36:27,800
+اربعة Zero واحد واتنين وتلاتة اربع عناصر بس مش
+
+306
+00:36:27,800 --> 00:36:33,460
+غيرهم خليني نجرب اي رقمين فيهم وليكن مثلا واحد
+
+307
+00:36:33,460 --> 00:36:40,580
+وثلاثة لو أخد X بواحد و Y تساوي تلاتة بهذا الشكل
+
+308
+00:36:40,580 --> 00:36:49,250
+تمام؟ وبتاجر أقولهذا يريد أن يعطينا ان الـ x زائد
+
+309
+00:36:49,250 --> 00:36:59,090
+y to the power 4 يساوي 1 زائد 3 to the power 4
+
+310
+00:36:59,090 --> 00:37:09,310
+فبتشوف كده يساوي هذا كده 1 زائد 3 فزيت 4 صفر صفر
+
+311
+00:37:09,310 --> 00:37:17,140
+هذا بزيتبتادي واخد واحد أُص أربعة ثلاثة أُص أربعة
+
+312
+00:37:17,140 --> 00:37:29,700
+واحد أُص أربعة أبواحد ثلاثة أُص أربعة واحد أكيد
+
+313
+00:37:29,700 --> 00:37:35,380
+ثلاثة تربية تسعة مشيل منها أربعتين بيظل واحد
+
+314
+00:37:35,380 --> 00:37:40,860
+والتاني بيظل واحد في واحد أبواحدأو تسعة فى تسعة
+
+315
+00:37:40,860 --> 00:37:45,480
+بواحد و تمانين التمانين بتقسمها لاربعه مانشيلها
+
+316
+00:37:45,480 --> 00:37:50,440
+بيظهر الواحد هذي والله هذي سيان واحد يبقى النتج
+
+317
+00:37:50,440 --> 00:37:56,640
+يسوى ايش اتنين هذا بدي أكيد ان واحد زائد تلاته أُص
+
+318
+00:37:56,640 --> 00:38:02,720
+أربعه لا يساوي واحد أُص أربعه زائد تلاته أُص أربعه
+
+319
+00:38:02,720 --> 00:38:08,910
+وهو المطلوب هذا سؤال خمسة واربعين بروحي الآنلسؤال
+
+320
+00:38:08,910 --> 00:38:15,430
+640 بيقول الـ R commutative ring with unity و
+
+321
+00:38:15,430 --> 00:38:24,030
+prime characteristic يبقى السؤال 640 الـ R
+
+322
+00:38:24,030 --> 00:38:36,130
+commutative ring with unity اللي هو الواحد و prime
+
+323
+00:38:36,130 --> 00:38:47,370
+characteristicwill be prime as the characteristic
+
+324
+00:38:47,370 --> 00:38:58,650
+of R تمام أخد ال A موجودة في R نيل بوتن ال A اللي
+
+325
+00:38:58,650 --> 00:39:06,750
+موجودة في R is Neil Pottenما هو المطلوب بعد هذه
+
+326
+00:39:06,750 --> 00:39:12,790
+المعلومات بيقول ان ال botan prove there is a
+
+327
+00:39:12,790 --> 00:39:21,030
+positive integer k such that اثبت ان في عندك
+
+328
+00:39:21,030 --> 00:39:27,410
+positive integer k بحيث واحد زائد a to the power k
+
+329
+00:39:27,410 --> 00:39:30,830
+يساوي واحد صحيح
+
+330
+00:39:51,250 --> 00:39:56,670
+أحنا الآن عندنا R commutative with unity واحد و ال
+
+331
+00:39:56,670 --> 00:40:01,170
+P prime هو ال characteristic لل ring اللي عندنا R
+
+332
+00:40:01,170 --> 00:40:09,270
+ال A هو لبوتن بداية من واحد زاد اتو رفعته كوصل ل
+
+333
+00:40:09,270 --> 00:40:13,810
+positive integer P منه المهم يجيبلي positive
+
+334
+00:40:13,810 --> 00:40:17,830
+integer أيش ما يكون شكله يكونبدي يا يطلع هذا
+
+335
+00:40:17,830 --> 00:40:23,210
+الكلام يسوى قدر واحد صحيح بنقول الحلقة التالية
+
+336
+00:40:23,210 --> 00:40:34,390
+solution الان ال potent اش يتطلب هذا يتطلب ان ال a
+
+337
+00:40:34,390 --> 00:40:43,230
+to the power n تسوى zero for some positive انتجة
+
+338
+00:40:51,120 --> 00:40:58,740
+أحنا الآن لو خدنا ال prime مثلا تلاتة وال K يساوي
+
+339
+00:40:58,740 --> 00:41:05,780
+عشر مثلا على سبيل المثال يبقى ال P تربيع P تربيع
+
+340
+00:41:05,780 --> 00:41:10,500
+يعني تلاتة تربيع أقل من عشرةلكن لو أخدنا K تكعيب
+
+341
+00:41:10,500 --> 00:41:15,160
+يعني تلاتة تكعيب بيصير ايه؟ بيصير أكبر من عشر صحيح
+
+342
+00:41:15,160 --> 00:41:20,660
+ولا لأ؟ يبقى أنا بدي أخد L prime لو رفعتها لأس
+
+343
+00:41:20,660 --> 00:41:28,120
+يكون أكبر من مين؟ أكبر من K اللي عندنا، تمام؟ يبقى
+
+344
+00:41:28,120 --> 00:41:39,080
+هنا let P to the power I greater than Nأكبر من N
+
+345
+00:41:39,080 --> 00:41:44,740
+then بتاخد
+
+346
+00:41:44,740 --> 00:41:54,380
+على مين؟ واحد زائد A to the power P أُس I من سؤال
+
+347
+00:41:54,380 --> 00:42:00,840
+خمسة وأربعين يجب أقول واحد to the power P أُس I
+
+348
+00:42:00,840 --> 00:42:10,990
+زائد A to the power P أُس Iطبعا ؟ طيب هذا الكلام
+
+349
+00:42:10,990 --> 00:42:15,990
+بقدر اكتره على صيغة هذا كله جداشا مناهي يبقى هذا
+
+350
+00:42:15,990 --> 00:42:23,250
+الكلام from exercises خمسة و أربعين مش عشوائي يعني
+
+351
+00:42:23,250 --> 00:42:30,790
+هذا الكلام يسوى واحد زائد هذه a to the power inf
+
+352
+00:42:30,790 --> 00:42:37,700
+of a to the power of P أُص I ناقص Mبقدر اكتب هذا
+
+353
+00:42:37,700 --> 00:42:45,020
+اكثر صح ليش لأن ال P و PY أكبر من ال N وبالتالي
+
+354
+00:42:45,020 --> 00:42:50,740
+بقدر اخد هذه منها طيب هذه كلها بقدر ايش؟ نشيب Zero
+
+355
+00:42:50,740 --> 00:42:55,840
+من ال Quotient هيبقى لكم ب Zero يبقى صارت النتيجة
+
+356
+00:42:55,840 --> 00:43:00,180
+واحد زائد Zero يسوى كده يعني يسوى واحد يبدأ يعني
+
+357
+00:43:00,180 --> 00:43:07,690
+قدرت هجيبله رقم Kرفعته لل أُس هذا طلع النتج يساوي
+
+358
+00:43:07,690 --> 00:43:15,910
+قدر واحد يبقى ساعة الـ K تساوي P أُس I قال جيبلي
+
+359
+00:43:15,910 --> 00:43:22,590
+any positive integer K يحقق مين؟ يحقق هذه المعادلة
+
+360
+00:43:22,590 --> 00:43:29,130
+إذا كنت هنا من ستة واربعين وصلنا لاتنين وخمسين
+
+361
+00:43:29,130 --> 00:43:36,420
+ولسة ضالة أربعة أسئلةطيب لأن لو جينا لسؤال 52 جالي
+
+362
+00:43:36,420 --> 00:43:42,460
+find all solutions سؤال
+
+363
+00:43:42,460 --> 00:43:50,340
+52 جالي هاتلي ال solutions للمعادلة x تربيع ماقص x
+
+364
+00:43:50,340 --> 00:43:58,780
+زائد 2 يسوى 0 ان هذا
+
+365
+00:43:59,570 --> 00:44:12,350
+ن زد تلاتة I ن زد تلاتة I يبني
+
+366
+00:44:12,350 --> 00:44:16,950
+احنا عندنا معادلة والمعادلة هذه طلب الحلول لها
+
+367
+00:44:16,950 --> 00:44:22,930
+تمين في زد تلاتة I عظم زد تلاتة I كتبنا عناصرها
+
+368
+00:44:22,930 --> 00:44:29,800
+قبل هيك كم عنصر فيها تسعة عناصرلو جيت للعناصر هذي
+
+369
+00:44:29,800 --> 00:44:35,120
+الدمسك كل عنصر معوض في المعادلة تمام؟ طبعا زي
+
+370
+00:44:35,120 --> 00:44:39,220
+التلاتة عتمت ب zero واحد و اتنين ولا واحد فيهم
+
+371
+00:44:39,220 --> 00:44:47,300
+بيحقق المعادلة لكن لو جيتي اتنين زائد I اندي اتنين
+
+372
+00:44:47,300 --> 00:44:57,220
+زائد اتنين I هذول satisfy the above equation
+
+373
+00:44:58,880 --> 00:45:07,960
+موليكي واحدة فيهم ناخد هذه تربيع يبقى I أربعة زائد
+
+374
+00:45:07,960 --> 00:45:17,740
+أربعة I ناقص واحد ناقص X يبقى ناقص اتنين ناقص I
+
+375
+00:45:17,740 --> 00:45:26,900
+زائد اتنين ويسبب هدول قداش ناقص ثلاثة وزائد اتنين
+
+376
+00:45:27,250 --> 00:45:33,430
+بظل ناقص واحد وعندك أربعة بظل تلاتة تلاتة بزد
+
+377
+00:45:33,430 --> 00:45:40,190
+تلاتة بزيرو يبقى الأرقام كلها بزيرو تمام الأربعة I
+
+378
+00:45:40,190 --> 00:45:46,910
+بدي أشيل منها تلاتة بظل I واحدة I واحدة و سالف I
+
+379
+00:45:46,910 --> 00:45:53,330
+كله راح بزيرو يبقى هالي حققتها طويلة والتالي نفسه
+
+380
+00:45:53,330 --> 00:45:58,620
+بالصبابةنفس الرقم اللي هو عند هذا ال complex بشرة
+
+381
+00:45:58,620 --> 00:46:03,820
+سالف زي الاتنين بتلاقي zero يبقى هدول فقط هم اللي
+
+382
+00:46:03,820 --> 00:46:08,760
+بحلوا المعادلة السؤال اللي بعده إزاي؟ بس اللي بعده
+
+383
+00:46:08,760 --> 00:46:13,600
+أربع مطالب لإن كل واحدة فيهم شكل يعطيك معادلة
+
+384
+00:46:13,600 --> 00:46:23,180
+ويعطيك ring تانية تلترها بحط عناصرها وبجيب عوضوحدة
+
+385
+00:46:23,180 --> 00:46:27,760
+منهم هتلاقي فيها حلين وحدة بتلاقي فيها ثلاثة حلول
+
+386
+00:46:27,760 --> 00:46:34,940
+وحدة مثلا أربعة حلول إلى آخرين فمثلا فمثلا لو جيتي
+
+387
+00:46:34,940 --> 00:46:47,660
+لسؤال 53 سؤال 53 سؤال 53 بتلاقي عندك نمرة A نمرة A
+
+388
+00:46:47,660 --> 00:46:56,380
+الحل تبعه اللي هو عبارة عنالـ X يساوي 2 و 3 ونمره
+
+389
+00:46:56,380 --> 00:47:09,100
+B الحل تبعه نمره B الحل تبعه كمان 2 و 3 ونمره C
+
+390
+00:47:09,100 --> 00:47:21,140
+ونمره C الحل تبعه 2 و 3 و 6 و 11 ونمره D الحل تبعه
+
+391
+00:47:21,380 --> 00:47:28,400
+إتنين و تلاتة و تسعة و عشرة لإن كل واحدة فيهم ring
+
+392
+00:47:28,400 --> 00:47:32,880
+شكله بتختلف عن التانية المحاضرة القادمة نبدأ ال
+
+393
+00:47:32,880 --> 00:47:38,420
+chapter الجديد ان شاء الله تعليه ال ideals and
+
+394
+00:47:38,420 --> 00:47:40,240
+quotient rings
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b99876e5641a00432996d37a7f9238dd7f8a3cd1
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M_postprocess.srt
@@ -0,0 +1,1692 @@
+1
+00:00:20,860 --> 00:00:25,640
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا به في المرة
+
+2
+00:00:25,640 --> 00:00:30,860
+الماضية في نهاية المحاضرة الماضية كتبنا ال remark
+
+3
+00:00:30,860 --> 00:00:36,140
+التالية أنه لو كان عندي function من Z كله ل square
+
+4
+00:00:36,140 --> 00:00:42,300
+root ل D ل Z plus معرفة N of A زائد B ل square
+
+5
+00:00:42,300 --> 00:00:47,120
+root ل D بتساوي ال absolute value لل A ترابية نقص
+
+6
+00:00:47,120 --> 00:00:54,800
+ال D بيه ترابيةالنقطة الأولى والثانية برهنهم المرة
+
+7
+00:00:54,800 --> 00:01:00,200
+الماضية ووصلنا الى النقطة الثالثة والرابعة إذا كلا
+
+8
+00:01:00,200 --> 00:01:07,280
+كتر بدنا نيجي لنمرى الـC نمرى الـC قال X is a unit
+
+9
+00:01:07,280 --> 00:01:14,220
+if and only if ال N X يسوى 101 هذا العشري نسبته ال
+
+10
+00:01:14,220 --> 00:01:18,660
+1000 يبقى أبراد ال N أكتر
+
+11
+00:01:21,070 --> 00:01:26,790
+الـ X هو اللي موجودة هذه في
+
+12
+00:01:26,790 --> 00:01:32,770
+ذات الاسم وعود لـ D هي كمعنى هذا الكلام اللي هي N
+
+13
+00:01:32,770 --> 00:01:40,990
+of A زائد B جادر الـ D بديه سوى 1 if and only if
+
+14
+00:01:40,990 --> 00:01:47,290
+وده يجيب روح نستخدم التعريف نشيل هذا ونحط التعريف
+
+15
+00:01:47,290 --> 00:01:54,570
+اللي احنا حاطينااللي همين a تربيع ناقص d بي تربيع
+
+16
+00:01:54,570 --> 00:02:05,450
+كل هذا الكلام بدي يساوي واحدة if and only if يبقى
+
+17
+00:02:05,450 --> 00:02:11,630
+ال a تربيع ناقص d بي تربيع يساوي زائد او ناقص
+
+18
+00:02:11,630 --> 00:02:17,070
+واحدة يشيلنا ال absolute valueحطينا لل element
+
+19
+00:02:17,070 --> 00:02:21,990
+واحد زايد او ناقص واحد هذا ممكن احلله كفارق بين
+
+20
+00:02:21,990 --> 00:02:29,090
+المرابعين يبقى هذا الكلام صحيح اذا كان ال a ناقص b
+
+21
+00:02:29,090 --> 00:02:37,150
+في جذر ال D في ال a زايد b جذر ال D بيكون زايد او
+
+22
+00:02:37,150 --> 00:02:46,840
+ناقص واحد if and only if هذا صحيح لو كانهه مدام
+
+23
+00:02:46,840 --> 00:02:51,980
+واحد واحد هو ال unity مظبوط ولا لا يبقى بناء عليه
+
+24
+00:02:51,980 --> 00:02:58,100
+هذا الكلام صحيح لو كان هداش unit يبقى if and only
+
+25
+00:02:58,100 --> 00:03:07,800
+if ال X اللي تساوي ال A زائد B جذر ال D is a unit
+
+26
+00:03:07,800 --> 00:03:17,270
+وهو المفروض حيث نبردالنمرة دي بتاعي أقول له assume
+
+27
+00:03:17,270 --> 00:03:27,130
+افترض ان ال N of X is a prime ايش
+
+28
+00:03:27,130 --> 00:03:35,310
+بدنا نثبت؟ ايش بدنا نثبت يا بنات؟ ايش بدنا نثبت؟
+
+29
+00:03:35,310 --> 00:03:40,330
+ان ال X is irreducible المرة اللي فاتت عرفنا ال
+
+30
+00:03:40,330 --> 00:03:45,380
+prime وعرفنا ال irreducibleيبقى ال element a بقول
+
+31
+00:03:45,380 --> 00:03:53,460
+عنه irreducible إذا حقق شرطين الشرط الأول أن ال a
+
+32
+00:03:53,460 --> 00:03:58,900
+is non unit الشرط التاني لو جدرت أكتبه على صيغة
+
+33
+00:03:58,900 --> 00:04:04,520
+حصل ضرب عنصرين يبقى واحد فيهم يكون unit يعني لو
+
+34
+00:04:04,520 --> 00:04:09,920
+كان ال a كتبته على شكل b في c يبقى ال a is unit أو
+
+35
+00:04:09,920 --> 00:04:15,320
+ال b is unit هذا ال irreducibleطيب ليه prime الشرط
+
+36
+00:04:15,320 --> 00:04:20,720
+الأولاني هو الشرط نفسه ان ال a بقول عنه prime إذا
+
+37
+00:04:20,720 --> 00:04:26,180
+كان ال a non unit اتنين مش كان يسوى حصر ضرب ب two
+
+38
+00:04:26,180 --> 00:04:31,220
+elements لأ كان ال a بيقسم ال b في c إذا ال a
+
+39
+00:04:31,220 --> 00:04:34,560
+بيقسم ال b or ال b بيقسم ال c هذا ال two
+
+40
+00:04:34,560 --> 00:04:39,940
+definitions اللي معاكم في بداية المحاضرة الماضية
+
+41
+00:04:39,940 --> 00:04:45,810
+طيب نمشي هناان احنا افترضنا ان ال N of X is a
+
+42
+00:04:45,810 --> 00:04:54,170
+prime مطلوب يثبت ان ال X is a reducer ممتاز جدا طب
+
+43
+00:04:54,170 --> 00:05:00,790
+لما اقول N of X is a prime تمام يبقى ال N of X
+
+44
+00:05:00,790 --> 00:05:07,370
+ممكن تكون unit ممكن
+
+45
+00:05:07,370 --> 00:05:18,590
+تكون واحديبقى ذلك ال n of x does not equal to one
+
+46
+00:05:18,590 --> 00:05:25,110
+مش ممكن تكون واحد طب لو ماكنتش واحد يبقى إيش بدها
+
+47
+00:05:25,110 --> 00:05:33,150
+.. بدها تكون .. لأ من unit تمام؟ يبقى هذا بدي أقين
+
+48
+00:05:33,150 --> 00:05:38,090
+أن ال n of x is من unit
+
+49
+00:05:40,330 --> 00:05:47,050
+استغلني شوية بس يبقى هذا ال .. ال .. ال X is non
+
+50
+00:05:47,050 --> 00:05:53,590
+-unit تمام؟ طيب احنا الآن افترضنا ان ال N .. اه
+
+51
+00:05:53,590 --> 00:05:59,450
+وين افترضنا؟ طيب افترضنا ان ال N of X is prime و
+
+52
+00:05:59,450 --> 00:06:06,590
+ال N of X قلنا ممنوع تساوي واحد يبقى ال .. يبقى ال
+
+53
+00:06:06,590 --> 00:06:13,480
+N of X is non-unitطبعا طيب ممتاز جدا يبقى بدي اقعد
+
+54
+00:06:13,480 --> 00:06:21,220
+افترض ان عندي اللي هو ال element اللي عندنا هذا
+
+55
+00:06:21,220 --> 00:06:34,040
+ههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+56
+00:06:39,520 --> 00:06:47,480
+بتساوي A في B افترض ان ال X بيساوي حاصل ضرب A في B
+
+57
+00:06:47,480 --> 00:06:55,540
+ال X هذا مشان يكون عندي irreducible بيكون واحد من
+
+58
+00:06:55,540 --> 00:07:01,580
+هذول عبارة عن unit صحيح ولا لأ طيب تعالى نشوف الان
+
+59
+00:07:01,580 --> 00:07:08,520
+لو أخد تأثير ال function N على X مش يساوي تأثير ال
+
+60
+00:07:08,520 --> 00:07:16,610
+Nعلى ال A في ال B صحيح؟ طيب هذا الكلام يعني ان ال
+
+61
+00:07:16,610 --> 00:07:27,790
+N of X يساوي ال N of A في ال N of B طب ال N of X
+
+62
+00:07:27,790 --> 00:07:36,070
+is a prime ايش معناه؟ ونجاه ان ال N of X يساوي حصل
+
+63
+00:07:36,070 --> 00:07:41,840
+ضرب الاتنين هدوليبقى واحد فيهم بده يسوى واحد على
+
+64
+00:07:41,840 --> 00:07:51,000
+الأقل صحيح يبقى بجي بقول since ال N of X is a
+
+65
+00:07:51,000 --> 00:08:01,780
+prime we have يبقى
+
+66
+00:08:01,780 --> 00:08:11,560
+we have ان ال N of A بده يسوى واحداو ال N of B
+
+67
+00:08:11,560 --> 00:08:23,100
+يسوى واحد مظبوط ؟ طيب هذا مظبوط تعالى ايه ال
+
+68
+00:08:23,100 --> 00:08:29,180
+N of A يسوى واحد معناته ال A is unit هذا يسوى واحد
+
+69
+00:08:29,180 --> 00:08:36,260
+لأن معناته ال B is unit يبقى ضروري اقوله by part C
+
+70
+00:08:39,430 --> 00:08:51,170
+إن الـ A is A unit أو الـ B is A unit إذا واحد
+
+71
+00:08:51,170 --> 00:08:59,090
+منهم unit فبإيش صار عندي؟ ال X is irreducible
+
+72
+00:08:59,090 --> 00:09:06,350
+صحيح؟ لإن ال X هي فرضناها حاصل ضرب اتنين طالع واحد
+
+73
+00:09:06,350 --> 00:09:17,370
+فيهم unit يبقى thismeans that ان ال X is
+
+74
+00:09:17,370 --> 00:09:26,670
+irreducible over .. irreducible
+
+75
+00:09:26,670 --> 00:09:33,270
+over Z of the square root of D
+
+76
+00:09:39,100 --> 00:09:47,880
+طيب ننتقل الآن الى الأول نظرية على هذا الموضوع نقل
+
+77
+00:09:47,880 --> 00:09:54,600
+integral
+
+78
+00:09:54,600 --> 00:10:00,280
+domain integral
+
+79
+00:10:00,280 --> 00:10:02,500
+domain
+
+80
+00:10:06,600 --> 00:10:17,900
+every prime is a reducer every prime is a reducer
+
+81
+00:10:17,900 --> 00:10:29,380
+every prime is a reducer افترض
+
+82
+00:10:29,380 --> 00:10:33,820
+يجب
+
+83
+00:10:33,820 --> 00:10:38,980
+ان افترضإنه في عندي integral domain اللي بجيه هنا
+
+84
+00:10:38,980 --> 00:10:51,280
+فده اقول له left دي be an integral domain طبعا
+
+85
+00:10:51,280 --> 00:10:57,960
+جالس اي prime بده يكون ال reducer إذا بده اخد
+
+86
+00:10:57,960 --> 00:11:03,260
+element و اثرضه انه prime وروح اثبتله انه reducer
+
+87
+00:11:03,890 --> 00:11:12,950
+يرجع هنا فجأة بيقولوا let ال A اللي موجودة في D ب
+
+88
+00:11:12,950 --> 00:11:22,830
+A prime وانت شارف ان
+
+89
+00:11:22,830 --> 00:11:31,950
+نحاول نثبت ان ال A is irreducible يبقى
+
+90
+00:11:31,950 --> 00:11:38,270
+كل شغلنا منصفعلى التعريفات تبعات المحاضرة الماضية
+
+91
+00:11:38,270 --> 00:11:45,430
+طيب الان فرضنا ان a is a prime ال a معناته ممكن
+
+92
+00:11:45,430 --> 00:11:55,910
+يكون unit لأ يبقى هنا باجي بقول send ال a since ال
+
+93
+00:11:55,910 --> 00:12:06,820
+a is a prime ال a is my unitيجي الشرط الأول من شرط
+
+94
+00:12:06,820 --> 00:12:12,800
+ال irreducible يتحقق بدنا نيجي لمين للشرط الثاني
+
+95
+00:12:12,800 --> 00:12:20,560
+الشرط الثاني بد أثبت irreducible يعني اه بس في
+
+96
+00:12:20,560 --> 00:12:28,060
+عندك بدنا نستفيد من مين نستفيد من مين من
+
+97
+00:12:28,060 --> 00:12:33,330
+المعطيات ال A is a primeماذا يعني الـ Time؟ لو كان
+
+98
+00:12:33,330 --> 00:12:38,330
+الـ A بيقسم حاصل الضرب يبقى فانت بيقسم واحد فيه،
+
+99
+00:12:38,330 --> 00:12:51,630
+مظبوط؟ يبقى الـ A and if ال A بيقسم ال B، C then
+
+100
+00:12:51,630 --> 00:12:57,750
+ال A بيقسم ال B or ال A بيقسم ال C
+
+101
+00:13:00,820 --> 00:13:08,220
+بدأ أخد لو كان الـ A بيقسم الـ B إيش اللي بده
+
+102
+00:13:08,220 --> 00:13:17,580
+يحصل؟ مشان نثبتها Irreducible يبقى None، Zero و
+
+103
+00:13:17,580 --> 00:13:22,660
+بده كتبتها علاقة ما كتبناش على شكل حاصل ضرب نكتبها
+
+104
+00:13:22,660 --> 00:13:25,100
+على شكل حاصل ضرب
+
+105
+00:13:31,120 --> 00:13:39,820
+الـ A بدها تساوي الـ B في C مشان
+
+106
+00:13:39,820 --> 00:13:43,760
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+107
+00:13:43,760 --> 00:13:44,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+108
+00:13:44,260 --> 00:13:44,720
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+109
+00:13:44,720 --> 00:13:45,220
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+110
+00:13:45,220 --> 00:13:46,600
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+111
+00:13:46,600 --> 00:13:46,800
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+112
+00:13:46,800 --> 00:13:50,820
+انا انا انا انا انا
+
+113
+00:13:50,820 --> 00:13:50,900
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+114
+00:13:50,900 --> 00:13:58,360
+انا انا
+
+115
+00:13:58,360 --> 00:14:04,600
+اناالـ A non-unit فالـ A تقسم الـ C فالترضيه ان
+
+116
+00:14:04,600 --> 00:14:13,780
+الـ A بده يساوي مين؟ P في C الان since ال A بتقسم
+
+117
+00:14:13,780 --> 00:14:22,640
+ال بي سي أكيد ما هي ال A تساوي مين؟ ال P في C يعني
+
+118
+00:14:22,640 --> 00:14:28,440
+ال A بتقسم نفسها صح ولا لأ يبقى ال A بتقسم ال P في
+
+119
+00:14:28,440 --> 00:14:40,430
+C يبقىwe have ان ال A تقسم ال B او ال A تقسم ال C
+
+120
+00:14:40,430 --> 00:14:51,010
+لش؟ لأن ال A is a prime because ال
+
+121
+00:14:51,010 --> 00:14:55,790
+A is a prime فهي تمام
+
+122
+00:15:00,870 --> 00:15:06,490
+احنا بنثبت يا اما ال B unit يا اما ال C unit
+
+123
+00:15:06,490 --> 00:15:18,410
+مظبوط؟ طيب الان لو جيت قولتلك ال A او F ال A
+
+124
+00:15:18,410 --> 00:15:28,570
+بتقسمين تقسمي ال B then ال B تساوي A في T مثلا
+
+125
+00:15:31,780 --> 00:15:42,220
+وهو sum T اللي موجودة في دي طب
+
+126
+00:15:42,220 --> 00:15:50,440
+لو جتنا العنصر B وضربته في واحد ضربته في واحد يبقى
+
+127
+00:15:50,440 --> 00:15:57,900
+هذا مش هو عبارة عن ال B تمام طب و ال B هو عبارة عن
+
+128
+00:15:57,900 --> 00:16:08,470
+مين A FTصح؟ مافجدش ال ايه تساوي؟ P في C يبقى هنا P
+
+129
+00:16:08,470 --> 00:16:19,850
+في C في T تمام؟ طيب هذا قد يعطيني ال P في C T الان
+
+130
+00:16:19,850 --> 00:16:23,290
+احنا بنشتغل وين؟ في ring ولا في integral domain؟
+
+131
+00:16:23,290 --> 00:16:27,850
+ال integral domain أخدنا علاقة بتقولي لو عندك
+
+132
+00:16:27,850 --> 00:16:32,320
+integral domainو A في B بده يسوي A في C بقى بال
+
+133
+00:16:32,320 --> 00:16:36,280
+left cancellation ال B بده يسوي مين؟ بده يسوي C
+
+134
+00:16:36,280 --> 00:16:48,340
+يجينا By left cancellation لأ
+
+135
+00:16:48,340 --> 00:16:56,540
+We have بده يصير الواحد بده يسوي C في T إيش معنى
+
+136
+00:16:56,540 --> 00:17:03,210
+هذا الكلام؟إن الـC is a unit يبقى هذا معناته إن
+
+137
+00:17:03,210 --> 00:17:11,490
+الـC is a unit طبعا؟ طب ال irreducible قلنا يا إما
+
+138
+00:17:11,490 --> 00:17:15,570
+الـB unit يا إما الـC unit يبقى لما طلعت الـC unit
+
+139
+00:17:15,570 --> 00:17:20,790
+أروح أدور على B مافيش داعي يبقى معنى هذا الكلام
+
+140
+00:17:20,790 --> 00:17:31,050
+يبقى this means thatهذا يعني ان ال A is
+
+141
+00:17:31,050 --> 00:17:36,970
+irreducible over
+
+142
+00:17:36,970 --> 00:17:46,270
+اللي هو Z over
+
+143
+00:17:46,270 --> 00:17:51,230
+D على
+
+144
+00:17:51,230 --> 00:17:52,530
+D فقط لإيه
+
+145
+00:18:15,190 --> 00:18:20,550
+طيب النظرية هذه كان بيقول في ال integral domain لو
+
+146
+00:18:20,550 --> 00:18:26,370
+عندي A' بصير irreducible السؤال هو طب لو كان ال A
+
+147
+00:18:26,370 --> 00:18:33,190
+irreducible بصير A' قد يكون و قد لا يكون، إذا
+
+148
+00:18:33,190 --> 00:18:39,290
+العكس النظرية ليس بالضرورة صحيحة، تبقى بنا نكتب
+
+149
+00:18:39,290 --> 00:18:42,790
+هذه الملاحظة في Gary Mark
+
+150
+00:18:47,180 --> 00:18:56,240
+the converse of
+
+151
+00:18:56,240 --> 00:19:01,560
+the
+
+152
+00:19:01,560 --> 00:19:16,400
+above theorem نظريتي على 100.100 مرتر
+
+153
+00:19:17,300 --> 00:19:28,580
+ليس بالضرورة صحيحا that is I am ال
+
+154
+00:19:28,580 --> 00:19:43,460
+A is a radio source لا يعني ان ال A is right
+
+155
+00:19:45,570 --> 00:19:54,750
+بنعطي مثال على ذلك طبعا
+
+156
+00:19:54,750 --> 00:20:02,930
+الكتاب أعطاني المثال في الأول ثم النظرية ثم ال
+
+157
+00:20:02,930 --> 00:20:08,350
+remark تمام فالترتيب مش دقيق احنا أعطينا النظرية
+
+158
+00:20:08,350 --> 00:20:13,170
+ثم أعطينا ال remark ثم بدنا نجيب counter example
+
+159
+00:20:13,170 --> 00:20:17,820
+يثبت مينيثبت هذه الـ remark يبقى أنا بدأ أخد
+
+160
+00:20:17,820 --> 00:20:21,920
+integral domain و أثبت أنه على ال integral domain
+
+161
+00:20:21,920 --> 00:20:26,540
+هنا في عندي element irreducible لكنه في الحقيقة
+
+162
+00:20:26,540 --> 00:20:34,180
+ليس prime تمام؟ for example بيقول ما يأتي consider
+
+163
+00:20:34,180 --> 00:20:41,880
+the integral domain consider the integral
+
+164
+00:20:44,920 --> 00:20:51,340
+domain افترض انه عندك integral domain اللى هو D
+
+165
+00:20:51,340 --> 00:21:03,620
+يساوي Z of الجدرق الترابيعى اللى سارب تلاتة
+
+166
+00:21:03,620 --> 00:21:09,220
+يبقى
+
+167
+00:21:09,220 --> 00:21:15,040
+انا بروح اخد elementفي هذا الـ integral domain و
+
+168
+00:21:15,040 --> 00:21:19,720
+أثبت ان هذا ال element في الأول is irreducible
+
+169
+00:21:19,720 --> 00:21:25,020
+يعني في الحل انا همشي خطواتين مش انا قولت لك خلاص
+
+170
+00:21:25,020 --> 00:21:29,260
+خد هال element is irreducible لأ بدي أثبت ان في
+
+171
+00:21:29,260 --> 00:21:33,880
+عندي element irreducible وفي الحقيقة هذا ال
+
+172
+00:21:33,880 --> 00:21:38,080
+element ليس a prime يبقى الخطوة الحل بيكون على
+
+173
+00:21:38,080 --> 00:21:47,050
+مرحلتينإيش بدالي أقوله الواحد زائد جدد سالب تلاتة
+
+174
+00:21:47,050 --> 00:21:59,050
+belong to z of the square root لسالبين بعدين
+
+175
+00:21:59,050 --> 00:22:09,210
+بدالي أقول له assume افترض ان there exist x و y
+
+176
+00:22:09,660 --> 00:22:20,100
+موجودة في Z of الجذر السالب تلاتة such that وبحيث
+
+177
+00:22:20,100 --> 00:22:28,520
+ان ال X في ال Y يساوي الواحد زائد الجذر السالب
+
+178
+00:22:28,520 --> 00:22:50,890
+تلاتة with ال X and ال Y arenot units يبقى
+
+179
+00:22:50,890 --> 00:22:55,730
+احنا ايش سوينا هنا اخدنا element في ال integral
+
+180
+00:22:55,730 --> 00:23:01,350
+domain اللي عندنا وجينا افترضنا انه في عندي عمصرين
+
+181
+00:23:01,350 --> 00:23:05,850
+حاصل ضربه ما يساوي هذا ال element و ال two
+
+182
+00:23:05,850 --> 00:23:10,500
+elements هدول are not unitsطيب و لا واحد فيهم
+
+183
+00:23:10,500 --> 00:23:17,580
+عبارة عن ايش عن units تمام تمام طيب تشوف حالي هل
+
+184
+00:23:17,580 --> 00:23:23,720
+بوصل لتناقض و لا بوصلش لتناقض من هذا الكلام نرجع
+
+185
+00:23:23,720 --> 00:23:30,540
+مرة تانية احنا أخدنا قبل قليل ال function من z of
+
+186
+00:23:30,540 --> 00:23:31,980
+z of z of z of z of z of z of z of z of z of z of
+
+187
+00:23:31,980 --> 00:23:33,480
+z of z of z of z of z of z of z of z of z of z of
+
+188
+00:23:33,480 --> 00:23:33,660
+z of z of z of z of z of z of z of z of z of z of
+
+189
+00:23:33,660 --> 00:23:33,760
+z of z of z of z of z of z of z of z of z of z of
+
+190
+00:23:33,760 --> 00:23:33,860
+z of z of z of z of z of z of z of z of z of z of
+
+191
+00:23:37,230 --> 00:23:44,630
+تخليها تأثر على XY تأثير ال N على 1 زائد جدر ناقص
+
+192
+00:23:44,630 --> 00:23:49,230
+تلاتة الخاصية
+
+193
+00:23:49,230 --> 00:23:57,170
+التانية هذه معناها ايش ان ال N X في ال N Y يساوي
+
+194
+00:23:57,170 --> 00:24:05,510
+هذه من التعريف مربع الأول زائد ناقص تلاتة في مربع
+
+195
+00:24:05,510 --> 00:24:09,390
+التاني الأول بواحدوالمعامل اللي جيبنا الجذر جداش
+
+196
+00:24:09,390 --> 00:24:16,310
+واحد يبقى هذه واحد تربيع بواحد ناقص دي اللي يبقى
+
+197
+00:24:16,310 --> 00:24:24,130
+ناقص ثلاثة في واحد يبقى ناتج جداش أربع تمام الأربع
+
+198
+00:24:24,130 --> 00:24:29,810
+هذه لها تحليلين التحليل الأول اتنين في اتنين
+
+199
+00:24:29,810 --> 00:24:37,940
+والتحليل التاني واحد في أربع يعني ممكن تكونواحدة
+
+200
+00:24:37,940 --> 00:24:44,360
+منهم واحد وواحدة منهم أربعة بصوصهم شوية لو استفعدت
+
+201
+00:24:44,360 --> 00:24:50,100
+الواحد بظهر فيه إمكانية للأربعة؟ لأ طيب أنا الأن
+
+202
+00:24:50,100 --> 00:25:00,340
+أدعي أن ال N of X بده ساوين اتنين ليش؟ because
+
+203
+00:25:00,340 --> 00:25:05,520
+طالعش
+
+204
+00:25:05,520 --> 00:25:06,800
+كاتب هنا؟
+
+205
+00:25:09,320 --> 00:25:16,320
+ال X and Y are not units مظبوط يبقى لو قلت ال N of
+
+206
+00:25:16,320 --> 00:25:22,620
+X يساوي واحد مع انتهي X unit صحيح ولا لا يبقى لما
+
+207
+00:25:22,620 --> 00:25:26,700
+أقول ال N of X لا تساوي واحد معناته ال X is not a
+
+208
+00:25:26,700 --> 00:25:33,480
+unit مظبوط يبقى because ان ال N of X يساوي اتنين
+
+209
+00:25:33,480 --> 00:25:42,550
+because ال N of X لا تساوي واحدsince x is not a
+
+210
+00:25:42,550 --> 00:25:48,730
+unit يبقى حكايته باربع حطيها على الشكل بظل مين؟
+
+211
+00:25:48,730 --> 00:25:55,810
+بظل عندى اتنين و اتنين يبقى ندل ال N of X ال N of
+
+212
+00:25:55,810 --> 00:26:03,790
+X يا بناه أليست هي N of A زائد B generally سالب
+
+213
+00:26:03,790 --> 00:26:11,780
+تلاتة يساوي اتنين؟ بظبططيب هذا الكلام بدي أروح
+
+214
+00:26:11,780 --> 00:26:19,400
+أستخدم تعريف ال N يبقى A ترابية absolute value
+
+215
+00:26:19,400 --> 00:26:26,700
+ناقص ال D اللي هي بناقص تلاتة في ال B ترابية يساوي
+
+216
+00:26:26,700 --> 00:26:36,140
+اتنين طيب هذا معناه ان ال A ترابية زائد تلاتة B
+
+217
+00:26:36,140 --> 00:26:40,960
+ترابيةيساوى اتنى، احط ال absolute value، مافيش
+
+218
+00:26:40,960 --> 00:26:45,680
+داعي لها، مافيش داعي لها، لإن الكمية مربعة اتنين
+
+219
+00:26:45,680 --> 00:26:51,280
+بالموجة، طيب هذا الكلام يساوي اتنى، طب ال A و ال B
+
+220
+00:26:51,280 --> 00:26:58,680
+وين موجودة هذه؟ في Z، صح ولا لأ؟ يبقى هنا لو جلنا
+
+221
+00:26:58,680 --> 00:27:05,140
+جنب هذي، و ال A و ال B belong to Zبعد اتنين حطيلي
+
+222
+00:27:05,140 --> 00:27:08,380
+فاصفة و أقولي الـA و الـB موجودة وين في الـZ
+
+223
+00:27:08,380 --> 00:27:19,240
+السؤال هو ممكن ألاقي A و B في Z يحقق هذه المعاملة؟
+
+224
+00:27:19,240 --> 00:27:23,160
+ممكن ألاقي انت؟ مش مهم سالم موجة بصفر اللي بدك
+
+225
+00:27:23,160 --> 00:27:29,420
+إياه ممكن ألاقي؟ ولا واحد تمام؟ يعني هذا كلام
+
+226
+00:27:29,420 --> 00:27:35,290
+ممكن؟ this is impossibleيبدأ هنا فروح بقول له this
+
+227
+00:27:35,290 --> 00:27:45,230
+is impossible because there
+
+228
+00:27:45,230 --> 00:27:56,110
+is no integers او
+
+229
+00:27:56,110 --> 00:27:59,410
+no integers
+
+230
+00:27:59,410 --> 00:28:07,740
+a andالـ B satisfied the
+
+231
+00:28:07,740 --> 00:28:14,580
+equation المعادلة اللي هو A ترابية زائد تلاتة B
+
+232
+00:28:14,580 --> 00:28:21,820
+ترابية يساوية نكت. إذن في شغل غلط. هي اللي وصلتني
+
+233
+00:28:21,820 --> 00:28:29,420
+إلى نتيجة غلط. هذول فرطب انهم ايش؟not units معناته
+
+234
+00:28:29,420 --> 00:28:39,220
+واحدة منهم unit أو 10 يبقى هذا contradiction تناقض
+
+235
+00:28:39,220 --> 00:28:49,520
+مادام تناقض هذا يعطينا ان ال X is a unit او ال Y
+
+236
+00:28:49,520 --> 00:28:57,200
+is a unit طبعا هذا تعريف مين؟طبعا هي في ال
+
+237
+00:28:57,200 --> 00:29:05,200
+reducibility يبقى هنا ساق ال X is ايه ال .. مش ال
+
+238
+00:29:05,200 --> 00:29:13,020
+X ال element اللي عندنا الواحد زائد جدر ناقص تلاتة
+
+239
+00:29:13,020 --> 00:29:19,940
+is irreducible of
+
+240
+00:29:19,940 --> 00:29:24,180
+الجدر
+
+241
+00:29:24,180 --> 00:29:25,740
+اللي سالب تلاتة
+
+242
+00:29:33,440 --> 00:29:38,620
+لكن لو كانت Reduceable ده يعني ان ايه اذا بتعرف؟
+
+243
+00:29:38,620 --> 00:29:47,060
+اذا بتعرف لو كانت ايه؟ Reduceable بس ايش رايك
+
+244
+00:29:47,060 --> 00:29:52,560
+تصبري علينا شوية النظرية اللى جاية مربوطة بالنظرية
+
+245
+00:29:52,560 --> 00:29:57,780
+الاولانية ايه؟ بلب تجمع النظرية الاولانية او
+
+246
+00:29:57,780 --> 00:30:01,900
+النظرية اللى جاية نص النظرية الاولى ونص النظرية
+
+247
+00:30:01,900 --> 00:30:07,720
+التاليةيكون أجوبنا على سؤالك ان شاء الله يبقى ال
+
+248
+00:30:07,720 --> 00:30:12,720
+element هذه مرة يا بنات is irreducible يبقى احنا
+
+249
+00:30:12,720 --> 00:30:19,860
+حققنا مين؟ حققنا الأمر الأول من ال remark اللي كنا
+
+250
+00:30:19,860 --> 00:30:24,280
+كاتبينه هنا ان لو كان ال element is irreducible
+
+251
+00:30:24,280 --> 00:30:30,280
+ليس بالضرورة ان يكون fine يبقى الآن بدنا نثبت انه
+
+252
+00:30:30,280 --> 00:30:36,510
+ليس بالضرورة يكون ايهيكون افعال.طيب، شوفين يا شغل
+
+253
+00:30:36,510 --> 00:30:44,930
+غيرك. لو جيتني قولتلي consider واحد زائد جذر ناقص
+
+254
+00:30:44,930 --> 00:30:52,130
+تلاتة في واحد ناقص جذر لناقص تلاتة.يعني كأننا
+
+255
+00:30:52,130 --> 00:31:00,730
+حللنا فرق بين المربعين.أليس هذا هو واحد زائد
+
+256
+00:31:00,730 --> 00:31:08,690
+تلاتة؟اللي هو أربعة اللي هو بده يساوي كمان اتنين
+
+257
+00:31:08,690 --> 00:31:13,370
+في اتنين يعني
+
+258
+00:31:13,370 --> 00:31:17,930
+معناته ان ال element هذا بده يجسم اتنين في اتنين
+
+259
+00:31:17,930 --> 00:31:24,870
+صح؟ اللي حاصل ضربه مايساوي أربعة إذا بده يجسم و
+
+260
+00:31:24,870 --> 00:31:29,330
+الأربعة كتبتها اتنين في اتنين يبقى هذا بده يقينا
+
+261
+00:31:29,330 --> 00:31:36,600
+إيشبدي يعطينا ان واحد زي الجذر ناقص تلاتة divides
+
+262
+00:31:36,600 --> 00:31:44,540
+اتنين في اتنين لو كان ال prime بدي يقسم اتنين صح
+
+263
+00:31:44,540 --> 00:31:51,300
+ولا لا يبقى ابدا نشوفه هل هو بيقسم ولا بيقسمش طيب
+
+264
+00:31:51,300 --> 00:32:01,410
+if الواحد زي الجذر ناقص تلاتة يقسم لإتنينإذا لازم
+
+265
+00:32:01,410 --> 00:32:07,190
+ألاقي رقم تاني أو عنصر تاني أضرب فيه طبعا أنها
+
+266
+00:32:07,190 --> 00:32:18,450
+تجتنيه صح ولا لا يبقى هنا يساوي اتنين then for ال
+
+267
+00:32:18,450 --> 00:32:26,090
+a و ال b اللي موجود في z we have for some مش الكل
+
+268
+00:32:26,090 --> 00:32:34,650
+يعني for someالـ A و الـ B اللي موجودة في ذلك We
+
+269
+00:32:34,650 --> 00:32:44,470
+have ان الواحد زائد جذر ناقص تلاتة في A زائد B جذر
+
+270
+00:32:44,470 --> 00:32:52,050
+ناقص تلاتة يساوي اتنين بظبط يعنى؟ هذه بيقسم اتنين
+
+271
+00:32:52,050 --> 00:32:57,670
+يبقى لازم ألاقي عنصر أضربه في هذا يطلع اتنين بدي
+
+272
+00:32:57,670 --> 00:33:03,710
+أشوف هذه وين بتوصلطب بدفك القوس الأول دي عنها يبقى
+
+273
+00:33:03,710 --> 00:33:12,850
+هذا A ناقص تلاتة B زائد
+
+274
+00:33:12,850 --> 00:33:20,930
+بيجي نظر هذا في هذا ب A هذا في هذا ب A وهذا في هذا
+
+275
+00:33:20,930 --> 00:33:30,430
+ب B يبقى A زائد B في جدر ناقص تلاتة يسوى جداريساوي
+
+276
+00:33:30,430 --> 00:33:34,310
+اتنين طيب
+
+277
+00:33:34,310 --> 00:33:40,950
+هذه ممكن اكوّن منها معادلتين المعادلة الأولى A نقص
+
+278
+00:33:40,950 --> 00:33:45,870
+ثلاثة B يساوي اتنين والمعادلة التانية A زائد B
+
+279
+00:33:45,870 --> 00:33:50,390
+يساوي زين مصبوط
+
+280
+00:33:50,990 --> 00:33:56,190
+طيب إيش رايك؟ بتحلي المعادلتين هذول مع بعض يبقى a
+
+281
+00:33:56,190 --> 00:34:01,510
+ناقص ثلاثة بيه وهذه بتضربك بسالب واحد يبقى سالب a
+
+282
+00:34:01,510 --> 00:34:08,650
+سالب بيه ساوي زير لو جمعنا يبقى هذول مع السلام هذا
+
+283
+00:34:08,650 --> 00:34:14,570
+بده يعطيني سالب أربعة بيه ساوي اتنين يبقى بيه بده
+
+284
+00:34:14,570 --> 00:34:21,910
+يساوي قداش سالب نص موجود في ذلك؟إذا صار فيه تناقض،
+
+285
+00:34:21,910 --> 00:34:28,030
+مظبوط؟ طب التناقض هذا جابه شلة، شو الشلة؟ قلت إن
+
+286
+00:34:28,030 --> 00:34:36,270
+هذا بيقسم، مظبوط؟ يبقى هنا سواء الواحد زي الجذر
+
+287
+00:34:36,270 --> 00:34:41,450
+ناقص ثلاثة does not divide اتنين، لا يمكن نقسم
+
+288
+00:34:41,450 --> 00:34:48,140
+اتنين لما فرضت نقسم اتنين وصلت إلى تناقضوصلت إلى
+
+289
+00:34:48,140 --> 00:34:52,960
+عنصر مش موجود وان في الذات يبقى هذا لا يمكن ان
+
+290
+00:34:52,960 --> 00:34:58,260
+يحدث يعني لا يمكن لواحد ناقص جذر تلاتة انه يقسم
+
+291
+00:34:58,260 --> 00:35:04,220
+لاتنين يبقى ممكن يكون هذا try لا يبقى هذا بده
+
+292
+00:35:04,220 --> 00:35:10,740
+يعطينا آية ان الواحد زي جذر ناقص تلاتة is not a
+
+293
+00:35:10,740 --> 00:35:20,350
+try يبقى هذا ليس عادة أوليايبقى هذا مثل يوضح ان لو
+
+294
+00:35:20,350 --> 00:35:25,490
+كان عندى عنصر وعنصر irreducible على integral
+
+295
+00:35:25,490 --> 00:35:30,450
+domain يبقى ليس بالضرورة ان يكون هذا العنصر A'
+
+296
+00:35:30,610 --> 00:35:36,030
+يعني عكس النظرية اذا عكس النظرية ليس صحيحا الا ان
+
+297
+00:35:36,030 --> 00:35:43,290
+في نظرية تجمع النظرية الأولى و بتجيبلي كمان نص
+
+298
+00:35:43,290 --> 00:35:46,550
+نظرية جديدة ايش بتقول النظرية
+
+299
+00:35:51,040 --> 00:35:58,580
+بتقول النظرية من آياتك، او يا ريكو In
+
+300
+00:35:58,580 --> 00:36:06,600
+a principal ideal domain In a principal ideal
+
+301
+00:36:06,600 --> 00:36:09,800
+domain
+
+302
+00:36:09,800 --> 00:36:15,780
+اللي هاختصرها يا بنات إلى PID Principal Ideal
+
+303
+00:36:15,780 --> 00:36:18,160
+Domain An element
+
+304
+00:36:21,630 --> 00:36:32,090
+an element is irreducible is
+
+305
+00:36:32,090 --> 00:36:45,310
+irreducible if and only if it is prime لو كان لو
+
+306
+00:36:45,310 --> 00:36:46,630
+كان ال prime
+
+307
+00:36:52,400 --> 00:37:03,400
+الـ Pro تبقى
+
+308
+00:37:03,400 --> 00:37:11,540
+بدالي هقوله let D be a principal ideal domain
+
+309
+00:37:11,540 --> 00:37:14,800
+بتقفرك
+
+310
+00:37:14,800 --> 00:37:21,660
+انه عندي element و ال element هذا is irreducible
+
+311
+00:37:22,150 --> 00:37:27,210
+أها بتفترض انه is a prime في الأول ناخد الأسهم
+
+312
+00:37:27,210 --> 00:37:38,970
+يبقى هنا ل ال A B A prime D
+
+313
+00:37:38,970 --> 00:37:42,190
+النظرية
+
+314
+00:37:42,190 --> 00:37:49,430
+السابقة النظرية السابقة يبقى ال A is irreducible
+
+315
+00:37:49,430 --> 00:37:55,580
+وهو المطلوب المطلوب الأوليبقى هنا تلعبى A prime in
+
+316
+00:37:55,580 --> 00:38:08,320
+D by the above theorem النظرية الأعلى ال A is
+
+317
+00:38:08,320 --> 00:38:18,280
+irreducible in D هذا
+
+318
+00:38:18,280 --> 00:38:40,290
+الاتجاه الأولبنروح من اتجاه الثاني كونزر
+
+319
+00:38:40,290 --> 00:38:46,370
+احنا
+
+320
+00:38:46,370 --> 00:38:56,260
+اخدنا هنا A'بدنا ناخد ال a irreducible assume that
+
+321
+00:38:56,260 --> 00:39:08,020
+ان ال a is irreducible one
+
+322
+00:39:08,020 --> 00:39:19,900
+to show that one to show thatإن ال A is a prime
+
+323
+00:39:19,900 --> 00:39:26,300
+إيش
+
+324
+00:39:26,300 --> 00:39:31,640
+يعني ال A is a prime؟ يعني لو كان ال A بيقسم ال B
+
+325
+00:39:31,640 --> 00:39:44,260
+C يقسم ال B أو يقسم ال C تفهم؟ يعني that is if ال
+
+326
+00:39:44,260 --> 00:39:51,120
+Aبيقسم ال بي سي then
+
+327
+00:39:51,120 --> 00:40:03,260
+ال A بيقسم ال بي او ال A بيقسم ال بي سي
+
+328
+00:40:03,260 --> 00:40:11,240
+تجاهنا بفترض ان ال A بيقسم ال بي سي هذا بيكون معطى
+
+329
+00:40:11,240 --> 00:40:16,490
+وهذا اللي احنا عايزينه يعني عايزين نفريبقى باجي
+
+330
+00:40:16,490 --> 00:40:21,690
+بقوله هنا ال CEO ان
+
+331
+00:40:21,690 --> 00:40:28,230
+ال A بيقسم ال VC طيب
+
+332
+00:40:28,230 --> 00:40:42,370
+بدي أجي أقوله define an idea I و بده يساوي Ax زي
+
+333
+00:40:42,370 --> 00:40:47,600
+بي ورح بحيث الـ X والـ Y موجودة في دي.
+
+334
+00:40:50,680 --> 00:40:55,900
+طب واحنا مليش نرانا يا بنات؟
+
+335
+00:40:55,900 --> 00:41:00,220
+ال principle of ideal دماغيه؟ يبقى أي ideal يبقى
+
+336
+00:41:00,220 --> 00:41:08,140
+inside، صح؟ يبقى ده الـ
+
+337
+00:41:08,140 --> 00:41:14,750
+I هذا بدي ساوي دييعني هو ال principle idea
+
+338
+00:41:14,750 --> 00:41:21,430
+generated by D تمام؟ بنقوله كويسة. الآن السؤال هو
+
+339
+00:41:21,430 --> 00:41:30,770
+هل ال A موجود في ال I؟ موجود
+
+340
+00:41:30,770 --> 00:41:38,470
+ليش؟ لأن ال A بقدر أكتبه A في واحد زي ال B في Zero
+
+341
+00:41:41,580 --> 00:41:45,560
+على الصيغة اللى موجودة يبقى هذا Zero و F واحد في
+
+342
+00:41:45,560 --> 00:41:54,500
+اي مصدر ايه ابتدأ يبقى هذه عارفين اللي هي شملات ال
+
+343
+00:41:54,500 --> 00:41:58,600
+I يساوي دي؟ principle I دي ايه لإن principle I دي
+
+344
+00:41:58,600 --> 00:42:08,620
+domain تمام كويس طيب الآن then ال A موجود وين؟
+
+345
+00:42:09,070 --> 00:42:13,930
+موجود في ال principle ideal generated by D يعني
+
+346
+00:42:13,930 --> 00:42:26,630
+بقدر اكتره ان ال A بدر ساوي D في A for some A اللي
+
+347
+00:42:26,630 --> 00:42:27,890
+موجودة في D
+
+348
+00:42:40,170 --> 00:42:46,910
+الان ..الان انا بقول ان ال A تسوى ال mean دي R
+
+349
+00:42:46,910 --> 00:42:55,510
+واحنا ايش فرضنا ان ال A is reducible مظبوط؟ انا من
+
+350
+00:42:55,510 --> 00:43:05,470
+جباجي بقوله since بما ان ال A is irreducible we
+
+351
+00:43:05,470 --> 00:43:13,270
+have هاهذه irreducible وقدرنا نكتبها على الشكل
+
+352
+00:43:13,270 --> 00:43:20,010
+الحاصل تضارب two elements يبقى واحد unit مظبوط we
+
+353
+00:43:20,010 --> 00:43:32,230
+have ان ال D is a unit or ال R is a unit طيب
+
+354
+00:43:32,230 --> 00:43:39,620
+بتاخدهم واحدة واحدة وشوف لون بتوصلنا Fالـ D is a
+
+355
+00:43:39,620 --> 00:43:40,120
+unit.
+
+356
+00:43:42,840 --> 00:43:50,360
+Then بدك تكتبها العبارة شفوانة صحيحة ولا لأ. يبقى
+
+357
+00:43:50,360 --> 00:43:55,880
+الواحد موجود في ال principle idea generated from
+
+358
+00:43:55,880 --> 00:44:03,820
+D. لأنه D unit. مظبوط؟ طيب، مدام الواحد موجود في D
+
+359
+00:44:04,310 --> 00:44:09,370
+لو كان ال unity موجود في ال id اللي بيبقى ال id
+
+360
+00:44:09,370 --> 00:44:15,690
+بتسوى ميه؟ ال ring كلها، مظبوط ان هذا يرجع there
+
+361
+00:44:15,690 --> 00:44:27,950
+او هذا بيبقى موجود هنا implies that ان ال D هذا
+
+362
+00:44:27,950 --> 00:44:30,930
+كله بيبقى يسوى كل ال
+
+363
+00:44:34,840 --> 00:44:42,240
+طيب الواحد موجود في D الان هل الواحد موجود في A
+
+364
+00:44:42,240 --> 00:44:46,960
+ماهي
+
+365
+00:44:46,960 --> 00:44:55,960
+I E D صح ولا لأ ال E هذي R تمام؟ اذا هذا بدي
+
+366
+00:44:55,960 --> 00:45:03,130
+يعطينا معين مدينة موجود في I يبقى الواحدبدي ساول
+
+367
+00:45:03,130 --> 00:45:09,670
+ax زائد b مصبوط
+
+368
+00:45:09,670 --> 00:45:18,690
+اضرب كله في c إذا ضربنا كله في c بصير c بيساوي a c
+
+369
+00:45:18,690 --> 00:45:27,030
+x زائد b c y ده
+
+370
+00:45:27,030 --> 00:45:31,090
+جيبوا النظر معايا هل a تقسم هذا term
+
+371
+00:45:34,160 --> 00:45:43,560
+هل ال A تقسم هذا ال term؟ مظبوط؟ يبقى فاجب يقوله
+
+372
+00:45:43,560 --> 00:45:55,520
+now ال A تقسم ال A C X هذه واحدة and ال A تقسم ال
+
+373
+00:45:55,520 --> 00:46:08,490
+B C Y becauseال A تقسم ال B C هذا يتطلب ان ال A
+
+374
+00:46:08,490 --> 00:46:17,930
+تقسم ال A C X زائد ال B C Y طب هذي مين هي؟ C هذا
+
+375
+00:46:17,930 --> 00:46:24,630
+معناته ان ال A تقسم ال C هتجيبها المطلب الأول
+
+376
+00:46:32,190 --> 00:46:39,030
+خلصنا نمشي مرة تانية احنا اخدنا لو كانت ال E unit
+
+377
+00:46:39,030 --> 00:46:44,930
+طلعنا منها ان اذا تقسم ال C الان لو كانت ال R is
+
+378
+00:46:44,930 --> 00:47:01,580
+unit if ال R is unit then احنا اخدنا الالـ A بدأ
+
+379
+00:47:01,580 --> 00:47:08,120
+تساوي الـ D A صح؟ أخدنا الـ A بدأ تساوي الـ D R M
+
+380
+00:47:08,120 --> 00:47:14,320
+I الـ R هدا unit يعني إيه معكوس لو ضربنا في
+
+381
+00:47:14,320 --> 00:47:23,940
+المعكوس إيش بده يصير؟ A R inverse بده يساوي D سكت
+
+382
+00:47:23,940 --> 00:47:32,820
+الشعر لإنها A تساوي D Aأيها فوق بدي أضربها في R
+
+383
+00:47:32,820 --> 00:47:38,800
+inverse كيف يبقى بصير A R inverse بدي أساوي D طيب،
+
+384
+00:47:38,800 --> 00:47:47,700
+مين هو هذا بنا؟ تعريف مين؟ مش كل العناصر على الشكل
+
+385
+00:47:47,700 --> 00:47:54,020
+هذا element A في element من R وفي element من D مش
+
+386
+00:47:54,020 --> 00:48:00,400
+بشكل الisomal ideal generated by A صح ولا لأ؟يفقى
+
+387
+00:48:00,400 --> 00:48:05,120
+هذا معناه ان ال principle ideal generated by ايه؟
+
+388
+00:48:05,120 --> 00:48:13,940
+هو ال principle ideal generated by دي صحيح ولا لأ؟
+
+389
+00:48:13,940 --> 00:48:21,580
+انا سكت ولا اشتغل؟ مظبوط ولا لأ؟ هذه العبارة اللي
+
+390
+00:48:21,580 --> 00:48:27,460
+عندك هذه مش العنصر هذا هو العنصر هذا يبقىال ideal
+
+391
+00:48:27,460 --> 00:48:31,440
+اللي يولد بهذا العمصر هو ال ideal اللي يولد بهذا
+
+392
+00:48:31,440 --> 00:48:35,140
+العمصر ال principle ideal، مظبوط؟ هذا ال principle
+
+393
+00:48:35,140 --> 00:48:39,640
+ideal تبع ال D هذا لو جيت أعرف ال principle ideal
+
+394
+00:48:39,640 --> 00:48:44,980
+generated by A، مش هو كل العلاصر A في R حيث R
+
+395
+00:48:44,980 --> 00:48:49,340
+موجودة في R أو R موجودة في D اللي عندنا هنا؟ R
+
+396
+00:48:49,340 --> 00:48:53,060
+والله Rين بس، بس هو ليه شدله معكس؟ يبقى هو ولا مش
+
+397
+00:48:53,060 --> 00:48:57,380
+هومش غير ان العنصر او المعكس يولد نفس ال subgroup
+
+398
+00:48:57,380 --> 00:49:02,560
+زمان نفس القسم يبقى صار هذا ال principle هو هذا ال
+
+399
+00:49:02,560 --> 00:49:08,260
+principle طيب بدأ أسألكوا سؤال هل ال B موجود في ال
+
+400
+00:49:08,260 --> 00:49:12,200
+I؟
+
+401
+00:49:12,200 --> 00:49:21,200
+ممكن أخد X ب Zero و Y ب أحد صح؟ يبقى ال B موجود في
+
+402
+00:49:21,200 --> 00:49:29,290
+ال Iطيب ال I هذه مش هي ال D صح ولا لأ؟ هي ال A
+
+403
+00:49:29,290 --> 00:49:36,310
+يبقى implies ان ال B موجودة في ال principle I D
+
+404
+00:49:36,310 --> 00:49:43,050
+generated by A يبقى هذا معناه ان ال B بدها تسوي
+
+405
+00:49:43,050 --> 00:49:55,550
+مثلا AT for some Tاللي موجودة في دي طب ايش تفسيرك
+
+406
+00:49:55,550 --> 00:50:06,470
+لهذا العبارة؟ ان ال A بتقسمين تقسمين B يبقى هذا
+
+407
+00:50:06,470 --> 00:50:13,570
+بده يعطينا ان ال A تقسم ال B اتطلعيلي هنا هاي واحد
+
+408
+00:50:13,570 --> 00:50:20,410
+وهي اتنين يبقى Trump واحد
+
+409
+00:50:20,930 --> 00:50:33,830
+أمس اتنين we have ان ال a تقسم ال b or ال a تقسم
+
+410
+00:50:33,830 --> 00:50:41,450
+ال c يبقى تفسير من تفسير من ال prime يبقى هذا بدي
+
+411
+00:50:41,450 --> 00:50:51,690
+يعطينا انه وان بدأنا ان ال a is a primeوهو اتبعه
+
+412
+00:50:51,690 --> 00:50:57,370
+طبعا
+
+413
+00:50:57,370 --> 00:51:03,590
+طبعا الى هنا نكتفي بهذا القدر من هذا ال section
+
+414
+00:51:03,590 --> 00:51:08,490
+لان عندكم امتحانات تبدأ من الغد فمشان هيك نقول ان
+
+415
+00:51:08,490 --> 00:51:14,270
+يكفينا ما أخدناه حتى هذه اللحظة واتمنى ان تكونوا
+
+416
+00:51:14,270 --> 00:51:20,290
+قد استمتعتم بهذا المساق خلال الدراسة في هذا الفصل
+
+417
+00:51:20,700 --> 00:51:26,740
+ولن يستمتع الطالب إلا إذا اشتغل بدينه، مش بس رسم
+
+418
+00:51:26,740 --> 00:51:31,200
+من على الصبح لو خلصناه. وهدفي كل مسرح كان سواء كان
+
+419
+00:51:31,200 --> 00:51:37,280
+جبر أو غيره على أي حال نتمنى لكم التوفيق والنجاح
+
+420
+00:51:37,280 --> 00:51:42,240
+في هذا المساء وفي جميع المساقات الأخرى. وتمنى لكم
+
+421
+00:51:42,240 --> 00:51:48,360
+التوفيق والنجاح في حياتكننا إلى أن يأتي الأجالي
+
+422
+00:51:48,360 --> 00:51:54,620
+المحتوملكل واحدة منكنا ولكل واحد مننا بارك الله
+
+423
+00:51:54,620 --> 00:51:59,580
+فيكم وشكر لكم و السلام عليكم ورحمة الله وبركته
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7fe29320ad9934f719af1b05394d47fd41fb10e9
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ.srt
@@ -0,0 +1,1385 @@
+1
+00:00:21,600 --> 00:00:26,440
+بسم الله الرحمن الرحيم، احنا انتهينا المرة الماضية من
+
+2
+00:00:26,440 --> 00:00:31,420
+chapter الـ ideas and factoring وبدأنا في حل
+
+3
+00:00:31,420 --> 00:00:35,560
+الأسئلة في نصف الساعة من المحاضرة، واليوم إن شاء
+
+4
+00:00:35,560 --> 00:00:41,780
+الله نكمل حل الأسئلة اللي كلفناها بحلها في البيت
+
+5
+00:00:41,780 --> 00:00:48,120
+طبعًا آخر سؤال مرة اتعرضنا له هو سؤال 17، اليوم سؤال
+
+6
+00:00:48,120 --> 00:00:54,390
+17 يقول لو كان الـ I هو ideal من R، و هذا الـ ID
+
+7
+00:00:54,390 --> 00:00:59,570
+الاحتواء unit، بدا نثبت أن الـ I بده يساوي R، يبقى
+
+8
+00:00:59,570 --> 00:01:13,670
+السؤال 17 كان: I ideal of R، و الـ I contains a unit
+
+9
+00:01:13,670 --> 00:01:20,260
+هذا الكلام بده يعطينا أن الـ I  من R بده يساوي
+
+10
+00:01:20,260 --> 00:01:27,160
+الـ Ring R itself. مشان نحل هذا السؤال، بنرجع
+
+11
+00:01:27,160 --> 00:01:32,400
+بمعلوماتنا قليلًا إلى الأوراق. الـ Set Theory،
+
+12
+00:01:32,400 --> 00:01:36,520
+بجينا نثبت أن الـ two sets are equal، وبنثبت أن
+
+13
+00:01:36,520 --> 00:01:40,440
+الأولى subset من الثانية والثانية subset من الأولى،
+
+14
+00:01:40,440 --> 00:01:45,100
+إن حدث ذلك، بقول يبقى الـ two sets are equal، بأن
+
+15
+00:01:45,100 --> 00:01:50,770
+نفسه، نمشي بنفس  الطريقة. الآن يا بنات، I هو ideal من
+
+16
+00:01:50,770 --> 00:01:57,410
+R، يبقى... يبقى هذا يجعل الـ R أقل منه، صح ولا لأ؟
+
+17
+00:01:57,410 --> 00:02:04,010
+يعني subset من الـ R وقد يساويها، يبقى in a sense بما
+
+18
+00:02:04,010 --> 00:02:16,710
+أن الـ I is an ideal of R، we have أنه الـ I subset من
+
+19
+00:02:16,710 --> 00:02:22,470
+الـ R، وسمّيلي هذه العلاقة رقم واحد. بعد هيك بدنا
+
+20
+00:02:22,470 --> 00:02:34,850
+نيجي نقول: افترض أن A is a unit in I.
+
+21
+00:02:34,850 --> 00:02:40,590
+يبقى بنفترض أن العنصر A هو unit، والـ unit هذا
+
+22
+00:02:40,590 --> 00:02:42,270
+موجود في I، زي ما هو قال
+
+23
+00:02:46,200 --> 00:02:55,940
+لأثبت أن الـ R subset من الـ I، يبقى لو أخدت الآن عنصر من الـ R
+
+24
+00:02:55,940 --> 00:03:01,640
+موجود في R، لو قدرت أثبت أن هذا العنصر
+
+25
+00:03:01,640 --> 00:03:09,360
+موجود في I، بتمام المطلوب. يبقى then هذا العنصر بقدر
+
+26
+00:03:09,360 --> 00:03:16,610
+أكتبه على شكل R في A⁻¹ في A، لأن الـ inverse
+
+27
+00:03:16,610 --> 00:03:23,250
+يعني معكوس العنصر exist. هذا كله، الـ R يساوي R في A
+
+28
+00:03:23,250 --> 00:03:30,190
+اللي بقدر أقول هو عبارة عن R في A⁻¹ في مين؟ في
+
+29
+00:03:30,190 --> 00:03:40,130
+الـ A. هذا الآن موجود في I، صح؟ وهذا موجود وين؟ في R
+
+30
+00:03:40,130 --> 00:03:46,440
+يبقى، والـ I ideal، اللي يبقى حاصل ضرب مين؟ موجود في I
+
+31
+00:03:46,440 --> 00:03:57,820
+يبقى هذا موجود في I، since لأن الـ I is an ideal، لأن الـ
+
+32
+00:03:57,820 --> 00:04:04,180
+I ideal، يبقى هذا موجود فيها، تمام؟ يبقى أخدنا عنصر
+
+33
+00:04:04,180 --> 00:04:10,880
+R موجود في R، أثبتنا إنه موجود وين؟ موجود في I، يبقى
+
+34
+00:04:10,880 --> 00:04:17,080
+إذاً الـ R subset من مين؟ من I، وهذه العلاقة رقم
+
+35
+00:04:17,080 --> 00:04:26,640
+اثنين. بروح بقول: from واحد and اثنين we have أن الـ
+
+36
+00:04:26,640 --> 00:04:34,900
+ideal I يساوي الـ ring R كله. إذًا حتى الآن استنتجنا
+
+37
+00:04:34,900 --> 00:04:40,020
+يعني حصلنا على معلومتين مهمتين. المعلومة الأولى
+
+38
+00:04:40,020 --> 00:04:44,440
+قلناها سابقًا، والمعلومة الثانية هي بيننا الآن
+
+39
+00:04:44,440 --> 00:04:48,420
+المعلومة السابقة، بجينا نقول: إذا الـ ideal اللي احتوى
+
+40
+00:04:48,420 --> 00:04:53,160
+على الـ unity، على عنصر الوحدة، يبقى الـ ideal اللي بده
+
+41
+00:04:53,160 --> 00:04:57,420
+يساوي مين؟ في الـ ring itself. وهنا نقول: لو الـ ideal اللي
+
+42
+00:04:57,420 --> 00:05:02,600
+احتوى على unit واحد، يبقى هذا الـ ideal بده يساوي
+
+43
+00:05:02,600 --> 00:05:08,870
+مين؟ بيساوي الـ ring R. يبقى من الآن فصاعدًا هذا أخذنا
+
+44
+00:05:08,870 --> 00:05:13,270
+ideal من الـ ring، ولجأنا فيه الـ unity أو لجأنا فيه
+
+45
+00:05:13,270 --> 00:05:17,790
+unit، يبقى على طول الخط هذا الـ ideal بده يساوي مين؟
+
+46
+00:05:17,790 --> 00:05:23,690
+بده يساوي نفس الـ ring. هذا كان سؤال سبعة عشر. بعد ذلك
+
+47
+00:05:23,690 --> 00:05:29,190
+معنا سؤال اثنين وعشرين، جاي يحكي عن الـ ideal والـ
+
+48
+00:05:29,190 --> 00:05:35,550
+principle ideal generated by اثنين. يبقى سؤال اثنين
+
+49
+00:05:35,550 --> 00:05:40,790
+وعشرين: الـ I هو الـ principle ideal generated by
+
+50
+00:05:40,790 --> 00:05:50,110
+اثنين، ومعطيني بعد ذلك I of X، وإن I of X is not
+
+51
+00:05:50,110 --> 00:05:56,890
+maximal ideal في Z، even though I is maximal. يبقى
+
+52
+00:05:56,890 --> 00:06:04,830
+هنا sure إن I of X is not
+
+53
+00:06:07,860 --> 00:06:19,740
+maximal in Z of X، الرغم أن الـ principle ideal
+
+54
+00:06:19,740 --> 00:06:25,660
+generated by اثنين هو عبارة عن maximal من مين؟ في Z
+
+55
+00:06:25,660 --> 00:06:30,840
+وعندنا الـ principle ideal generated by اثنين هو
+
+56
+00:06:30,840 --> 00:06:40,370
+maximal in Z. يعني برغم أن هذا الـ ideal maximal في Z
+
+57
+00:06:40,370 --> 00:06:46,510
+لكن I of X ماهيش maximal في مين؟ في Z of X. يبقى
+
+58
+00:06:46,510 --> 00:06:54,490
+خلونا شوية نشوف الـ principle ideal generated by
+
+59
+00:06:54,490 --> 00:07:01,270
+اثنين، هذا معروف، بالنسبة لمين؟ اللي هم مين؟ الـ zero
+
+60
+00:07:01,270 --> 00:07:03,990
+وزائد أو ناقص اثنين
+
+61
+00:07:09,670 --> 00:07:17,830
+طب الـ I of X مين؟
+
+62
+00:07:17,830 --> 00:07:23,610
+الـ I of X؟ مين الـ Z of X؟ كثيرات الحدود التي
+
+63
+00:07:23,610 --> 00:07:29,830
+المعاملات تبعها أعداد صحيحة، صح ولا لأ؟ قياسًا عليها الـ
+
+64
+00:07:29,830 --> 00:07:39,400
+I of X هو كثيرات الحدود التي معاملاتها أعداد زوجية
+
+65
+00:07:39,400 --> 00:07:44,760
+2، 4، 6، 8، إلى آخره، صح؟ نعم، لأن هاي الـ principle
+
+66
+00:07:44,760 --> 00:07:48,680
+ideal generated by اثنين: اثنين، أربعة، ستة، كلها أعداد
+
+67
+00:07:48,680 --> 00:07:56,340
+زوجية، تمام؟ يبقى I of X هو عبارة عن كل الـ functions
+
+68
+00:07:56,340 --> 00:08:05,480
+F of X such that الـ F of X has
+
+69
+00:08:07,160 --> 00:08:11,420
+even، أو
+
+70
+00:08:11,420 --> 00:08:21,500
+has even coefficients، أو polynomial، أو
+
+71
+00:08:21,500 --> 00:08:29,640
+polynomial with even
+
+72
+00:08:29,640 --> 00:08:32,320
+coefficients
+
+73
+00:08:42,410 --> 00:08:48,450
+كل كثيرات الحدود التي المعاملات تبعها أعداد زوجية
+
+74
+00:08:48,450 --> 00:08:54,810
+even،  أعداد زوجية، منطقي، هيها من
+
+75
+00:08:54,810 --> 00:08:59,250
+اثنين، أربعة، ستة، ثمانية، بالسابق أو في الموجب، عرفنا
+
+76
+00:08:59,250 --> 00:09:04,950
+الـ I of X، قال لي أثبت إنه هذا ليس maximal، لو
+
+77
+00:09:04,950 --> 00:09:10,090
+رجعنا لتعريف الـ maximal ideal، بنقول الـ ideal بقول
+
+78
+00:09:10,090 --> 00:09:15,250
+عنه maximal لو وجدنا ولاقي ideal ثاني بحيث هذا الـ
+
+79
+00:09:15,250 --> 00:09:21,050
+ideal subset منه ولا يساويه، وهذا الـ ideal إذا
+
+80
+00:09:21,050 --> 00:09:25,970
+كان بيساويه، يبقى بيساوي ring كله، إن
+
+81
+00:09:25,970 --> 00:09:30,010
+حدث ذلك، يبقى بقول هذا الـ ideal ليس maximal
+
+82
+00:09:30,010 --> 00:09:37,510
+ideal. طيب احنا لو قدرنا نجيب ideal ثاني بحيث الـ I
+
+83
+00:09:37,510 --> 00:09:43,970
+of X هو subset منه ولا يساويه، وهذا الـ ideal subset من الـ
+
+84
+00:09:43,970 --> 00:09:50,250
+ring ولا يساويه، يبقى ليس maximal. ما نقومش على
+
+85
+00:09:50,250 --> 00:09:55,450
+طول الخط نجيب من المريخ الـ ideal، لأ لأ لأ، من
+
+86
+00:09:55,450 --> 00:10:00,090
+اللي أخذناه. أخذنا فيه principle ideal generated by
+
+87
+00:10:00,090 --> 00:10:10,180
+X و 2. تذكروا الـ polynomial اللي كل الـ... كل العدد
+
+88
+00:10:10,180 --> 00:10:15,940
+الأخير، أو العدد الثابت، هو عدد زوجي، مظبوط؟ فجأة
+
+89
+00:10:15,940 --> 00:10:22,340
+بدنا نروح نطبق صحة هذا الكلام. فبعدين بيقول: أخذنا
+
+90
+00:10:22,340 --> 00:10:29,340
+part ولكن هو seminary principle ideal
+
+91
+00:10:29,340 --> 00:10:33,720
+generated by X و 2
+
+92
+00:10:37,970 --> 00:10:46,710
+بحيث أن الـ F of X تساوي X في G of X زائد اثنين H
+
+93
+00:10:46,710 --> 00:10:55,210
+of X، صح؟ طيب تعالوا ندقق النظر في الاثنين هدول: الـ
+
+94
+00:10:55,210 --> 00:11:01,470
+I of X، كل الـ F of X كثيرات الحدود التي المعاملات
+
+95
+00:11:01,470 --> 00:11:09,900
+تبعها أعداد زوجية، صح؟ هذا مهم. هذا كل العناصر التي
+
+96
+00:11:09,900 --> 00:11:16,920
+الحد الأخير فيها بيكون عدد زوجي، تمام؟ ممتاز جدًا،
+
+97
+00:11:16,920 --> 00:11:22,140
+طيب هل الأولى subset من الثانية، والثانية subset
+
+98
+00:11:22,140 --> 00:11:26,240
+من الأولى؟ لأن
+
+99
+00:11:26,240 --> 00:11:32,140
+الأولى كلها أعداد زوجية. هذا العدد الزوجي هو مين؟
+
+100
+00:11:32,140 --> 00:11:36,550
+العدد الأخير، وقبل هيك فردي والله زوجي ما بتفرقش معنا
+
+101
+00:11:36,550 --> 00:11:45,790
+لما بروح بقول له هنا clearly واضح أن الـ I of X
+
+102
+00:11:45,790 --> 00:11:53,730
+subset من الـ principle ideal generated by X و 2،
+
+103
+00:11:53,730 --> 00:12:01,350
+ولا يساويه. طيب السؤال: والـ principle ideal
+
+104
+00:12:04,170 --> 00:12:10,570
+subset من الـ R ولا لا؟ يساويه؟ لأ، لأن الحد الذي
+
+105
+00:12:10,570 --> 00:12:16,030
+قد يكون زوجي وقد يكون صفر وقد يكون فرديًا، يبقى
+
+106
+00:12:16,030 --> 00:12:23,010
+subset منه ولا يساويه. يبقى جبت ideal موجود ما بين
+
+107
+00:12:23,010 --> 00:12:29,330
+الـ ring وما بين الـ ideal وهو proper، شرط أساسي، وقدْرت
+
+108
+00:12:29,330 --> 00:12:33,990
+أثبت أن الـ ideal عندي ما هو ليس maximal، واللي
+
+109
+00:12:33,990 --> 00:12:37,830
+جبناه لا يساوي الـ R، يبقى الـ I هذا ليس maximal؟
+
+110
+00:12:37,830 --> 00:12:52,790
+لأ، if this means that الـ I of X is not maximal
+
+111
+00:12:52,790 --> 00:12:56,670
+in Z
+
+112
+00:13:01,380 --> 00:13:06,780
+إذًا كان سؤال اللي هو الاثنين وعشرين، رغم أنه الـ
+
+113
+00:13:06,780 --> 00:13:09,980
+principle ideal generated by اثنين هو maximal
+
+114
+00:13:09,980 --> 00:13:16,840
+ideal في Z وهو أعلى ideal ممكن آخذه من مين؟ آخذه من
+
+115
+00:13:16,840 --> 00:13:21,860
+الـ Z. بعد اثنين وعشرين، عندنا أربعة وعشرين: جاي يقول: هات
+
+116
+00:13:21,860 --> 00:13:26,680
+مثال a commutative ring that has a maximal ideal
+
+117
+00:13:26,680 --> 00:13:34,170
+that is not a prime ideal. يبقى أربعة وعشرين بدنا
+
+118
+00:13:34,170 --> 00:13:46,470
+مثال: commutative ring، commutative ring، commutative
+
+119
+00:13:46,470 --> 00:13:51,970
+ring that has a maximal، ما هو؟ عشان five، و has
+
+120
+00:13:51,970 --> 00:13:58,650
+a maximal ideal but
+
+121
+00:14:14,840 --> 00:14:25,120
+الحمد لله. لو جينا وقلنا: set of integers، a commutative
+
+122
+00:14:25,120 --> 00:14:26,260
+ring، و لا لأ؟
+
+123
+00:14:29,460 --> 00:14:35,760
+with usual
+
+124
+00:14:35,760 --> 00:14:44,560
+addition، يعني تحت عملية الجمع العادية، and
+
+125
+00:14:44,560 --> 00:14:47,600
+multiplication
+
+126
+00:14:47,600 --> 00:14:52,480
+defined
+
+127
+00:14:52,480 --> 00:14:58,460
+by ...
+
+128
+00:15:21,490 --> 00:15:30,880
+معروف؟ أي سؤال يحتاج إلى إجابة، هو إحنا لكي نثبت أن
+
+129
+00:15:30,880 --> 00:15:36,700
+الـ six conditions تحت الـ two operations اللي عليها مش
+
+130
+00:15:36,700 --> 00:15:41,560
+لازم نثبت الـ six conditions، تمام؟ طيب لما بيقول لنا
+
+131
+00:15:41,560 --> 00:15:46,000
+الـ usual addition، الجمع العادي، يعني الأول أربعة
+
+132
+00:15:46,000 --> 00:15:52,200
+الشروط محققة، صح ولا لأ؟ اللي اختلفوا مين؟ آخر شرطين
+
+133
+00:15:52,200 --> 00:15:57,640
+آخر شرطين هم اللي مين؟ هم اللي اختلفوا. ليش؟ ليش
+
+134
+00:15:57,640 --> 00:16:03,990
+اختلفوا؟ لأن هدول مش عملية الضرب العادية، عملية ضرب
+
+135
+00:16:03,990 --> 00:16:08,250
+خاصة، يمسك، يعطلهم جُرم، ويساويهم بالصفر. هي بتعرف
+
+136
+00:16:08,250 --> 00:16:14,010
+عملية الضرب. بدي أثبت له إن هذا الـ ring وكذلك
+
+137
+00:16:14,010 --> 00:16:19,610
+commutative ring، يبقى أول أربعة شروط محققة لعملية
+
+138
+00:16:19,610 --> 00:16:23,890
+الجمع العادي. دول شرطين، الشرط الأول: خاصية الـ
+
+139
+00:16:23,890 --> 00:16:29,180
+associativity، الخاصية الثانية هي خاصية التوزيع
+
+140
+00:16:29,180 --> 00:16:33,380
+distributive law. طيب نجرّب الخاصية دي: الـ
+
+141
+00:16:33,380 --> 00:16:42,460
+associativity. بقى بقى بقى بقول: that if four
+
+142
+00:16:42,460 --> 00:16:48,700
+conditions of
+
+143
+00:16:48,700 --> 00:16:53,240
+a ring are satisfied
+
+144
+00:16:58,670 --> 00:17:02,470
+ننتقل لعملية الجمع العادية. نيجي للثانية: الـ
+
+145
+00:17:02,470 --> 00:17:07,650
+associativity. فبداية أقول له: لو أخدت الـ A والـ B والـ C
+
+146
+00:17:07,650 --> 00:17:17,690
+موجودة في Z، لأن لو أخدت الـ A في الـ B في الـ C، هي موجودة
+
+147
+00:17:17,690 --> 00:17:25,910
+هي A في صفر.  حاصل ضرب اثنين فيدي يساوي صفر. أحوالنا
+
+148
+00:17:28,750 --> 00:17:39,330
+يساوي الـ Z. يعني لو أخدت الـ A والـ B كلها في الـ C، بدي
+
+149
+00:17:39,330 --> 00:17:45,430
+أساوي صفر في الـ C، يساوي صفر. معنى هذا الكلام
+
+150
+00:17:45,430 --> 00:17:53,630
+أن الـ A والـ B في الـ C، بدي أساوي صفر في الـ C لكل الـ
+
+151
+00:17:53,630 --> 00:17:56,390
+A والـ B والـ C الموجودة
+
+152
+00:17:59,260 --> 00:18:05,220
+distributive law صحيحة. طيب الآن هذه الخاصية
+
+153
+00:18:05,220 --> 00:18:10,760
+الثانية، الخاصية السادسة، بدنا distributive
+
+154
+00:18:10,760 --> 00:18:23,260
+law: A في (B زائد C)، تمام؟ هذا الكلام بده
+
+155
+00:18:23,260 --> 00:18:24,100
+يساوي
+
+156
+00:18:28,500 --> 00:18:33,280
+لأن هذا كله يعتبر element وهذا element ثاني، وكان
+
+157
+00:18:33,280 --> 00:18:36,880
+اللي حاصل ضربهم يساوي صفر لأي two elements
+
+158
+00:18:36,880 --> 00:18:46,040
+موجودة فيها. امين لو أخذت الـ A في B زي أن الـ A في C صفر،
+
+159
+00:18:46,040 --> 00:18:53,060
+أخذ صفر اللي هو يساوي صفر، فإتبعنا هذا الكلام أن
+
+160
+00:18:53,060 --> 00:19:03,160
+A في (B زائد C) يساوي A في B زائد A في C، و
+
+161
+00:19:03,160 --> 00:19:09,880
+بنفس الطريقة، Similarly، بنفس
+
+162
+00:19:09,880 --> 00:19:20,080
+الطريقة B في (A زائد C) يساوي B في A زائد C في A
+
+163
+00:19:20,080 --> 00:19:32,530
+Plus وهكذا. الـ Z هذا غير B، عملية
+
+164
+00:19:32,530 --> 00:19:41,490
+مين؟ commutative. الآن A في B، كده تساوي مين؟ حسب
+
+165
+00:19:41,490 --> 00:19:48,150
+الـ definition. طيب و B في A؟ صفر. يبقى معنا هذا
+
+166
+00:19:48,150 --> 00:19:56,960
+الكلام أن A في B، لكل الـ A والـ B موجودة في Z
+
+167
+00:19:56,960 --> 00:20:04,300
+هذا اللي هو commutative point.
+
+168
+00:20:04,300 --> 00:20:11,960
+لما إحنا جبنا مثل لـ commutative ring، ها يبدو
+
+169
+00:20:11,960 --> 00:20:15,720
+commutative ring، جبنا له  commutative ring، هذا
+
+170
+00:20:15,720 --> 00:20:22,140
+maximal ideal. إحنا عطينا الفعل، السؤال هو: لما يكون
+
+171
+00:20:24,840 --> 00:20:33,640
+maximal ideal، انتهى، صحيح ولا لأ؟ طيب السؤال هو: هل
+
+172
+00:20:33,640 --> 00:20:42,260
+هذا هو prime؟ بنقول: آه، إذا بتاخد رقمين حاصل ضربهما
+
+173
+00:20:42,260 --> 00:20:45,340
+موجود في هذا الـ ideal،
+
+174
+00:20:49,630 --> 00:20:56,450
+موجود في هذا الـ ideal، إن حدث ذلك، بقول هذا هو prime ideal،
+
+175
+00:20:56,450 --> 00:21:02,450
+ما حدثش، يبقى ليس prime ideal. طيب، لو جاءت
+
+176
+00:2
+
+223
+00:26:42,960 --> 00:26:54,540
+و y one و شكل الـ b ثلاثة x two و y two تمام؟ كل
+
+224
+00:26:54,540 --> 00:26:59,440
+عنصر على شكل أو ضارب a مزود مرتب زي ما أنتم
+
+225
+00:26:59,440 --> 00:27:06,460
+شايفينه الـ element ده ياخد الـ a معكوس الـ b يبقى هذا
+
+226
+00:27:06,460 --> 00:27:13,960
+الكلام بالدرجة تلاتة x one و y one ناقص تلاتة x
+
+227
+00:27:13,960 --> 00:27:20,300
+two و y two الطرح أو الجمع component twice يبقى
+
+228
+00:27:20,300 --> 00:27:27,540
+هذا الكلام بالدرجة تلاتة x one ناقص x two و y one
+
+229
+00:27:27,540 --> 00:27:35,070
+ناقص y two هل هذا على الشكل اللي عندنا؟ صح؟ الـ C
+
+230
+00:27:35,070 --> 00:27:39,390
+موجود في الـ A خلاصة من الـ condition الثالث،
+
+231
+00:27:39,390 --> 00:27:45,110
+الثاني، ضارب الـ condition الثالث والأخير، إذا
+
+232
+00:27:45,110 --> 00:27:51,410
+ناخد element من الـ ring الأصلية، و ناخد element من
+
+233
+00:27:51,410 --> 00:27:58,610
+هنا، يبقى بالتالي أقول للـ L، الـ C و الـ D موجودة
+
+234
+00:27:58,610 --> 00:28:02,870
+في الـ Z-direct sum Z، and
+
+235
+00:28:05,290 --> 00:28:13,070
+الـ A اللي بدها تساوي تلاتة X1 و Y1 موجودة في الـ
+
+236
+00:28:13,070 --> 00:28:20,750
+A ثم بدي أشوف حاصل ضربهما إذا موجود في A، بيكون
+
+237
+00:28:20,750 --> 00:28:25,090
+صار الـ A عفر عن الـ Ideal سواء ما كان ضارب من
+
+238
+00:28:25,090 --> 00:28:33,170
+اليمين أو من الشمال يبقى الأخيرين C وD مضروب في من؟
+
+239
+00:28:33,170 --> 00:28:44,630
+في الـ A بتساوي C و D في تلاتة X one و Y one هذا
+
+240
+00:28:44,630 --> 00:28:58,370
+الكلام يساوي تلاتة C X one و هذا D Y one موجود؟
+
+241
+00:29:00,380 --> 00:29:08,700
+يبقى هذا موجود في A بنفس الطريقة اللي هو
+
+242
+00:29:08,700 --> 00:29:18,020
+A في C وD موجود في الـ A يبقى الـ A معلوم is
+
+243
+00:29:18,020 --> 00:29:24,780
+an ideal سواء الـ A is an ideal
+
+244
+00:29:29,710 --> 00:29:35,630
+خلصنا؟ لما قلنا إلى أين؟ إلى أين خلصت؟ أنت كل
+
+245
+00:29:35,630 --> 00:29:43,170
+اللي اتبعته أنه ideal فقط، بقى عليك تثبت أنه إيش؟
+
+246
+00:29:43,170 --> 00:29:50,790
+not maximum ليس maximum ideal  لك maximum؟ اه
+
+247
+00:29:50,790 --> 00:29:56,050
+هذا صحيح، طيب كملتوا صحيح معانا ماشي الآن
+
+248
+00:29:56,050 --> 00:30:02,410
+طيب يبقى المطلوب أن نثبت أن هذا هو عبارة عن maximum
+
+249
+00:30:02,410 --> 00:30:09,750
+ايديل لذلك قدامي بدأت بطريقة اثنين، طريقة ثانية
+
+250
+00:30:09,750 --> 00:30:15,090
+يعني ناخد أ، أو طريقة اثنين يعني طريقة التعريف هي
+
+251
+00:30:15,090 --> 00:30:19,610
+طريقة النظرية ليست النظرية اللي هو تقول لو كان
+
+252
+00:30:19,610 --> 00:30:24,370
+عندي ring  commutative with unity يبقى الـ a module
+
+253
+00:30:24,370 --> 00:30:30,030
+is a في الـ F عنده دقة is maximum يعني لو كان أرهد
+
+254
+00:30:30,030 --> 00:30:34,390
+يقوله إيه كانت فيه يبقى لإيه maximum أو على
+
+255
+00:30:34,390 --> 00:30:39,210
+التعريض، قبل شوية احنا أثبتنا ذلك بواسطة التعريض،
+
+256
+00:30:39,210 --> 00:30:44,670
+المثبتنا الماكسيماليتي، ده استخدمنا التعريض، هنا،
+
+257
+00:30:44,670 --> 00:30:49,410
+ده استخدمنا ضغط، وشو المشكلة؟ بلاش، اه، فاستنى
+
+258
+00:30:49,410 --> 00:30:52,270
+شوية، وين تبقى التعريض؟
+
+259
+00:31:01,270 --> 00:31:08,510
+السؤال هو هل هذه commutative؟ أكيد
+
+260
+00:31:08,510 --> 00:31:12,390
+ميل ميل، لأن الـ Z أصلاً commutative فلما يكون حاصل
+
+261
+00:31:12,390 --> 00:31:15,990
+ضرب عنصرين في الـ Z، يقل بيهم أو بداية الـ Z، يبقى
+
+262
+00:31:15,990 --> 00:31:23,170
+commutative و الـ Unity لهما إيه؟ واحد و واحد، يبقى
+
+263
+00:31:23,170 --> 00:31:23,570
+الـ Unity
+
+264
+00:31:28,040 --> 00:31:38,200
+Is plus is plus is plus is plus is plus is
+
+265
+00:31:38,200 --> 00:31:39,640
+plus is plus is plus is plus is plus is plus is
+
+266
+00:31:39,640 --> 00:31:41,360
+plus is plus is plus is plus is plus is plus is
+
+267
+00:31:41,360 --> 00:31:46,460
+plus is plus is plus is plus is plus is plus is
+
+268
+00:31:46,460 --> 00:31:46,760
+plus is plus is plus is plus is plus is plus is
+
+269
+00:31:46,760 --> 00:31:47,040
+plus is plus is plus is plus is plus is plus is
+
+270
+00:31:47,040 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+271
+00:31:47,140 --> 00:31:47,180
+plus is plus is plus is plus is plus is plus is
+
+272
+00:31:47,180 --> 00:31:47,200
+plus is plus is plus is plus is plus is plus is
+
+273
+00:31:47,200 --> 00:31:50,760
+plus is plus
+
+274
+00:31:50,760 --> 00:31:58,930
+is plus is plus يبقى بس باقي علينا لو نثبت أن الـ
+
+275
+00:31:58,930 --> 00:32:05,270
+direct sum بينه و بين Z  مدهوله إيه لفتنا إنها فيه
+
+276
+00:32:05,270 --> 00:32:10,710
+اللي بيكون خلصنا، فالسؤال هو كم عنصر في الـ direct
+
+277
+00:32:10,710 --> 00:32:22,250
+sum تبع Z plus Z مدهوله إيه؟ كم عنصر؟ كده؟ مديني
+
+278
+00:32:22,250 --> 00:32:29,680
+هذه العناصر؟ لا؟ علمية مثلا؟ بقى حسب إيه؟ قد إيش
+
+279
+00:32:29,680 --> 00:32:33,920
+متجدر يعني قيمة إيه؟ قيمة إيه؟ اه وين قيمة إيه؟
+
+280
+00:32:33,920 --> 00:32:39,860
+إيه الـ R & D؟ إيه الـ R & D؟ فيه عناصر كتير ثلاثة
+
+281
+00:32:39,860 --> 00:32:44,860
+ثلاثة عناصر؟ لأ، عدد عناصر Z، Z إيه؟ عدد عناصر
+
+282
+00:32:44,860 --> 00:32:49,980
+Z؟ Z فيها  ملانهاية من العناصر يعني ممكن يكون فيها
+
+283
+00:32:49,980 --> 00:32:51,780
+ملانهاية من العناصر؟
+
+284
+00:32:58,770 --> 00:33:07,170
+أنا أزعم أنه لا يوجد ثلاثة تعريفات عشان وجود
+
+285
+00:33:07,170 --> 00:33:13,970
+الثلاثة مهاجورة، قبل نهيئة الثلاثة بتلعب؟ صحيح؟
+
+286
+00:33:13,970 --> 00:33:18,650
+و ليش؟ ثلاثة؟ و ليش؟ كمان، مش يا ثلاثة أي أخ قطر
+
+287
+00:33:18,650 --> 00:33:19,730
+يبقى هناك، لأ
+
+288
+00:33:27,330 --> 00:33:39,630
+يبقى F وE شادة إذا قدرنا نثبت أنه دائرة صغيرة ما
+
+289
+00:33:39,630 --> 00:33:43,610
+بين الـ Z و الـ Z موديول A
+
+290
+00:33:52,850 --> 00:34:01,190
+We have a prison يعني
+
+291
+00:34:01,190 --> 00:34:05,530
+بالاسم هذه فيه نجيبه و نقول إيه is maximum و نقول
+
+292
+00:34:05,530 --> 00:34:15,070
+فلسطين I am الهدف الباريكي الصاممي بين الذنب و
+
+293
+00:34:15,070 --> 00:34:18,550
+الذنب متى قدر فيه الأزر
+
+294
+00:34:33,700 --> 00:34:42,420
+بس تلاتة أنصار؟ اه بس التلاتة هذول؟ اه بس التلاتة
+
+295
+00:34:42,420 --> 00:34:47,960
+هذول، مش لذا طيب واحد هذول  قبخل لكل أنصار وشوفوا
+
+296
+00:34:47,960 --> 00:34:52,740
+من التلاتة هذول ولا إيش هاتيلي عنصر جاله على بانه و
+
+297
+00:34:52,740 --> 00:34:56,800
+القرة وخنيه كبيرة شوية مش يعني اتنين أو اتنين
+
+298
+00:34:56,800 --> 00:34:59,140
+اتنين خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+299
+00:34:59,140 --> 00:35:00,280
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+300
+00:35:00,280 --> 00:35:02,580
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+301
+00:35:02,580 --> 00:35:02,860
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+302
+00:35:02,860 --> 00:35:15,900
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+303
+00:35:15,900 --> 00:35:18,000
+خل
+
+304
+00:35:21,050 --> 00:35:25,430
+كيف؟ يبقى الـ God ما يطرحش، يبقى واحد وصفر كما
+
+305
+00:35:25,430 --> 00:35:32,670
+تقول، زي ما جالس، لأن لو
+
+306
+00:35:32,670 --> 00:35:36,910
+أخذنا خمسة وعشرين وانت، أن أحدث واحد ثالث وواحد
+
+307
+00:35:36,910 --> 00:35:45,020
+ثالث، تمام؟ هذا الكلام زي الـ 2007بادر أبوتي واحد
+
+308
+00:35:45,020 --> 00:35:53,400
+وزير زائد أربعة وعشرين واتنين زائد الآية هذا
+
+309
+00:35:53,400 --> 00:36:01,180
+الكلام يساوي واحد وزير زائد أربعة وعشرين تلاتة في
+
+310
+00:36:01,180 --> 00:36:06,820
+ثمانية واتنين زائد الآية هذا موجود في A ولا لا؟
+
+311
+00:36:06,820 --> 00:36:10,120
+اه موجود في A، صح؟ اه، اه، اه، اه، اه، اه، اه،
+
+312
+00:36:10,120 --> 00:36:14,160
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+313
+00:36:14,160 --> 00:36:15,180
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+314
+00:36:15,180 --> 00:36:16,680
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+315
+00:36:16,680 --> 00:36:20,780
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+316
+00:36:20,780 --> 00:36:32,860
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+317
+00:36:32,860 --> 00:36:42,810
+عشرين وأربعة وعشرين وأربعة وعشرين وأربعة زائد الـ
+
+318
+00:36:42,810 --> 00:36:51,650
+عشرين بقدر أكسبها اتنين وزيرو زائد ثمانية عشر
+
+319
+00:36:51,650 --> 00:36:58,170
+وأربعة زائد الـ A تمام؟
+
+320
+00:36:58,170 --> 00:37:00,150
+هللي بردودة دي ولا ده؟
+
+321
+00:37:03,140 --> 00:37:12,300
+يبقى هنا اتنين وزيرو زائد ثلاثة في ستة وأربعة زائد
+
+322
+00:37:12,300 --> 00:37:18,000
+الـ A هذه الموجودة في الـ A يبقى اتنين وزيرو زائد
+
+323
+00:37:18,000 --> 00:37:18,660
+الـ A
+
+324
+00:37:23,530 --> 00:37:28,270
+الحين لو جبت مضاعفات، الرقم الأول مضاعفات التلاتة،
+
+325
+00:37:28,270 --> 00:37:35,510
+بيطلع الـ 0، بيطلع الـ 3، بيطلع الـ 6، بيطلع
+
+326
+00:37:35,510 --> 00:37:35,550
+بيطلع الـ 9، بيطلع الـ 12، بيطلع الـ 15، بيطلع
+
+327
+00:37:35,550 --> 00:37:35,650
+الـ 18، بيطلع الـ 21، بيطلع الـ 24، بيطلع
+
+328
+00:37:35,650 --> 00:37:36,350
+الـ 27، بيطلع الـ 30، بيطلع الـ 33، بيطلع
+
+329
+00:37:36,350 --> 00:37:44,550
+الـ 36، بيطلع الـ 39، بيطلع الـ 42، بيطلع الـ 45،
+
+330
+00:37:44,550 --> 00:37:50,050
+بيطلع
+
+331
+00:37:50,050 --> 00:37:52,610
+الـ
+
+332
+00:37:53,630 --> 00:37:58,050
+أه و الباقي كله روتينيًا، فهذا شغال روتيني، هذا صورة
+
+333
+00:37:58,050 --> 00:38:01,850
+واحدة في إجاباتك، تبقى الإجابة هذا، و كله قدامي في
+
+334
+00:38:01,850 --> 00:38:09,050
+طريقين، يا جيبي ايديل ثاني، يا إما على النظرية،
+
+335
+00:38:09,050 --> 00:38:13,770
+فإذا بتقدر يبقى أنا ممتن، وإن شغلت، كنت يبقى أضافتي
+
+336
+00:38:13,770 --> 00:38:18,630
+للمعلومات اللي كمان معلومة، فيبقى أنا بفكر
+
+337
+00:38:18,630 --> 00:38:23,590
+بالطريقة اللي هي اسم ناسبني، وكل واحد فكر في الأول
+
+338
+00:38:23,590 --> 00:38:28,090
+ممكن إحنا اتنين نقصد والتفكير ممكن نقصد النتيجة
+
+339
+00:38:28,090 --> 00:38:31,970
+يعني ليس صعب نروح ندور على عيون ثانية ونقول هذا
+
+340
+00:38:31,970 --> 00:38:37,050
+صرصت منه وهذا صرصت منها ونثبت أن هذا كذا إلى آخره
+
+341
+00:38:37,050 --> 00:38:43,750
+طيب على أي حال صار عندنا Factoring جديدة وهذا ليس
+
+342
+00:38:43,750 --> 00:38:51,690
+بالجديد لأن موضوعنا كان Ideals and Factoring تمام؟
+
+343
+00:38:51,790 --> 00:38:58,190
+هل هدف الـ shattering
+
+344
+00:38:58,190 --> 00:39:02,610
+فيه الـ unity؟
+
+345
+00:39:02,610 --> 00:39:10,190
+واحد وزيره زي ده هو الـ unity  قصدنا فيه هدف هذا
+
+346
+00:39:10,190 --> 00:39:16,470
+الحاجة ده وزيره زي ده ده لما ملهمي إن هو يشمل نفس
+
+347
+00:39:16,470 --> 00:39:26,430
+الشيء يبقى هدف هو الـ unity يرجع هذه هما هذه الكلمة
+
+348
+00:39:26,430 --> 00:39:39,570
+Factor ring Factor ring و الـ unity اللي هو واحد و
+
+349
+00:39:39,570 --> 00:39:44,810
+zero ذات الـ two السؤال،
+
+350
+00:39:44,810 --> 00:39:52,270
+هل هذه field؟ يعني هل every non-zero element is a
+
+351
+00:39:52,270 --> 00:39:59,010
+unit؟ هذا unity يبقى unit، بل هذا، لو ضربته في
+
+352
+00:39:59,010 --> 00:40:06,910
+هذا، يبقى unity؟ طبعًا لا، طب لو ضربته في نفسه؟
+
+353
+00:40:06,910 --> 00:40:12,910
+طبعًا الـ unity هو الـ unity، يبقى صح unity ولا لا؟
+
+354
+00:40:12,910 --> 00:40:20,910
+يبقى هنا، ما نروح بأمرنا الواحد وزيره زائد الـ a is a
+
+355
+00:40:20,910 --> 00:40:32,030
+unit and الإتنين وزيره زائد الـ a is a unit السبب
+
+356
+00:40:32,030 --> 00:40:35,950
+because إنه
+
+357
+00:40:35,950 --> 00:40:44,270
+الإتنين وزيره زائد الـ a لو ضربتوا إتنين وزيره زائد
+
+358
+00:40:44,270 --> 00:40:51,200
+الـ a بتشير، بتساوي اتنين وزيره اتنين وزيره زائد الـ a
+
+359
+00:40:51,200 --> 00:40:59,180
+يعني أربعة وزيره زائد الـ a يعني واحد وزيره زائد
+
+360
+00:40:59,180 --> 00:41:05,400
+تلاتة وزيره زائد الـ a هذا موجود في الـ a يبقى بيبقى
+
+361
+00:41:05,400 --> 00:41:12,320
+بيساوي واحد وزيره زائد الـ L و الـ unity مظلوم؟ يبقى
+
+362
+00:41:12,320 --> 00:41:19,600
+صح هذا is a unit طيب مادة unit يبقى every non zero
+
+363
+00:41:19,600 --> 00:41:28,260
+is a unit تبقى صرفيت ولا لأ طيب شاهد تيب every non
+
+364
+00:41:28,260 --> 00:41:44,200
+zero is a unit
+
+365
+00:42:05,700 --> 00:42:11,080
+طيب يبقى صار هذا هو عبارة عن maximal ideal هذا
+
+366
+00:42:11,080 --> 00:42:16,510
+المقبول الأول من السؤال، قال لي بيجيلي إن هذا
+
+367
+00:42:16,510 --> 00:42:23,090
+maximum و بعدين كني generalized لذالك لملة التلاتة
+
+368
+00:42:23,090 --> 00:42:29,890
+يا بنات prime ولا لا؟ أو لو سبدلته بخمسة أو لو
+
+369
+00:42:29,890 --> 00:42:36,410
+سبدلته باتنين أو لو سبدلته بسبعة، أحد عشر، ثلاثة عشر،
+
+370
+00:42:36,410 --> 00:42:42,790
+سبعة عشر كله كانت الكلام صحيح و هذا maximum يبقى
+
+371
+00:42:43,990 --> 00:42:58,330
+the ideal اللي هو A بدرساه P X وY such that X وY
+
+372
+00:42:58,330 --> 00:43:13,330
+موجودة في ذلك I الـ P is prime is maximum طيب
+
+373
+00:43:13,770 --> 00:43:17,310
+نمر الـ C طب ليش بقى يا أستاذ باقي الأرقام مقتنعة؟
+
+374
+00:43:17,310 --> 00:43:24,050
+باقي الأرقام؟ أنا جايك لباقي الأرقام، أطلعت، فخلص،
+
+375
+00:43:24,050 --> 00:43:30,370
+مخلصش، قال لي هنا عامة، بقوله لو كان الرقم بدل ما
+
+376
+00:43:30,370 --> 00:43:34,370
+هو التلاتة، أي prime ideal، بيكون الـ ideal
+
+377
+00:43:34,370 --> 00:43:39,790
+maximum، طب لو جينا لأرقام، نمر الـ C قال إيش بيحصل
+
+378
+00:43:39,790 --> 00:43:46,170
+لو شيلت التلاتة X وحطيت مكانها أربعة X بقوله بسيطة
+
+379
+00:43:46,170 --> 00:43:54,730
+بدي أخد الـ A تساوي كل الأربعة X وY بحيث الـ X و الـ Y
+
+380
+00:43:54,730 --> 00:44:03,070
+موجودة في Z قال هذا maximum ideal هذا ideal في
+
+381
+00:44:03,070 --> 00:44:14,920
+الأول يبقى هذا is an ideal غير هيك الـ ring commutative
+
+382
+00:44:14,920 --> 00:44:24,640
+with unity أخذناها من الأول و الـ Z بس Z is
+
+383
+00:44:24,640 --> 00:44:29,900
+commutative with
+
+384
+00:44:29,900 --> 00:44:32,120
+unity
+
+385
+00:44:36,880 --> 00:44:43,760
+الآن نشوف هل هي field ولا ماهيّاش field أنا أزعم
+
+386
+00:44:43,760 --> 00:44:55,840
+أن Z direct sum Z موديول A هي الـ A و مين؟ واحد
+
+387
+00:44:55,840 --> 00:45:08,600
+و Zero زائد الـ A إثنين و Zero زائد الـ A زائد MA
+
+388
+00:45:08,600 --> 00:45:19,100
+ثلاثة و Zero زائد A فلو بدلنا ثلاثة X بأربعة X بصير
+
+389
+00:45:19,100 --> 00:45:24,820
+بدل ما كان فيها هنا تلات عناصر بس بصير عندي قد إيش
+
+390
+00:45:24,820 --> 00:45:30,940
+أربعة، إذا لو بدلتها بخمسة خمسة، ستة ستة عناصر وهكذا
+
+391
+00:45:30,940 --> 00:45:36,060
+كل ما تغير رقم بيزداد عدد العناصر في الـ factor،
+
+392
+00:45:36,060 --> 00:45:40,440
+الـ group، الـ unit. طيب، هدول ثلاثة، السؤال هو،
+
+393
+00:45:40,4
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..776c6f7c9c5b8018d7f09c8ea29c44e056deb040
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_raw.srt
@@ -0,0 +1,1704 @@
+1
+00:00:21,600 --> 00:00:26,440
+رحمان الله الرحيم احنا انتهينا المرة الماضية من
+
+2
+00:00:26,440 --> 00:00:31,420
+chapter ال ideas and factoring وبدأنا في حل
+
+3
+00:00:31,420 --> 00:00:35,560
+الأسئلة في نصف التانية من المحاضرة واليوم ان شاء
+
+4
+00:00:35,560 --> 00:00:41,780
+الله نكمل حل الأسئلة اللي كلفناها بحلها في البيت
+
+5
+00:00:41,780 --> 00:00:48,120
+طبعا اخر سؤال مرة اتعرضنا له هو سؤال 17 اليوم سؤال
+
+6
+00:00:48,120 --> 00:00:54,390
+17يقول لو كان الـ I هو ID المنازل و هذا الـ ID
+
+7
+00:00:54,390 --> 00:00:59,570
+الاحتواء unit بدا نثبت ان الـ I بدي ساوي R يبقى
+
+8
+00:00:59,570 --> 00:01:13,670
+السؤال 17 كان I ID of R و الـ I contains a unit
+
+9
+00:01:13,670 --> 00:01:20,260
+هذا الكلام بدي يعطينا ان الـ ID الـ Rبدو يساوي
+
+10
+00:01:20,260 --> 00:01:27,160
+الـRing R itself.مشان نحل هذا السؤال، بنرجع
+
+11
+00:01:27,160 --> 00:01:32,400
+بمعلوماتنا قليلا إلى الأوراق. الـ Set Theory،
+
+12
+00:01:32,400 --> 00:01:36,520
+بجينا نثبت أن الـ two sets are equal و بنثبت أن
+
+13
+00:01:36,520 --> 00:01:40,440
+الأولى صبست من التانية و التانية صبست من الأولى،
+
+14
+00:01:40,440 --> 00:01:45,100
+إن حدث ذلك، بقول يبقى الـ two sets are equal، بأن
+
+15
+00:01:45,100 --> 00:01:50,770
+نفسي نمشي نفسي التفتيق.الأن يا بنات I هو ideal من
+
+16
+00:01:50,770 --> 00:01:57,410
+R يبقى .. يبقى هذا يجد الـ R أقل منه صح ولا لأ؟
+
+17
+00:01:57,410 --> 00:02:04,010
+يعني صدست من الـ R وقد يساويها يبقى in a sense بما
+
+18
+00:02:04,010 --> 00:02:16,710
+أن ال I is an ideal of R we have أنهالـ I سادسة من
+
+19
+00:02:16,710 --> 00:02:22,470
+الـ A وسمّيلي هذه العلاقة رقم واحد بعد هيك بدنا
+
+20
+00:02:22,470 --> 00:02:34,850
+نيجي نقول افترضي ان A is a unit in A in X in
+
+21
+00:02:34,850 --> 00:02:40,590
+I يبقى بنفترض ان العمصر A هو unit و ال unit هذا
+
+22
+00:02:40,590 --> 00:02:42,270
+موجود في I زي انه قال
+
+23
+00:02:46,200 --> 00:02:55,940
+لأثبت أن الـR صبست من الـI يبقى لو أخدت الآن الـR
+
+24
+00:02:55,940 --> 00:03:01,640
+موجودة في R لو قدرت أثبت أن الـR اسمه الهادي
+
+25
+00:03:01,640 --> 00:03:09,360
+موجودة في I بتمام المطلوب يبقى then الـR هادي بقدر
+
+26
+00:03:09,360 --> 00:03:16,610
+أكتبها على شكل الـR في A inverse Aلأن الـinity
+
+27
+00:03:16,610 --> 00:03:23,250
+يعني معكوث العنصر exist هذا كله الـR يسوى R في A
+
+28
+00:03:23,250 --> 00:03:30,190
+اللي بقدر أقول هو عبارة عن R A inverse في مين في
+
+29
+00:03:30,190 --> 00:03:40,130
+الـA هذا الآن موجود في I صح؟ و هذا موجود وين؟ في R
+
+30
+00:03:40,130 --> 00:03:46,440
+يبقى و الـI ID اللي يبقى حاصر ضربه مين موجودفي I
+
+31
+00:03:46,440 --> 00:03:57,820
+يبقى هذا موجود في I since لإن ال I is an ID لإن ال
+
+32
+00:03:57,820 --> 00:04:04,180
+I ideally يبقى هذا موجود فيها تمام يبقى أخدنا عنصر
+
+33
+00:04:04,180 --> 00:04:10,880
+R موجود في R أثبتنا إنه موجود وين؟ موجود في I يبقى
+
+34
+00:04:10,880 --> 00:04:17,080
+ساق ال R subset من مين؟من I و هذه العلاقة رقم
+
+35
+00:04:17,080 --> 00:04:26,640
+اتنين بروح بقول from واحد and اتنين we have ان ال
+
+36
+00:04:26,640 --> 00:04:34,900
+ideal R تسوى ال ring R كله إذا حتى الآن استمعنا
+
+37
+00:04:34,900 --> 00:04:40,020
+يعني حصلنا على معلومتين مهماتالمعلومة الأولى
+
+38
+00:04:40,020 --> 00:04:44,440
+قلتلناها سابقا والمعلومة الثانية هي بيننا الآن
+
+39
+00:04:44,440 --> 00:04:48,420
+المعلومة السابقة بجينا نقول إذا ال ID اللي احتوى
+
+40
+00:04:48,420 --> 00:04:53,160
+على ال unity على عنصر الوحدة يبقى ال ID اللي بدي
+
+41
+00:04:53,160 --> 00:04:57,420
+أسوأ مين في ال ring itself وهنا نقول لو ال ID اللي
+
+42
+00:04:57,420 --> 00:05:02,600
+احتوى على unit واحدة يبقى ال ID اللي هذا بدي أسوأ
+
+43
+00:05:02,600 --> 00:05:08,870
+مين بيسوء ال ring R يبقى من الأن أساعداهذا أخدنا
+
+44
+00:05:08,870 --> 00:05:13,270
+ideal من ال ring و لجأت فيه ال unity أو لجأت فيه
+
+45
+00:05:13,270 --> 00:05:17,790
+unit يبقى على كل الخط ال ideal هذا بده يساوي مين؟
+
+46
+00:05:17,790 --> 00:05:23,690
+بده يساوي نفس ال ring هذا كان سؤال سبعتاشر بعد ذلك
+
+47
+00:05:23,690 --> 00:05:29,190
+معانا سؤال اتنين و عشرين جال يخد لل ideal و ال
+
+48
+00:05:29,190 --> 00:05:35,550
+principle ideal generated by اتنين يبقى سؤال اتنين
+
+49
+00:05:35,550 --> 00:05:40,790
+و عشرينالـ I هو الـ principle IG generated by
+
+50
+00:05:40,790 --> 00:05:50,110
+إتنين ومعطيني بعد ذلك I of X وإن I of X is not
+
+51
+00:05:50,110 --> 00:05:56,890
+maximal ideal في Z even though I is maximal يبقى
+
+52
+00:05:56,890 --> 00:06:04,830
+هنا sure إن I of X is not
+
+53
+00:06:07,860 --> 00:06:19,740
+maximum in z of x الرغم ان ال principle ideal
+
+54
+00:06:19,740 --> 00:06:25,660
+generated by a هو عبارة عن maximum من مين في z
+
+55
+00:06:25,660 --> 00:06:30,840
+وعندنا ال principle ideal generated by a هو
+
+56
+00:06:30,840 --> 00:06:40,370
+maximum in zيعني برغم ان هذا ال ideal maximal في Z
+
+57
+00:06:40,370 --> 00:06:46,510
+لكن I of X ماهياش maximal في ماين في Z of X يبقى
+
+58
+00:06:46,510 --> 00:06:54,490
+خلوم شده اظهر ال principle ideal generated by
+
+59
+00:06:54,490 --> 00:07:01,270
+اتنين هذا معروف بالنسبة ايه؟ اللي همين ال zero
+
+60
+00:07:01,270 --> 00:07:03,990
+وزاد او ناقص اتنين
+
+61
+00:07:09,670 --> 00:07:17,830
+طب ال I of X مين
+
+62
+00:07:17,830 --> 00:07:23,610
+ال I of X؟ مين ال Z of X؟ كثيرات الحدود إلى
+
+63
+00:07:23,610 --> 00:07:29,830
+المعاملة تبعها تعدد صحيح صح ولا لأ؟ قياسا عليها ال
+
+64
+00:07:29,830 --> 00:07:39,400
+I of X هو كثيرات الحدود لمعاملتهاإنها عدالة زوجية
+
+65
+00:07:39,400 --> 00:07:44,760
+2 4 6 8 إلى أخرى صح؟ نعم لأن هاي ال principle
+
+66
+00:07:44,760 --> 00:07:48,680
+ideal generated by اتنين اتنين اربع ستة كلها عدالة
+
+67
+00:07:48,680 --> 00:07:56,340
+زوجية تمام يبقى I of X هو عبارة عن كل ال functions
+
+68
+00:07:56,340 --> 00:08:05,480
+F of X such that ال F of X has
+
+69
+00:08:07,160 --> 00:08:11,420
+even او
+
+70
+00:08:11,420 --> 00:08:21,500
+has even coefficients او كولونوميال او
+
+71
+00:08:21,500 --> 00:08:29,640
+كولونوميال with even
+
+72
+00:08:29,640 --> 00:08:32,320
+coefficients
+
+73
+00:08:42,410 --> 00:08:48,450
+كل كثيرات الحدود اللي المعاملات تبعتها أعداد زوجية
+
+74
+00:08:48,450 --> 00:08:54,810
+even إنتجاه يبقى أعداد زوجية، منطقية، هيها من
+
+75
+00:08:54,810 --> 00:08:59,250
+أربعة، ستة، تمانية، بالسالف أو في الموجة عرفنا
+
+76
+00:08:59,250 --> 00:09:04,950
+الـI of X، قال لي أثبت إنه هذه الماكسيمال، لو
+
+77
+00:09:04,950 --> 00:09:10,090
+رجعنا لتعريف الماكسيمال idealبنقول ال ideal بقول
+
+78
+00:09:10,090 --> 00:09:15,250
+عنه maximum لو جدت و لاقي ideal تاني بعيط هذا ال
+
+79
+00:09:15,250 --> 00:09:21,050
+ideal subset منه و لا يساويه و هذا ال ideal إذا
+
+80
+00:09:21,050 --> 00:09:25,970
+كان بيسويش يبقى بيساوي 100 بيساوي ال R itself إن
+
+81
+00:09:25,970 --> 00:09:30,010
+حدث ذلك يبقى بيقول هذا ال ideal ما له maximal
+
+82
+00:09:30,010 --> 00:09:37,510
+ideal طيب احنا لو قدرنا نجيب ideal تاني بحيث ال I
+
+83
+00:09:37,510 --> 00:09:43,970
+of Xهو لا يساويه و ال ideal التاني الصبصت من ال
+
+84
+00:09:43,970 --> 00:09:50,250
+ring هو لا يساويها يبقاش من السنة تانية ماقوم على
+
+85
+00:09:50,250 --> 00:09:55,450
+طول الخط مش هنجيب من المريخ ال ideal لأ لأ لأ من
+
+86
+00:09:55,450 --> 00:10:00,090
+اللي أخدناه أخدنا فيه principle ideal generated by
+
+87
+00:10:00,090 --> 00:10:10,180
+X و 2 تذكروا ال polynomialاللي كل ال .. كل العدد
+
+88
+00:10:10,180 --> 00:10:15,940
+الأخير أو العدد الثابت هو عدد زوجي، مظبوط؟ يفجأة
+
+89
+00:10:15,940 --> 00:10:22,340
+بدنا نروح نطبق صحة هذا الكلام، فبعدين بيقول أخدنا
+
+90
+00:10:22,340 --> 00:10:29,340
+part ولكن اللي هو seminary principle ideal
+
+91
+00:10:29,340 --> 00:10:33,720
+generated by X و 2
+
+92
+00:10:37,970 --> 00:10:46,710
+بحيث أن ال F of X تسادي X في G of X زائد اتنين H
+
+93
+00:10:46,710 --> 00:10:55,210
+of X صح؟ طيب تعالوا ندقق النظر في الأتنين هدولة ال
+
+94
+00:10:55,210 --> 00:11:01,470
+I of X كل ال F of X كتيرات الحدود اللي المعاملات
+
+95
+00:11:01,470 --> 00:11:09,900
+تبعتها أعداد زوجية صح؟ هذا مهمهذا كل العناصر اللي
+
+96
+00:11:09,900 --> 00:11:16,920
+الحد الأخير فيها بيكون عدد زوجي، تمام؟ ممتاز جدا،
+
+97
+00:11:16,920 --> 00:11:22,140
+طيب هل الأولى صبست من التانية و الله التانى صبست
+
+98
+00:11:22,140 --> 00:11:26,240
+من التانية؟ لأن
+
+99
+00:11:26,240 --> 00:11:32,140
+الأولى كلهم عدد زوجية، هذا العدد الزوجي هو مين؟
+
+100
+00:11:32,140 --> 00:11:36,550
+العدد الأخير و قبل هيكفردي والله زوجي مابتفرقش عنا
+
+101
+00:11:36,550 --> 00:11:45,790
+لما بروح بقوله هنا clearly واضح انه ال I or X
+
+102
+00:11:45,790 --> 00:11:53,730
+subset من ال principle ideal generated by X ذأ و
+
+103
+00:11:53,730 --> 00:12:01,350
+اتنين ولا يساوي طيب السؤال and ال principle ideal
+
+104
+00:12:04,170 --> 00:12:10,570
+subset من ال R ولا لا؟ يساويها؟ لأ لأن الحد اللي
+
+105
+00:12:10,570 --> 00:12:16,030
+قد يكون زوجي و قد يكون صفر و قد يكونه فرديا يبقى
+
+106
+00:12:16,030 --> 00:12:23,010
+subset منها ولا تساويه يبقى جبت ideal موجود ما بين
+
+107
+00:12:23,010 --> 00:12:29,330
+ال ring و ما بين ال ideal و proper شرط أساسي وقدرت
+
+108
+00:12:29,330 --> 00:12:33,990
+أثبت أن ال ideal عندي ما هواشأي لا يساوي و اللي
+
+109
+00:12:33,990 --> 00:12:37,830
+جبناه لا يساوي ال R، يبقى ال I دي لديه maximum؟
+
+110
+00:12:37,830 --> 00:12:52,790
+لأ، if this means that ان ال I of X is not maximum
+
+111
+00:12:52,790 --> 00:12:56,670
+in Z
+
+112
+00:13:01,380 --> 00:13:06,780
+أدا كان سؤال اللي هو الأتنين وعشرين رغم انه ال
+
+113
+00:13:06,780 --> 00:13:09,980
+principle ideal generated by اتنين هو maximum
+
+114
+00:13:09,980 --> 00:13:16,840
+ideal في Z وهو أعلى ideal ممكن أخده من مين أخده من
+
+115
+00:13:16,840 --> 00:13:21,860
+الـ Z بعد اتنين وعشرين عندنا أربعة وعشرين جالي هات
+
+116
+00:13:21,860 --> 00:13:26,680
+مثال a commutative ring that has maximal ideal
+
+117
+00:13:26,680 --> 00:13:34,170
+that is not a prime idealيبقى اربعة و عشرين بدنا
+
+118
+00:13:34,170 --> 00:13:46,470
+مثال لكميوتاتيف رينج كوميوتاتيف رينج كوميوتاتيف
+
+119
+00:13:46,470 --> 00:13:51,970
+رينج that has maximal ما هو عشان five و has
+
+120
+00:13:51,970 --> 00:13:58,650
+maximal idea but
+
+121
+00:14:14,840 --> 00:14:25,120
+الحمد لله لو جينا وقلنا set of integers community
+
+122
+00:14:25,120 --> 00:14:26,260
+of ring و لا لأ
+
+123
+00:14:29,460 --> 00:14:35,760
+zev and usual
+
+124
+00:14:35,760 --> 00:14:44,560
+addition يعني تحت عملية الجمعين العادية and
+
+125
+00:14:44,560 --> 00:14:47,600
+multiplication
+
+126
+00:14:47,600 --> 00:14:52,480
+defined
+
+127
+00:14:52,480 --> 00:14:58,460
+by الملء
+
+128
+00:15:21,490 --> 00:15:30,880
+معروف؟ أي سؤال يحتاج إلى إجابة هو أحنا لكي نثبتإن
+
+129
+00:15:30,880 --> 00:15:36,700
+ال six strings تحت ال two operations اللي عليها مش
+
+130
+00:15:36,700 --> 00:15:41,560
+لازم نثبت ال six conditions تمام؟ طيب لما بقولنا
+
+131
+00:15:41,560 --> 00:15:46,000
+ال usual addition الجامعة العادى يعني الأول أربعة
+
+132
+00:15:46,000 --> 00:15:52,200
+الشروط محققة صح ولا لأ اللي اختلفوا مين؟ أخر شرطين
+
+133
+00:15:52,200 --> 00:15:57,640
+أخر شرطين هم اللي مين؟ هم اللي اختلفوا ليش؟ ليش
+
+134
+00:15:57,640 --> 00:16:03,990
+اختلفوا؟لأن هدول مش عملية الضرب العادية، عملية ضرب
+
+135
+00:16:03,990 --> 00:16:08,250
+خاصة، يمسك، يعطلهم جرم ويسويهم بالصبر، هي أتعرف
+
+136
+00:16:08,250 --> 00:16:14,010
+عملية الضرب، بدى أثبتله إن هذه ال ring و كذلك
+
+137
+00:16:14,010 --> 00:16:19,610
+كميوتة ال ring، يبقى أول أربعة شهور محققة لعملية
+
+138
+00:16:19,610 --> 00:16:23,890
+الجمع العالمي، دول شرطين، الشرط الأول خاصية ال
+
+139
+00:16:23,890 --> 00:16:29,180
+accessibility، الخاصية التانية هي خاصيةالتوزيع
+
+140
+00:16:29,180 --> 00:16:33,380
+Distributive law طيب نجرى الخاصية دي ال
+
+141
+00:16:33,380 --> 00:16:42,460
+sociability بقى بقى بقى بقول that if four
+
+142
+00:16:42,460 --> 00:16:48,700
+conditions of
+
+143
+00:16:48,700 --> 00:16:53,240
+a ring are satisfied
+
+144
+00:16:58,670 --> 00:17:02,470
+نقلت ما عملى فى الجامعة العادية نيجى للتانى ال
+
+145
+00:17:02,470 --> 00:17:07,650
+associativity فبداية أقوله لفت ال a و ال b و ال c
+
+146
+00:17:07,650 --> 00:17:17,690
+مويزة فى z لأن لو أخدت ال a فى ال b و ال z هميزة
+
+147
+00:17:17,690 --> 00:17:25,910
+هي a فى zero عصر ضرب اتنين فدي سوى z أحوالنا
+
+148
+00:17:28,750 --> 00:17:39,330
+يساوي الـ Z يعني لو أخدت ال A وB كلها في الـ C بدي
+
+149
+00:17:39,330 --> 00:17:45,430
+أساوي Zero في الـ C يساوي الـ D معناه هذا الكلام
+
+150
+00:17:45,430 --> 00:17:53,630
+أن ال A وB في الـ C بدي أساوي KB في الـ C لكل الـ
+
+151
+00:17:53,630 --> 00:17:56,390
+A وB وC الموجودة
+
+152
+00:17:59,260 --> 00:18:05,220
+distributive law صحيحة طيب الآن هذه الخاصية
+
+153
+00:18:05,220 --> 00:18:10,760
+التانية الخالصة الخاصية السادسة بدنا distributive
+
+154
+00:18:10,760 --> 00:18:23,260
+law داخل ال a ال b زائد ال c تمام هذا الكلام بده
+
+155
+00:18:23,260 --> 00:18:24,100
+يساوي
+
+156
+00:18:28,500 --> 00:18:33,280
+لأن هذا كله يعتبر element وهذا element تاني وكان
+
+157
+00:18:33,280 --> 00:18:36,880
+اللي حاصد الطريق يساوي zero لأي two elements
+
+158
+00:18:36,880 --> 00:18:46,040
+موجودة فيها امين لو أخدت ال A P زي ان ال A C Zero
+
+159
+00:18:46,040 --> 00:18:53,060
+زاخد Zero اللي هو يساوي Zero فإتبعنا هذا الكلام أن
+
+160
+00:18:53,060 --> 00:19:03,160
+ال A ال Bزايد الـ C يساوي بـ A B زايد بـ A C و
+
+161
+00:19:03,160 --> 00:19:09,880
+بنفس الطريقة Similarly بنفس
+
+162
+00:19:09,880 --> 00:19:20,080
+الطريقة الـ B زايد الـ C كل K يساوي بـ A زايد C A
+
+163
+00:19:20,080 --> 00:19:32,530
+Plus وهكذا الـ Zis A غير B عملية
+
+164
+00:19:32,530 --> 00:19:41,490
+مين؟ commutative الأن ال A في B كده تسوية منها حسب
+
+165
+00:19:41,490 --> 00:19:48,150
+ال definition طيب و ال B في A؟ Zero يبقى معنا هذا
+
+166
+00:19:48,150 --> 00:19:56,960
+الكلام أن ال A بيلكل الـ A و الـ B موجودة في نزل
+
+167
+00:19:56,960 --> 00:20:04,300
+هذا اللي هو commutative point
+
+168
+00:20:04,300 --> 00:20:11,960
+لما احنا جبنا مثل لـ commutative ring ها يبدو
+
+169
+00:20:11,960 --> 00:20:15,720
+commutative ring جبنا له commutative ring هذا
+
+170
+00:20:15,720 --> 00:20:22,140
+maximum ideal باطناطي الفعل السؤال هو لما نزل
+
+171
+00:20:24,840 --> 00:20:33,640
+maximum ideal انزل، صحيح ولا لا؟ طيب السؤال هو هل
+
+172
+00:20:33,640 --> 00:20:42,260
+هذا هو prime؟ بنقول آه، إذا بتاخد رقم حاسم ضرهم
+
+173
+00:20:42,260 --> 00:20:45,340
+موجود في هذا ال ideal
+
+174
+00:20:49,630 --> 00:20:56,450
+موجود في هذا ID، إن حدث ذلك، بقول هذا هو prime ID،
+
+175
+00:20:56,450 --> 00:21:02,450
+ماحدثش، يبقى هو نقطة prime ID، طيب، لو جاءت
+
+176
+00:21:02,450 --> 00:21:11,430
+conflict، مثلا، قد يلي ثلاثة في سبعة، ثلاثة في
+
+177
+00:21:11,430 --> 00:21:12,490
+سبعة، كم سنة؟
+
+178
+00:21:17,840 --> 00:21:23,420
+في الشغل العادى، لأن 3×7 يساوي 0، لماذا؟ لأن 3
+
+179
+00:21:23,420 --> 00:21:28,820
+موجود في الـ Z وال7 موجود في الـ Z، وعملية الضرب
+
+180
+00:21:28,820 --> 00:21:33,840
+علي حصة الضرب أي اتنين يساوي 0، طيب، هذا الكلام
+
+181
+00:21:33,840 --> 00:21:38,660
+يساوي 0، طيب، هل الـ Zero موجودة في اتنين Z ولا
+
+182
+00:21:38,660 --> 00:21:45,820
+لا؟ هل موجودة في اتنين Z؟اللي هو مين؟ اللي فيه الـ
+
+183
+00:21:45,820 --> 00:21:51,400
+Zero وزاد أو نقص اتنين وزاد أو نقص اربع وانا مجرد
+
+184
+00:21:51,400 --> 00:21:57,980
+موجودة في هذه الـ Zero، بطل ولكن هذه التلاتة
+
+185
+00:21:57,980 --> 00:22:05,500
+موجودة في اتنين زرد؟ لأ، مش موجودة أنزل السبعة مش
+
+186
+00:22:05,500 --> 00:22:11,860
+موجودة في اتنين زرد كذلك صحيح ولا لأ؟يبقى صرحد ما
+
+187
+00:22:11,860 --> 00:22:23,440
+هواش بيه إسرائيل، يبقى هنا ساعة ننزل الناس إسرائيل
+
+188
+00:22:23,440 --> 00:22:30,400
+قاعدين الزجاج
+
+189
+00:22:30,400 --> 00:22:33,760
+فالرياضات
+
+190
+00:22:33,760 --> 00:22:39,200
+عموما، كما يقولك برهم، أسهر اللي يقولك تاتي مثال
+
+191
+00:22:40,440 --> 00:22:47,440
+تكون عملية جالب المثال صعبة، لكن الورهان أسهل من
+
+192
+00:22:47,440 --> 00:22:53,000
+مفروض البراجين الرياضيات معروفة تلاتة طرق، طرق
+
+193
+00:22:53,000 --> 00:22:58,320
+تاعتها بنقدر عليها و بنحاول نحقق السؤال، ابتعدوا.
+
+194
+00:22:58,840 --> 00:23:04,200
+هذا كان سؤال أربع وعشرين، ثم سؤال تلاتين.
+
+195
+00:23:06,340 --> 00:23:17,340
+سؤال تلاتين بيقولأعفر مطالب مطلوب الأول شراء ذات
+
+196
+00:23:17,340 --> 00:23:26,220
+ما يلغ أنه لقيت يساوي كل الأزواج المغتلة تلاتة x و
+
+197
+00:23:26,220 --> 00:23:33,880
+y بحيث ال x و ال y موجودة في z شراء ذات is a
+
+198
+00:23:33,880 --> 00:23:39,640
+maximal idea is a maximal
+
+199
+00:23:41,760 --> 00:23:52,760
+Ideal أن زرق ضايق صنع زرق المطلوب
+
+200
+00:23:52,760 --> 00:24:05,140
+التالي مربي بنرع لايك عم المطلوب التالي what
+
+201
+00:24:05,140 --> 00:24:15,580
+happen شو اللي بده يحصلwhen تلاتة
+
+202
+00:24:15,580 --> 00:24:21,220
+X replace باربع
+
+203
+00:24:21,220 --> 00:24:30,740
+X، شو اللي بده يحصل؟ D generalized،
+
+204
+00:24:30,740 --> 00:24:31,780
+برضه عامل
+
+205
+00:24:46,380 --> 00:24:55,060
+هذا فيكو أثبتت أن هذا ID لبنات بس؟ كيف؟ لأ
+
+206
+00:24:55,060 --> 00:25:00,820
+هو هذا، هل تثبت أنه ID؟ لأ، هو قال أثبت أنه
+
+207
+00:25:00,820 --> 00:25:04,240
+maximal ID، لم يمرش علينا قبل الليلة أثبتنا أنه
+
+208
+00:25:04,240 --> 00:25:08,380
+ID، يبقى الخبرة ويبقى الابنانية، بيثبت أنه ID، ثم
+
+209
+00:25:08,380 --> 00:25:12,960
+نذهب إلى ال максимالين، كتير ID ولا حد يعمل فيش؟
+
+210
+00:25:13,750 --> 00:25:18,330
+مده ما مرش علينا قبل هير كمان لازم نكفت أولا إنه
+
+211
+00:25:18,330 --> 00:25:24,930
+ideal ثم نذهب نبحث عن ماكسيمالي أه حد عارف أولا
+
+212
+00:25:24,930 --> 00:25:30,090
+إنه ideal؟ طب عارف هذا الفيلم لازم تتكتر أنه ideal
+
+213
+00:25:30,090 --> 00:25:34,430
+أولا ثم بقعد أدرك أن هو تتكتر أنه maximum ideal
+
+214
+00:25:34,430 --> 00:25:41,490
+نفنجي الأول بدنا نكفت أنه ideal كيف جبالي بيقولونه
+
+215
+00:25:41,490 --> 00:25:49,650
+نمرأيهمبتجد النقطة الأولى بدي أكتر من M يبقى الـ A
+
+216
+00:25:49,650 --> 00:26:02,470
+أزمن M because الـ Zero و Zero موجود في .. اللي هو
+
+217
+00:26:02,470 --> 00:26:09,130
+المسافر تلاتة مضروف في Zero و Zero صار على الصيلة
+
+218
+00:26:09,130 --> 00:26:13,950
+هذهما جاليش الـ Nox بتسوي و لا بتسوي حرب خد زي ما
+
+219
+00:26:13,950 --> 00:26:22,030
+بدها يبقى A موجودة في A يبقى بشأن هاتمان M يبقى
+
+220
+00:26:22,030 --> 00:26:26,790
+تحقق ال condition الأول ال condition التاني فتروح
+
+221
+00:26:26,790 --> 00:26:35,350
+أخد عنصرين موجودات في A يبقى net A و B موجودة في A
+
+222
+00:26:35,350 --> 00:26:42,960
+then شكل ال A إيش بدي يكون؟يبقى بيكون ثلاثة x one
+
+223
+00:26:42,960 --> 00:26:54,540
+و y one and شكل ال b ثلاثة x two و y two تمام؟ كل
+
+224
+00:26:54,540 --> 00:26:59,440
+عنصر على شكل or ضارف a مزود مرتب زي ما انتوا
+
+225
+00:26:59,440 --> 00:27:06,460
+شايفينه الاند ده ياخد ال a ماعقرس ال bيبقى هذا
+
+226
+00:27:06,460 --> 00:27:13,960
+الكلام بالدرسان تلاتة x one و y one ناقص تلاتة x
+
+227
+00:27:13,960 --> 00:27:20,300
+two و y two الطرح أو الجمع component twice يبقى
+
+228
+00:27:20,300 --> 00:27:27,540
+هذا الكلام بالدرسان تلاتة x one ناقص x two و y one
+
+229
+00:27:27,540 --> 00:27:35,070
+ناقص y two هل هذا على الشكل اللي عندنا؟ صح؟الـ C
+
+230
+00:27:35,070 --> 00:27:39,390
+موجود في الـ A خلاصة من ال condition الثالث،
+
+231
+00:27:39,390 --> 00:27:45,110
+الثاني، ضالان ال condition الثالث والأخير، إذا
+
+232
+00:27:45,110 --> 00:27:51,410
+ناخد element من ال ring الأصلية، و ناخد element من
+
+233
+00:27:51,410 --> 00:27:58,610
+هنا، يبقى بالتالي أقول للـ L، الـ C و الـ D موجودة
+
+234
+00:27:58,610 --> 00:28:02,870
+في الـ Z-direct صمع Z، and
+
+235
+00:28:05,290 --> 00:28:13,070
+الـ A اللي بدها تساوي تلاتة X1 و Y1 موجودة في الـ
+
+236
+00:28:13,070 --> 00:28:20,750
+A ثم بدي أشوف حاصل ضاربهم إذا موجود في A، بيكون
+
+237
+00:28:20,750 --> 00:28:25,090
+صار الـ A عفر عن الـ Ideal سواء ما كان ضارب من
+
+238
+00:28:25,090 --> 00:28:33,170
+اليمين أو من الشمال يبقى الأواخر C وD مضروب في من؟
+
+239
+00:28:33,170 --> 00:28:44,630
+في الـ Aبتي ساوى C و D LLي تلاتة X one و Y one هذا
+
+240
+00:28:44,630 --> 00:28:58,370
+الكلام يساوى تلاتة C X one و هذا D Y one موجود؟
+
+241
+00:29:00,380 --> 00:29:08,700
+يبقى هذا موجود في A Similarي بنفس الطريقة اللي هو
+
+242
+00:29:08,700 --> 00:29:18,020
+A في C وD موجود في الـ A يبقى الـ A معلوم is
+
+243
+00:29:18,020 --> 00:29:24,780
+unideal سواء الـ A is unideal
+
+244
+00:29:29,710 --> 00:29:35,630
+خلصنا؟ لما قلتوا إلى أين؟ إلى أين خلصت؟ انت كل
+
+245
+00:29:35,630 --> 00:29:43,170
+اللي اتبعته انه ideal فقط بقى عليك تثبت انه ايش؟
+
+246
+00:29:43,170 --> 00:29:50,790
+not maximum ماهواش maximum ideal لك maximum؟ اه
+
+247
+00:29:50,790 --> 00:29:56,050
+هذا صحييني كويس طيب كليتوا صحيين معانا ماشي الآن
+
+248
+00:29:56,050 --> 00:30:02,410
+طيبيبقى المطموع أن نثبت أن هذا هو عبارة عن maximum
+
+249
+00:30:02,410 --> 00:30:09,750
+ايدين لذلك قدامي بدأت بطريقة اثنين طريقة ثانية
+
+250
+00:30:09,750 --> 00:30:15,090
+يعني ناخد ا او طريقة اثنين يعني طريقة التعريف هي
+
+251
+00:30:15,090 --> 00:30:19,610
+طريقة النظرية ليست النظرية اللي هو تقول لو كان
+
+252
+00:30:19,610 --> 00:30:24,370
+عندي range commutative with unity يبقى ال a module
+
+253
+00:30:24,370 --> 00:30:30,030
+is a في ال F عنده دقة is maximumيعني لو كان ارهد
+
+254
+00:30:30,030 --> 00:30:34,390
+يقوله ايه كانت فيه يبقى لإيه maximum أو على
+
+255
+00:30:34,390 --> 00:30:39,210
+التعريض، قبل شوية احنا أثبتنا ذلك بواسطة التعريض،
+
+256
+00:30:39,210 --> 00:30:44,670
+المثبتنا الماكسيماليتي، ده استخدمنا التعريض، هنا،
+
+257
+00:30:44,670 --> 00:30:49,410
+ده استخدمنا ضغيط، وشو المشكلة؟ بلاش، اه، فاستنى
+
+258
+00:30:49,410 --> 00:30:52,270
+شوية، وين تبقى التعريض؟
+
+259
+00:31:01,270 --> 00:31:08,510
+السؤال هو هل هذه commutative؟ أكيد
+
+260
+00:31:08,510 --> 00:31:12,390
+ميل ميل، لأن الـZ أصلاً commutative فلما يكون حاصل
+
+261
+00:31:12,390 --> 00:31:15,990
+ضرب عنصرين في الـZ، يقل بيهم أو بداية الـZ، يبقى
+
+262
+00:31:15,990 --> 00:31:23,170
+commutative و الـUnity لهم إيه؟ واحد و واحد، يبقى
+
+263
+00:31:23,170 --> 00:31:23,570
+الـUnity
+
+264
+00:31:28,040 --> 00:31:38,200
+Is plus is plus is plus is plus is plus is plus is
+
+265
+00:31:38,200 --> 00:31:39,640
+plus is plus is plus is plus is plus is plus is
+
+266
+00:31:39,640 --> 00:31:39,640
+plus is plus is plus is plus is plus is plus is
+
+267
+00:31:39,640 --> 00:31:41,360
+plus is plus is plus is plus is plus is plus is
+
+268
+00:31:41,360 --> 00:31:46,460
+plus is plus is plus is plus is plus is plus is
+
+269
+00:31:46,460 --> 00:31:46,760
+plus is plus is plus is plus is plus is plus is
+
+270
+00:31:46,760 --> 00:31:47,040
+plus is plus is plus is plus is plus is plus is
+
+271
+00:31:47,040 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+272
+00:31:47,140 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+273
+00:31:47,140 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+274
+00:31:47,140 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+275
+00:31:47,140 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+276
+00:31:47,140 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+277
+00:31:47,140 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+278
+00:31:47,140 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+279
+00:31:47,140 --> 00:31:47,180
+plus is plus is plus is plus is plus is plus is
+
+280
+00:31:47,180 --> 00:31:47,180
+plus is plus is plus is plus is plus is plus is
+
+281
+00:31:47,180 --> 00:31:47,200
+plus is plus is plus is plus is plus is plus is
+
+282
+00:31:47,200 --> 00:31:50,760
+plus is plus
+
+283
+00:31:50,760 --> 00:31:58,930
+is plus is plusيبقى بس بايلة علينا لو نثبت أن الـ
+
+284
+00:31:58,930 --> 00:32:05,270
+direct sum بينه زي وزي مدهوله إيه لفتنا إنها فيه
+
+285
+00:32:05,270 --> 00:32:10,710
+اللي بيكون خلصنا فالسؤال هو أكم عنصر في ال direct
+
+286
+00:32:10,710 --> 00:32:22,250
+sum تبع زي plus زي مدهوله إيه؟ أكم عنصر؟ كده؟ مدني
+
+287
+00:32:22,250 --> 00:32:29,680
+هذا العناصر؟لا؟ علمية مثلا؟ بقى حسب ايه؟ قداش
+
+288
+00:32:29,680 --> 00:32:33,920
+متجدر يعني قيمة ايه؟ قيمة ايه؟ اه وين قيمة ايه؟
+
+289
+00:32:33,920 --> 00:32:39,860
+ايه ال R & D؟ ايه ال R & D؟ فى عناصر كتير ثلاثة
+
+290
+00:32:39,860 --> 00:32:44,860
+ثلاثة عناصر؟ لأ، عدد العناصر زد، زد ايه؟ عدد عناصر
+
+291
+00:32:44,860 --> 00:32:49,980
+زد؟ زد فيها ملنهاد من العناصر يعني ممكن يكون فيها
+
+292
+00:32:49,980 --> 00:32:51,780
+ملنهاد من العناصر؟
+
+293
+00:32:58,770 --> 00:33:07,170
+أنا أزعم أنه لا يوجد ثلاثة تعارفين عشان وجود
+
+294
+00:33:07,170 --> 00:33:13,970
+الثلاثة مهاجورة، قبل نهيئة الثلاثة بتلعب؟ صحيح؟
+
+295
+00:33:13,970 --> 00:33:18,650
+وليش؟ ثلاثة؟ وليش؟ كمان، مش يا ثلاثة أي أخ قطر
+
+296
+00:33:18,650 --> 00:33:19,730
+يبقى هناك، لأ
+
+297
+00:33:27,330 --> 00:33:39,630
+يبقى F وE شادة إذا قدرنا نظبر إنه دائرة صغيرة ما
+
+298
+00:33:39,630 --> 00:33:43,610
+بين الـ Z و الـ Z موديولة A
+
+299
+00:33:52,850 --> 00:34:01,190
+We have a prison يعني
+
+300
+00:34:01,190 --> 00:34:05,530
+بالاسم هذه فيه نجيبه و نقول ايه is maximum و نقول
+
+301
+00:34:05,530 --> 00:34:15,070
+فلسطين I am الهدف الباريكي الصاممي بين الذنب و
+
+302
+00:34:15,070 --> 00:34:18,550
+الذنب مُتي قُدر فيه الازر
+
+303
+00:34:33,700 --> 00:34:42,420
+بس تلاتة انصار؟ اه بس التلاتة هذول؟ اه بس التلاتة
+
+304
+00:34:42,420 --> 00:34:47,960
+هذول، مش لذا طيب واحد هذول قبخل لكل انصار وشوفوا
+
+305
+00:34:47,960 --> 00:34:52,740
+من التلاتة هذول ولايلا هاتيلي عمصر جاله على بانه و
+
+306
+00:34:52,740 --> 00:34:56,800
+القره و خنيه كبيرة شوية مش يعني اتنين او اتنين
+
+307
+00:34:56,800 --> 00:34:59,140
+اتنين خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+308
+00:34:59,140 --> 00:35:00,280
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+309
+00:35:00,280 --> 00:35:02,580
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+310
+00:35:02,580 --> 00:35:02,860
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+311
+00:35:02,860 --> 00:35:02,860
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+312
+00:35:02,860 --> 00:35:15,900
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+313
+00:35:15,900 --> 00:35:18,000
+خل
+
+314
+00:35:21,050 --> 00:35:25,430
+كيف؟ يبقى الـ God ما يطرحش، يبقى واحد وصفر كما
+
+315
+00:35:25,430 --> 00:35:32,670
+تقول، زي ما جالس، لأن لو
+
+316
+00:35:32,670 --> 00:35:36,910
+أخدنا خمسة وعشرين وانت، أن أحدث واحد ثالث وواحد
+
+317
+00:35:36,910 --> 00:35:45,020
+ثالث، تمام؟ هذا الكلام زي الـ 2007بادر أبوتي واحد
+
+318
+00:35:45,020 --> 00:35:53,400
+وزير زائد اربعة وعشرين واتنين زائد الاية هذا
+
+319
+00:35:53,400 --> 00:36:01,180
+الكلام يساوي واحد وزير زائد اربعة وعشرين تلاتة في
+
+320
+00:36:01,180 --> 00:36:06,820
+تمانية واتنين زائد الايةهذا موجود في ايه ولا لا؟
+
+321
+00:36:06,820 --> 00:36:10,120
+اه موجود في ايه، صح؟ اه، اه، اه، اه، اه، اه، اه،
+
+322
+00:36:10,120 --> 00:36:14,160
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+323
+00:36:14,160 --> 00:36:15,180
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+324
+00:36:15,180 --> 00:36:16,680
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+325
+00:36:16,680 --> 00:36:20,780
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+326
+00:36:20,780 --> 00:36:32,860
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+327
+00:36:32,860 --> 00:36:42,810
+اعشرين واربع عشرين واربع عشرين واربع زائد الان
+
+328
+00:36:42,810 --> 00:36:51,650
+العشرين بقدر اكسبها اتنين وزيرو زائد تمانبعشر
+
+329
+00:36:51,650 --> 00:36:58,170
+واربع زائد الان تمام؟
+
+330
+00:36:58,170 --> 00:37:00,150
+هللي بردودة دي ولا ده؟
+
+331
+00:37:03,140 --> 00:37:12,300
+يبقى هنا اتنين وزيرو زائد ثلاثة في ستة وأربعة زائد
+
+332
+00:37:12,300 --> 00:37:18,000
+الـA هذه الموجودة في الـA يبقى اتنين وزيرو زائد
+
+333
+00:37:18,000 --> 00:37:18,660
+الـA
+
+334
+00:37:23,530 --> 00:37:28,270
+الحين لو جبت مضاعفات، الرقم الأول مضاعفات التلاتة،
+
+335
+00:37:28,270 --> 00:37:35,510
+بيطلع الـ00، بيطلع الـ100، بيطلع الـ100، بيطلع
+
+336
+00:37:35,510 --> 00:37:35,510
+الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع الـ100،
+
+337
+00:37:35,510 --> 00:37:35,550
+بيطلع الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع
+
+338
+00:37:35,550 --> 00:37:35,650
+الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع الـ100،
+
+339
+00:37:35,650 --> 00:37:36,350
+بيطلع الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع
+
+340
+00:37:36,350 --> 00:37:44,550
+الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع الـ100،
+
+341
+00:37:44,550 --> 00:37:50,050
+بيطلع
+
+342
+00:37:50,050 --> 00:37:52,610
+الـ
+
+343
+00:37:53,630 --> 00:37:58,050
+أه و البقى كله روتينيا، فهذا شغال روتيني، هذا صورة
+
+344
+00:37:58,050 --> 00:38:01,850
+واحدة في تجابتك، تبقى الإفرار هذا، و كله قدامي في
+
+345
+00:38:01,850 --> 00:38:09,050
+طريقين، يا جيبي ايديل ثاني، يا اما على النظرية،
+
+346
+00:38:09,050 --> 00:38:13,770
+فإذا بتقدر يبقى أنا ممتن وانشغل، كنت يبقى أضافتي
+
+347
+00:38:13,770 --> 00:38:18,630
+للمعلومات اللي كمان معلومة، فيبقى أنا بفكر
+
+348
+00:38:18,630 --> 00:38:23,590
+بالطريقة اللي هي اسم ناسبني،وكل واحد فكر في الأول
+
+349
+00:38:23,590 --> 00:38:28,090
+ممكن احنا اتنين نقصد والتفكير ممكن نقصد النتيجة
+
+350
+00:38:28,090 --> 00:38:31,970
+يعني ليس صعب نروح ندور على عيون تاريو ونقول هذا
+
+351
+00:38:31,970 --> 00:38:37,050
+صرصت منه وهذا صرصت منها ونثبت أن هذا كذا إلى آخرية
+
+352
+00:38:37,050 --> 00:38:43,750
+طيب على أي حال صار عندنا Factoring جديدة وهذا ليس
+
+353
+00:38:43,750 --> 00:38:51,690
+بالجديدة لأن مضوانا كان Ideals and Factoring تمام؟
+
+354
+00:38:51,790 --> 00:38:58,190
+هل هدفي الـshattering
+
+355
+00:38:58,190 --> 00:39:02,610
+فيها ال unity؟
+
+356
+00:39:02,610 --> 00:39:10,190
+واحد وزيره زي ده هو ال unity قضوه فيه هدفي هذا
+
+357
+00:39:10,190 --> 00:39:16,470
+الحاجة ده وزيره زي ده ده لما ملهمي ان هو يشمل نفس
+
+358
+00:39:16,470 --> 00:39:26,430
+الشيء يبقى هدفي هو ال unityيرجع هذه هما هذه كلمة
+
+359
+00:39:26,430 --> 00:39:39,570
+فاكتور رينج فاكتور رينج وال unity اللي هو واحد و
+
+360
+00:39:39,570 --> 00:39:44,810
+zero ذات ال two السؤال،
+
+361
+00:39:44,810 --> 00:39:52,270
+هل هذه field؟يعني هل every non-zero element is a
+
+362
+00:39:52,270 --> 00:39:59,010
+unit؟ هذا unity يبقى unit، بل هذا، لو ضربته في
+
+363
+00:39:59,010 --> 00:40:06,910
+هذا، يبقى unity؟ طبعا لا، طب لو ضربته في نفسه؟
+
+364
+00:40:06,910 --> 00:40:12,910
+طبعا ال unity هو ال unity، يبقى صح unity ولا لا؟
+
+365
+00:40:12,910 --> 00:40:20,910
+يبقى هنا، ماروح بامرناالواحد وزيره زائد ال a is a
+
+366
+00:40:20,910 --> 00:40:32,030
+unit and الإتنين وزيره زائد ال a is unit السبب
+
+367
+00:40:32,030 --> 00:40:35,950
+because إنه
+
+368
+00:40:35,950 --> 00:40:44,270
+الإتنين وزيره زائد ال a لو طردتوا إتنين وزيره زائد
+
+369
+00:40:44,270 --> 00:40:51,200
+ال a بتشيربساوي اتنين وزيرا اتنين وزيرا زائد ال a
+
+370
+00:40:51,200 --> 00:40:59,180
+يعني اربعة وزيرا زائد ال a يعني واحد وزيرا زائد
+
+371
+00:40:59,180 --> 00:41:05,400
+تلاتة وزيرا زائد ال a هذا موجود في ال a يبقى بيبقى
+
+372
+00:41:05,400 --> 00:41:12,320
+بيساوي واحد وزيرا زائد ال L و ال unity مظلوم؟ يبقى
+
+373
+00:41:12,320 --> 00:41:19,600
+صح هذا is a unitطيب مادة unit يبقى every non zero
+
+374
+00:41:19,600 --> 00:41:28,260
+is a unit تبقى صرفيت ولا لأ طيب شاهد تيب every non
+
+375
+00:41:28,260 --> 00:41:44,200
+zero is a unit
+
+376
+00:42:05,700 --> 00:42:11,080
+طيب يبقى صار هذا هو عبارة عن maximal ideal هذا
+
+377
+00:42:11,080 --> 00:42:16,510
+المقبول الأول من السؤالقال لي بيجيلي إن هذا
+
+378
+00:42:16,510 --> 00:42:23,090
+maximum و بعدين كني generalized لذالي لملة التلاتة
+
+379
+00:42:23,090 --> 00:42:29,890
+يا بنات prime ولا لا؟ أو لو سبدلته بخمسة أو لو
+
+380
+00:42:29,890 --> 00:42:36,410
+سبدلته باتنين أو لو سبدلته بسبعة، احداشر، تلتاشر،
+
+381
+00:42:36,410 --> 00:42:42,790
+سبعتاشر كله كانت الكلام صحيح و هذا maximum يبقى
+
+382
+00:42:43,990 --> 00:42:58,330
+the ideal اللي هو A بدرساه P X وY such that X وY
+
+383
+00:42:58,330 --> 00:43:13,330
+موجودة في ذلك I ال P is prime is maximum طيب
+
+384
+00:43:13,770 --> 00:43:17,310
+نمر الـ C طب ليش بقى يا أستاذ باقي الأرقام مقتنعة؟
+
+385
+00:43:17,310 --> 00:43:24,050
+باقي الأرقام؟ أنا جايك لباقي الأرقام، أطلعت، فخلص،
+
+386
+00:43:24,050 --> 00:43:30,370
+مخلصش، قال لي هنا عامة، بقوله لو كان الرقم بدل ما
+
+387
+00:43:30,370 --> 00:43:34,370
+هو التلاتة، أي track ideal، بيكون ال ideal
+
+388
+00:43:34,370 --> 00:43:39,790
+maximum، طب لو جينا لأرقام، نمر ال Cقال إيش بيحصل
+
+389
+00:43:39,790 --> 00:43:46,170
+لو شيلت التلاتة X وحطيت مكانها أربعة X بقوله بسيطة
+
+390
+00:43:46,170 --> 00:43:54,730
+بدي أخد ال A تساوي كل الأربعة X وY بحيث ال X وY
+
+391
+00:43:54,730 --> 00:44:03,070
+موجودة في Z قال هذا maximum ideal هذا ideal في
+
+392
+00:44:03,070 --> 00:44:14,920
+الأول يبقى هذا isID غير هيك ال ring commutative
+
+393
+00:44:14,920 --> 00:44:24,640
+with unity أخذناها من الأول و ال Z بس Z is
+
+394
+00:44:24,640 --> 00:44:29,900
+commutative with
+
+395
+00:44:29,900 --> 00:44:32,120
+unity
+
+396
+00:44:36,880 --> 00:44:43,760
+الأن نشوف هل هي field و لا ماهياش field أنا أزعم
+
+397
+00:44:43,760 --> 00:44:55,840
+أن زر دارف صمم مع زر موديول A هي الـ A و مين؟ واحد
+
+398
+00:44:55,840 --> 00:45:08,600
+و Zero زائد الـ A نين و Zero زائد الـ Aزائد MA
+
+399
+00:45:08,600 --> 00:45:19,100
+ثلاثة و Zero زائد A فلو بدلنا ثلاثة X باربع X بصير
+
+400
+00:45:19,100 --> 00:45:24,820
+بدل ما كان فيها هنا تلات عناصر بس بصير عندى جداش
+
+401
+00:45:24,820 --> 00:45:30,940
+اربع اذا لو بدلتها بخمسة خمسة ستة ستة عناصر و هكذا
+
+402
+00:45:30,940 --> 00:45:36,060
+كل ما تغير رقمبيزداد عدد العناصر في الـ factor،
+
+403
+00:45:36,060 --> 00:45:40,440
+الـ group، الـ unit. طيب، هدول ثلاثة، السؤال هو،
+
+404
+00:45:40,440 --> 00:45:44,780
+هل هذا field؟
+
+405
+00:45:44,780 --> 00:45:51,340
+في ال field، كل عنصر غير الصفر يبقى unit، هذا
+
+406
+00:45:51,340 --> 00:45:57,500
+unit، وهذا unit، لأن تلاتة بتلاتة، تسعة، اثنين،
+
+407
+00:45:57,500 --> 00:46:01,820
+اربعتين، بضلين ال unit اللي بيبقى unit، هل هذا
+
+408
+00:46:01,820 --> 00:46:08,280
+unit؟لأن هذا الـ Potent Element لو ضربته في نفسه
+
+409
+00:46:08,280 --> 00:46:29,720
+بتظهر الـ Zero و Zero تمام؟ إذن باجي بقوله باجي
+
+410
+00:46:29,720 --> 00:46:39,050
+بقوله الآن اتنينوزيره زائد ال a في اتنين وزيره
+
+411
+00:46:39,050 --> 00:46:47,470
+زائد ال a يساوي اربعة وزيره زائد ال a اللي هو قد
+
+412
+00:46:47,470 --> 00:46:54,610
+يساوي ال a itself يبقى هنا ساعة اتنين وزيره زائد
+
+413
+00:46:54,610 --> 00:47:09,430
+ال a is a من الportent من الportentEleven المفروض
+
+414
+00:47:09,430 --> 00:47:19,070
+ليش؟ لأنه مربع أعطاني Zero But Not Unit يبقى قدرت
+
+415
+00:47:19,070 --> 00:47:26,150
+أجيب عنصر واحد مالوش معكوس يبقى هل هذا فيه؟ يبقى
+
+416
+00:47:26,150 --> 00:47:32,940
+هنا هذا بدي يعطينا أن ال direct sum ما عزيزيموديول
+
+417
+00:47:32,940 --> 00:47:43,100
+A is not A فيه هذا بيعطينا ان ال A is not maximum
+
+418
+00:47:43,100 --> 00:47:46,660
+طيب
+
+419
+00:47:46,660 --> 00:47:52,780
+الآن اخر حاجة اللي امر دي بقولي عن مم يبقى باجي
+
+420
+00:47:52,780 --> 00:48:05,090
+بقوله الان ال A بتساوي N X و Ysuch that ال X و ال
+
+421
+00:48:05,090 --> 00:48:14,590
+Y موجودة في Z and ال N هذه not a prime يبقى and ال
+
+422
+00:48:14,590 --> 00:48:30,310
+M is not a prime is not maximum طبعا
+
+423
+00:48:30,310 --> 00:48:40,200
+مثالشكله بسيط كإثبات إنه أرضيل ولكن .. ولكن بده
+
+424
+00:48:40,200 --> 00:48:46,240
+شغل كتير طبعا المرة القادمة إن شاء الله سناخد حل
+
+425
+00:48:46,240 --> 00:48:50,640
+بقية الأسلة مش هنخش في الشكرة اللي بعد إلا لما
+
+426
+00:48:50,640 --> 00:48:53,300
+نخلص هذا إن شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/N-D4GQAtXSk_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/N-D4GQAtXSk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ce665c5cda1724d906022fb42ed9b5f9f8280e23
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/N-D4GQAtXSk_raw.srt
@@ -0,0 +1,1736 @@
+1
+00:00:20,990 --> 00:00:24,710
+بسم الله الرحمن الرحيم اليوم ان شاء الله هنقش في
+
+2
+00:00:24,710 --> 00:00:27,790
+ال chapter الثاني اللي هو ال integral domains بس
+
+3
+00:00:27,790 --> 00:00:32,210
+بقى من المرة الماضية ثلاثة أسئلة بدنا نشيل اليها
+
+4
+00:00:32,210 --> 00:00:37,350
+أو بدنا نعطي الحل تبعها ثم نبدأ في ال chapter
+
+5
+00:00:37,350 --> 00:00:41,390
+الجديد اللي هو chapter 13 ال integral domains
+
+6
+00:00:41,390 --> 00:00:46,610
+وصلنا إلى سؤال واحد واربعين بيقول Pro or Deci Pro
+
+7
+00:00:47,180 --> 00:00:53,820
+الـ 6R التي تساوي كل المص و فات لنظام 2X2 و اللي
+
+8
+00:00:53,820 --> 00:00:58,420
+على الشكل اللي قدامنا هذا الـ A و الـ B و العنصر
+
+9
+00:00:58,420 --> 00:01:04,800
+هذا هو نفس العنصر هذا و هو الفرق بين هذين العنصرين
+
+10
+00:01:04,800 --> 00:01:17,250
+يبقى A A-B A-B نفس العنصر B بحيث الـ A و Bهل هو
+
+11
+00:01:17,250 --> 00:01:21,110
+subring من
+
+12
+00:01:21,110 --> 00:01:29,090
+الارنج ال M2 of Z M2 of Z هي عبارة عن مجموعة كل
+
+13
+00:01:29,090 --> 00:01:35,310
+المصحفات اللي الارقام
+
+14
+00:01:35,310 --> 00:01:41,420
+تبعها تبقى أعداد صحيحةيبقى نشوف prove or
+
+15
+00:01:41,420 --> 00:01:45,980
+disapprove يعني شوف حالك انك تقدر تبره انها sub
+
+16
+00:01:45,980 --> 00:01:51,060
+ring ولا لأ ان كدرت تبره ان كان بيها ماكانش يبقى
+
+17
+00:01:51,060 --> 00:01:57,460
+ممكن تكون ماهياش sub ring اذا احنا هنبتدي نشوف هل
+
+18
+00:01:57,460 --> 00:02:03,240
+ثلاثة شروط تبعات ال sub ring بنقدر نطبقهم على هذه
+
+19
+00:02:03,240 --> 00:02:09,370
+السيطرة ولا لأ لو جد يا بنات قلنا النقطة الأولىبدي
+
+20
+00:02:09,370 --> 00:02:15,450
+اثبت ان الـ a هدق is non-empty حطلي شروط على a و b
+
+21
+00:02:15,450 --> 00:02:20,690
+غير انهم انتجار لا لإذا ممكن يكونوا وصفاء بحو ولا
+
+22
+00:02:20,690 --> 00:02:27,730
+لا لإذا بدي بقول if ال a تساوي ال b تساوي ال 0
+
+23
+00:02:27,730 --> 00:02:37,220
+then الآن ال element 0 0 ناقص 0 0 ناقص 0 و 0اللي
+
+24
+00:02:37,220 --> 00:02:44,340
+هو عبارة عن Zero Zero Zero إذا موجود في R هذا بيجي
+
+25
+00:02:44,340 --> 00:02:53,960
+يقينا ان ال R is non-empty يبقى تحقق الشرط الأول
+
+26
+00:02:53,960 --> 00:03:01,700
+من شروط الصبرين بتروح للشرط التالف بتاخد عنصرين
+
+27
+00:03:01,700 --> 00:03:07,830
+مختلفين و أثبت أن الفرق فيما بينهماموجود هنا ان
+
+28
+00:03:07,830 --> 00:03:12,530
+قدرت فدوري على الشرطة التالت ماقدرت بكون كف الله
+
+29
+00:03:12,530 --> 00:03:18,290
+المؤمنين و قتال يبقى انا لو جيت قلت ذيت ال a و ال
+
+30
+00:03:18,290 --> 00:03:24,950
+b مصفوفتين موجودات في ال set R اللي عندنا يبقى
+
+31
+00:03:24,950 --> 00:03:34,740
+then المصفوفة a بدها تساوي a a ناقص ال bA ناقص ال
+
+32
+00:03:34,740 --> 00:03:44,720
+B وB والمصفوفة B بدي يكون C وهنا D وهنا C ناقص D
+
+33
+00:03:44,720 --> 00:03:52,220
+وهنا C ناقص D بالشكل اللي عندها بدي أجى أطرح ال A
+
+34
+00:03:52,220 --> 00:03:57,480
+ناقص ال B انطلع مصفوفة على الشكل اللي عندها ده
+
+35
+00:03:57,480 --> 00:04:03,370
+بيكون الفرق فيما بينهما موجوديبقى هذا الكلام بده
+
+36
+00:04:03,370 --> 00:04:11,630
+يساعد فطرحه بنطرح كل عنصر مع نظيره يبقى هنا A ناقص
+
+37
+00:04:11,630 --> 00:04:21,250
+ال C هنا ال A ناقص ال B ناقص ال C زائد ال D هنا ال
+
+38
+00:04:21,250 --> 00:04:32,990
+A ناقص ال B ناقص ال C زائد ال Dهنا ال B ناقص ال D
+
+39
+00:04:32,990 --> 00:04:40,290
+طيب هي عنصرين مختلفين وهي هذا الفرق ما بين العنصر
+
+40
+00:04:40,290 --> 00:04:47,250
+هذا لإنه A ناقص C هي ال A ناقص ال C وB ناقص D يعني
+
+41
+00:04:47,250 --> 00:04:53,710
+بقدر أكتب هذه على الشكل التالي اللي هو ال A ناقص
+
+42
+00:04:53,710 --> 00:05:01,190
+ال Cو هذه ال a ناقص ال c كلها مع بعض ضال ال b و ال
+
+43
+00:05:01,190 --> 00:05:09,710
+d بقدر اخد ناقص عامل مشترك ل b ناقص ال d هنا بنفس
+
+44
+00:05:09,710 --> 00:05:19,510
+الطريقة a ناقص ال c ناقص ال b ناقص ال d تمام؟ و
+
+45
+00:05:19,510 --> 00:05:27,670
+هذه ال b ناقص ال dبالشكل اللي انا طلعه، هاي عنصر،
+
+46
+00:05:27,670 --> 00:05:32,750
+هاي عنصر مختلف، هذا هو الفرق فيما بينهما، وهذا هو
+
+47
+00:05:32,750 --> 00:05:36,950
+الفرق فيما بينهما، إذا الشكل هذا على الشكل اللي
+
+48
+00:05:36,950 --> 00:05:42,610
+فوق، يبقى هذه موجودة وين؟ موجودة في الست أعلى اللي
+
+49
+00:05:42,610 --> 00:05:47,450
+عنده، إذا انت حقق ال condition التاني، بتروح لمين؟
+
+50
+00:05:47,450 --> 00:05:52,250
+لل condition التالت، ال condition التالت والأخر
+
+51
+00:05:52,250 --> 00:05:59,440
+إذا طلعحاصل ضرب ال two matrices ال A في ال B على
+
+52
+00:05:59,440 --> 00:06:03,580
+الشكل اللي عندنا هذا بنقوله خلاص ما كده وبالتالي
+
+53
+00:06:03,580 --> 00:06:09,280
+بصير sub ring ال condition هذا لم يتحقق بقوله يبقى
+
+54
+00:06:09,280 --> 00:06:15,940
+ال R ماهياش sub ring يبقى بده أروح أخد ال A في ال
+
+55
+00:06:15,940 --> 00:06:21,700
+B يبقى المصروف اللي عندنا A يناقص ال B
+
+56
+00:06:41,530 --> 00:06:48,110
+الصف الأول في العمود الأول ونجمع بيعطينا العنصر
+
+57
+00:06:48,110 --> 00:06:55,810
+الأول من مصفوفة حاصل الضغطيبقى باجي بقول A في C A
+
+58
+00:06:55,810 --> 00:07:04,470
+في C هذول بتغربهم في بعض زائد A ناقص ال B فاهمين
+
+59
+00:07:04,470 --> 00:07:11,470
+ال A ناقص ال B في ال C ناقص ال D هايضربنا كل عنصر
+
+60
+00:07:11,470 --> 00:07:18,310
+معناظه وجامعنا اعطاني مين؟ العنصر الأول نيجي الصف
+
+61
+00:07:18,310 --> 00:07:28,060
+الأول في العمود الثانييبقى A في C ناقص ال D زائد
+
+62
+00:07:28,060 --> 00:07:36,280
+اللي هو ال A ناقص ال B تمين في ال D شكل عنانا
+
+63
+00:07:36,280 --> 00:07:42,420
+خلصنا الصف الأول نروح للصف الثاني يبقى الصف الثاني
+
+64
+00:07:42,420 --> 00:07:49,500
+في العمود الأول يبقى ال C أو خليها مرتبة زي ما هي
+
+65
+00:07:50,070 --> 00:07:58,610
+الـ A ناقص الـ B كلها في C آه answer في نظيره B
+
+66
+00:07:58,610 --> 00:08:07,210
+يبقى زائد B في C ناقص الـ D أي خلصنا الصف الأول في
+
+67
+00:08:07,210 --> 00:08:10,690
+العمود الأول بدنا نجي الصف الثاني في العمود الأول
+
+68
+00:08:10,690 --> 00:08:18,230
+نجي الصف الثاني في العمود الأول يبقى A ناقص الـ B
+
+69
+00:08:18,230 --> 00:08:29,700
+في الـ Cناقص ال D وبعده زائد BD يبقى زائد BD بيحنا
+
+70
+00:08:29,700 --> 00:08:35,480
+نشوف شكل المصطفى هذا وين وصلنا يبقى هذا الكلام
+
+71
+00:08:35,480 --> 00:08:44,020
+يبدو يساوي ال A C وهنا زائد A C يبقى بصير قداش
+
+72
+00:08:44,020 --> 00:08:51,130
+عندي نين A C مرة تانية هذه A Cبدي اضرب A في C
+
+73
+00:08:51,130 --> 00:09:01,890
+بتطلعي AC وعقدي AC بتنقل AC ناقص AD يفجأ ناقص AD
+
+74
+00:09:01,890 --> 00:09:11,890
+ناقص BC زائد BD هيخلصنا العمصر اللي عندنا هنا نيجي
+
+75
+00:09:11,890 --> 00:09:26,400
+لهذا AC زي ما هو يفجأ هذا ACناقص AD ناقص AD زائد
+
+76
+00:09:26,400 --> 00:09:35,560
+AD وناقص AD مع السلامة طبعا هاي مرة تانية هاي ناقص
+
+77
+00:09:35,560 --> 00:09:44,220
+AD وعندك هنا زائد AD مع السلامة بيظهر ان هي ناقص
+
+78
+00:09:44,220 --> 00:09:52,670
+BD ناقصBD طيب
+
+79
+00:09:52,670 --> 00:10:00,710
+هنا ممكن يصير اختصارات المهم طيب هذه AC ناقص BD
+
+80
+00:10:00,710 --> 00:10:11,030
+خلصناها نجي لهذه هذه اللي هو AC يبقى هذه AC تمام؟
+
+81
+00:10:11,030 --> 00:10:21,220
+هذه A في Cناقص BC وزائد BC وروحوا مع السلامة ويبقى
+
+82
+00:10:21,220 --> 00:10:30,640
+ناقص BD يبقى ناقص BD ندى لهذا العنصر هذا العنصر
+
+83
+00:10:30,640 --> 00:10:45,460
+بصير عندنا A في C ناقص AD ناقص BCزائد BD وزائد BD
+
+84
+00:10:45,460 --> 00:10:54,500
+زائد اتنين BD وهي خلصنا.طيب هل هذه يعني الشكل اللي
+
+85
+00:10:54,500 --> 00:10:59,220
+فوق ولا لأ؟ بنقول الله هو أعلى.طلعيني ال element
+
+86
+00:10:59,220 --> 00:11:04,900
+هذا هو ال element هذا بالضبط؟طيب تمام يبقى صار
+
+87
+00:11:04,900 --> 00:11:12,360
+العنصر هذا هو العنصر هذا.الان طب خليني اجربالاتنين
+
+88
+00:11:12,360 --> 00:11:18,960
+هدول لو طرحتهم من بعض طلع هذا يكون مية لمية مرة
+
+89
+00:11:18,960 --> 00:11:24,940
+تانية العنصر هذا هو العنصر هذا لو طرحت هذول من بعض
+
+90
+00:11:24,940 --> 00:11:30,600
+بده يطلع مين اللي هو العنصر هذا ليه؟ هاي و هذول
+
+91
+00:11:30,600 --> 00:11:34,660
+طرحيهم من بعض بده يطلع .. الآن طلعوا اتنين هذول من
+
+92
+00:11:34,660 --> 00:11:39,580
+بعض زي بعض بالضبط إذا بدي أطرح حد ناقص هذا بده
+
+93
+00:11:39,580 --> 00:11:44,470
+يعطينيإنها تجي لأنك تعالى في الها مش هيك نطرحهم من
+
+94
+00:11:44,470 --> 00:11:51,110
+بعض يبقى لو جيت في الها مش هيك قولت هذا ما يعني
+
+95
+00:11:51,110 --> 00:12:05,270
+هاي اتنين A C اتنين A C ناقص A D وناقص B C وزائد B
+
+96
+00:12:05,270 --> 00:12:12,760
+Dو هدول بدي اكتبهم بإشارة ناقص لإن ايه ناقص ال b
+
+97
+00:12:12,760 --> 00:12:21,240
+يبقى هد بالناقص تصير ناقص a c هد بيصير زائد a d
+
+98
+00:12:21,240 --> 00:12:31,820
+وهد زائد b c وهد ناقص اتنين b d اظن هد مع بعض بضل
+
+99
+00:12:31,820 --> 00:12:40,390
+جداش a c وهدوهذه مع السلامة بظل ناقص PD وال
+
+100
+00:12:40,390 --> 00:12:48,090
+element هذا يبقى على طول الخط بس تنتج ان هذا ال A
+
+101
+00:12:48,090 --> 00:12:55,390
+في B موجود وين؟ موجود في ال R من هنا تحققت الشروط
+
+102
+00:12:55,390 --> 00:13:03,210
+التلاتة يبقى ال R is a صفرين هذا بدي يقين ان ال R
+
+103
+00:13:03,720 --> 00:13:16,660
+is a sub ring of
+
+104
+00:13:16,660 --> 00:13:21,000
+M2Z
+
+105
+00:13:21,000 --> 00:13:24,500
+هذا
+
+106
+00:13:24,500 --> 00:13:29,640
+كان طبعا في عندك كمان سؤالين زي رسول اربعين و رسول
+
+107
+00:13:29,640 --> 00:13:34,510
+اتنين و اربعين بنفس الفكرةسؤال اربعين بدل الناقص
+
+108
+00:13:34,510 --> 00:13:40,530
+الزائد هذا الناقص لاربع أناصر منفصلة عن بعض.طيب
+
+109
+00:13:40,530 --> 00:13:49,150
+نجي لسؤال ستة واربعين يبقى هنا شوف بيليلي ان اتنين
+
+110
+00:13:49,150 --> 00:13:58,790
+زد اتحاد تلاتة زد is not a sovereign
+
+111
+00:14:02,210 --> 00:14:11,970
+is not subring of z.مشان
+
+112
+00:14:11,970 --> 00:14:15,550
+أثبت ال subring يقول لنا بناروح نثبت الشروط
+
+113
+00:14:15,550 --> 00:14:20,490
+التلاتة أول شي اتنين z non-empty وتلاتة z non
+
+114
+00:14:20,490 --> 00:14:24,790
+-empty يبقى اليوم انتباههم non-empty.حطيه على شجرة
+
+115
+00:14:24,790 --> 00:14:31,430
+وقال لي أثبت ان هذا ماهياش subring.إذا هذا متحقق
+
+116
+00:14:31,430 --> 00:14:39,050
+.تنينتعالى نجرب الطرح طب السؤال هل اتنين موجودة في
+
+117
+00:14:39,050 --> 00:14:43,030
+ال subset اللى عندها هذى؟ في ال union طب و التلاتة
+
+118
+00:14:43,030 --> 00:14:49,370
+موجودة تمام يعني لو احنا كتبنا اتنين زد و كتبنا
+
+119
+00:14:49,370 --> 00:14:53,450
+تلاتة زد و جبنا ال union بيكون عناصر ال union هي
+
+120
+00:14:53,450 --> 00:14:58,490
+عناصر اتنين زد و كذلك عناصر التلاتة زد يبقى باجي
+
+121
+00:14:58,490 --> 00:15:06,250
+بقوله ان الحال كتالةاحنا عندنا اللي هو الاتنين
+
+122
+00:15:06,250 --> 00:15:16,550
+وثلاثة موجودة في الاتنين زد اتحاد تلاتة زد تمام؟
+
+123
+00:15:16,550 --> 00:15:23,270
+بطء ولكن لو جيت تقول تلاتة ناقص اتنين الفرق بين
+
+124
+00:15:23,270 --> 00:15:32,380
+هذين العمصرين هل الواحد موجود هنا؟ لأيبقى الواحد
+
+125
+00:15:32,380 --> 00:15:40,040
+does not belong لإتنين Z اتحاد تلاتة Z معناه ان ال
+
+126
+00:15:40,040 --> 00:15:44,740
+condition التاني من ال subgroup is not satisfied
+
+127
+00:15:44,740 --> 00:15:55,720
+يبقى هنا Sir إتنين Z union تلاتة Z is not a
+
+128
+00:15:55,720 --> 00:15:59,920
+subring of Z
+
+129
+00:16:03,020 --> 00:16:08,980
+طيب سؤال خمسين سؤال
+
+130
+00:16:08,980 --> 00:16:15,640
+خمسين الحقيقة مشهور في كل كتب الجبر أي كتاب جبر
+
+131
+00:16:15,640 --> 00:16:20,280
+دورك في الهامش اللي في الآخر في ال index علي كلمة
+
+132
+00:16:20,280 --> 00:16:24,900
+Boolean ring بقولك موجودة وين في الصفحة الفولانية
+
+133
+00:16:24,900 --> 00:16:30,840
+لذلك ال a is
+
+134
+00:16:34,830 --> 00:16:41,870
+الـ A تربيع الـ A لكل الـ A الموجودة في R
+
+135
+00:16:41,870 --> 00:16:49,590
+بلاستيكتنات الـ ring اللي في هذه الخاصية بسميها
+
+136
+00:16:49,590 --> 00:16:56,170
+bullion ring نسبة الاكتشافة يفجأها باسمها بنات
+
+137
+00:16:56,170 --> 00:16:59,070
+bullion ring
+
+138
+00:17:01,580 --> 00:17:07,000
+السؤال بيقوللي show .. طبعا هذه لكل اللي موجودة في
+
+139
+00:17:07,000 --> 00:17:17,160
+الأرض بيقوللي show that any Boolean ring
+
+140
+00:17:17,160 --> 00:17:21,860
+is commutative
+
+141
+00:17:35,380 --> 00:17:41,520
+يبقى انا في عندى ring ال ring فيها خاصية انه مربع
+
+142
+00:17:41,520 --> 00:17:47,820
+اي عنصر فيها بيعطيني مين نفس العنصر تمام بقول كويس
+
+143
+00:17:47,820 --> 00:17:53,640
+ان حدث ذلك هذا ال ring بسميها Boolean ring السؤال
+
+144
+00:17:53,640 --> 00:17:59,540
+بيقول اثبت ان اي Boolean ring is commutative يعني
+
+145
+00:17:59,540 --> 00:18:04,980
+لو أخدت عنصرين فيها a و bبدي اثبت ان ال A في B بدي
+
+146
+00:18:04,980 --> 00:18:10,160
+ساوي B في A لكل ال A و ال B اللي موجودة فى ال ring
+
+147
+00:18:10,160 --> 00:18:16,080
+A بحكي ان A تنتمي لل R و B تنتمي لل R يعني AB
+
+148
+00:18:16,080 --> 00:18:22,260
+تنتمي لل R AB تربيه تساوي AB اذا قدرت اثبت انه
+
+149
+00:18:22,260 --> 00:18:28,300
+يساوي بي A بيتمي المطول اشتغل شوية احنا بروحنا فى
+
+150
+00:18:28,300 --> 00:18:35,090
+طريقإن عندنا عمص وين موجودة في R يبقى بقى بقوله if
+
+151
+00:18:35,090 --> 00:18:42,350
+ال A و ال B belongs to R then ال A تربيع بده يساوي
+
+152
+00:18:42,350 --> 00:18:48,550
+ال A and ال B تربيع بده يساوي بيهك بدنا بداية
+
+153
+00:18:48,550 --> 00:18:57,890
+صحيحة طيب الآن ال A و ال B موجودة في R هل هذا يعني
+
+154
+00:18:58,280 --> 00:19:07,940
+إن ال A زائد ال B موجودة في R، صح؟
+
+155
+00:19:07,940 --> 00:19:14,620
+مش العملية الجمع وعملية الضرب على ال ring A اتنين
+
+156
+00:19:14,620 --> 00:19:20,400
+R، إيش بنسميها؟ binary operation، binary operation
+
+157
+00:19:20,400 --> 00:19:24,960
+يعني إن جمعت، والضرب بدي يكون النتج موجود في R
+
+158
+00:19:24,960 --> 00:19:29,110
+itselfيعني closed under addition and closed under
+
+159
+00:19:29,110 --> 00:19:34,290
+multiplication يبقى إن حدث ذلك بقول يبقى ال A زائد
+
+160
+00:19:34,290 --> 00:19:41,150
+B يبقى ينطبق علميا الخاصية اللي عندنا يبقى هذا
+
+161
+00:19:41,150 --> 00:19:49,110
+معناه ان ال A زائد ال B بدي ساوي ال A زائد ال B
+
+162
+00:19:49,110 --> 00:19:56,720
+لكل تربيع ليش since ان ال Aبتساوي ال a تربيع لكل
+
+163
+00:19:56,720 --> 00:20:03,380
+ال a اللي موجودة فيها يبقى نظرا لأنه مربع العنصر
+
+164
+00:20:03,380 --> 00:20:08,540
+بيعطينا العنصر نفسه فمربع هذا العنصر بيعطينا من؟
+
+165
+00:20:08,540 --> 00:20:14,360
+العنصر نفسه يبقى صار عند مين؟ ال a زي ال b بتفك
+
+166
+00:20:14,360 --> 00:20:23,000
+التربيع هذا يبقى a تربيع زي ال ab زي ال baزائد B
+
+167
+00:20:23,000 --> 00:20:28,360
+تربيع بقولش اتنين AB لإنه أنا ماثبتش انه
+
+168
+00:20:28,360 --> 00:20:31,600
+commutative بعد ما اثبت انه commutative بكبر
+
+169
+00:20:31,600 --> 00:20:38,320
+كلامنا هذا معنو صحيح طيب الان ال A تربيع ايش تزاوي
+
+170
+00:20:38,320 --> 00:20:44,180
+و ال B تربيع اذا بقدر استبدل ال A تربيع و ال B
+
+171
+00:20:44,180 --> 00:20:49,700
+تربيع بال A و ال B يبقى هذا بده يعطيلك انه A زائد
+
+172
+00:20:49,700 --> 00:20:59,180
+ال Bبتساوي ال a زائد ال a b زائد ال b a زائد ال b
+
+173
+00:20:59,180 --> 00:21:07,340
+طب لو أضفت المعكوس الجمعي ل a زائد ال b للطرفين
+
+174
+00:21:07,340 --> 00:21:15,320
+هذا ايش هيعطيكي؟ هيعطيكي ان ال zero تساوي a b زائد
+
+175
+00:21:15,320 --> 00:21:25,270
+b فااو ان شئتم فقولوا ان ال A بيبدو ساوي سالب B في
+
+176
+00:21:25,270 --> 00:21:32,570
+A السؤال اللي بدي اسأله سالب B في A هدى موجود فى
+
+177
+00:21:32,570 --> 00:21:40,310
+ال ring R صح؟ فكت الشعب مظبوط؟ اذا المربع هدى
+
+178
+00:21:40,310 --> 00:21:47,460
+بتكون موجود فى ال ring R صح؟ يبقى هدى بدى ساويسالب
+
+179
+00:21:47,460 --> 00:21:55,460
+بي الكل تربيع مظبوط؟ ليش؟ لأن ال A تربيع يسوي لك
+
+180
+00:21:55,460 --> 00:22:00,320
+كل العناصر اللي موجودة في ال link إذا سالب بي في A
+
+181
+00:22:00,320 --> 00:22:05,800
+هو نفسه سالب بي في A الكل تربيع هذا لو أتبعت
+
+182
+00:22:05,800 --> 00:22:14,010
+وبيعطيني بي الكل تربيع صحيح ولا لا؟طبقا للخاصية
+
+183
+00:22:14,010 --> 00:22:20,650
+اللي عندنا هذا بدي يعطيني مين بي في ايه لأنه مربع
+
+184
+00:22:20,650 --> 00:22:25,290
+اي element بدي يعطيني نفس ال element ايه صار عندنا
+
+185
+00:22:25,290 --> 00:22:32,010
+هنا صار ال a في b بدي ساوي ال b في a هدول ال a و b
+
+186
+00:22:32,010 --> 00:22:38,400
+عناصر محددة ولا اخدتم any elementيبقى ما ينطبق
+
+187
+00:22:38,400 --> 00:22:44,280
+عليهم ينطبق على كل بياطي عناصر ال ring يبقى هذا
+
+188
+00:22:44,280 --> 00:22:50,100
+الكلام صحيح لكل ال A و ال B اللي موجودة في R هذا
+
+189
+00:22:50,100 --> 00:22:58,840
+بدي يعطينا ان R is commutative يبقى من الآن تصعد
+
+190
+00:22:58,840 --> 00:23:05,100
+ال any Boolean ring is commutative او اي ringفيها
+
+191
+00:23:05,100 --> 00:23:10,960
+هذه الخاصية هي حلقات إبداعية
+
+192
+00:23:32,840 --> 00:23:40,260
+هك مكون انهينا ثلاثة مثال الموجودة من الماضي والان
+
+193
+00:23:40,260 --> 00:23:45,120
+بدنا ندخل في الشفتر الجديد اللي هو ال integral
+
+194
+00:23:45,120 --> 00:23:54,820
+domains شفتر 13 يبقى الشفتر 13 ال integral domains
+
+195
+00:23:54,820 --> 00:24:00,860
+هذا
+
+196
+00:24:00,860 --> 00:24:07,000
+الشفترفيه ثلاثة عناصر رئيسة كل شغلنا هيكون يدور
+
+197
+00:24:07,000 --> 00:24:12,460
+حول هذه الثلاثة عناصر الأولى ال integral domain
+
+198
+00:24:12,460 --> 00:24:19,600
+والتانية ال field والتالتة ال characteristic ring
+
+199
+00:24:19,600 --> 00:24:25,820
+هذول الثلاثة هم العمود الفقري لمين لموضوع ال
+
+200
+00:24:25,820 --> 00:24:31,530
+integral domain هنبدأ بتعريف ماخدهوش قبل هيكثم
+
+201
+00:24:31,530 --> 00:24:37,250
+نذهب الى تعريف الـ Integral domain لأن هذا التعريف
+
+202
+00:24:37,250 --> 00:24:49,770
+كان تالي Definition a zero divisor is a
+
+203
+00:24:49,770 --> 00:24:51,270
+non-zero element
+
+204
+00:25:00,810 --> 00:25:08,450
+of a commutative ring A of a commutative
+
+205
+00:25:08,450 --> 00:25:14,650
+ring A
+
+206
+00:25:14,650 --> 00:25:22,830
+such that such
+
+207
+00:25:22,830 --> 00:25:24,870
+that there is
+
+208
+00:25:32,320 --> 00:25:44,040
+such that there is a non-zero element non-zero
+
+209
+00:25:44,040 --> 00:25:55,300
+element B in R with AB بده يساوي مين؟ بده يساوي
+
+210
+00:25:55,300 --> 00:25:55,800
+Zero
+
+211
+00:26:19,090 --> 00:26:22,770
+نرجع للتعريف اللي احنا كدوينه و نقرأ مرة تانية و
+
+212
+00:26:22,770 --> 00:26:30,050
+نحاول نفهم يبدأ zero divisor يعني القاسم الصفري
+
+213
+00:26:30,050 --> 00:26:36,730
+مين هو هو non-zero element هو عنصر غير الصفري هه
+
+214
+00:26:36,730 --> 00:26:44,510
+سميته ايه؟ لمين؟ لحلقة إبدالية سميتها R بحيث انه
+
+215
+00:26:44,510 --> 00:26:51,220
+ممكن نلاقي عنصر تاني غير الصفريB في A يعني لو
+
+216
+00:26:51,220 --> 00:26:57,140
+ضربتهم يسوى مين بده يسوى الـ Zero يبقى مرة ثانية
+
+217
+00:26:57,140 --> 00:27:03,820
+من خلال هذا التعريف العنصر A صفري ولا غير صفري غير
+
+218
+00:27:03,820 --> 00:27:10,540
+صفري طب ال B غير صفري حصل ضربه يسوى الصفري إن حدث
+
+219
+00:27:10,540 --> 00:27:15,560
+ذلك يبقى ال A بسميه Zero divisor يبقى ال Zero
+
+220
+00:27:15,560 --> 00:27:21,620
+divisor هو عنصرلو لقيت عمصر اخر من ال ring اللي
+
+221
+00:27:21,620 --> 00:27:26,660
+عندنا ضربنا العمصرين في بعض طالع الناتج يسوى صفر
+
+222
+00:27:26,660 --> 00:27:31,080
+يبقى العمصر اللي عندنا بيسميه zero divisor بالشرط
+
+223
+00:27:31,080 --> 00:27:36,080
+ولا واحد فيهم يكون مياه زيه نوضح لك الفكرة for
+
+224
+00:27:36,080 --> 00:27:45,140
+example مثلا for example in
+
+225
+00:27:45,140 --> 00:27:54,730
+مثلا thereRing Z6 Z6 مين العناصر تبعها Zero واحد
+
+226
+00:27:54,730 --> 00:28:01,110
+اتنين تلاتة اربع خمسة اول شي بنقول يا زيكي بتصف
+
+227
+00:28:01,110 --> 00:28:06,910
+على شجر مالاكش دعوة بدي امسك الواحد هل بقدر الاجي
+
+228
+00:28:06,910 --> 00:28:11,170
+او ااخد اي عنصر من العناصر اللي انا اضربه في واحد
+
+229
+00:28:11,170 --> 00:28:17,980
+يطلع النتج صفر مش ممكنيبقى الواحد is not easy هو
+
+230
+00:28:17,980 --> 00:28:24,520
+the advisor طيب سؤال لو ضربت الواحد في نفسه يعني
+
+231
+00:28:24,520 --> 00:28:33,280
+ايش معنى هذا الكلام ان الواحد عبارة عن unit تمام
+
+232
+00:28:33,280 --> 00:28:37,820
+ال unity هنا الواحد يبقى الواحد is a unit هل هناك
+
+233
+00:28:37,820 --> 00:28:41,840
+unit أخرى لأ بالمرة
+
+234
+00:28:44,050 --> 00:28:50,150
+طب الخمسة في خمسة يبقى ايه؟ خمسة و اشد ستة في واحد
+
+235
+00:28:50,150 --> 00:28:53,950
+يبقى الواحد
+
+236
+00:28:53,950 --> 00:28:59,470
+و الخمسة are units يبقى هنا طبعا هذا ليس دوام في
+
+237
+00:28:59,470 --> 00:29:06,110
+الإجابة بس مجرد معلومة يبقى الواحد and الخمسة are
+
+238
+00:29:06,110 --> 00:29:13,610
+units ايش السبب؟ sinceإن واحد تربيع بده يساوي خمسة
+
+239
+00:29:13,610 --> 00:29:18,990
+تربيع بده يساوي واحد طيب نيدي اتنين لو ضربتها في
+
+240
+00:29:18,990 --> 00:29:23,830
+تلتة قداش انها تانية لا اتنين في زيرو ولا تلتة في
+
+241
+00:29:23,830 --> 00:29:29,070
+زيرو يبقى zero divisor ولا لا طب التلتة في الأربعة
+
+242
+00:29:29,070 --> 00:29:34,830
+مارتش يعني ستة تنتين يبقى zero يبقى كمان zero
+
+243
+00:29:34,830 --> 00:29:41,480
+divisor يبقى صار اتنينوالتلاتة والاربعة كمان are
+
+244
+00:29:41,480 --> 00:29:50,680
+zero divisors يبقى هنا اتنين والتلاتة والاربعة اها
+
+245
+00:29:50,680 --> 00:30:01,000
+zero divisors ليش؟ since ان اتنين في تلاتة بده
+
+246
+00:30:01,000 --> 00:30:08,100
+يسوي zero andالتلاتة في الأربعة بدل ساعة كمان Zero
+
+247
+00:30:08,100 --> 00:30:13,160
+كل مودي له ستة درهم كل مودي له ستة يبقى هذول صاروا
+
+248
+00:30:13,160 --> 00:30:18,080
+Zero divisors يبقى هناك Ring بسيطة لقينا بعض
+
+249
+00:30:18,080 --> 00:30:25,190
+العناصر فيها units والبعض الآخر Zero divisorsطيب
+
+250
+00:30:25,190 --> 00:30:30,390
+الان بدنا نروح نعطي امثلة توضحية بس الامثلة
+
+251
+00:30:30,390 --> 00:30:33,570
+التوضحية قبل ما نعطي امثلة بدنا نعرف ايش ال
+
+252
+00:30:33,570 --> 00:30:39,130
+integral domain احنا عرفنا zero divisors تمام ال
+
+253
+00:30:39,130 --> 00:30:43,330
+integral domain بسيطة جدا communicative ring فيهاش
+
+254
+00:30:43,330 --> 00:30:49,230
+zero divisors بسماذا يعني Zero Divisor؟ يعني لو
+
+255
+00:30:49,230 --> 00:30:53,770
+لاقيت عنصرين حاصل ضربهم بده يساوي Zero يبقى واحد
+
+256
+00:30:53,770 --> 00:30:59,070
+فيهم على الأقل بده يساوي Zero أي معناه طبعا يبقى
+
+257
+00:30:59,070 --> 00:31:04,070
+روح نقطة بتعريف ال integral domain يبقى definition
+
+258
+00:31:04,070 --> 00:31:08,650
+an
+
+259
+00:31:08,650 --> 00:31:10,010
+integral domain
+
+260
+00:31:17,430 --> 00:31:20,950
+and integral domain is a commutative ring with
+
+261
+00:31:20,950 --> 00:31:35,550
+unity is a commutative ring with unity commutative
+
+262
+00:31:35,550 --> 00:31:43,910
+ring with unity and no zero divisors and no zero
+
+263
+00:31:43,910 --> 00:31:45,770
+divisors
+
+264
+00:31:49,250 --> 00:31:58,930
+this means that توضيح ليس الا this means that هذا
+
+265
+00:31:58,930 --> 00:32:15,090
+يعني ان ال integral domain ال a
+
+266
+00:32:15,090 --> 00:32:25,820
+b بده يسوى zeroonly بيحصل when ال a تساوي zero or
+
+267
+00:32:25,820 --> 00:32:34,880
+ال b تساوي zero for
+
+268
+00:32:34,880 --> 00:32:39,040
+example كتوضيح
+
+269
+00:32:39,040 --> 00:32:45,200
+بمثال بسيط زي ما وضحنا في المثال البسيط لو المثال
+
+270
+00:32:45,200 --> 00:32:51,120
+البسيط الأولبيلنا ان بعض العناصر units و بعضهم له
+
+271
+00:32:51,120 --> 00:33:01,860
+zero divisors الان لو جيت زد سبعة هنا اخدنا زد ستة
+
+272
+00:33:01,860 --> 00:33:09,300
+تكون هنا زد سبعة اها عناصرها zero واحد اتنين تلاتة
+
+273
+00:33:09,300 --> 00:33:20,300
+اربع خمسة ستة سؤال هو فيأي رقم من هدول أضربه في
+
+274
+00:33:20,300 --> 00:33:27,720
+نفسه يطلع صفر أو أضربه في رقم تاني يطلع صفر؟ هاي
+
+275
+00:33:27,720 --> 00:33:37,380
+من قدامك كله؟ فيه؟ ولا واحد طيب هل الواحد is a
+
+276
+00:33:37,380 --> 00:33:44,480
+unit؟ ال three بالكيس هل اتنين unit؟ ليش اتنين
+
+277
+00:33:44,480 --> 00:33:51,720
+فاربع بقداش؟يعني unit صح؟ وبتنين في أربعة، بعد
+
+278
+00:33:51,720 --> 00:33:59,620
+هالتلاتة؟ تلاتة في خمسة، جدت؟ واحد، يبقى كمان
+
+279
+00:33:59,620 --> 00:34:06,040
+هادول units، خلصنا؟ ضايق ليش ما خدناهوش؟ ضايق ستة؟
+
+280
+00:34:06,040 --> 00:34:09,040
+ستة بدنا احنا سبعة
+
+281
+00:34:22,050 --> 00:34:27,250
+لو جابها لخمسة ومفيشها ابنها سبعةستة في خمسة في
+
+282
+00:34:27,250 --> 00:34:30,350
+تلاتين واربعة في سبعة واتنين وعشرين لأ، ستة في
+
+283
+00:34:30,350 --> 00:34:34,170
+أربعة في أربعة وعشرين لأ، ستة في تلاتة في تمانتين،
+
+284
+00:34:34,170 --> 00:34:37,950
+ستة في ستة في ستة في تلاتين، ستة في ستة في تلاتين،
+
+285
+00:34:37,950 --> 00:34:41,450
+ستة في ستة في تلاتين، ستة في ستة في تلاتين، ستة في
+
+286
+00:34:41,450 --> 00:34:44,130
+تلاتين، ستة في تلاتين، ستة في تلاتين، ستة في
+
+287
+00:34:44,130 --> 00:34:44,130
+تلاتين، ستة في تلاتين، ستة في تلاتين، ستة في
+
+288
+00:34:44,130 --> 00:34:44,510
+تلاتين، ستة في تلاتين، ستة في تلاتين، ستة في
+
+289
+00:34:44,510 --> 00:34:50,890
+تلاتين، ستة
+
+290
+00:34:50,890 --> 00:35:03,270
+في تلاتين، ستة في تلintegral domain because
+
+291
+00:35:03,270 --> 00:35:07,990
+ان
+
+292
+00:35:07,990 --> 00:35:13,210
+ال Z7 is commutative
+
+293
+00:35:13,210 --> 00:35:19,490
+ring
+
+294
+00:35:19,490 --> 00:35:21,990
+with unity
+
+295
+00:35:25,980 --> 00:35:31,800
+اللي هو one and no
+
+296
+00:35:31,800 --> 00:35:46,080
+zero divisors يبقى
+
+297
+00:35:46,080 --> 00:35:50,060
+تحققت الشروط التلاتة لل Integral domain وهي
+
+298
+00:35:50,060 --> 00:35:54,380
+commutative ring و ال unit الشرط التاني و مافيش
+
+299
+00:35:54,380 --> 00:35:58,750
+فيها zero divisorإذا هذه كلها بتكون ايه بتكون
+
+300
+00:35:58,750 --> 00:36:03,050
+integral domain نبدأ ناخد أمثلة مختلفة عن ال
+
+301
+00:36:03,050 --> 00:36:12,390
+integral domain نبقى examples أول مثال بقول the
+
+302
+00:36:12,390 --> 00:36:22,030
+ring of integers that ring of integers that
+
+303
+00:36:24,150 --> 00:36:33,850
+مالة is an integral domain is an integral domain
+
+304
+00:36:33,850 --> 00:36:44,450
+طب ليش يا مانا؟ السؤال فيها unity؟ اللي هو الواحد
+
+305
+00:36:44,450 --> 00:36:45,950
+و الواحد و الواحد و الواحد و الواحد و الواحد و
+
+306
+00:36:45,950 --> 00:36:46,170
+الواحد و الواحد و الواحد و الواحد و الواحد و
+
+307
+00:36:46,170 --> 00:36:47,650
+الواحد و الواحد و الواحد و الواحد و الواحد و
+
+308
+00:36:47,650 --> 00:36:47,830
+الواحد و الواحد و الواحد و الواحد و الواحد و
+
+309
+00:36:47,830 --> 00:36:47,910
+الواحد و الواحد و الواحد و الواحد و الواحد و
+
+310
+00:36:47,910 --> 00:36:47,910
+الواحد و الواحد و الواحد و الواحد و الواحد و
+
+311
+00:36:47,910 --> 00:36:47,910
+الواحد و الواحد و الواحد و الواحد و الواحد و
+
+312
+00:36:47,910 --> 00:36:47,910
+الواحد و الواحد و الواحد و الواحد و الواحد و
+
+313
+00:36:47,910 --> 00:36:48,430
+الواحد و الواحد و الواحد و الواحد و الواحد و
+
+314
+00:36:48,430 --> 00:36:55,820
+الواحد و الواحد و الوايبقى commutative ring with
+
+315
+00:36:55,820 --> 00:37:04,960
+unity يبقى هنا integral domain because z is a
+
+316
+00:37:04,960 --> 00:37:17,840
+commutative ring with unity و ال unity هو الواحد
+
+317
+00:37:17,840 --> 00:37:18,700
+الصحيح
+
+318
+00:37:21,360 --> 00:37:28,380
+تعالى نسأل السؤال التالى عمرك شوفتي عددين صحيحين
+
+319
+00:37:28,380 --> 00:37:35,080
+غير صفريين طلبناهم في بعض الانتجة سوى zero مفيش
+
+320
+00:37:35,080 --> 00:37:46,380
+يبقى هنا also ال ال ال z has
+
+321
+00:37:48,120 --> 00:37:57,960
+zero divisors because if
+
+322
+00:37:57,960 --> 00:38:09,200
+ال a و ال b موجودة في z then a في b بدي سوى zero
+
+323
+00:38:09,200 --> 00:38:18,810
+implies ان ال a تسوى zero او ال b تسوى zeroهذا
+
+324
+00:38:18,810 --> 00:38:24,310
+الكلام في الأعداد الصحيحة. لا يوجد عددان صحيحان
+
+325
+00:38:24,310 --> 00:38:30,110
+حاصل ضربهما يساوي صفر، ماعنديش بالمرة في الأعداد
+
+326
+00:38:30,110 --> 00:38:34,310
+الصحيحة. لو حدث إنهم يكونوا يساوي صفر، يبقى هذا لن
+
+327
+00:38:34,310 --> 00:38:40,690
+يحدث إلا إذا كان أحدهم أو كلاهما يساوي صفر. واحنا
+
+328
+00:38:40,690 --> 00:38:45,030
+Zero Divisor قلنا ممنوع الأصفات. إيه non-zero
+
+329
+00:38:45,030 --> 00:38:49,620
+element طبق لل definition؟وبدي ألاقي non-zero قلب
+
+330
+00:38:49,620 --> 00:39:02,460
+يبقى thus z is an integral domain ليش؟ لأنها حققت
+
+331
+00:39:02,460 --> 00:39:08,020
+الشروط التلاتة طب خلينا نسأل سؤال آخر ال set of
+
+332
+00:39:08,020 --> 00:39:13,740
+rational numbers مجموعة الأعداد النسبية تحت عملية
+
+333
+00:39:13,740 --> 00:39:16,040
+الجمع والضرب العادية
+
+334
+00:39:18,490 --> 00:39:25,510
+فيها zero divisor؟ طيب ال set of real numbers عمرك
+
+335
+00:39:25,510 --> 00:39:31,490
+شفتي عددين حقيقيين نظروفهم في بعض يطلع النتج صفر
+
+336
+00:39:31,490 --> 00:39:37,130
+وممكن يكون واحد فيهم هوش صفر؟ عمراش حصل في التاريخ
+
+337
+00:39:37,130 --> 00:39:42,190
+طيب ال set of complex numbers set of complex
+
+338
+00:39:42,190 --> 00:39:47,960
+numbersنفس الشيء يبقى هدول التلاتة rings are
+
+339
+00:39:47,960 --> 00:39:52,480
+commutative with unity with no zero divisor يبقى
+
+340
+00:39:52,480 --> 00:39:58,420
+هنا هدول integral دلوقتي يبقى similarly بنفس
+
+341
+00:39:58,420 --> 00:40:05,160
+الطريقة ال set of rational number ل Q و ال set of
+
+342
+00:40:05,160 --> 00:40:11,580
+real numbers R and ال set of complex numbers اللي
+
+343
+00:40:11,580 --> 00:40:19,060
+هي Care integral domains
+
+344
+00:40:19,060 --> 00:40:35,820
+طيب هذا المثال الأول المثال الثاني the ring of
+
+345
+00:40:35,820 --> 00:40:45,400
+Gaussian integralThe ring of Johnson integers.اللي
+
+346
+00:40:45,400 --> 00:40:53,860
+هي مين؟ Z of I، العدد التخيلي، لقيمته يساوي سالب
+
+347
+00:40:53,860 --> 00:41:00,520
+واحد، اللي على الصيرة A زائد BI، بحيث الـA والـB
+
+348
+00:41:00,520 --> 00:41:07,560
+أداداً صحيحة.هل
+
+349
+00:41:07,560 --> 00:41:16,460
+هذا integral domain؟دعونا نشوف يبقى هذا is an
+
+350
+00:41:16,460 --> 00:41:24,260
+integral domain اظن
+
+351
+00:41:24,260 --> 00:41:30,420
+هذه اثبتناها قبل ذلك انها communicative with unity
+
+352
+00:41:30,420 --> 00:41:34,860
+انت ما تظل علينا بس حكاية ال zero divisor هذه ما
+
+353
+00:41:34,860 --> 00:41:38,060
+اثبتناها يبقى هنا because
+
+354
+00:41:42,190 --> 00:41:53,990
+اللي هو Z of I is a commutative ring
+
+355
+00:41:53,990 --> 00:41:57,010
+with
+
+356
+00:41:57,010 --> 00:42:02,490
+unity اللي
+
+357
+00:42:02,490 --> 00:42:08,350
+هو واحد اللي بده يساوي واحد زائد zero في I اللي
+
+358
+00:42:08,350 --> 00:42:20,350
+موجودة في Z of Iإيش ضايق علينا؟ لثبت إنه ماعنديش
+
+359
+00:42:20,350 --> 00:42:26,410
+Zero Divisor أو لو فرضت إنه عندي عددين حاصل ضربهم
+
+360
+00:42:26,410 --> 00:42:32,010
+بده يسوي Zero بده أثبت إنه العددين هذول على الأقل
+
+361
+00:42:32,010 --> 00:42:38,800
+واحد فيهم بده يسوي مين؟بدرسها و easy مش هي subset
+
+362
+00:42:38,800 --> 00:42:42,720
+من ال complex number خصائصها نفس خصائص ال complex
+
+363
+00:42:42,720 --> 00:42:45,240
+و ال complex هي انتجار دو ما مافيش فيها zero
+
+364
+00:42:45,240 --> 00:42:47,980
+divisor يعني كان نفس الاشي طب مش عرفنا ان ال
+
+365
+00:42:47,980 --> 00:42:53,420
+complex مش فيها zero divisor انا كل الشيء من اغلبي
+
+366
+00:42:53,420 --> 00:42:58,540
+انا في عملية انا فتشتغلت في عملية كما اشتغلت هذا
+
+367
+00:42:58,540 --> 00:43:04,390
+لكن احنا بنوثبش هذا الكلام رياضيا يعني احنامن هنا
+
+368
+00:43:04,390 --> 00:43:08,210
+اتكلمنا عن خطواتين communicative with unity، ضال
+
+369
+00:43:08,210 --> 00:43:15,590
+علينا الخطوة الثانية، فبدي ااخد عددين او عنصرين
+
+370
+00:43:15,590 --> 00:43:21,230
+موجودين في هالست هذين، وافترض ان حصل ضربهم ما
+
+371
+00:43:21,230 --> 00:43:28,250
+يساوي Zero، و اثبت ان هدول اتنين ال Zero حصل لان
+
+372
+00:43:28,250 --> 00:43:33,840
+واحد فيهم Zero او كلهما كان ب Zero، تمام؟يبقى
+
+373
+00:43:33,840 --> 00:43:43,440
+بيانات اتداجية كله افترضي ان ال a زائد bi و ال c
+
+374
+00:43:43,440 --> 00:43:55,200
+زائد di موجودة في z of i و اتنين بيسووش بعض and ال
+
+375
+00:43:55,200 --> 00:44:09,460
+a زائد bi لا يساوي ال cزائد DI and ال A زائد ال BI
+
+376
+00:44:09,460 --> 00:44:18,000
+في C زائد ال DI بده يساوي 0 يبقى
+
+377
+00:44:18,000 --> 00:44:25,300
+أنا أخدت أنصرين موجودات في ZI و هدول بيساووش بعض و
+
+378
+00:44:25,300 --> 00:44:31,040
+افترض انه حاصل ضربه ما بده يساوي 100 بده يساوي 0
+
+379
+00:44:32,090 --> 00:44:36,310
+بدي أروح أضرب هذا يفجأة لو ضربته إيش بيصير يا فنان
+
+380
+00:44:36,310 --> 00:44:45,450
+ال C هذا الجزء الحقيقي ال B I في ال D I بيصير B D
+
+381
+00:44:45,450 --> 00:44:52,170
+في سالب واحد لإن ال I تربيع سالب واحد يفجأة ناقص B
+
+382
+00:44:52,170 --> 00:44:59,710
+في D ناقص B في D هذا ال term الأولأو الجزء الأول
+
+383
+00:44:59,710 --> 00:45:05,570
+من العدد المُركّب أو الجزء الحقيقي من العدد
+
+384
+00:45:05,570 --> 00:45:09,150
+المُركّب إننا نيجي للجزء التفيّلي من العدد
+
+385
+00:45:09,150 --> 00:45:22,490
+المُركّب زائد A D زائد B C في I زائد A D زائد B C
+
+386
+00:45:22,490 --> 00:45:29,670
+كله في I هذا الكلام يساوي Zeroمن الأعداد التخيّلية
+
+387
+00:45:29,670 --> 00:45:35,670
+إذا عندي عدد تخيّلي ب Zero يبقى الجزء الحقيقي ب
+
+388
+00:45:35,670 --> 00:45:42,210
+Zero وجزء التخيّلي ب Zero يبقى هذا بده يعطينا ان
+
+389
+00:45:42,210 --> 00:45:52,810
+ال AC ناقص BD بده يسوى Zero وال AD زائد BC بده
+
+390
+00:45:52,810 --> 00:46:01,130
+يسوى Zero تمام؟ طيبإيش رأيك من المعادلة هذه بقدر
+
+391
+00:46:01,130 --> 00:46:12,430
+أقول ان دي تساوي ناقص بي سي على ايه من المعادلة
+
+392
+00:46:12,430 --> 00:46:18,190
+التانية صح؟ طب إيش رأيك؟ بدي أمسك هذه و أعوضها في
+
+393
+00:46:18,190 --> 00:46:23,330
+المعادلة التانية و أشوف إيش بدي يعطينا هذايبقى
+
+394
+00:46:23,330 --> 00:46:31,430
+بتشير المعادلة التانية A C ناقص B في D D اللي هي
+
+395
+00:46:31,430 --> 00:46:40,110
+ناقص B C على A كله بده يساوي Zero بده أضرب الطرفين
+
+396
+00:46:40,110 --> 00:46:50,890
+في A هذا الكلام بده يعطينا ال A تارى بيع C ناقص
+
+397
+00:46:51,200 --> 00:46:58,920
+زائد الـ B ترابيع الـ C بده يساوي Zero من الـ
+
+398
+00:46:58,920 --> 00:47:05,120
+Distributive Law يبقى الـ A ترابيع زائد الـ B
+
+399
+00:47:05,120 --> 00:47:12,620
+ترابيع كل هذا في الـ C بده يساوي Zero هذا إيش
+
+400
+00:47:12,620 --> 00:47:20,250
+معناه؟ إما الـ C تساوي Zeroيبقى M A تربيع زائد B
+
+401
+00:47:20,250 --> 00:47:26,030
+تربيع يساوي Zero يبقى هذا الكلام بده يساوي C بده
+
+402
+00:47:26,030 --> 00:47:33,990
+يساوي Zero O A تربيع زائد B تربيع يساوي Zero طب
+
+403
+00:47:33,990 --> 00:47:42,690
+الآن لو كان ال C تساوي Zero يبقى F C تساوي Zero
+
+404
+00:47:43,960 --> 00:47:49,020
+شايفين انه في الموقع هذه يا بناه يبقى دي بقداش
+
+405
+00:47:49,020 --> 00:47:58,200
+Zero يبقى هذه سامعها ل start يبقى then D تساوي
+
+406
+00:47:58,200 --> 00:48:07,120
+Zero هذه from start طبعا إذا C ب Zero وD ب Zero
+
+407
+00:48:07,120 --> 00:48:15,420
+يبقى C زائد D I تساوي Zeroيبقى هذا بده يعطيك انه C
+
+408
+00:48:15,420 --> 00:48:39,640
+زائد DI بده ساوينين بده ساوي Zero طيب
+
+409
+00:48:40,230 --> 00:48:44,310
+أخدنا الحالة الأولى لو كان يساوي C تساوي Zero
+
+410
+00:48:44,310 --> 00:48:49,250
+أثبتنا ان D تساوي Zero وبالتالي صار العدل هو Zero
+
+411
+00:48:49,250 --> 00:48:54,550
+وهذا يتفق مع تعريف main ال integral domain بقيت
+
+412
+00:48:54,550 --> 00:49:02,710
+عندنا الحالة الثانية وهي ان ال A تربيع زائد B
+
+413
+00:49:02,710 --> 00:49:08,110
+تربيع بدل ساوي Zero السؤال هو ال A و ال B
+
+414
+00:49:08,110 --> 00:49:15,130
+integers، راح؟طيب السؤال هو هل يعقل انه مربع two
+
+415
+00:49:15,130 --> 00:49:20,850
+integers نجمعهم يسوى zero لا ولا مرة واحدة في
+
+416
+00:49:20,850 --> 00:49:26,990
+التاريخ مرة واحدة إذا ال a ساوة ال b ساوة ال zero
+
+417
+00:49:26,990 --> 00:49:39,170
+إذا هذا then this is this is a true only
+
+418
+00:49:40,980 --> 00:49:49,100
+عندما ال A تساوي ال B تساوي Zero غير هيك يبقى
+
+419
+00:49:49,100 --> 00:49:55,420
+السرعه ال A زائد ال B في I قد مش بده يساوي Zero
+
+420
+00:49:55,680 --> 00:50:00,920
+يبقى هاي اثبتنا له انه C زائد DI بده يساوي Zero
+
+421
+00:50:00,920 --> 00:50:06,820
+وهنا اثبتنا له انه ال A زائد BI يساوي Zero واحنا
+
+422
+00:50:06,820 --> 00:50:13,520
+افترضنا ان حاصل ضربه ما يساوي Zero نتج انه على
+
+423
+00:50:13,520 --> 00:50:18,300
+الأقل واحد فيهم يساوي Zero إذا ماكانش اتنين يبقى
+
+424
+00:50:18,300 --> 00:50:24,040
+هذا أو هذا تمام؟يبقى بناء عليه ايش معنى هذا الكلام
+
+425
+00:50:24,040 --> 00:50:30,020
+انتجرال دومين فاكرين اللي بنجو سين كتبناه عندما
+
+426
+00:50:30,020 --> 00:50:33,900
+أعرفنا الانتجرال دومين؟ كنا في الانتجرال دومين لو
+
+427
+00:50:33,900 --> 00:50:38,080
+كان حاصل ضرب عددين a في b يبدو يسوى zero يبقى ايا
+
+428
+00:50:38,080 --> 00:50:43,060
+اما a تسوى zero او b وهي اللي أثبتناها احنا بضبط
+
+429
+00:50:43,060 --> 00:50:48,140
+يبقى بناء على يسار z of i is an integral domain
+
+430
+00:50:48,140 --> 00:51:01,270
+يبقى هنا thismeans that ان ال Z of I is an
+
+431
+00:51:01,270 --> 00:51:11,430
+integral domain يبقى من الآن يبقى نطفح ساعدا Z of
+
+432
+00:51:11,430 --> 00:51:17,930
+I الجوش الهدية commuted ring with unity وفيهاش
+
+433
+00:51:17,930 --> 00:51:25,040
+zero divisors تمامليزال هناك المزيد من الأمثلة
+
+434
+00:51:25,040 --> 00:51:29,600
+للمرة القادمة، ان شاء الله تعالى. أفضل العافية.
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..37925de8eb9757a0918f7702eb2b298e9f4f153e
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc.srt
@@ -0,0 +1,1344 @@
+
+1
+00:00:20,640 --> 00:00:25,720
+بسم الله الرحمن الرحيم.  عوضًا عن البدء، نذكر بما
+
+2
+00:00:25,720 --> 00:00:31,160
+أعطيناه المرة الماضية، لأن هذه الكورلري تعتمد على
+
+3
+00:00:31,160 --> 00:00:35,500
+ما درسناه في المحاضرة الماضية. المحاضرة الماضية
+
+4
+00:00:35,500 --> 00:00:39,860
+كانت عمودًا شُقريًا هو نظريتان. النظرية الأولى تقول:
+
+5
+00:00:39,860 --> 00:00:44,370
+لو كانت الـ R commutative ring with unity، يبقى من
+
+6
+00:00:44,370 --> 00:00:48,390
+الـ R modulo A is an integral domain if and only
+
+7
+00:00:48,390 --> 00:00:53,630
+if الـ A is a prime ideal. والنظرية الثانية أيضًا
+
+8
+00:00:53,630 --> 00:00:58,990
+نفس منطلق النظرية الأولى، اللي هو الـ R
+
+9
+00:00:58,990 --> 00:01:02,310
+commutative ring with unity. لكن النتيجة عند
+
+10
+00:01:02,310 --> 00:01:07,930
+المطلوب، فنقول: الـ R modulo A is a field if and
+
+11
+00:01:07,930 --> 00:01:14,040
+only if الـ A is a maximal ideal. هذا آخر شيء أثبتناه
+
+12
+00:01:14,040 --> 00:01:18,000
+المرة الماضية. الكورلري عبارة عن نتيجة على
+
+13
+00:01:18,000 --> 00:01:22,240
+النظريتين، تقول: لو كانت الـ R commutative ring with
+
+14
+00:01:22,240 --> 00:01:29,880
+unity، يبقى every maximal ideal is prime. يبقى الـ
+
+15
+00:01:29,880 --> 00:01:39,840
+proof كالتالي: الـ R is a commutative ring with unity.
+
+16
+00:01:44,120 --> 00:01:50,080
+طبعًا، يبقى بدي أَفترض أنه عندي ideal، والـ ideal is
+
+17
+00:01:50,080 --> 00:02:01,580
+maximal. Let A be a maximal ideal
+
+18
+00:02:01,580 --> 00:02:11,880
+of R. بالنظرية الثانية، يبقى الـ R modulo A is a
+
+19
+00:02:11,880 --> 00:02:20,600
+field. يبقى بروح بقوله: by the second theorem،
+
+20
+00:02:20,600 --> 00:02:32,860
+بالنظرية الثانية، الـ R modulo A is a field. طبعًا
+
+21
+00:02:32,860 --> 00:02:40,680
+احنا قلنا قبل ذلك: any field is an integral domain.
+
+22
+00:02:41,190 --> 00:02:48,770
+هذا بدي يعطينا أن الـ R modulo A is an integral
+
+23
+00:02:48,770 --> 00:02:54,070
+domain. يبقى
+
+24
+00:02:54,070 --> 00:03:04,290
+بروحة نقوله: by the first theorem، النظرية
+
+25
+00:03:04,290 --> 00:03:13,960
+الأولى، الـ A is a prime ideal. يبقى أثبتنا أن الـ
+
+26
+00:03:13,960 --> 00:03:20,420
+maximal ideal عبارة عن prime ideal، إذا كانت الـ R
+
+27
+00:03:20,420 --> 00:03:26,620
+is commutative with unity. وصلنا لآخر مثال في
+
+28
+00:03:26,620 --> 00:03:34,840
+هذا الـ section، وهو يقول:
+
+29
+00:03:34,840 --> 00:03:35,960
+the ideal
+
+30
+00:03:39,630 --> 00:03:46,970
+أو الـ principal ideal generated by X is a prime
+
+31
+00:03:46,970 --> 00:03:55,510
+ideal in Z[X] but not maximal.
+
+32
+00:04:18,540 --> 00:04:24,720
+هذا المثال، لحله، بيعتمد على سؤالين موجودين في
+
+33
+00:04:24,720 --> 00:04:29,980
+الكتاب، مثل ما ذكر الكتاب. احنا هنحل السؤالين، وأنتم
+
+34
+00:04:29,980 --> 00:04:36,200
+مش دارين، من خلال إثباتنا أو خلال حلنا لهذا السؤال.
+
+35
+00:04:36,200 --> 00:04:40,840
+أول شيء، بيقول لي: الـ principal ideal generated by X هو
+
+36
+00:04:40,840 --> 00:04:45,340
+عبارة عن prime ideal في هذه الـ ring، لكنه ليس
+
+37
+00:04:45,340 --> 00:04:49,720
+maximal. يبقى بدي أثبت شيء ثاني: أن الـ principal
+
+38
+00:04:49,720 --> 00:04:54,260
+ideal generated by X هو prime ideal، وفي نفس الوقت
+
+39
+00:04:54,260 --> 00:05:00,380
+ليس maximal ideal أيضًا في Z[X]. علشان هيك، بدنا
+
+40
+00:05:00,380 --> 00:05:04,300
+نبدأ نثبت الـ maximality، لأن بدنا نثبت اللي هو يفتقر
+
+41
+00:05:04,300 --> 00:05:09,460
+إلى أن يكون prime ideal. لكن قبل ذلك، خلينا نرجع لتعريف الـ
+
+42
+00:05:09,460 --> 00:05:16,210
+principal ideal generated by X. قلنا سابقًا: كل الـ
+
+43
+00:05:16,210 --> 00:05:23,070
+elements X في R بحيث أن R موجودة في RX، والـ R
+
+44
+00:05:23,070 --> 00:05:26,290
+و RX الاثنين، الـ R ده similar لأن الـ ring commutative.
+
+45
+00:05:26,290 --> 00:05:32,510
+تمام؟ يبقى كل الـ X في R بحيث أن الـ R موجودة في R، هذا
+
+46
+00:05:32,510 --> 00:05:36,930
+الـ general definition لمين؟ للـ principal ideal
+
+47
+00:05:36,930 --> 00:05:42,050
+generated by X. بدي أروح أطبق هذا التعريف على
+
+48
+00:05:42,050 --> 00:05:47,270
+الـ ring اللي عندنا. يبقى بقدر أقول: هذا كل الـ
+
+49
+00:05:47,270 --> 00:05:59,870
+elements x، كل الـ elements f(x) اللي موجودة في الـ Z
+
+50
+00:05:59,870 --> 00:06:10,110
+[X] such that أن x في g(x)، أن f(x) شو
+
+51
+00:06:10,110 --> 00:06:16,930
+شكلها.. شو شكلها؟ بحيث أن f(x) يساوي x في
+
+52
+00:06:16,930 --> 00:06:25,650
+g(x)، والـ g(x) هذه موجودة في Z[X]. الشكل
+
+53
+00:06:25,650 --> 00:06:32,290
+اللي عندنا. إذا أنا قاعد أعرف اللي هو الـ principal
+
+54
+00:06:32,290 --> 00:06:37,510
+ideal generated by X، بما يناسب طبيعة المسألة اللي
+
+55
+00:06:37,510 --> 00:06:42,850
+عندنا. يبقى كل الـ functions أو الـ polynomials اللي
+
+56
+00:06:42,850 --> 00:06:47,830
+المعاملات تبعها أعداد صحيحة، اللي بتكون على الشكل
+
+57
+00:06:47,830 --> 00:06:53,990
+التالي: x في g(x). أنا قلنا x في R، بدي أخد R من
+
+58
+00:06:53,990 --> 00:06:58,890
+الـ Z[X]، يعني بدي أخد الـ g(x) من الـ Z[X]، مضروبة
+
+59
+00:06:58,890 --> 00:07:06,010
+في مين؟ في الـ x. الآن، بدي أَفترض أن عندنا  ideal
+
+60
+00:07:06,510 --> 00:07:18,130
+يبقى باجي بقوله: consider the ideal I. الـ
+
+61
+00:07:18,130 --> 00:07:22,490
+I هذا، أثبتناه قبل ذلك أنه ideal. كل الـ polynomials
+
+62
+00:07:22,490 --> 00:07:27,750
+اللي المقدار الثابت فيها يساوي الصفر. تذكروا المرة
+
+63
+00:07:27,750 --> 00:07:33,630
+الماضية، وأثبتناه أنه ideal. يبقى الـ ideal I: كل الـ f
+
+64
+00:07:33,630 --> 00:07:40,740
+(x) such that f(0) بده يساوي مين؟ 0. طب
+
+65
+00:07:40,740 --> 00:07:44,480
+إيش علاقة هذا بالموضوع؟ آه، دلوقت بنوريك إيش علاقة
+
+66
+00:07:44,480 --> 00:07:54,360
+هذا الموضوع الآن، يا عزيزي، إننا ندّعي
+
+67
+00:07:54,360 --> 00:07:59,810
+أن الـ principal ideal generated by X بده يساوي I. أنا
+
+68
+00:07:59,810 --> 00:08:05,230
+أَدّعي أن هذا الـ ideal هو هذا الـ ideal، مضبوط تمامًا.
+
+69
+00:08:05,230 --> 00:08:09,630
+شكله مش مبين، هذا في شيء وهذا في شيء، لكن احنا
+
+70
+00:08:09,630 --> 00:08:15,150
+بنشتغل شغل رياضي، بحيث فعلًا نثبت أن هذا يساوي هذا.
+
+71
+00:08:15,150 --> 00:08:24,230
+إذا، علشان هيك، أَفترض أن f(x) موجود في الـ principal
+
+72
+00:08:24,230 --> 00:08:30,760
+ideal generated by X. يبقى في هذه الحالة، الـ f(x)
+
+73
+00:08:30,760 --> 00:08:36,080
+بدها تساوي هاي، يبقى الـ f(x) بدها تساوي مين؟ الـ x
+
+74
+00:08:36,080 --> 00:08:43,520
+في g(x). يبقى x في g(x). طيب، لو جيت وقلت: بدي
+
+75
+00:08:43,520 --> 00:08:49,180
+أشوف قد ايش الـ f(0) بدها تساوي، يبقى بدها تساوي
+
+76
+00:08:49,180 --> 00:08:56,230
+0 في g(0). 0 في 0 = 0. والله، أي رقم آخر
+
+77
+00:08:56,230 --> 00:09:01,270
+أضربه في 0 بده يعطيني 0. element. إيش تفسيرك
+
+78
+00:09:01,270 --> 00:09:07,210
+لهذا الكلام؟ أن الـ f(x) موجودة وين؟ في الـ I، ده في
+
+79
+00:09:07,210 --> 00:09:13,710
+الـ I، مظبوط. يبقى هذا بده يعطينا مين؟ أن الـ f(x)
+
+80
+00:09:13,710 --> 00:09:20,200
+موجودة وين؟ في الـ I. الـ I هذا بده يعطينا أن الـ
+
+81
+00:09:20,200 --> 00:09:24,660
+principal ideal generated by X subset من مين؟
+
+82
+00:09:24,660 --> 00:09:31,120
+subset من I. وهذه الخطوات الأولى. On the other hand،
+
+83
+00:09:31,120 --> 00:09:34,980
+يبقى
+
+84
+00:09:34,980 --> 00:09:42,880
+on the other hand، من الناحية الأخرى، بدي أجي أقوله:
+
+85
+00:09:42,880 --> 00:09:49,770
+أفترض أن الـ f(x) موجودة وين؟ موجودة في الـ I. الـ I، بدي أحاول أثبت أن الـ f(x) موجودة في الـ x.
+
+86
+00:09:49,770 --> 00:09:53,930
+الـ I، بدي أحاول أثبت أن الـ f(x) موجودة في الـ x
+
+87
+00:09:53,930 --> 00:10:04,950
+موجودة في الـ x. then الـ f(x)، بدي أثبت أن f(x)
+
+88
+00:10:04,950 --> 00:10:05,170
+موجودة في الـ x
+
+89
+00:10:05,170 --> 00:10:07,410
+موجودة في الـ x
+
+90
+00:10:07,410 --> 00:10:08,310
+موجودة في الـ x
+
+91
+00:10:08,310 --> 00:10:08,390
+موجودة في الـ x
+
+92
+00:10:08,390 --> 00:10:08,430
+موجودة في الـ x
+
+93
+00:10:08,430 --> 00:10:13,450
+موجودة في الـ x
+
+94
+00:10:17,070 --> 00:10:23,150
+ليش؟ لأن الـ I عندها فيه الـ term الأخير بـ 0.
+
+95
+00:10:23,150 --> 00:10:26,990
+تمام؟ يبقى فقط الـ term الأخير اللي هو الـ
+
+96
+00:10:26,990 --> 00:10:31,790
+constant term، والـ mean 0. لأن f(0) = 0 = 0 = 0. كلهم 0.  مضّلش إلا الـ term الأخير. تمام؟ طيب
+
+97
+00:10:31,790 --> 00:10:37,170
+كويس. يبقى الـ f(x)  على الشكل اللي عندها ده، أليس
+
+98
+00:10:37,170 --> 00:10:42,150
+كذلك؟ هذه عبارة عن x في a<sub>n</sub>x<sup>n-1</sup> + a<sub>n-1</sub>x<sup>n-2</sup> + a<sub>1</sub>. يعني أخذنا x
+
+99
+00:10:51,720 --> 00:10:59,700
+عامل مشترك. هذه كلها functions موجودة في Z[x] ولا
+
+100
+00:10:59,700 --> 00:11:07,420
+لا؟ صح. إذا بقدر أقول: هذه x، وشكلها على الشكل التالي.
+
+101
+00:11:15,390 --> 00:11:19,490
+هذه موجودة في الـ principal ideal generated by X.
+
+102
+00:11:19,490 --> 00:11:26,330
+طبعًا، بالتعريف تبعه، مظبوط؟ يعني إيش استفدنا؟ أخذنا
+
+103
+00:11:26,330 --> 00:11:33,610
+f(x) موجودة في I، وجينا الـ f(x) موجودة في الـ
+
+104
+00:11:33,610 --> 00:11:37,850
+principal ideal generated by X، يبقى باجي أقول له:
+
+105
+00:11:37,850 --> 00:11:42,830
+الـ principal ideal generated by X يساوي الـ I.
+
+106
+00:11:42,830 --> 00:11:51,520
+كما زعمنا قبل قليل. إذا صار عندنا هذا، معناه هو هذا.
+
+107
+00:11:51,520 --> 00:11:57,460
+يبقى الـ principal ideal generated by X هو الـ I،
+
+108
+00:11:57,460 --> 00:12:03,460
+الـ I بالضبط تمامًا. طيب، احنا حتى الآن ما سوّينا
+
+109
+00:12:03,460 --> 00:12:09,180
+شيء، سوّينا مقدمة، المقدمة هذه لِزمان، ديروا بالكم.
+
+110
+00:12:09,180 --> 00:12:13,640
+مثل هذا في الكتاب، وبيعتمد على سؤالين من الكتاب.
+
+111
+00:12:13,980 --> 00:12:17,800
+هنحل السؤالين، واحنا مش دارين أن احنا حلناهم، و
+
+112
+00:12:17,800 --> 00:12:24,120
+احنا بنبرهن في السؤال. طيب، ندخل الآن للمعلومات اللي
+
+113
+00:12:24,120 --> 00:12:29,860
+احنا عارفينها ومقتنعين بها. الـ ideal هذا، بدي أثبت
+
+114
+00:12:29,860 --> 00:12:34,500
+أنه prime ideal. يبقى بدي آخذ two functions هنا،
+
+115
+00:12:34,500 --> 00:12:41,860
+بحيث يكون حاصل ضربهما موجود هنا، وبالتالي أثبت يا إما
+
+116
+00:12:41,860 --> 00:12:45,680
+الدالة الأولى موجودة في الـ principal ideal generated by
+
+117
+00:12:45,680 --> 00:12:52,900
+X، يا إما الثانية. بقوله: كويس، يبقى لأن بتجي
+
+118
+00:12:52,900 --> 00:13:01,820
+أقوله: أَفترض أن عندي دالتين، g و h، موجودتين تمّامًا في Z
+
+119
+00:13:01,820 --> 00:13:12,010
+[X] such that بحيث أن gh موجودة موجودة في الـ
+
+120
+00:13:12,010 --> 00:13:16,870
+principal ideal generated by X. مش هو هذا اللي بثبت
+
+121
+00:13:16,870 --> 00:13:22,910
+أنه prime؟ يبقى آخذ two elements من الـ ring الأصلية،
+
+122
+00:13:22,910 --> 00:13:29,050
+بحيث حاصل ضربهما موجود هنا. بيقولوا: كويس، يبقى بناءً
+
+123
+00:13:29,050 --> 00:13:34,350
+على هذا، بدي أحاول أثبت يا إما الـ g موجودة في الـ
+
+124
+00:13:34,350 --> 00:13:38,130
+principal ideal generated by X، يا إما الـ h اللي
+
+125
+00:13:38,130 --> 00:13:47,310
+موجودة. مظبوط. طيب، كويس. Then، لو أخذت يا بنات gh،
+
+126
+00:13:47,310 --> 00:13:54,710
+تأثيرها على الـ 0، الشكل ده عندنا هنا، طبقًا
+
+127
+00:13:54,710 --> 00:14:01,410
+للكورلاري، أليس هذا هو g(0) في h(0)؟
+
+128
+00:14:01,410 --> 00:14:08,210
+نعم. احنا أخذنا حاصل الضرب، موجود هنا، اللي هو في الـ x.
+
+129
+00:14:08,210 --> 00:14:14,750
+طيب، من الـ x؟ مش هي الـ I، صح؟ يعني بتقدر تقول:
+
+130
+00:14:14,750 --> 00:14:20,890
+الموجودة في الـ I، اللي هي بدها تساوي الـ I، هي
+
+131
+00:14:20,890 --> 00:14:24,110
+أخذناها، الموجودة في الـ x، اللي هي بدها تساوي الـ I.
+
+132
+00:14:24,110 --> 00:14:29,690
+يبقى تأثيرها على الـ 0 بده يساوي قد ايش؟ بده يساوي
+
+133
+00:14:29,690 --> 00:14:35,710
+الـ 0 itself. طب، الـ g(0) والـ h(0)، أنتم
+
+134
+00:14:35,710 --> 00:14:42,070
+جارين ولا لا؟ أنتم جارين؟ هل يُعقل أن حاصل ضربهما يكون
+
+135
+00:14:42,070 --> 00:14:49,270
+بـ 0 إلا إذا كان كلاهما بـ 0؟ يبقى فادي بيقول لهم: but
+
+136
+00:14:49,270 --> 00:15:01,650
+ولكن g(0) and h(0) are integers. يبقى
+
+137
+00:15:01,650 --> 00:15:11,270
+so g(0)h(0) = 0 imply أن g(0)
+
+138
+00:15:11,270 --> 00:15:18,810
+بتساوي 0 أو h(0) هو اللي بتساوي 0. طيب، إذا g
+
+139
+00:15:18,810 --> 00:15:24,770
+(0) تساوي 0، يبقى موجودة في x ولا لا؟ يعني في I.
+
+140
+00:15:24,770 --> 00:15:31,710
+يبقى هذا بده يعطينا أن g(x) موجودة في
+
+141
+00:15:31,710 --> 00:15:38,660
+الـ principal ideal generated by X، أو h(x) موجودة
+
+142
+00:15:38,660 --> 00:15:43,980
+في، في الـ principal ideal generated by X. فمش
+
+143
+00:15:43,980 --> 00:15:49,840
+معنى هذا الكلام؟ prime ideal. يبقى هذا بده يعطينا
+
+144
+00:15:49,840 --> 00:15:57,360
+أن الـ principal ideal generated by X is a prime
+
+145
+00:15:57,360 --> 00:16:05,330
+ideal. يبقى أثبتنا الشطر الأول من هذا المثال. بدا
+
+146
+00:16:05,330 --> 00:16:09,250
+نَجي للشطر الثاني، نثبت أن الـ principal ideal
+
+147
+00:16:09,250 --> 00:16:16,430
+generated by X is not maximal. نرجع بالذاكرة إلى
+
+148
+00:16:16,430 --> 00:16:21,400
+الدرس. الـ maximal ideal. كيف بثبت أنه maximal؟ نجيب
+
+149
+00:16:21,400 --> 00:16:28,100
+ideal ثاني، هذا الـ ideal يكون subset منه،
+
+150
+00:16:28,100 --> 00:16:32,660
+والـ ideal الثاني هذا subset من R، وبالتالي الـ
+
+151
+00:16:32,660 --> 00:16:37,100
+ideal اللي عندنا يا إما بده يساوي الـ ideal الجديد،
+
+152
+00:16:37,100 --> 00:16:41,960
+يا الـ ideal الجديد بده يساوي ring R. صح ولا لا؟ طيب
+
+153
+00:16:41,960 --> 00:16:47,530
+تعالوا نشوف هالشيء هانيبقى. بالداخل، أقول: consider
+
+154
+00:16:47,530 --> 00:16:56,710
+the set، الـ set بالرموز، اللي هي: x و 2. الجديد.
+
+155
+00:16:56,710 --> 00:17:04,530
+هذا علينا، صح؟ نشوف مين هي هذه. يبدو هذه كل العناصر f
+
+156
+00:17:04,530 --> 00:17:12,180
+(x) اللي موجودة في Z[x] such that f(x)
+
+157
+00:17:12,180 --> 00:17:23,880
+بيساوي x في g(x) + 2h(x). إيش
+
+158
+00:17:23,880 --> 00:17:30,900
+يعني؟ يعني كل الـ functions اللي المقدار الثابت هنا
+
+159
+00:17:30,900 --> 00:17:37,260
+تبعها بيكون عدد زوجي. h(x)  جد ما تضربه في 2. بيصير عدد زوجي صحيح ولا لأ؟ يعني بالبلدي، زي ما
+
+160
+00:17:43,200 --> 00:17:47,600
+عرفنا، الاثنين هذول بيقولوا: كل الـ f(x) في حيث f(
+
+161
+00:17:47,600 --> 00:17:52,740
+0) بده يساوي 2k. 2k اللي هو أي عدد زوجي.
+
+162
+00:17:52,740 --> 00:17:57,260
+بيه، 2 في h(x). هذا ما يعنيه الـ set اللي
+
+163
+00:17:57,260 --> 00:18:02,840
+عندنا. هل هي ideal؟ إذا أثبتنا أنها ideal، خلاص هنحِلّ
+
+164
+00:18:02,840 --> 00:18:09,320
+مشكلتنا نهائيًا. يبقى أنا أَزعم أن هذه ideal، بس
+
+165
+00:18:09,320 --> 00:18:24,430
+بتَكتسب. يبقى now،  x و 2 is an ideal because ليش؟
+
+166
+00:18:24,430 --> 00:18:31,950
+بتدل النقطة الأولى: x و 2 is subset من
+
+167
+00:18:35,820 --> 00:18:40,620
+يبقى هذه الدالة، الشفرة فيها على الأقل ولو عنصر
+
+168
+00:18:40,620 --> 00:18:48,240
+واحد. ليش؟ since
+
+223
+00:25:45,830 --> 00:25:53,890
+احنا جيبنا ideal جديد، الـ ID الجديد، شو علاقته بالـ ID
+
+224
+00:25:53,890 --> 00:25:59,110
+للأصلي؟ تمام
+
+225
+00:25:59,110 --> 00:26:09,170
+Subset منه ولا يساوي أكيد، هاي الـ ID الأصلي، هاي X في
+
+226
+00:26:09,170 --> 00:26:15,430
+G of X، وهذا أضفنا عليه كمان الـ term اللي عندنا
+
+227
+00:26:15,430 --> 00:26:23,230
+مش صفر، أضفنا عليه اللي هو عدد صحيح زوجي، تمام؟ طيب
+
+228
+00:26:23,230 --> 00:26:31,210
+كويس، إذن واضح إن هذا Subset من هذا، تمام؟ بس
+
+229
+00:26:31,210 --> 00:26:39,630
+لأن هل الـ principle ideal generated by X و 2 بده
+
+230
+00:26:39,630 --> 00:26:46,060
+يساوي Z of X؟ يعني هل كل الـ elements اللي في الـ Z و
+
+231
+00:26:46,060 --> 00:26:51,040
+X بقدر أكتبهم على الشكل هذا؟ لأ، هذا ممكن يكون
+
+232
+00:26:51,040 --> 00:26:55,480
+الزوج، وممكن يكون الفرد، وممكن يكون الصفر، صحيح؟
+
+233
+00:26:55,480 --> 00:27:02,120
+إذا لا يمكن لهذا الـ ID أنه يساوي مين؟ أنه يساوي الـ
+
+234
+00:27:02,120 --> 00:27:07,820
+ring الأصلية، يبقى هذا لا يمكن أن يساوي الـ ring
+
+235
+00:27:07,820 --> 00:27:12,760
+الأصلية من خلال الـ definition اللي عندنا، يبقى أنا
+
+236
+00:27:12,760 --> 00:27:19,200
+جبت ID آخر، الـ ID اللي عندي Subset منه ولا يساوي
+
+237
+00:27:19,200 --> 00:27:24,480
+يعني proper subset، وهذا في نفس الوقت proper
+
+238
+00:27:24,480 --> 00:27:30,360
+ولا يساوي الـ ring الأصلية، يبقى بناء عليه لا يمكن
+
+239
+00:27:30,360 --> 00:27:36,880
+لهذا أن يكون maximal ID، يبقى الـ principle
+
+240
+00:27:36,880 --> 00:27:40,340
+ideal generated by X is
+
+241
+00:27:44,440 --> 00:27:50,300
+not maximal، ممكن يكون maximum أبداً، هيك بكون أجبنا
+
+242
+00:27:50,300 --> 00:27:54,140
+على سؤالين من التمرين، ما بعرف سبعة و ثلاثين أظن، و
+
+243
+00:27:54,140 --> 00:27:59,400
+تسعة و عشرين، أو شغل رجل من أسئلة الكتاب، لأنه
+
+244
+00:27:59,400 --> 00:28:05,020
+مدخلهم في، في الحل، طيب، احنا هيك انتهينا
+
+245
+00:28:05,020 --> 00:28:09,720
+من هذا الـ section، والآن بنتقل إلى مناقشة بعض
+
+246
+00:28:09,720 --> 00:28:17,160
+المسائل، من، هنحدد بعض المسائل للمحاضرة القادمة، إن
+
+247
+00:28:17,160 --> 00:28:18,300
+شاء الله
+
+248
+00:28:40,070 --> 00:28:45,970
+بنرجع للـ exercises على chapter أربعة عشر، الـ exercises
+
+249
+00:28:45,970 --> 00:28:54,470
+of chapter أربعة عشر، سؤال
+
+250
+00:28:54,470 --> 00:29:04,690
+رابع، سؤال رابع، بقول find a subring، find a
+
+251
+00:29:04,690 --> 00:29:15,160
+subring of the Z plus Z direct sum that is not an
+
+252
+00:29:15,160 --> 00:29:32,860
+ideal، so find a subring that is not an ideal، solution
+
+253
+00:29:32,860 --> 00:29:37,580
+طبعاً
+
+254
+00:29:38,560 --> 00:29:42,940
+الـ direct sum، الـ element اللي هنا بيكون على شكل
+
+255
+00:29:42,940 --> 00:29:49,420
+ordered pair، يعني ذكر تذكير بس، الـ Z direct sum مع Z
+
+256
+00:29:49,420 --> 00:29:56,100
+يعني كل العناصر A و B، بحيث الـ A و الـ B موجودة
+
+257
+00:29:56,100 --> 00:30:01,780
+يعني موجودة في Z، أي العناصر اللي عليها، والجمع
+
+258
+00:30:01,780 --> 00:30:07,160
+componentwise، والضرب componentwise، طيب بقول
+
+259
+00:30:07,660 --> 00:30:16,060
+أثبت لي إنه هذه الـ subring، بدك تأخذ لي set S مثلاً
+
+260
+00:30:16,060 --> 00:30:21,560
+subset من هذه، وتحاول تثبت إنها الـ subring، يبقى
+
+261
+00:30:21,560 --> 00:30:29,900
+هذه بيكون عليها شكل قوس مركب من عنصرين، يلا مين
+
+262
+00:30:29,900 --> 00:30:36,460
+بأخذ عنصرين أبدًا؟ عنصرين منزل؟ يلا، بيحتوي على الـ
+
+263
+00:30:36,460 --> 00:30:45,180
+subring، وفي نفس الوقت مش ideal، يلا
+
+264
+00:30:45,180 --> 00:30:50,340
+ذكر ايش
+
+265
+00:30:50,340 --> 00:30:55,000
+ممكن يجي في بارك، أهو، اتنين، أو اتنين، أو اتنين
+
+266
+00:30:55,000 --> 00:31:02,240
+مثلاً، أخذت A و 2 كعنصر، يعني الـ A موجود في Z،
+
+267
+00:31:02,240 --> 00:31:08,220
+مين مكان يكون؟ و 2 صار ثابت، تمام، بنشوف هالـ subring
+
+268
+00:31:08,220 --> 00:31:14,400
+ولا لأ؟ طبعاً، non-empty، صحيح
+
+269
+00:31:14,400 --> 00:31:19,280
+موجود، والجمع، ناخذ عنصرين، ونطرحهم من بعض، حتى
+
+270
+00:31:19,280 --> 00:31:23,580
+يكون موجود، لأن 2 ممكن ناخذها عامل مشترك، والله
+
+271
+00:31:23,580 --> 00:31:32,620
+يطلع صفر، لو طرحناهم من بعض، بيطلع صفر، صح؟ يبقى بطل
+
+272
+00:31:32,620 --> 00:31:39,200
+الـ subring، بطل subring، صح ولا لأ؟ عادي عندنا الطرح، سقط اللي
+
+273
+00:31:39,200 --> 00:31:43,920
+هو الشرط الثاني، يبقى غيرها، اه، 2A و 2B
+
+274
+00:31:43,920 --> 00:31:50,920
+2A و 2B، طب ما تخليها A و B خلاص، طب
+
+275
+00:31:50,920 --> 00:31:55,360
+و يساوي، شو المشكلة؟ بتأخذها A و A، شو المشكلة؟
+
+276
+00:31:55,360 --> 00:32:04,000
+يبقى (A,A)، بحيث الـ A موجودة في Z، شوفوا
+
+277
+00:32:04,000 --> 00:32:10,900
+شوفوا، (0,0) موجودة في S ولا لأ؟ طيب الشرط
+
+278
+00:32:10,900 --> 00:32:18,320
+الأول صحيح، نجي للثاني، بتأخذ (a,a) و (b,b) موجودة
+
+279
+00:32:18,320 --> 00:32:22,120
+في S، يبقى (a-b, a-b) موجودة في S، الشرط
+
+280
+00:32:22,120 --> 00:32:27,500
+الثاني مظبوط، ثاني بارك، هنا (a,a) و خذ الرقم اللي
+
+281
+00:32:27,500 --> 00:32:34,760
+يعجبك، بعد ذلك من مين؟ من الـ S، (b,b)، يبقى بيصير
+
+282
+00:32:34,760 --> 00:32:41,320
+من؟ (ab,ab)، نفس الرقم موجود في S ولا يوجد في S؟ ليه
+
+283
+00:32:41,320 --> 00:32:53,860
+subring؟ يبقى هنا S هذه is a subring، يبقى check
+
+284
+00:32:53,860 --> 00:32:57,820
+بدك تروح تعمليها في الدفتر، أنا بقول سهل كده، أي شفوي
+
+285
+00:32:57,820 --> 00:33:03,100
+وأنت بدك تروح تعمليها تحريري، أنا بامن إنها ماهيش
+
+286
+00:33:03,100 --> 00:33:03,540
+ID
+
+287
+00:33:13,130 --> 00:33:18,970
+مش هنجيب في S، إذا ما نجتوش في S، يبقى بطل subring
+
+288
+00:33:18,970 --> 00:33:25,370
+اللي جاته في S، يبقى صارت main subring، أو صارت
+
+289
+00:33:25,370 --> 00:33:35,380
+ideal، طيب، بدنا نقول let X موجودة في S، and مثلاً (1،
+
+290
+00:33:35,380 --> 00:33:43,660
+3) موجودة في direct sum، عزيزي، عنصر هنا من الـ
+
+291
+00:33:43,660 --> 00:33:51,720
+ring الأصلية، وعنصر من الـ S، ثاني، الـ
+
+292
+00:33:51,720 --> 00:34:03,710
+X في (1،3)، بالضرب الـ A و الـ A مضروبة في (1،
+
+293
+00:34:03,710 --> 00:34:11,110
+3)، هذه بدها تساوي مين؟ ايه؟ (A،3A)؟
+
+294
+00:34:11,110 --> 00:34:17,390
+موجودة في S؟ لأ، يبقى this is not belonging to S
+
+295
+00:34:17,390 --> 00:34:24,990
+يبقى هنا S، الـ S is not ID
+
+296
+00:34:26,390 --> 00:34:30,490
+أنت ممكن تأخذ (2،3)، ممكن تأخذ (2،5)،
+
+297
+00:34:30,490 --> 00:34:34,950
+المهم الرقمين ما يكونوش زي بعض، وعندي جوداش مالة
+
+298
+00:34:34,950 --> 00:34:39,510
+لها من الأرقام، يبقى هذا مثال بسيط على أن الـ
+
+299
+00:34:39,510 --> 00:34:44,630
+subset اللي أخذتها هي subring، لكنها ليست
+
+300
+00:34:44,630 --> 00:34:55,830
+ideal. طيب، سؤال آخر، مثلاً زي سؤال ستة، سؤال ستة،
+
+301
+00:34:56,620 --> 00:35:02,560
+بيقول لي اوجد كل الـ maximal ideals، واعين الـ
+
+302
+00:35:02,560 --> 00:35:06,780
+maximal ideals
+
+303
+00:35:06,780 --> 00:35:23,060
+في Z8، Z10، Z12، Z n
+
+304
+00:35:25,670 --> 00:35:33,010
+نبدأ شكل الـ maximal ideal فيهم، احنا
+
+305
+00:35:33,010 --> 00:35:37,910
+أخذنا مثال Z12، وجبنا الـ maximal ideal فيهم
+
+306
+00:35:37,910 --> 00:35:44,870
+كمثال، تذكروا، والله راحت أدراج الرياح، وطبعاً
+
+307
+00:35:44,870 --> 00:35:49,550
+رسمنا، وعملنا لها الـ lattice، والمثال الوحيد اللي
+
+308
+00:35:49,550 --> 00:35:55,220
+عملنا الشبكية تبعته خلال هذا الـ section، وقلنا عندها
+
+309
+00:35:55,220 --> 00:35:58,800
+إن (2) و (3)، و الـ principle ideal generated
+
+310
+00:35:58,800 --> 00:36:02,780
+by 2، و الـ principle ideal generated by 3
+
+311
+00:36:02,780 --> 00:36:09,320
+are maximal ideals in Z12، مظبوط، لقيته في الدفاتر
+
+312
+00:36:09,320 --> 00:36:15,700
+ممتاز، يبقى هذا يا بنات، بياننا سابقاً، إن الـ
+
+313
+00:36:15,700 --> 00:36:20,020
+principle ideal generated by 2، و الـ principle
+
+314
+00:36:20,020 --> 00:36:25,000
+ideals generated by 3، هدول are maximal ideals
+
+315
+00:36:25,000 --> 00:36:31,400
+هدول الإثنين هما الـ maximal، خلي هالمعلومة عندك
+
+316
+00:36:31,400 --> 00:36:37,780
+هذه لزمان، طيب، نيجي لـ Z8، لـ Z8 بدي
+
+317
+00:36:37,780 --> 00:36:43,740
+أدور على الـ ideals تبعها، الآن لو جيت على الـ
+
+318
+00:36:43,740 --> 00:36:48,570
+principle ideals generated by 1، بتلاقيها هي الـ
+
+319
+00:36:48,570 --> 00:36:53,790
+principle ideal generated by 3، بتلاقيها هي الـ
+
+320
+00:36:53,790 --> 00:36:58,510
+principle ideal generated by 5، بتلاقيها هي الـ
+
+321
+00:36:58,510 --> 00:37:03,270
+principle ideal generated by 7، يعني كل primes
+
+322
+00:37:03,270 --> 00:37:09,290
+من 1 إلى 8، بيعطوني مين؟ بيعطوني نفس الـ
+
+323
+00:37:09,290 --> 00:37:15,750
+ring الأصلية، ليه؟ Z8، كل هذا بيساوي Z8
+
+324
+00:37:16,580 --> 00:37:22,960
+طيب، تمام، راح الـ 1 والـ 3 والـ 5 والـ 7، بقى
+
+325
+00:37:22,960 --> 00:37:32,520
+اللي عندي 2 و 4 و 6 وبس، مظبوط، والـ 0 صح؟
+
+326
+00:37:32,520 --> 00:37:36,920
+طيب، عندك الـ principle ideal generated by 0، اللي
+
+327
+00:37:36,920 --> 00:37:42,880
+هو 0 itself، عندك الـ principle ideal generated by
+
+328
+00:37:42,880 --> 00:37:49,560
+2، اللي هو {0، 2، 4، 6}، تمام؟ عندك الـ
+
+329
+00:37:49,560 --> 00:37:54,200
+principle ideal generated by 4، اللي هو {0،
+
+330
+00:37:54,200 --> 00:38:01,660
+4}، خلصنا؟ لأ، ما خلصناش، By الـ
+
+331
+00:38:01,660 --> 00:38:05,680
+principle ideal generated by 6، بيكون كله عندي
+
+332
+00:38:05,680 --> 00:38:13,630
+بيصير عندي {0}، وهي {2}، وهي {4}، وهي {6}، وهي
+
+333
+00:38:13,630 --> 00:38:17,790
+{0, 2, 4, 6}، بيضل الـ principle ideal generated by
+
+334
+00:38:17,790 --> 00:38:22,910
+6، بدي أعرفه من هنا، يبقى الـ principle ideal
+
+335
+00:38:22,910 --> 00:38:28,510
+generated by 6، هو {0، 6}، 6+6=12، من
+
+336
+00:38:28,510 --> 00:38:35,030
+8 بيضل 4، 6 في 3 =18، من 16
+
+337
+00:38:35,030 --> 00:38:40,830
+بيضل 2، 6 في 4 = 24، اللي هو مضاعفاتها {0،
+
+338
+00:38:40,830 --> 00:38:48,430
+2، 4، 6}، يبقى طالع هذه هي مين؟ يا Z2، يا Z6، يبقى
+
+339
+00:38:48,430 --> 00:38:53,530
+أنا بقول، ده ليه، أعمل الـ lattice، الشبكية تبعت هذه
+
+340
+00:38:53,530 --> 00:39:01,710
+الـ ring، مظبوط؟ يبقى بعدين بقول الأولاني، يا Z
+
+341
+00:39:01,710 --> 00:39:09,550
+8، أو هذه، أو هذه، أو هذه، كل واحد طلع
+
+342
+00:39:09,550 --> 00:39:16,370
+عندنا مين؟ principle ideal generated by 2، وطلع
+
+343
+00:39:16,370 --> 00:39:21,610
+منه الـ principle ideal generated by 4، وطلع الـ
+
+344
+00:39:21,610 --> 00:39:25,470
+principle ideal generated by 0، اللي هو يساوي
+
+345
+00:39:25,470 --> 00:39:31,530
+{0}، في غيرهم من الـ maximal، اللي هو الـ proper ولا
+
+346
+00:39:31,530 --> 00:39:38,160
+يساوي الـ ring الأصلي، منهم، الإثنين، طيب، ممتاز جداً، يبقى
+
+347
+00:39:38,160 --> 00:39:44,980
+هذه طلعت ليه الإثنين؟ طيب هنا، هنا بنات، 2 و 3
+
+348
+00:39:44,980 --> 00:39:51,880
+prime numbers، وكل واحد فيهم بيقسم 8، هذه طلعت
+
+349
+00:39:51,880 --> 00:39:58,180
+2 هو prime number بيقسم 8، بناء عليه هذه
+
+350
+00:39:58,180 --> 00:40:03,580
+منهم، الـ maximal، 2 و 5، 2 و 5، ممتازة
+
+351
+00:40:03,670 --> 00:40:08,210
+تبقى الـ principle ideal generated by 2، و الـ
+
+352
+00:40:08,210 --> 00:40:12,850
+principle ideal generated by 5، لو جيتي حسبتيهم
+
+353
+00:40:12,850 --> 00:40:18,230
+هيطلع الكلام اللي عندك هنا، طبعاً، طيب لو جيت أعمل
+
+354
+00:40:18,230 --> 00:40:24,450
+إنها الشبكية تبعها، فبيصير اللي بقول ايه، Z10، في
+
+355
+00:40:24,450 --> 00:40:28,910
+عند الـ principle ideal generated by 2، وفي الـ
+
+356
+00:40:28,910 --> 00:40:34,690
+principle ideal generated by 5، بعد هيك في الـ
+
+357
+00:40:34,690 --> 00:40:40,010
+principle ideal generated by 0، وهذا الـ principle ideal
+
+358
+00:40:40,010 --> 00:40:48,410
+generated by 0، هذه 5 وهذه 2، طبعاً، يبقى هذه
+
+359
+00:40:48,410 --> 00:40:54,790
+الشبكية تبعت الـ Z10، الـ باقي كل الأرقام الأخرى
+
+360
+00:40:54,790 --> 00:40:59,110
+مثلاً Z10، عزيزي، الـ principle هذه generated by
+
+361
+00:40:59,110 --> 00:41:04,340
+1، principle ideal generated by 3، principle
+
+362
+00:41:04,340 --> 00:41:08,640
+ideal generated by 7، principle ideal
+
+363
+00:41:08,640 --> 00:41:13,140
+generated by 9، by 9، كلهم هذول بيساووا بعض
+
+364
+00:41:13,140 --> 00:41:17,460
+يبقى كله هي الـ ring، هذول، والباقي هتلاقي واحدة
+
+365
+00:41:17,460 --> 00:41:21,460
+بتساوي ثانية، وما أظنش عندي إلا مين؟ إلا الأربعة اللي
+
+366
+00:41:21,460 --> 00:41:26,660
+بيبقى الـ maximal ideals هم مين؟ الإثنين و 5، مثل
+
+367
+00:41:26,660 --> 00:41:32,240
+ما قلنا، بناءً عليه، بدي الـ maximal ideals، هذه بيكونوا
+
+368
+00:41:32,240 --> 00:41:39,180
+هم كل الـ primes بحيث هذه الـ primes بتقسم الـ N، تقسم
+
+369
+00:41:39,180 --> 00:41:47,100
+الـ N، يبقى هذه كل الـ principle ideals generated by P
+
+370
+00:41:47,100 --> 00:41:58,550
+والـ P is prime divisor of N، يعني اللي بيكون
+
+371
+00:41:58,550 --> 00:42:03,450
+relatively prime in itself، جوداش جود ما يكون، إن
+
+372
+00:42:03,450 --> 00:42:07,950
+شاء الله تكون الـ result 500، ما عندناش مشكلة فيها،
+
+373
+00:42:07,950 --> 00:42:12,530
+يظهر هاي حلّيناها، طبعاً هذا حلّيناها سابقاً، وهي حل
+
+374
+00:42:12,530 --> 00:42:19,290
+ذلك الـ 3، الأخيرة سنتج بناءً على مين؟ بناءً على
+
+375
+00:42:19,290 --> 00:42:21,810
+الـ rings الـ 3 اللي عندنا
+
+376
+00:42:24,920 --> 00:42:33,640
+طيب، نروح لسؤال أربعة عشر، مثلاً، نفترض سؤال أربعة
+
+377
+00:42:33,640 --> 00:42:39,640
+عشر، سؤال أربعة عشر بيقول،  ليكن الـ A والـ B ideals،
+
+378
+00:42:39,640 --> 00:42:50,980
+الـ A والـ B ideals، أثبت أن الـ A intersection B
+
+379
+00:42:50,980 --> 00:42:52,920
+يساوي الـ A
+
+380
+00:43:17,180 --> 00:43:21,780
+الآن، تعلمنا من الـ set theory، لكي نثبت أن set هي
+
+381
+00:43:21,780 --> 00:43:25,480
+subset من set، بدي آخذ element في الـ set الأولى، وأثبت
+
+382
+00:43:25,480 --> 00:43:28,900
+إنه موجود في الـ set الثانية، وأبسط اللي أشاء
+
+383
+00:43:28,900 --> 00:43:33,680
+في مبادئ رياضية على كل المعلومات اللي عندنا، إثنين
+
+384
+00:43:33,680 --> 00:43:38,680
+هذول ideals، بس حصل ضرب الـ A في B، ما شفتاش له تعريف
+
+385
+00:43:38,680 --> 00:43:42,520
+جديد لك، طب
+
+386
+00:43:42,520 --> 00:43:46,260
+إذا بدنا نروح و نحط التعريف اللي حطه الكتاب من
+
+387
+00:43:46,260 --> 00:43:53,310
+خلال التمرين، يبقى solution، في سؤال 12 اللي جاب له
+
+388
+00:43:53,310 --> 00:44:00,250
+راح حطّني حاصل الضرب، قرفلّي حاصل الضرب A في B، وكل
+
+389
+00:44:00,250 --> 00:44:11,610
+العنصر A1 B1 + A2 B2 + ... + An Bn، بحيث أن الـ Ai موجودة
+
+390
+00:44:11,610 --> 00:44:20,350
+في A، وأنكوا كمان منه، والـ Bi موجودة
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d71752215a8821c5d89df2220cda799850a0b770
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_postprocess.srt
@@ -0,0 +1,1768 @@
+1
+00:00:20,640 --> 00:00:25,720
+بسم الله الرحمن الرحيم عوض على بدء نذكر بما
+
+2
+00:00:25,720 --> 00:00:31,160
+أعطيناه المرة الماضية لأن هذه الكترولري تعتمد على
+
+3
+00:00:31,160 --> 00:00:35,500
+ما درسناه في المحاضرة الماضية المحاضرة الماضية
+
+4
+00:00:35,500 --> 00:00:39,860
+كانت عمود شقري هو نظري تاني النظرية الأولى بتقول
+
+5
+00:00:39,860 --> 00:00:44,370
+لو كانت ال R is commutative ring with unityيبقى من
+
+6
+00:00:44,370 --> 00:00:48,390
+الـ R modulo A is an integral domain if and only
+
+7
+00:00:48,390 --> 00:00:53,630
+if الـ ID الـ A is a prime والنظرية التانية برضه
+
+8
+00:00:53,630 --> 00:00:58,990
+نفس الموطنة تبع النظرية الأولى اللي هو الـ R
+
+9
+00:00:58,990 --> 00:01:02,310
+committed to bring with unity لكن القلاف عند
+
+10
+00:01:02,310 --> 00:01:07,930
+المطلوب فبنقول الـ R modulo A is a field if and
+
+11
+00:01:07,930 --> 00:01:14,040
+only if الـ A is a maximal IDهذا آخر حاجة أثبتناها
+
+12
+00:01:14,040 --> 00:01:18,000
+المرة الماضية الكرولري عبارة عن نتيجة على
+
+13
+00:01:18,000 --> 00:01:22,240
+النظريتين بتقول لو كانت ال R commutative ring with
+
+14
+00:01:22,240 --> 00:01:29,880
+unity يبقى every maximal ideal is prime يبقى ال
+
+15
+00:01:29,880 --> 00:01:39,840
+proof كالتالي ال R is commutative ring with unity
+
+16
+00:01:44,120 --> 00:01:50,080
+طبعا يبقى بدي افترض انه عندي ideal و ال ideal is
+
+17
+00:01:50,080 --> 00:02:01,580
+maximum let ال a be a maximal ideal
+
+18
+00:02:01,580 --> 00:02:11,880
+of R بالنظرية الثانية يبقى ال R modulo a is a
+
+19
+00:02:11,880 --> 00:02:20,600
+fieldيبقى بروح بقوله by the second theorem
+
+20
+00:02:20,600 --> 00:02:32,860
+بالنظرية الثانية ال a modulo a is a field طبعا
+
+21
+00:02:32,860 --> 00:02:40,680
+احنا قلنا قبل ذلك any field is an integral domain
+
+22
+00:02:41,190 --> 00:02:48,770
+هذا بدي يعطينا ان ال R موديول A is an integral
+
+23
+00:02:48,770 --> 00:02:54,070
+domain يبقى
+
+24
+00:02:54,070 --> 00:03:04,290
+بروحنا نقوله by the first theorem النظرية
+
+25
+00:03:04,290 --> 00:03:13,960
+الأولى ال A is a prime IDيبقى أثبتنا إن الـ
+
+26
+00:03:13,960 --> 00:03:20,420
+maximal ideal عبارة عن prime ideal إذا كانت الـR
+
+27
+00:03:20,420 --> 00:03:26,620
+is commutative with unity وصلنا إلى آخر مثال في
+
+28
+00:03:26,620 --> 00:03:34,840
+هذا ال section وهو الاردن يقول
+
+29
+00:03:34,840 --> 00:03:35,960
+the ideal
+
+30
+00:03:39,630 --> 00:03:46,970
+أو الـ principal ideal generated by X is a prime
+
+31
+00:03:46,970 --> 00:03:55,510
+ideal in Z of X but not maximum
+
+32
+00:04:18,540 --> 00:04:24,720
+هذا المثال مشان نحله بيعتمد على سؤالين موجودين في
+
+33
+00:04:24,720 --> 00:04:29,980
+الكتاب مثل ما ذكر الكتاب احنا هنحل السؤالين وانتوا
+
+34
+00:04:29,980 --> 00:04:36,200
+مش دارين من خلال اثباتنا أو خلال حلنا لهذا السؤال
+
+35
+00:04:36,200 --> 00:04:40,840
+أول شي بقوللي ال principle id generated by X هو
+
+36
+00:04:40,840 --> 00:04:45,340
+عبارة عن ال prime ideal في هذه ال ring لكنه ليس
+
+37
+00:04:45,340 --> 00:04:49,720
+maximumيبقى بدي أثبت شغل تاني ان ال principle
+
+38
+00:04:49,720 --> 00:04:54,260
+ideal generated by X هو prime ideal وفي نفس الوقت
+
+39
+00:04:54,260 --> 00:05:00,380
+ليس maximum ideal كمان في Z of X علشان هيك بدنا
+
+40
+00:05:00,380 --> 00:05:04,300
+نبدأ نثبت ال maximum لإن بدنا نثبت اللي هو يفتقر
+
+41
+00:05:04,300 --> 00:05:09,460
+انه prime ideal لكن قبل ذلك خلينا نرجع لتعريف ال
+
+42
+00:05:09,460 --> 00:05:16,210
+principle ideal generated by X قلنا سابقاكل ال
+
+43
+00:05:16,210 --> 00:05:23,070
+elements ال X في R بحيث ال R موجودة في R X R والله
+
+44
+00:05:23,070 --> 00:05:26,290
+R X الاتنين R ده similar لإن ال ring commuted
+
+45
+00:05:26,290 --> 00:05:32,510
+تمام؟ يبقى كل ال X في R بحيث ال R موجودة في R هذا
+
+46
+00:05:32,510 --> 00:05:36,930
+ال general definition لمين؟ لل principle ideal
+
+47
+00:05:36,930 --> 00:05:42,050
+generated by X بدي أروح أطبق هذا التعريف عالميا
+
+48
+00:05:42,050 --> 00:05:47,270
+على ال ring اللي عندنايبقى بقدر أقول هذا كل ال
+
+49
+00:05:47,270 --> 00:05:59,870
+element x كل ال element f of x اللي موجودة في ال z
+
+50
+00:05:59,870 --> 00:06:10,110
+of x such that ان ال x في ال g ان ال f of xشو
+
+51
+00:06:10,110 --> 00:06:16,930
+شكلها .. شو شكل سبعها بحيث ال F of X يساوي ال X في
+
+52
+00:06:16,930 --> 00:06:25,650
+ال G of X وال G of X هذه موجودة في Z of X الشكل
+
+53
+00:06:25,650 --> 00:06:32,290
+اللي عندنا إذا أنا قاعد تعريف اللي هو ال principle
+
+54
+00:06:32,290 --> 00:06:37,510
+ideal generated by X بما يناسب طبيعة المسألة اللي
+
+55
+00:06:37,510 --> 00:06:42,850
+عندنايبقى كل الـ Functions أو الـ Polynomials اللي
+
+56
+00:06:42,850 --> 00:06:47,830
+المعاملات تبعتها أعداد صحيحة اللي بتكون على الشكل
+
+57
+00:06:47,830 --> 00:06:53,990
+التالي X في G of X أنا قولنا X في R بدي أخد R من
+
+58
+00:06:53,990 --> 00:06:58,890
+الـ Z يعني بدي أخد الـ G of X من الـ Z of X مضروبة
+
+59
+00:06:58,890 --> 00:07:06,010
+في المين في الـ F X الآن بدي أفترض أن عندنا ستانية
+
+60
+00:07:06,510 --> 00:07:18,130
+يبقى باجي بقوله consider the ideal I ال
+
+61
+00:07:18,130 --> 00:07:22,490
+I هذا أثبتناه قبل ذلك أنه ideal كل ال polynomials
+
+62
+00:07:22,490 --> 00:07:27,750
+اللي المقدار الثابت فيها يساوي الصفر تذكروا المرة
+
+63
+00:07:27,750 --> 00:07:33,630
+علينا و أثبتناه أنه ideal يبقى ال ideal I كل ال F
+
+64
+00:07:33,630 --> 00:07:40,740
+of Xsuch that ال F of Zero بده يساوي مين؟ Zero طب
+
+65
+00:07:40,740 --> 00:07:44,480
+إيش علاقة هذا بالموضوع؟ آه دلوقت بنريك إيش علاقة
+
+66
+00:07:44,480 --> 00:07:54,360
+هذا الموضوع الان يا عزيزي اننا ندعي
+
+67
+00:07:54,360 --> 00:07:59,810
+ان ال principle ID generated by X بده يساوي Iأنا
+
+68
+00:07:59,810 --> 00:08:05,230
+أدّعي أن هذا ال ideal هو هذا ال ideal مضبط تماما
+
+69
+00:08:05,230 --> 00:08:09,630
+شكله مش مبين هذا في شجه و هذا في شجه لكن احنا
+
+70
+00:08:09,630 --> 00:08:15,150
+بنشتغل شغل رياضي بحيث فعلا نثبت أن هذا يساوي هذا
+
+71
+00:08:15,150 --> 00:08:24,230
+إذا مشان هيك أفترض أن F of X موجود في ال principle
+
+72
+00:08:24,230 --> 00:08:30,760
+ideal generated by Xيبقى في هذه الحالة ال F of X
+
+73
+00:08:30,760 --> 00:08:36,080
+بدها تساوي هاي يبقى ال F of X بدها تساوي مين؟ ال X
+
+74
+00:08:36,080 --> 00:08:43,520
+في G of X يبقى ال X في G of X طيب لو جيت و قلت بدي
+
+75
+00:08:43,520 --> 00:08:49,180
+أشوف قداشي ال F of Zero بدها تساوي يبقى بدها تساوي
+
+76
+00:08:49,180 --> 00:08:56,230
+Zero في G of ZeroD of Zero Zero والله اي رقم اخر
+
+77
+00:08:56,230 --> 00:09:01,270
+اضربه في Zero بده يعطيني Zero element ايش تفسيرك
+
+78
+00:09:01,270 --> 00:09:07,210
+لهذا الكلام ان ال F of X موجودة وين في ال I ده في
+
+79
+00:09:07,210 --> 00:09:13,710
+ال I مظبوط يبقى هذا بده يعطينا مين ان ال F of X
+
+80
+00:09:13,710 --> 00:09:20,200
+موجودة وين في ال I دي ال Iهذا بدّه يعطينا ان ال
+
+81
+00:09:20,200 --> 00:09:24,660
+principle ideal generated by X subset من مين؟
+
+82
+00:09:24,660 --> 00:09:31,120
+subset من I وهذه الخطوات الأولى on the other hand
+
+83
+00:09:31,120 --> 00:09:34,980
+يبقى
+
+84
+00:09:34,980 --> 00:09:42,880
+on the other hand من الناحية الأخرى بدّه اجي أقوله
+
+85
+00:09:42,880 --> 00:09:49,770
+افترضي ان ال F of X موجودة وين؟موجودة في الـ I دي
+
+86
+00:09:49,770 --> 00:09:53,930
+الـ I بدي أحاول أثبت أن ال F of X موجودة في ال X
+
+87
+00:09:53,930 --> 00:10:04,950
+موجودة في ال X then ال F of X بدي أثبت أن F of X
+
+88
+00:10:04,950 --> 00:10:05,170
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+89
+00:10:05,170 --> 00:10:07,410
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+90
+00:10:07,410 --> 00:10:08,310
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+91
+00:10:08,310 --> 00:10:08,390
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+92
+00:10:08,390 --> 00:10:08,430
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+93
+00:10:08,430 --> 00:10:13,450
+موجودة في ال X موجودة في ال X موجودة في ال
+
+94
+00:10:17,070 --> 00:10:23,150
+ليش؟ لإن ال I عندها فيه ال term الأخير ب zero
+
+95
+00:10:23,150 --> 00:10:26,990
+تمام؟ يبقى طيارة ال term الأخير اللي هو ال
+
+96
+00:10:26,990 --> 00:10:31,790
+constant and ال mean zero لإن F of zero زيرو زيرو
+
+97
+00:10:31,790 --> 00:10:37,170
+زيرو كلهم زيرو مضلش إلا ال term الأخير تمام؟ طيب
+
+98
+00:10:37,170 --> 00:10:42,150
+كويس يبقى ال F of X سوى الشكل اللي عندها ده أليس
+
+99
+00:10:42,150 --> 00:10:51,720
+كذلك؟ هذه عبارة عن X ب A Mx in minus one زائد a in
+
+100
+00:10:51,720 --> 00:10:59,700
+minus one x in minus two زائد a one يعني أخدنا x
+
+101
+00:10:59,700 --> 00:11:07,420
+عامل مشترك هذه كلها function موجودة في z of x ولا
+
+102
+00:11:07,420 --> 00:11:15,060
+لا صح إذا بقدر أقول هذه x وشكلها على الشكل التالي
+
+103
+00:11:15,390 --> 00:11:19,490
+هذه موجودة في الـ Principle ID الـ generated by X
+
+104
+00:11:19,490 --> 00:11:26,330
+طبعاً للتعريف تبعه، مظبوط؟ يعني إيش استفدنا؟ أخدنا
+
+105
+00:11:26,330 --> 00:11:33,610
+F of X موجودة في I، دجينا الـ F of X موجودة في الـ
+
+106
+00:11:33,610 --> 00:11:37,850
+Principle ID الـ generated by X، يبقى بجيب أقول له
+
+107
+00:11:37,850 --> 00:11:42,830
+الـ Principle ID الـ generated by X يساوي الـ I
+
+108
+00:11:42,830 --> 00:11:51,520
+كما زعمناقبل قليل، إذا صار عندنا هذا معناه هو هذا
+
+109
+00:11:51,520 --> 00:11:57,460
+يبقى ال principle ideal generated by X هو الـ I،
+
+110
+00:11:57,460 --> 00:12:03,460
+الـ I بالضبط تماماً. طيب، إحنا حتى الآن ما سوناش
+
+111
+00:12:03,460 --> 00:12:09,180
+شيء، سونا مقدمة، المقدمة هذه لزمان، ديرا بالكم
+
+112
+00:12:09,180 --> 00:12:13,640
+مثلها ده في الكتاب، وبيعتمد على سؤالين من الكتاب.
+
+113
+00:12:13,980 --> 00:12:17,800
+هنحل السؤالين و احنا مش دارين ان احنا حلناهم و
+
+114
+00:12:17,800 --> 00:12:24,120
+احنا بنبرهن في السؤال طيب ندل الان للمعلومات اللي
+
+115
+00:12:24,120 --> 00:12:29,860
+احنا عارفينها و مقمنين اليها ال ideal هذا بدي اثبت
+
+116
+00:12:29,860 --> 00:12:34,500
+انه prime ideal يبقى بدي اخد two functions هنا
+
+117
+00:12:34,500 --> 00:12:41,860
+بحيث يكون حصل ضربهم موجود هنا وبالتالي اثبت يا اما
+
+118
+00:12:41,860 --> 00:12:45,680
+الدالة الأولىموجودة في ال principle I D generated
+
+119
+00:12:45,680 --> 00:12:52,900
+I X يا إما دلّه الثاني بقوله كويسة يبقى لان بتاجي
+
+120
+00:12:52,900 --> 00:13:01,820
+اقوله افترض ان عندي دالتين G وH موجودة تمين في Z
+
+121
+00:13:01,820 --> 00:13:12,010
+of X such that بحيث ان الـ G H موجودةموجودة في ال
+
+122
+00:13:12,010 --> 00:13:16,870
+principle ideal generated by X مش هو هذا اللي بثبت
+
+123
+00:13:16,870 --> 00:13:22,910
+انه prime يبقى أخد two elements من ال ring الأصلية
+
+124
+00:13:22,910 --> 00:13:29,050
+بحيث حصل ضربهما موجود هنا بيقولوا كويس يبقى بناء
+
+125
+00:13:29,050 --> 00:13:34,350
+ان عليه بدي أحاول أثبت يا إما ال G موجودة في ال
+
+126
+00:13:34,350 --> 00:13:38,130
+principle ideal generated by X يا إما ال H اللي
+
+127
+00:13:38,130 --> 00:13:47,310
+موجودة مظبوططيب كويس then لو أخدت يا بنات gh
+
+128
+00:13:47,310 --> 00:13:54,710
+تأثيرها على ال zero الشكل دي عندنا هنا طبقا
+
+129
+00:13:54,710 --> 00:14:01,410
+للكلكورات أليس هذا هو g of zero في ال h of zero
+
+130
+00:14:01,410 --> 00:14:08,210
+نعم احنا أخدنا حاصل ضرب موجود هنا اللي هو في ال x
+
+131
+00:14:08,210 --> 00:14:14,750
+طيب من ال x؟مش هي ال I صح؟ يعني بتقدر تقول
+
+132
+00:14:14,750 --> 00:14:20,890
+الموجودة في ال H اللي هي بدها تساوي ال I هي
+
+133
+00:14:20,890 --> 00:14:24,110
+أخدناها الموجودة في ال X اللي هي بدها تساوي ال I
+
+134
+00:14:24,110 --> 00:14:29,690
+يبقى تأثيرها على ال Zero بده يساوي قداش؟ بده يساوي
+
+135
+00:14:29,690 --> 00:14:35,710
+ال Zero itself طب ال G of Zero و ال H of Zero انت
+
+136
+00:14:35,710 --> 00:14:42,070
+جارز ولا لا؟ انت جارز؟هل يُعقل إن حاصل ضربهما يكون
+
+137
+00:14:42,070 --> 00:14:49,270
+بـ0 إلا إذا كان حضرهما بـ0 يبقى فادي بيقول لهم but
+
+138
+00:14:49,270 --> 00:15:01,650
+ولكن الـG of 0 and الـH of 0 are integers يبقى
+
+139
+00:15:01,650 --> 00:15:11,270
+so الـG of 0 الـH of 0 بدي سوى 0imply ان الـG of 0
+
+140
+00:15:11,270 --> 00:15:18,810
+بتساوي 0 او الـH of 0 هو اللي بتساوي 0 طيب اذا G
+
+141
+00:15:18,810 --> 00:15:24,770
+of 0 تساوي 0 يبقى موجودة في X ولا لا يعني في I
+
+142
+00:15:24,770 --> 00:15:31,710
+يبقى هذا بيدي يعطينا ان الـG of X موجودة في
+
+143
+00:15:31,710 --> 00:15:38,660
+الـprinciple ID generated by X او الـH of Xموجودة
+
+144
+00:15:38,660 --> 00:15:43,980
+في من في ال principle ideal generated by X فمش
+
+145
+00:15:43,980 --> 00:15:49,840
+معناه هذا الكلام؟ prime ideal يبقى هذا بده يعطينا
+
+146
+00:15:49,840 --> 00:15:57,360
+ان ال principle ideal generated by X is a prime
+
+147
+00:15:57,360 --> 00:16:05,330
+ideal يبقى أثبتنا الشطر الأول من هذا المثالبدا
+
+148
+00:16:05,330 --> 00:16:09,250
+نيجي للشطر الثاني نثبت ان ال principle ideal
+
+149
+00:16:09,250 --> 00:16:16,430
+generated by X is not maximum نرجع بالذاكرة الى
+
+150
+00:16:16,430 --> 00:16:21,400
+الوراقالـ Maximum Ideal كيف بثبت انه Maximum؟ نجيب
+
+151
+00:16:21,400 --> 00:16:28,100
+Ideal تاني هات ال Ideal اللي عندنا يكون subset منه
+
+152
+00:16:28,100 --> 00:16:32,660
+و ال Ideal الثاني هذا subset من R وبالتالي ال
+
+153
+00:16:32,660 --> 00:16:37,100
+Ideal اللي عندنا يا إما بدي يسوى ال Ideal الجديد
+
+154
+00:16:37,100 --> 00:16:41,960
+يا ال Ideal الجديد بدي يسوى Ring R صح ولا ده؟ طيب
+
+155
+00:16:41,960 --> 00:16:47,530
+تعالوا نشوف هالست هانيبقى بالداخل اقول consider
+
+156
+00:16:47,530 --> 00:16:56,710
+the set ال set بالدرموز اللي هي x و 2 جديد
+
+157
+00:16:56,710 --> 00:17:04,530
+هذا علينا صح نشوف مين هي هذه يبدو هذه كل العناصر f
+
+158
+00:17:04,530 --> 00:17:12,180
+of x اللي موجودة في z of x such thatالـ F of X
+
+159
+00:17:12,180 --> 00:17:23,880
+بيتساور X الـ G of X زائد 2H of X إيش
+
+160
+00:17:23,880 --> 00:17:30,900
+يعني؟ يعني كل ال functions اللي المقدار الثابت هنا
+
+161
+00:17:30,900 --> 00:17:37,260
+تبعها بيكون عدد زوجي H of X جد ما تقطع تظهر بيها
+
+162
+00:17:37,260 --> 00:17:43,200
+في 2 بيصير عدد زوجي صحيح ولا لأ؟يعني بالبلد زي ما
+
+163
+00:17:43,200 --> 00:17:47,600
+عرفنا اتنين هدول بيقول كل ال F of X في حيث F of
+
+164
+00:17:47,600 --> 00:17:52,740
+Zero بده يساوي اتنين K اتنين K اللي هو على زوجيك
+
+165
+00:17:52,740 --> 00:17:57,260
+بيه اتنين في H of X هذا ما يعني ايه الست اللي
+
+166
+00:17:57,260 --> 00:18:02,840
+عندنا هل هي ايدين اذا أثبتنا انها ايدين خلاص هنحلت
+
+167
+00:18:02,840 --> 00:18:09,320
+مشكلتنا نهائيا يبقى انا ازعم ان هذه ايدين بس
+
+168
+00:18:09,320 --> 00:18:24,430
+بتكتسبيبقى now ال X والإتنين is an ID because ليش؟
+
+169
+00:18:24,430 --> 00:18:31,950
+بتدل النقطة الأولة ال X والإتنين is من M
+
+170
+00:18:35,820 --> 00:18:40,620
+يبقى هذه المهنية الشفرة فيها على الأقل ولو عمصر
+
+171
+00:18:40,620 --> 00:18:48,240
+واحد لإيش؟ since لو أخدت ال F of Zero هناك كدهش
+
+172
+00:18:48,240 --> 00:18:55,100
+بده يساوي؟ Zero زائد اتنين H of Zero يبقى Zero
+
+173
+00:18:55,100 --> 00:19:03,240
+زائد اتنين H of Zero يبقى موجودة هنا ولا هناك صح؟
+
+174
+00:19:03,520 --> 00:19:08,820
+يبقى هذه موجودة في الـ principle في الـ 6 اللي
+
+175
+00:19:08,820 --> 00:19:15,240
+عندناها طيب النقطة الثانية إذا أخدت elements مثلًا
+
+176
+00:19:15,240 --> 00:19:27,100
+F1 و F2 موجودة في الـ 6 اللي عندناها ثاني ال F1 of
+
+177
+00:19:27,100 --> 00:19:32,860
+X تساوي خطة موجودة يبقى اش بده تساوي بده تساوي ال
+
+178
+00:19:32,860 --> 00:19:46,180
+Xالـ G1 of X زائد 2H1 of X والـ F2 of X بتساوي الـ
+
+179
+00:19:46,180 --> 00:19:55,960
+X في الـ G2 of X زائد 2H2 of X هي أحتياط عمصرين
+
+180
+00:19:55,960 --> 00:20:02,500
+موجودات في هذه الستة بتشوف الفرق في ما بينهماقداش
+
+181
+00:20:02,500 --> 00:20:10,560
+بده يساوي يبقى هادي بدي أقوله بده ال F1 ناقص F2 as
+
+182
+00:20:10,560 --> 00:20:16,540
+a function of X طبقا لمعلوماتنا في ال calculus F1
+
+183
+00:20:16,540 --> 00:20:24,200
+of X ناقص F2 of X بده أطرح هدول من بعض يبقى لو
+
+184
+00:20:24,200 --> 00:20:34,330
+طرحته من هناك بده يصير X في G1 of X-G2 of X زائد
+
+185
+00:20:34,330 --> 00:20:47,250
+اتنين في H1 of X ناقص H2 of X ويسافر هذه بقدر
+
+186
+00:20:47,250 --> 00:20:57,150
+اكتبها على الشكل X في G1 ناقص G2 of X وهذه زائد
+
+187
+00:20:57,150 --> 00:21:04,200
+اللي هو الاتنينفمين في H واحد ناقص H اتنين كل هذا
+
+188
+00:21:04,200 --> 00:21:09,980
+a function of X أليس تهالي على الصيغة اللي فوق هذه
+
+189
+00:21:09,980 --> 00:21:18,340
+صح يبقى صار الفرق فيما بينهما موجود وين موجود يبقى
+
+190
+00:21:18,340 --> 00:21:25,940
+هذا بدي يعطينا ان ال F واحد ناقص F اتنين موجودةفي
+
+191
+00:21:25,940 --> 00:21:32,360
+الـ 6 اللي هو الـ X و 2 ضايل علينا مين؟ النقطة
+
+192
+00:21:32,360 --> 00:21:42,140
+الأخيرة يبقى النقطة الثالثة بقول مافي خدلي ال F of
+
+193
+00:21:42,140 --> 00:21:54,820
+X موجودة في مين؟ في ال ring الأساسية أن ال F1 of X
+
+194
+00:21:55,080 --> 00:22:03,660
+و من F1 هاجر اللي هي باتنية موجودة و موجودة في
+
+195
+00:22:03,660 --> 00:22:11,120
+الست اللي عندناها then بتاخد حاصل الطرق إلها then
+
+196
+00:22:11,120 --> 00:22:23,500
+if F1 of X بدل ساول F of X فالـ F1 of X بدل ساول F
+
+197
+00:22:23,500 --> 00:22:38,180
+of Xالـ F1 هي جازة يبقى X G1 يبقى X G1 of X زائد 2
+
+198
+00:22:38,180 --> 00:22:52,640
+H1 of X شكل اللي عندنا هذا طيب هذه صارت الـ F F1
+
+199
+00:22:52,640 --> 00:22:58,450
+of Xيساوى هذي بقدر .. طبعا ال ring قبلنا
+
+200
+00:22:58,450 --> 00:23:06,510
+commutative يبقى هذي X في ال F of X في ال G1 of X
+
+201
+00:23:06,510 --> 00:23:16,830
+زائد اتنين F of X في ال H1 of X اللي بقدر اكتبها
+
+202
+00:23:16,830 --> 00:23:28,420
+على الشكل التالي X اللي هي LXفي ال FG1 as a
+
+203
+00:23:28,420 --> 00:23:38,740
+function of X زائد اتنين F F1 F F1 كله as a
+
+204
+00:23:38,740 --> 00:23:44,720
+function of X يبقى هذه هنا كتبتها على صيغة هذه
+
+205
+00:23:44,720 --> 00:23:49,260
+أليست الصيغة هذه هي الصيغة اللي عندنا؟ أستاذ اتنين
+
+206
+00:23:49,260 --> 00:24:00,720
+F H واحد مش F واحدH1 اتنين F H1 و هذه G1 مظبوط
+
+207
+00:24:00,720 --> 00:24:04,660
+كلامكوا صحيح مظبوطي بصرت على الصيغة اللي قدامنا
+
+208
+00:24:04,660 --> 00:24:08,840
+هذه ولا لا على الصيغة اللي قدامنا هذه ولا لا تمام
+
+209
+00:24:08,840 --> 00:24:14,920
+اذا الهدف اللي بده يعطينا انه مين ال F ال F1
+
+210
+00:24:14,920 --> 00:24:24,620
+موجودة في ال principal ideal generatedby x و 2 by
+
+211
+00:24:24,620 --> 00:24:32,300
+x و 2 يا ابنها أنا عليه هذا صار أيديل ولا لا يا
+
+212
+00:24:32,300 --> 00:24:37,900
+ابنها؟ كويس طب استاذ أنا سامحت سامحت ال g of x ولا
+
+213
+00:24:37,900 --> 00:24:43,120
+h of x موجودين برضه في ال ring الأصلية؟ أه بالضبط
+
+214
+00:24:43,120 --> 00:24:50,250
+سؤال تاني أيضا ال g of x ولا h of x في الأصلية؟هذه
+
+215
+00:24:50,250 --> 00:25:00,830
+وهذه يظهر في التعريف الـ G of X والـ H of X عبارة
+
+216
+00:25:00,830 --> 00:25:06,390
+عن كثيرات حدود في Z of X ليس من خلق جايبينها كل
+
+217
+00:25:06,390 --> 00:25:11,430
+شغل لداخل ال ring Z of X ماخلة ذلك ماليش علاقة فيه
+
+218
+00:25:11,430 --> 00:25:16,410
+يعني المعاملات كلها أعداد صحيحة من ال set of
+
+219
+00:25:16,410 --> 00:25:21,870
+integersطيب، لغاية هنا إيش اللي أثبتناها؟ أثبتناها
+
+220
+00:25:21,870 --> 00:25:30,910
+ده عبارة عن IE يبقى هنا بقولوا بص و هكذا ال X و 2
+
+221
+00:25:30,910 --> 00:25:38,270
+is an ideal أو is a principle، ideal generated by
+
+222
+00:25:38,270 --> 00:25:45,830
+X و 2 طيب، احنا إيش بدنا نثبت؟ Maximality، يبقى
+
+223
+00:25:45,830 --> 00:25:53,890
+احنا جيبنا ideal جديدال ID للجديد شو علاقته بال ID
+
+224
+00:25:53,890 --> 00:25:59,110
+للأصلي تمام
+
+225
+00:25:59,110 --> 00:26:09,170
+سبست منه ولا يساوي أكيد هاي ال ID للأصلي هاي X في
+
+226
+00:26:09,170 --> 00:26:15,430
+G of X وهذا لأ عضفنا عليه كمان ال term اللي عندنا
+
+227
+00:26:15,430 --> 00:26:23,230
+مش Zeroأضفنا عليه اللي هو عدد صحيح زوجي، تمام؟ طيب
+
+228
+00:26:23,230 --> 00:26:31,210
+كويس، إذن واضح إن هذا معنى سبسي من هذا، تمام؟ بس و
+
+229
+00:26:31,210 --> 00:26:39,630
+لأن هل ال principle ideal generated by X و 2 بده
+
+230
+00:26:39,630 --> 00:26:46,060
+يساوي Z of X؟يعني هل كل ال elements اللي في ال Z و
+
+231
+00:26:46,060 --> 00:26:51,040
+X بقدر أكتبهم على الشكل هذا؟ لأ، هذا ممكن يكون
+
+232
+00:26:51,040 --> 00:26:55,480
+الزوج و ممكن يكون الفرد و ممكن يكون الصفر، صحيح؟
+
+233
+00:26:55,480 --> 00:27:02,120
+إذا لا يمكن لهذا ال ID أنه يسوى مين؟ أنه يسوى ال
+
+234
+00:27:02,120 --> 00:27:07,820
+ring الأصلية، يبقى هذا لا يمكن أن يسوى ال ring
+
+235
+00:27:07,820 --> 00:27:12,760
+الأصلية من خلال ال definition اللي عندنايبقى أنا
+
+236
+00:27:12,760 --> 00:27:19,200
+جبت ID الآخر ال ID اللي عندي subset منه ولا يسوي
+
+237
+00:27:19,200 --> 00:27:24,480
+يعني proper subset وهذا في نفس الوقت ضال proper
+
+238
+00:27:24,480 --> 00:27:30,360
+ولا يسوي ال ring الأصلية يبقى بناء عليه لا يمكن
+
+239
+00:27:30,360 --> 00:27:36,880
+لهذا أن يكون maximal ID يبقى بصر ال principle
+
+240
+00:27:36,880 --> 00:27:40,340
+ideal generated by X is
+
+241
+00:27:44,440 --> 00:27:50,300
+maximal ممكن يكون maximum أبداً هيك يكون أجابنا
+
+242
+00:27:50,300 --> 00:27:54,140
+على سؤالين من التمرين ما بعرف سبعة و تلاتين اظن و
+
+243
+00:27:54,140 --> 00:27:59,400
+تسعة و عشرين او شغل رجل من أسئلات الكتاب لأنه
+
+244
+00:27:59,400 --> 00:28:05,020
+مدخلهم في من في الحل اللعنى طيب احنا هيك انتهينا
+
+245
+00:28:05,020 --> 00:28:09,720
+من هذا ال section و الآن بنتقل إلى مناقشة بعض
+
+246
+00:28:09,720 --> 00:28:17,160
+المسائل منهمونحدد بعض المسائل للمحاضرة القادمة إن
+
+247
+00:28:17,160 --> 00:28:18,300
+شاء الله
+
+248
+00:28:40,070 --> 00:28:45,970
+بنرجل ال exercises على شبتر اربعتاشر ب exercises
+
+249
+00:28:45,970 --> 00:28:54,470
+of شبتر اربعتاشر سؤال
+
+250
+00:28:54,470 --> 00:29:04,690
+رابع سؤال رابع بقول find a suffering find a
+
+251
+00:29:04,690 --> 00:29:15,160
+suffering of theplus z direct sum that is not an
+
+252
+00:29:15,160 --> 00:29:32,860
+id so bring that is not an id solution
+
+253
+00:29:32,860 --> 00:29:37,580
+طبعا
+
+254
+00:29:38,560 --> 00:29:42,940
+direct sum الـ element اللي هنا بيكون على شكل
+
+255
+00:29:42,940 --> 00:29:49,420
+order pair يعني ذكر تذكير بس الـ Z direct sum مع Z
+
+256
+00:29:49,420 --> 00:29:56,100
+يعني كل العناصر A و B بحيث الـ A و الـ B موجودة و
+
+257
+00:29:56,100 --> 00:30:01,780
+يعني موجودة في Z أي العناصر اللي عليها والجمع
+
+258
+00:30:01,780 --> 00:30:07,160
+component twice والضغط component twice طيب بقول
+
+259
+00:30:07,660 --> 00:30:16,060
+أثبتلي إنه هذه الـ Subring بدك تاخدلي set S مثلا
+
+260
+00:30:16,060 --> 00:30:21,560
+subset من هذه و تحاول تثبتها إنها الـ Subring يبقى
+
+261
+00:30:21,560 --> 00:30:29,900
+هذه بيكون عليها شكل قوس مُركّب من عنصرين يلّا مين
+
+262
+00:30:29,900 --> 00:30:36,460
+أخد عنصرين أبدا؟ عنصرين منزل؟ يلّا، بيحتفل على الـ
+
+263
+00:30:36,460 --> 00:30:45,180
+Subringوفي نفس الوقت مش ideal يالا
+
+264
+00:30:45,180 --> 00:30:50,340
+ذكر ايش
+
+265
+00:30:50,340 --> 00:30:55,000
+ممكن يجي في بارك اه او اتنين او اتنين او اتنين
+
+266
+00:30:55,000 --> 00:31:02,240
+مثلا اخدت ا و اتنين كعنصر يعني ال ا موجود في زي
+
+267
+00:31:02,240 --> 00:31:08,220
+مين مكان يكون و اتنين صار ثابت تمامبنشوف هالصبرينج
+
+268
+00:31:08,220 --> 00:31:14,400
+و لا لأ طبعا الجامعة و .. و لإنه non-empty صحيح
+
+269
+00:31:14,400 --> 00:31:19,280
+موجود و الجامعة ناخد عنصرين و نطرحهم من بعض حتى
+
+270
+00:31:19,280 --> 00:31:23,580
+يكون موجود لإن اتنين ممكن ناخدها عامل مشترك و الله
+
+271
+00:31:23,580 --> 00:31:32,620
+يطلع صفر لو طرحناهم من بعض بيطلع صفر صح يبقى بطلة
+
+272
+00:31:32,620 --> 00:31:39,200
+الصير بطلت صبركصح ولا لا؟ عادي عندنا طرح سقط اللي
+
+273
+00:31:39,200 --> 00:31:43,920
+هو الشرط الثاني يبقى غيريها اه اتنين A و اتنين B
+
+274
+00:31:43,920 --> 00:31:50,920
+اتنين A و اتنين B طب ما تخليها A و B خلاص طب
+
+275
+00:31:50,920 --> 00:31:55,360
+و يتساوي شو المشكلة؟ بتاخدها A و A شو المشكلة؟
+
+276
+00:31:55,360 --> 00:32:04,000
+يبقى من داخل A و A و بحيث ال A موجودة في ذلك شفوي
+
+277
+00:32:04,000 --> 00:32:10,900
+شفويzero و zero موجودة في S ولا لا؟ طيب الشرط
+
+278
+00:32:10,900 --> 00:32:18,320
+الأول صحيح نجي للثاني بتاخد a و a و b و b موجودة
+
+279
+00:32:18,320 --> 00:32:22,120
+في S يبقى a ناقص بي و a ناقص بي موجودة في S الشرط
+
+280
+00:32:22,120 --> 00:32:27,500
+التاني مظبوط تاني بارك هنا a و a و خدي الرقم اللي
+
+281
+00:32:27,500 --> 00:32:34,760
+يعجبك بعد ذلك من مين؟ من ال S بي و بي يبقى وصير
+
+282
+00:32:34,760 --> 00:32:41,320
+من؟ABAB نفس الرقم موجود في اس و لا يوجد اس اس ليه
+
+283
+00:32:41,320 --> 00:32:53,860
+subring يبقى هنا اس هذه is a sub ring يبقى check
+
+284
+00:32:53,860 --> 00:32:57,820
+بدك تروح تعمليها في الدار انا بقول سهل كده اي شفوي
+
+285
+00:32:57,820 --> 00:33:03,100
+و انت بده تروح تعمليها تحريري انا بهمن انها ماهياش
+
+286
+00:33:03,100 --> 00:33:03,540
+ID
+
+287
+00:33:13,130 --> 00:33:18,970
+مش هنجي في S إذا ما نجتوش في S يبقى بطلة suffering
+
+288
+00:33:18,970 --> 00:33:25,370
+اللي جاته في S يبقى صارت main suffering أو صارت
+
+289
+00:33:25,370 --> 00:33:35,380
+ideal طيب بدأت أقول let X موجودة في S and مثلاواحد
+
+290
+00:33:35,380 --> 00:33:43,660
+و تلاتة موجودة في direct sum عزيزي عنصر هنا من ال
+
+291
+00:33:43,660 --> 00:33:51,720
+ring الأصلية وعنصر من ال S ثاني ال
+
+292
+00:33:51,720 --> 00:34:03,710
+X في واحد و تلاتة بالدرسة ال A و ال Aمضربة في واحد
+
+293
+00:34:03,710 --> 00:34:11,110
+و تلاتة هذي بدها تساوي مين؟ ايه؟ و تلاتة ايه؟
+
+294
+00:34:11,110 --> 00:34:17,390
+موجودة في S؟ لأ يبقى the is not belonging to S
+
+295
+00:34:17,390 --> 00:34:24,990
+يبقى هنا س ال S is not ID
+
+296
+00:34:26,390 --> 00:34:30,490
+انت ممكن تاخد اتنين وثلاثة، ممكن تاخد اتنين وخمسة،
+
+297
+00:34:30,490 --> 00:34:34,950
+المهم الرقمين مايكونوش زي بعض، وعندي جداش مالة
+
+298
+00:34:34,950 --> 00:34:39,510
+ليها من الأرقام، يبقى هذا مثال بسيط على ان ال
+
+299
+00:34:39,510 --> 00:34:44,630
+subset اللي أخدتها هي ال sub ring، لكنها ليست
+
+300
+00:34:44,630 --> 00:34:55,830
+عادية. طيب سؤال آخر مثلا زي سؤال ستة، سؤال ستة،
+
+301
+00:34:56,620 --> 00:35:02,560
+بيقولّي اهدّي كل ال maximum ideas و اعين ال
+
+302
+00:35:02,560 --> 00:35:06,780
+maximum ideas
+
+303
+00:35:06,780 --> 00:35:23,060
+ان جالس زت تمانى و زد عشرة و زد اتناشر و زد ان
+
+304
+00:35:25,670 --> 00:35:33,010
+نبدأ شكل الـ maximal ideal فيهم احنا
+
+305
+00:35:33,010 --> 00:35:37,910
+خدنا مثال زبدة 12 و جبنا ال maximum ideal فيهم
+
+306
+00:35:37,910 --> 00:35:44,870
+كمثال تذكروا و الله راحت أدراجي الرياح و طبعا
+
+307
+00:35:44,870 --> 00:35:49,550
+بيرنا و عملنا لها ال lattice و المثال الوحيد اللي
+
+308
+00:35:49,550 --> 00:35:55,220
+عمله الشبكية تبعته خلال هذا ال sectionوقلنا عندها
+
+309
+00:35:55,220 --> 00:35:58,800
+ان اتنين والتلاتة و ال principle ideal generated
+
+310
+00:35:58,800 --> 00:36:02,780
+by اتنين و ال principle ideal generated by التلاتة
+
+311
+00:36:02,780 --> 00:36:09,320
+are maximal ideals in Z12 مظبوط لقيته في الدفاتر
+
+312
+00:36:09,320 --> 00:36:15,700
+ممتاز يبقى هذا يا بنات بياننا سابقا ان ال
+
+313
+00:36:15,700 --> 00:36:20,020
+principle ideal generated by اتنينو ال principle
+
+314
+00:36:20,020 --> 00:36:25,000
+ideals generated by ثلاثة هدول are maximum ideals
+
+315
+00:36:25,000 --> 00:36:31,400
+هدول الأتنين هما ال maximum خلّي هالمعلومة عندك
+
+316
+00:36:31,400 --> 00:36:37,780
+هذه لزمان طيب نيجي لزيد تمانية لزيد تمانية بدي
+
+317
+00:36:37,780 --> 00:36:43,740
+أدور على ال ideals تبعتها الان لو جيت على ال
+
+318
+00:36:43,740 --> 00:36:48,570
+principle ideals generated by oneبتلاقيها هي ال
+
+319
+00:36:48,570 --> 00:36:53,790
+principle ideal generated by تلاتة بتلاقيها هي ال
+
+320
+00:36:53,790 --> 00:36:58,510
+principle ideal generated by خمسة بتلاقيها هي ال
+
+321
+00:36:58,510 --> 00:37:03,270
+principle ideal generated by سبعة يعني كل primes
+
+322
+00:37:03,270 --> 00:37:09,290
+من واحد إلى تمانية بيعطوني مين؟ بيعطوني نفس ال
+
+323
+00:37:09,290 --> 00:37:15,750
+ring الأصلية ليه Z تمانية كل هذا بيساوي Z تمانية
+
+324
+00:37:16,580 --> 00:37:22,960
+طيب تمام راح الواحد والتلات والخمسة والسبعة بقى
+
+325
+00:37:22,960 --> 00:37:32,520
+اللي عندي اتنين واربعة وستة وبس مظبوط وال zero صح؟
+
+326
+00:37:32,520 --> 00:37:36,920
+طيب عندك ال principle ideal generated by zero اللي
+
+327
+00:37:36,920 --> 00:37:42,880
+هو zero itselfعندك ال principle ideal generated by
+
+328
+00:37:42,880 --> 00:37:49,560
+اتنين اللي هو Zero اتنين اربعة ستة تمام؟ عندك ال
+
+329
+00:37:49,560 --> 00:37:54,200
+principle ideal generated by اربعة اللي هو Zero
+
+330
+00:37:54,200 --> 00:38:01,660
+اربعة في الشريرة خلصنا؟ لأ ما خلصناش By ال
+
+331
+00:38:01,660 --> 00:38:05,680
+principle ideal generated by ستة بيكون كله عندي
+
+332
+00:38:05,680 --> 00:38:13,630
+بيصير عندي واحدوهي اتنين وهي تلاتة وهي أربعة وهي
+
+333
+00:38:13,630 --> 00:38:17,790
+خمسة وهي سبعة بيظل ال principle ideal generated by
+
+334
+00:38:17,790 --> 00:38:22,910
+ستة بدي أعرفه من هنا يبقى ال principle ideal
+
+335
+00:38:22,910 --> 00:38:28,510
+generated by ستة هو Zero والستة ستة وستة اتناش من
+
+336
+00:38:28,510 --> 00:38:35,030
+تمانية بيظل أربعة ستة في تلاتة بتمنتاش من ستاش
+
+337
+00:38:35,030 --> 00:38:40,830
+بيظلوا اتنين6 في 4 بـ 24 اللي هو مضاعفاتها Zero
+
+338
+00:38:40,830 --> 00:38:48,430
+يبقى طالع هذه هي مين؟ يا زد اتنين يا زد ستة يبقى
+
+339
+00:38:48,430 --> 00:38:53,530
+انا اقول ده ليه اعمل ال lattice الشباكية تبعت هذه
+
+340
+00:38:53,530 --> 00:39:01,710
+ال race مظبوط يبقى بعدين بقول الأولاني يا زد
+
+341
+00:39:01,710 --> 00:39:09,550
+تمانية اوهدى أو هدى أو هدى أو هدى كل واحد طلع
+
+342
+00:39:09,550 --> 00:39:16,370
+عندنا مين؟ principle ideal generated by اتنين وطلع
+
+343
+00:39:16,370 --> 00:39:21,610
+منه ال principle ideal generated by اربعة وطلع ال
+
+344
+00:39:21,610 --> 00:39:25,470
+principle ideal generated by zero اللي هو تساوي
+
+345
+00:39:25,470 --> 00:39:31,530
+Zero في غيرهم من ال maximum اللي هو ال proper ولا
+
+346
+00:39:31,530 --> 00:39:38,160
+يسوى ال ring الأصلي منهمالاتنين طيب ممتاز جدا يبقى
+
+347
+00:39:38,160 --> 00:39:44,980
+هذه طلعت ليه الاتنين طيب هنا هنا بنات اتنين وثلاثة
+
+348
+00:39:44,980 --> 00:39:51,880
+prime numbers وكل واحد فيهم بجسم نهار هذه طلعت
+
+349
+00:39:51,880 --> 00:39:58,180
+اتنين هو prime number بجسم التمانية بناء عليه هذه
+
+350
+00:39:58,180 --> 00:40:03,580
+من هم ال maximum اتنين وخمسة اتنين وخمسة ممتازة
+
+351
+00:40:03,670 --> 00:40:08,210
+تبقى ال principle ideal generated by اتنين و ال
+
+352
+00:40:08,210 --> 00:40:12,850
+principle ideal generated by خمسة لو جيتي حسب تهم
+
+353
+00:40:12,850 --> 00:40:18,230
+هيطلع الكلام اللي عندك هنا طبعا طيب لو جيت اعمل
+
+354
+00:40:18,230 --> 00:40:24,450
+انها الشبكية تبعتها فبقى اللي بقول ايه زاد عشرة في
+
+355
+00:40:24,450 --> 00:40:28,910
+عند ال principle ideal generated by اتنين و في ال
+
+356
+00:40:28,910 --> 00:40:34,690
+principle ideal generated by خمسةبعد هيك في ال
+
+357
+00:40:34,690 --> 00:40:40,010
+principle id generated by 0 و هذا ال principle id
+
+358
+00:40:40,010 --> 00:40:48,410
+generated by 0 هذه خمسة و هذه اتنين طبعا يبقى هذه
+
+359
+00:40:48,410 --> 00:40:54,790
+الشبكية تبعت ال z عشرة ال باقي كل الأرقام الأخرى
+
+360
+00:40:54,790 --> 00:40:59,110
+مثلا z عشرة عزيزي ال principle هذه generated by
+
+361
+00:40:59,110 --> 00:41:04,340
+oneprincipal ideal generated by three ,principal
+
+362
+00:41:04,340 --> 00:41:08,640
+ideal generated by seven ,principal ideal
+
+363
+00:41:08,640 --> 00:41:13,140
+generated by nine ,by تسعة كلهم هذول بيسووا بعض
+
+364
+00:41:13,140 --> 00:41:17,460
+يبقى كله هي ال ring هذول و الباقى هتلاقي واحدة
+
+365
+00:41:17,460 --> 00:41:21,460
+بتساوي تانية وماضنش عندى إلا مين إلا الأربعة اللي
+
+366
+00:41:21,460 --> 00:41:26,660
+بيبقى ال maximal ideals هم مين الاثنين وخمسة مثل
+
+367
+00:41:26,660 --> 00:41:32,240
+ما زعمنا بناءً عليهبدي الـ maximal ID اللي هذه بيه
+
+368
+00:41:32,240 --> 00:41:39,180
+هم كل الـprimes بحيث هذه الـprimes بتقسم الـN تقسم
+
+369
+00:41:39,180 --> 00:41:47,100
+الـL يبقى هذه كل الـprinciple ID generated by P
+
+370
+00:41:47,100 --> 00:41:58,550
+والـP is prime divisor of Nيعني اللي بيكون
+
+371
+00:41:58,550 --> 00:42:03,450
+relatively primal in itself، جداش جد ما يكون، ان
+
+372
+00:42:03,450 --> 00:42:07,950
+شاء الله تكون الـResult خمسمية، ماعناش مشكلة فيها،
+
+373
+00:42:07,950 --> 00:42:12,530
+يفجأ هاي حلناها، طبعا هذا حلناها السابقة، وهي حل
+
+374
+00:42:12,530 --> 00:42:19,290
+ذلك التلاتة، الأخيرة ستنتج بناء على مين؟ بناء على
+
+375
+00:42:19,290 --> 00:42:21,810
+ال rings التلاتة اللي عندنا
+
+376
+00:42:24,920 --> 00:42:33,640
+طيب نروح لأننا سؤال اربعة عشر مثلا نفجر سؤال اربعة
+
+377
+00:42:33,640 --> 00:42:39,640
+عشر سؤال اربعة عشر بيقول ما يتخذ ال A و ال B ايديل
+
+378
+00:42:39,640 --> 00:42:50,980
+ال A و ال B ايديل اثبت ان ال A بيستخدم ال A
+
+379
+00:42:50,980 --> 00:42:52,920
+intersection B
+
+380
+00:43:17,180 --> 00:43:21,780
+الان اتعلمنا من ال set theory لكي نثبت ان set هي
+
+381
+00:43:21,780 --> 00:43:25,480
+subset من setبدي أخد element في الست الأولى و أثبت
+
+382
+00:43:25,480 --> 00:43:28,900
+إنه موجود في الست التانية و الأعلى أبسط اللي أشاء
+
+383
+00:43:28,900 --> 00:43:33,680
+في مبادئ رياضية على كل المعلومات اللي عندنا اتنين
+
+384
+00:43:33,680 --> 00:43:38,680
+هذول ID بس حصل ضرب ال A في D ماشوفتاش له تعريف
+
+385
+00:43:38,680 --> 00:43:42,520
+جدليك طب
+
+386
+00:43:42,520 --> 00:43:46,260
+إذا بدنا نروح و نحط التعريف اللي حطه الكتاب من
+
+387
+00:43:46,260 --> 00:43:53,310
+خلال التمرين يبقى solutionفي سؤال 12 اللي جابله
+
+388
+00:43:53,310 --> 00:44:00,250
+راح حطني حاصن الضرب فقرفلي حاصن الضرب A في B وكل
+
+389
+00:44:00,250 --> 00:44:11,610
+العموظة A1 B1 B2 B2 plus ANBN بحيث أن ال AI موجودة
+
+390
+00:44:11,610 --> 00:44:20,350
+في I و أنكوا كمان منه و ال BI موجودة في Bالـ I
+
+391
+00:44:20,350 --> 00:44:27,270
+تأخذ من واحد لغاية الـ M والـ I تساوي واحد واتنين
+
+392
+00:44:27,270 --> 00:44:33,730
+لغاية الـ M هذا هو تعريف حاصل الضرر لـ Two Ideas
+
+393
+00:44:33,730 --> 00:44:40,630
+يبقى أنا بتروح اقول افترض ان ال X موجود في ال A في
+
+394
+00:44:40,630 --> 00:44:50,980
+B يبقى بلاء ان علي شكل ال Xالـ X متساوي A1 B1 زائد
+
+395
+00:44:50,980 --> 00:45:01,160
+ال A2 B2 زائد زائد ال A M B M بحيث ال AI موجودة في
+
+396
+00:45:01,160 --> 00:45:10,280
+A و ال BI موجودة في B و ال AI موجودة في ال A و ال
+
+397
+00:45:10,280 --> 00:45:16,360
+BI موجودة غير في ال B طيب
+
+398
+00:45:17,410 --> 00:45:25,850
+تعالى نشوف وين هذا بدها تصير هذا يا بنات ال A1
+
+399
+00:45:25,850 --> 00:45:34,470
+موجودة وين؟ فى ال A مظبوط و ال AID و ال B1 element
+
+400
+00:45:34,470 --> 00:45:38,870
+موجود فى B يعني موجود فى ال ring لما نقرأ ال B1
+
+401
+00:45:38,870 --> 00:45:45,790
+موجود فى A من زاوية أخرى ال B1 موجودة وين؟في الـB
+
+402
+00:45:45,790 --> 00:45:55,090
+والـA والموجودة في الـR في الـA
+
+403
+00:45:55,090 --> 00:46:00,590
+والموجودة في الـB بالمثل هذا موجود في A وB موجود
+
+404
+00:46:00,590 --> 00:46:08,050
+في AB وهذا كله موجود في AB يبقى هذا يقين إن الـX
+
+405
+00:46:08,050 --> 00:46:20,920
+موجودة في الـAو and ال X موجودة في ال B هذا موجودة
+
+406
+00:46:20,920 --> 00:46:26,180
+في ال اتنين موجودة وين ال intersection لهم يبقى
+
+407
+00:46:26,180 --> 00:46:32,840
+هذا يعطينا ان ال X موجودة في ال A intersection B
+
+408
+00:46:32,840 --> 00:46:39,140
+طبعا ستسأل واحدة فيكم ممكن يكون ال intersection
+
+409
+00:46:39,140 --> 00:46:46,780
+subset من أعصر الدارممكن بس في شوق بدنا نحطه زيادة
+
+410
+00:46:46,780 --> 00:46:53,820
+وهذا هو موضوع سؤال ستاشر سؤال ستاشر بيقول ال a و
+
+411
+00:46:53,820 --> 00:47:03,440
+ال b ideally commutative ال a و ال b ideals where
+
+412
+00:47:03,440 --> 00:47:06,020
+are commutative
+
+413
+00:47:09,550 --> 00:47:18,210
+و .. و كذلك ان ال A زائد ال B متساوي ال R كونها
+
+414
+00:47:18,210 --> 00:47:27,010
+اثبت ان ال intersection A intersection B بتساوي ال
+
+415
+00:47:27,010 --> 00:47:35,710
+A في B أول شيء ال A بيسلسل من ال A intersection B
+
+416
+00:47:35,710 --> 00:47:41,340
+هذا واحد هيه قدامك مظبوط؟يبقى الاتجاه الأول جاهز
+
+417
+00:47:41,340 --> 00:47:49,660
+الاتجاه الثاني فيه عندي معلومة ال R commutative
+
+418
+00:47:49,660 --> 00:47:55,700
+with unity فيها ال unity يبقى باجي بقوله الواحد
+
+419
+00:47:55,700 --> 00:48:00,740
+موجود في ال R اللي يبدأ تساوي A زائد ال B يبقى
+
+420
+00:48:00,740 --> 00:48:05,840
+معنى هذا الكلام ان الواحد بدي يساوي A زائد ال B
+
+421
+00:48:05,840 --> 00:48:16,380
+for someA موجود في A والـ B موجود في B الان بدأ
+
+422
+00:48:16,380 --> 00:48:24,440
+يقول خد ال X موجود في A intersection B then ال X
+
+423
+00:48:24,440 --> 00:48:32,280
+موجود في A and ال X موجود في B طيب
+
+424
+00:48:32,280 --> 00:48:39,530
+بدأ ياخد الآن ال X هذه أضربها في واحديبقى ال X
+
+425
+00:48:39,530 --> 00:48:45,670
+تساوي X في واحد يعني بدها تساوي ال X الواحد عندى
+
+426
+00:48:45,670 --> 00:48:54,130
+بقدرش ب A زائد ال B هذا الكلام بده يساوي ال X A
+
+427
+00:48:54,130 --> 00:49:02,910
+زائد ال X B ال R commutative يبقى هذا ب A X زائد
+
+428
+00:49:02,910 --> 00:49:10,780
+ال X B خلّالي هنا هذا موجود وينفى ال A و هذا موجود
+
+429
+00:49:10,780 --> 00:49:20,820
+وين فى B هذا موجود فى A و هذا موجود فى B إذا هذا
+
+430
+00:49:20,820 --> 00:49:28,440
+ال A X موجود فى ال A B بنفس الطريقة هذا موجود فى B
+
+431
+00:49:28,440 --> 00:49:36,600
+و هذا موجود وين فى A إذا هذا كله موجود وين فى ال A
+
+432
+00:49:36,600 --> 00:49:42,400
+Bيبقى X اللى خدتها في ال intersection اللى جيتها
+
+433
+00:49:42,400 --> 00:49:49,360
+موجودة وين في حاصل الدورة يبقى هنا ساعة ال
+
+434
+00:49:49,360 --> 00:49:56,260
+intersection بيه ساعة ست من مين من ال A بيه هذه
+
+435
+00:49:56,260 --> 00:50:05,700
+العلاقة رقم اتنين يبقى from واحد and اتنين we have
+
+436
+00:50:06,470 --> 00:50:15,210
+إن الـ A intersection B يساوي الـ A في B يلا صدلوا
+
+437
+00:50:15,210 --> 00:50:25,990
+عندكم exercises ليوم السبت خدوا
+
+438
+00:50:25,990 --> 00:50:30,970
+لسؤال 17 سؤال 22
+
+439
+00:50:36,220 --> 00:50:45,400
+أسئلة أربعة و عشرين سؤال تلاتين تمانية و تلاتين
+
+440
+00:50:45,400 --> 00:50:58,760
+واحد و أربعين نين و أربعين خمسة و أربعين ستة و
+
+441
+00:50:58,760 --> 00:51:03,260
+أربعين تمانية و أربعين
+
+442
+00:51:05,400 --> 00:51:12,300
+خمسين واحد وخمسين ستة وخمسين
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0d9d04a6d3bf90c9b1c0c1b3a9596c610e2697a1
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4316, "start": 20.64, "end": 43.16, "text": "بسم الله الرحمن الرحيم عوض على بدء نذكر بما أعطيناه المرة الماضية لأن هذه الكترولري تعتمد على ما درسناه في المحاضرة الماضية المحاضرة الماضية كانت عمود شقري هو نظري تاني النظرية الأولى بتقول لو كانت ال R is commutative ring with unity", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 6225, 2407, 11242, 15844, 47525, 38207, 8717, 8848, 37983, 4724, 15042, 5551, 3615, 9566, 1829, 8315, 3224, 9673, 25720, 9673, 46958, 10632, 5296, 33456, 29538, 33251, 2655, 2288, 12610, 16572, 6055, 34268, 2304, 3215, 15844, 19446, 11778, 2288, 3794, 8315, 3224, 8978, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 25961, 2655, 6225, 2304, 23328, 13412, 4587, 16572, 31439, 8717, 19913, 16572, 6055, 7649, 1829, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 39894, 39648, 45164, 25961, 2655, 2423, 497, 307, 800, 325, 1166, 4875, 365, 18205], "avg_logprob": -0.19914216022281087, "compression_ratio": 1.8009049773755657, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 20.64, "end": 20.94, "word": "بسم", "probability": 0.68359375}, {"start": 20.94, "end": 21.14, "word": " الله", "probability": 0.95068359375}, {"start": 21.14, "end": 21.6, "word": " الرحمن", "probability": 0.9580078125}, {"start": 21.6, "end": 22.14, "word": " الرحيم", "probability": 0.99169921875}, {"start": 22.14, "end": 23.46, "word": " عوض", "probability": 0.7405598958333334}, {"start": 23.46, "end": 23.78, "word": " على", "probability": 0.80029296875}, {"start": 23.78, "end": 24.36, "word": " بدء", "probability": 0.767578125}, {"start": 24.36, "end": 25.32, "word": " نذكر", "probability": 0.8450520833333334}, {"start": 25.32, "end": 25.72, "word": " بما", "probability": 0.957763671875}, {"start": 25.72, "end": 26.44, "word": " أعطيناه", "probability": 0.95458984375}, {"start": 26.44, "end": 26.96, "word": " المرة", "probability": 0.979248046875}, {"start": 26.96, "end": 28.14, "word": " الماضية", "probability": 0.99462890625}, {"start": 28.14, "end": 29.0, "word": " لأن", "probability": 0.8349609375}, {"start": 29.0, "end": 29.46, "word": " هذه", "probability": 0.92529296875}, {"start": 29.46, "end": 30.22, "word": " الكترولري", "probability": 0.5363525390625}, {"start": 30.22, "end": 30.94, "word": " تعتمد", "probability": 0.9407958984375}, {"start": 30.94, "end": 31.16, "word": " على", "probability": 0.75}, {"start": 31.16, "end": 31.34, "word": " ما", "probability": 0.89697265625}, {"start": 31.34, "end": 32.1, "word": " درسناه", "probability": 0.950390625}, {"start": 32.1, "end": 32.28, "word": " في", "probability": 0.92529296875}, {"start": 32.28, "end": 33.1, "word": " المحاضرة", "probability": 0.990234375}, {"start": 33.1, "end": 33.88, "word": " الماضية", "probability": 0.9944661458333334}, {"start": 33.88, "end": 35.12, "word": " المحاضرة", "probability": 0.957275390625}, {"start": 35.12, "end": 35.5, "word": " الماضية", 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"probability": 0.9365234375}, {"start": 58.41, "end": 58.79, "word": " الـ", "probability": 0.84814453125}, {"start": 58.79, "end": 58.99, "word": " R", "probability": 0.8642578125}, {"start": 58.99, "end": 59.41, "word": " committed", "probability": 0.1253662109375}, {"start": 59.41, "end": 59.67, "word": " to", "probability": 0.87109375}, {"start": 59.67, "end": 59.89, "word": " bring", "probability": 0.54345703125}, {"start": 59.89, "end": 60.15, "word": " with", "probability": 0.87060546875}, {"start": 60.15, "end": 60.63, "word": " unity", "probability": 0.953125}, {"start": 60.63, "end": 61.23, "word": " لكن", "probability": 0.90869140625}, {"start": 61.23, "end": 62.03, "word": " القلاف", "probability": 0.728515625}, {"start": 62.03, "end": 62.31, "word": " عند", "probability": 0.93017578125}, {"start": 62.31, "end": 62.95, "word": " المطلوب", "probability": 0.9888916015625}, {"start": 62.95, "end": 63.85, "word": " فبنقول", "probability": 0.864013671875}, {"start": 63.85, "end": 64.13, "word": " الـ", "probability": 0.903076171875}, {"start": 64.13, "end": 64.37, "word": " R", "probability": 0.892578125}, {"start": 64.37, "end": 65.01, "word": " modulo", "probability": 0.938720703125}, {"start": 65.01, "end": 65.57, "word": " A", "probability": 0.984375}, {"start": 65.57, "end": 66.21, "word": " is", "probability": 0.9423828125}, {"start": 66.21, "end": 66.77, "word": " a", "probability": 0.8662109375}, {"start": 66.77, "end": 67.31, "word": " field", "probability": 0.9404296875}, {"start": 67.31, "end": 67.65, "word": " if", "probability": 0.96728515625}, {"start": 67.65, "end": 67.93, "word": " and", "probability": 0.95947265625}, {"start": 67.93, "end": 68.23, "word": " only", "probability": 0.92138671875}, {"start": 68.23, "end": 68.67, "word": " if", "probability": 0.9794921875}, {"start": 68.67, "end": 69.39, "word": " الـ", "probability": 0.922607421875}, {"start": 69.39, "end": 69.69, "word": " A", "probability": 0.92724609375}, {"start": 69.69, 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"probability": 0.9959716796875}, {"start": 77.72, "end": 78.0, "word": " على", "probability": 0.83349609375}, {"start": 78.0, "end": 79.42, "word": " النظريتين", "probability": 0.79453125}, {"start": 79.42, "end": 79.92, "word": " بتقول", "probability": 0.61376953125}, {"start": 79.92, "end": 80.22, "word": " لو", "probability": 0.791015625}, {"start": 80.22, "end": 80.68, "word": " كانت", "probability": 0.8642578125}, {"start": 80.68, "end": 80.78, "word": " ال", "probability": 0.87109375}, {"start": 80.78, "end": 80.96, "word": " R", "probability": 0.43310546875}, {"start": 80.96, "end": 81.68, "word": " commutative", "probability": 0.7275390625}, {"start": 81.68, "end": 81.94, "word": " ring", "probability": 0.76611328125}, {"start": 81.94, "end": 82.24, "word": " with", "probability": 0.89599609375}, {"start": 82.24, "end": 82.8, "word": " unity", "probability": 0.97119140625}, {"start": 82.8, "end": 84.0, "word": " يبقى", "probability": 0.9666748046875}, {"start": 84.0, "end": 84.46, "word": " every", "probability": 0.734375}, {"start": 84.46, "end": 85.26, "word": " maximal", "probability": 0.83935546875}, {"start": 85.26, "end": 86.16, "word": " ideal", "probability": 0.92626953125}, {"start": 86.16, "end": 86.68, "word": " is", "probability": 0.86279296875}, {"start": 86.68, "end": 87.38, "word": " prime", "probability": 0.80615234375}, {"start": 87.38, "end": 89.66, "word": " يبقى", "probability": 0.8701171875}, {"start": 89.66, "end": 89.88, "word": " ال", "probability": 0.9423828125}, {"start": 89.88, "end": 90.34, "word": " proof", "probability": 0.87744140625}, {"start": 90.34, "end": 91.22, "word": " كالتالي", "probability": 0.91962890625}, {"start": 91.22, "end": 91.66, "word": " ال", "probability": 0.85498046875}, {"start": 91.66, "end": 92.28, "word": " R", "probability": 0.9052734375}, {"start": 92.28, "end": 93.1, "word": " is", "probability": 0.8330078125}, {"start": 93.1, "end": 95.62, "word": " commutative", "probability": 0.9607747395833334}, {"start": 95.62, "end": 98.12, "word": " ring", "probability": 0.9501953125}, {"start": 98.12, "end": 99.32, "word": " with", "probability": 0.9365234375}, {"start": 99.32, "end": 99.84, "word": " unity", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 4, "seek": 13268, "start": 104.12, "end": 132.68, "text": "طبعا يبقى بدي افترض انه عندي ideal و ال ideal is maximum let ال a be a maximal ideal of R بالنظرية الثانية يبقى ال R modulo a is a field", "tokens": [9566, 3555, 3615, 995, 7251, 3555, 4587, 7578, 4724, 16254, 1975, 5172, 2655, 43042, 16472, 3224, 18871, 16254, 7157, 4032, 2423, 7157, 307, 6674, 718, 2423, 257, 312, 257, 49336, 7157, 295, 497, 20666, 1863, 19913, 2288, 10632, 6024, 104, 7649, 10632, 7251, 3555, 4587, 7578, 2423, 497, 1072, 13455, 257, 307, 257, 2519], "avg_logprob": -0.26803975972262295, "compression_ratio": 1.3405797101449275, "no_speech_prob": 0.0, "words": [{"start": 104.12, "end": 104.8, "word": "طبعا", "probability": 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"end": 112.96, "word": " ال", "probability": 0.54296875}, {"start": 112.96, "end": 113.42, "word": " a", "probability": 0.3896484375}, {"start": 113.42, "end": 114.3, "word": " be", "probability": 0.459228515625}, {"start": 114.3, "end": 116.42, "word": " a", "probability": 0.982421875}, {"start": 116.42, "end": 118.5, "word": " maximal", "probability": 0.470703125}, {"start": 118.5, "end": 121.58, "word": " ideal", "probability": 0.935546875}, {"start": 121.58, "end": 123.96, "word": " of", "probability": 0.9501953125}, {"start": 123.96, "end": 124.92, "word": " R", "probability": 0.54248046875}, {"start": 124.92, "end": 127.6, "word": " بالنظرية", "probability": 0.9404296875}, {"start": 127.6, "end": 128.44, "word": " الثانية", "probability": 0.9586181640625}, {"start": 128.44, "end": 129.22, "word": " يبقى", "probability": 0.9775390625}, {"start": 129.22, "end": 129.34, "word": " ال", "probability": 0.9013671875}, {"start": 129.34, "end": 129.58, "word": " R", "probability": 0.8349609375}, {"start": 129.58, "end": 130.08, "word": " modulo", "probability": 0.6817626953125}, {"start": 130.08, "end": 130.38, "word": " a", "probability": 0.86279296875}, {"start": 130.38, "end": 131.06, "word": " is", "probability": 0.796875}, {"start": 131.06, "end": 131.88, "word": " a", "probability": 0.94677734375}, {"start": 131.88, "end": 132.68, "word": " field", "probability": 0.9423828125}], "temperature": 1.0}, {"id": 5, "seek": 16068, "start": 133.28, "end": 160.68, "text": "يبقى بروح بقوله by the second theorem بالنظرية الثانية ال a modulo a is a field طبعا احنا قلنا قبل ذلك any field is an integral domain", "tokens": [1829, 3555, 4587, 7578, 4724, 32887, 5016, 4724, 39648, 3224, 538, 264, 1150, 20904, 20666, 1863, 19913, 2288, 10632, 6024, 104, 7649, 10632, 2423, 257, 1072, 13455, 257, 307, 257, 2519, 23032, 3555, 3615, 995, 1975, 5016, 8315, 12174, 1211, 8315, 12174, 36150, 29910, 23275, 604, 2519, 307, 364, 11573, 9274], "avg_logprob": -0.2603665888309479, "compression_ratio": 1.3, "no_speech_prob": 0.0, "words": [{"start": 133.28, "end": 133.74, "word": "يبقى", "probability": 0.73895263671875}, {"start": 133.74, "end": 134.12, "word": " بروح", "probability": 0.91552734375}, {"start": 134.12, "end": 134.84, "word": " بقوله", "probability": 0.5840657552083334}, {"start": 134.84, "end": 135.3, "word": " by", "probability": 0.447509765625}, {"start": 135.3, "end": 136.72, "word": " the", "probability": 0.822265625}, {"start": 136.72, "end": 137.88, "word": " second", "probability": 0.7841796875}, {"start": 137.88, "end": 140.6, "word": " theorem", "probability": 0.73193359375}, {"start": 140.6, "end": 143.18, "word": " بالنظرية", "probability": 0.9568359375}, {"start": 143.18, "end": 144.04, "word": " الثانية", "probability": 0.953857421875}, {"start": 144.04, "end": 144.84, "word": " ال", "probability": 0.85205078125}, {"start": 144.84, "end": 145.38, "word": " a", "probability": 0.264404296875}, {"start": 145.38, "end": 146.6, "word": " modulo", "probability": 0.711181640625}, {"start": 146.6, "end": 147.14, "word": " a", "probability": 0.908203125}, {"start": 147.14, "end": 148.42, "word": " is", "probability": 0.5458984375}, {"start": 148.42, "end": 149.62, "word": " a", "probability": 0.96875}, {"start": 149.62, "end": 150.18, "word": " field", "probability": 0.92822265625}, {"start": 150.18, "end": 152.86, "word": " طبعا", "probability": 0.7626953125}, {"start": 152.86, "end": 153.76, "word": " احنا", "probability": 0.8131510416666666}, {"start": 153.76, "end": 154.06, "word": " قلنا", "probability": 0.8429361979166666}, {"start": 154.06, "end": 154.44, "word": " قبل", "probability": 0.980712890625}, {"start": 154.44, "end": 154.84, "word": " ذلك", "probability": 0.97802734375}, {"start": 154.84, "end": 155.3, "word": " any", "probability": 0.65869140625}, {"start": 155.3, "end": 157.82, "word": " field", "probability": 0.91943359375}, {"start": 157.82, "end": 158.56, "word": " is", "probability": 0.7265625}, {"start": 158.56, "end": 159.52, "word": " an", "probability": 0.6591796875}, {"start": 159.52, "end": 160.0, "word": " integral", "probability": 0.8203125}, {"start": 160.0, "end": 160.68, "word": " domain", "probability": 0.99560546875}], "temperature": 1.0}, {"id": 6, "seek": 19045, "start": 161.19, "end": 190.45, "text": "هذا بدي يعطينا ان ال R موديول A is an integral domain يبقى بروحنا نقوله by the first theorem النظرية الأولى ال A is a prime ID", "tokens": [3224, 15730, 4724, 16254, 37495, 9566, 1829, 8315, 16472, 2423, 497, 3714, 2407, 16254, 12610, 316, 307, 364, 11573, 9274, 7251, 3555, 4587, 7578, 4724, 32887, 5016, 8315, 8717, 39648, 3224, 538, 264, 700, 20904, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 2423, 316, 307, 257, 5835, 7348], "avg_logprob": -0.3223852040816326, "compression_ratio": 1.2361111111111112, "no_speech_prob": 0.0, "words": [{"start": 161.19, "end": 161.75, "word": "هذا", "probability": 0.927978515625}, {"start": 161.75, "end": 162.13, "word": " بدي", 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"word": " ID", "probability": 0.3037109375}], "temperature": 1.0}, {"id": 7, "seek": 21596, "start": 192.1, "end": 215.96, "text": "يبقى أثبتنا إن الـ maximal ideal عبارة عن prime ideal إذا كانت الـR is commutative with unity وصلنا إلى آخر مثال في هذا ال section وهو الاردن يقول the ideal", "tokens": [1829, 3555, 4587, 7578, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 39184, 49336, 7157, 6225, 3555, 9640, 3660, 18871, 5835, 7157, 11933, 15730, 25961, 2655, 2423, 39184, 49, 307, 800, 325, 1166, 365, 18205, 4032, 36520, 8315, 30731, 19753, 34740, 50113, 6027, 8978, 23758, 2423, 3541, 37037, 2407, 2423, 9640, 3215, 1863, 7251, 39648, 264, 7157], "avg_logprob": -0.40131578110812005, "compression_ratio": 1.311764705882353, "no_speech_prob": 0.0, "words": [{"start": 192.1, "end": 192.7, "word": "يبقى", "probability": 0.7235107421875}, {"start": 192.7, "end": 193.4, "word": " أثبتنا", "probability": 0.9310546875}, {"start": 193.4, "end": 193.6, "word": " إن", "probability": 0.3828125}, 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235.51, "word": " maximum", "probability": 0.49169921875}], "temperature": 1.0}, {"id": 9, "seek": 28592, "start": 258.54, "end": 285.92, "text": "هذا المثال مشان نحله بيعتمد على سؤالين موجودين في الكتاب مثل ما ذكر الكتاب احنا هنحل السؤالين وانتوا مش دارين من خلال اثباتنا أو خلال حلنا لهذا السؤال أول شي بقوللي ال principle id generated by X هو عبارة عن ال prime ideal في هذه ال ring لكنه ليس maximum", "tokens": [3224, 15730, 9673, 12984, 6027, 37893, 7649, 8717, 5016, 43761, 4724, 1829, 34268, 2304, 3215, 15844, 8608, 33604, 6027, 9957, 3714, 29245, 23328, 9957, 8978, 33251, 2655, 16758, 50113, 1211, 19446, 29910, 37983, 33251, 2655, 16758, 1975, 5016, 8315, 8032, 1863, 5016, 1211, 21136, 33604, 6027, 9957, 4032, 7649, 2655, 14407, 37893, 11778, 9640, 9957, 9154, 16490, 1211, 6027, 1975, 12984, 3555, 9307, 8315, 34051, 16490, 1211, 6027, 11331, 1211, 8315, 46740, 15730, 21136, 33604, 6027, 5551, 12610, 44049, 4724, 39648, 20292, 2423, 8665, 4496, 10833, 538, 1783, 31439, 6225, 3555, 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1314.82, "text": "في الـ 6 اللي هو الـ X و 2 ضايل علينا مين؟ النقطة الأخيرة يبقى النقطة الثالثة بقول مافي خدلي ال F of X موجودة في مين؟ في ال ring الأساسية أن ال F1 of X", "tokens": [41185, 2423, 39184, 1386, 13672, 1829, 31439, 2423, 39184, 1783, 4032, 568, 48812, 995, 26895, 25894, 8315, 3714, 9957, 22807, 28239, 47432, 3660, 16247, 9778, 48923, 7251, 3555, 4587, 7578, 28239, 47432, 3660, 6024, 104, 6027, 12984, 3660, 4724, 39648, 19446, 41185, 16490, 3215, 20292, 2423, 479, 295, 1783, 3714, 29245, 23328, 3660, 8978, 3714, 9957, 22807, 8978, 2423, 4875, 16247, 3794, 32277, 10632, 14739, 2423, 479, 16, 295, 1783], "avg_logprob": -0.2583626836118564, "compression_ratio": 1.5886075949367089, "no_speech_prob": 0.0, "words": [{"start": 1285.6, "end": 1285.94, "word": "في", "probability": 0.489501953125}, {"start": 1285.94, "end": 1286.92, "word": " الـ", "probability": 0.6376953125}, {"start": 1286.92, "end": 1287.26, "word": " 6", "probability": 0.2271728515625}, {"start": 1287.26, 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{"id": 58, "seek": 166034, "start": 1631.9, "end": 1660.34, "text": "يبقى أنا جبت ID الآخر ال ID اللي عندي subset منه ولا يسوي يعني proper subset وهذا في نفس الوقت ضال proper ولا يسوي ال ring الأصلية يبقى بناء عليه لا يمكن لهذا أن يكون maximal ID يبقى بصر ال principle ideal generated by X is", "tokens": [1829, 3555, 4587, 7578, 41850, 10874, 3555, 2655, 7348, 6024, 95, 34740, 2423, 7348, 13672, 1829, 18871, 16254, 25993, 9154, 3224, 49429, 7251, 3794, 45865, 37495, 22653, 2296, 25993, 37037, 15730, 8978, 8717, 36178, 2423, 30543, 2655, 48812, 6027, 2296, 49429, 7251, 3794, 45865, 2423, 4875, 16247, 36520, 10632, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 20193, 7251, 43020, 46740, 15730, 14739, 7251, 30544, 49336, 7348, 7251, 3555, 4587, 7578, 4724, 9381, 2288, 2423, 8665, 7157, 10833, 538, 1783, 307], "avg_logprob": -0.30864197530864196, "compression_ratio": 1.5809523809523809, "no_speech_prob": 0.0, "words": [{"start": 1631.9, "end": 1632.44, "word": "يبقى", "probability": 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2102.56, "end": 2103.5, "word": " maximum", "probability": 0.7236328125}, {"start": 2103.5, "end": 2106.78, "word": " ideas", "probability": 0.9306640625}, {"start": 2106.78, "end": 2109.18, "word": " ان", "probability": 0.1488037109375}, {"start": 2109.18, "end": 2111.32, "word": " جالس", "probability": 0.6376953125}, {"start": 2111.32, "end": 2111.62, "word": " زت", "probability": 0.4871826171875}, {"start": 2111.62, "end": 2113.2, "word": " تمانى", "probability": 0.6498209635416666}, {"start": 2113.2, "end": 2115.54, "word": " و", "probability": 0.177001953125}, {"start": 2115.54, "end": 2116.66, "word": " زد", "probability": 0.5438232421875}, {"start": 2116.66, "end": 2117.38, "word": " عشرة", "probability": 0.83642578125}, {"start": 2117.38, "end": 2119.48, "word": " و", "probability": 0.91015625}, {"start": 2119.48, "end": 2119.9, "word": " زد", "probability": 0.822509765625}, {"start": 2119.9, "end": 2121.24, "word": " اتناشر", "probability": 0.81240234375}, {"start": 2121.24, "end": 2122.22, "word": " و", "probability": 0.9423828125}, {"start": 2122.22, "end": 2122.64, "word": " زد", "probability": 0.873779296875}, {"start": 2122.64, "end": 2123.06, "word": " ان", "probability": 0.61474609375}], "temperature": 1.0}, {"id": 75, "seek": 215331, "start": 2125.67, "end": 2153.31, "text": "نبدأ شكل الـ maximal ideal فيهم احنا خدنا مثال زبدة 12 و جبنا ال maximum ideal فيهم كمثال تذكروا و الله راحت أدراجي الرياح و طبعا بيرنا و عملنا لها ال lattice و المثال الوحيد اللي عمله الشبكية تبعته خلال هذا ال section", "tokens": [1863, 44510, 10721, 13412, 28820, 2423, 39184, 49336, 7157, 8978, 16095, 1975, 5016, 8315, 16490, 3215, 8315, 50113, 6027, 30767, 3555, 41891, 2272, 4032, 10874, 3555, 8315, 2423, 6674, 7157, 8978, 16095, 9122, 2304, 12984, 6027, 6055, 8848, 37983, 14407, 4032, 21984, 12602, 39319, 2655, 5551, 3215, 2288, 26108, 1829, 2423, 16572, 39319, 4032, 23032, 3555, 3615, 995, 4724, 13546, 8315, 4032, 6225, 42213, 8315, 5296, 11296, 2423, 34011, 4032, 9673, 12984, 6027, 2423, 2407, 5016, 25708, 13672, 1829, 6225, 42213, 3224, 25124, 3555, 4117, 10632, 6055, 3555, 34268, 3224, 16490, 1211, 6027, 23758, 2423, 3541], "avg_logprob": -0.24693943298969073, "compression_ratio": 1.710144927536232, "no_speech_prob": 0.0, "words": [{"start": 2125.67, "end": 2126.17, "word": "نبدأ", "probability": 0.7338053385416666}, {"start": 2126.17, "end": 2126.61, "word": " شكل", "probability": 0.572021484375}, {"start": 2126.61, "end": 2126.95, "word": " الـ", "probability": 0.7064208984375}, {"start": 2126.95, "end": 2127.45, "word": " maximal", "probability": 0.38623046875}, {"start": 2127.45, "end": 2128.13, "word": " ideal", "probability": 0.66015625}, {"start": 2128.13, "end": 2129.23, "word": " فيهم", "probability": 0.864990234375}, {"start": 2129.23, "end": 2133.01, "word": " احنا", "probability": 0.65625}, {"start": 2133.01, "end": 2133.67, "word": " خدنا", "probability": 0.799072265625}, {"start": 2133.67, "end": 2134.19, "word": " مثال", "probability": 0.978515625}, {"start": 2134.19, "end": 2134.67, "word": " زبدة", "probability": 0.5843098958333334}, {"start": 2134.67, "end": 2135.49, "word": " 12", "probability": 0.46240234375}, {"start": 2135.49, "end": 2135.79, "word": " و", "probability": 0.67724609375}, {"start": 2135.79, "end": 2136.15, "word": " جبنا", "probability": 0.7618815104166666}, {"start": 2136.15, "end": 2136.33, "word": " ال", "probability": 0.888671875}, {"start": 2136.33, "end": 2136.77, "word": " maximum", "probability": 0.354736328125}, {"start": 2136.77, "end": 2137.39, "word": " ideal", "probability": 0.796875}, {"start": 2137.39, "end": 2137.91, "word": " فيهم", "probability": 0.9404296875}, {"start": 2137.91, "end": 2139.01, "word": " كمثال", "probability": 0.9833984375}, {"start": 2139.01, "end": 2140.73, "word": " تذكروا", "probability": 0.85595703125}, {"start": 2140.73, "end": 2140.95, "word": " و", "probability": 0.252197265625}, {"start": 2140.95, "end": 2141.09, "word": " الله", "probability": 0.7861328125}, {"start": 2141.09, "end": 2141.83, "word": " راحت", "probability": 0.7488606770833334}, {"start": 2141.83, "end": 2142.37, "word": " أدراجي", "probability": 0.77744140625}, {"start": 2142.37, "end": 2142.95, "word": " الرياح", "probability": 0.9069010416666666}, {"start": 2142.95, "end": 2144.41, "word": " و", "probability": 0.8447265625}, {"start": 2144.41, "end": 2144.87, "word": " طبعا", "probability": 0.958984375}, {"start": 2144.87, "end": 2145.89, "word": " بيرنا", "probability": 0.6787923177083334}, {"start": 2145.89, "end": 2146.17, "word": " و", "probability": 0.98193359375}, {"start": 2146.17, "end": 2146.59, "word": " عملنا", "probability": 0.95947265625}, {"start": 2146.59, "end": 2146.79, "word": " لها", "probability": 0.967529296875}, {"start": 2146.79, "end": 2146.99, "word": " ال", "probability": 0.93359375}, {"start": 2146.99, "end": 2147.51, "word": " lattice", "probability": 0.76171875}, {"start": 2147.51, "end": 2148.41, "word": " و", "probability": 0.58203125}, {"start": 2148.41, "end": 2148.89, "word": " المثال", "probability": 0.935546875}, {"start": 2148.89, "end": 2149.37, "word": " الوحيد", "probability": 0.847412109375}, {"start": 2149.37, "end": 2149.55, "word": " اللي", "probability": 0.901123046875}, {"start": 2149.55, "end": 2150.05, "word": " عمله", "probability": 0.7991536458333334}, {"start": 2150.05, "end": 2150.93, "word": " الشبكية", "probability": 0.9835205078125}, {"start": 2150.93, "end": 2151.77, "word": " تبعته", "probability": 0.967529296875}, {"start": 2151.77, "end": 2152.29, "word": " خلال", "probability": 0.9861653645833334}, {"start": 2152.29, "end": 2152.65, "word": " هذا", "probability": 0.8271484375}, {"start": 2152.65, "end": 2152.85, "word": " ال", "probability": 0.85400390625}, {"start": 2152.85, "end": 2153.31, "word": " section", "probability": 0.60302734375}], "temperature": 1.0}, {"id": 76, "seek": 217888, "start": 2154.06, "end": 2178.88, "text": "وقلنا عندها ان اتنين والتلاتة و ال principle ideal generated by اتنين و ال principle ideal generated by التلاتة are maximal ideals in Z12 مظبوط لقيته في الدفاتر ممتاز يبقى هذا يا بنات بياننا سابقا ان ال principle ideal generated by اتنين", "tokens": [2407, 4587, 1211, 8315, 43242, 11296, 16472, 1975, 2655, 1863, 9957, 16070, 2655, 1211, 9307, 3660, 4032, 2423, 8665, 7157, 10833, 538, 1975, 2655, 1863, 9957, 4032, 2423, 8665, 7157, 10833, 538, 16712, 1211, 9307, 3660, 366, 49336, 30956, 294, 1176, 4762, 3714, 19913, 3555, 2407, 9566, 5296, 4587, 36081, 3224, 8978, 32748, 5172, 9307, 2288, 3714, 2304, 2655, 31377, 7251, 3555, 4587, 7578, 23758, 35186, 4724, 8315, 2655, 4724, 1829, 7649, 8315, 8608, 16758, 4587, 995, 16472, 2423, 8665, 7157, 10833, 538, 1975, 2655, 1863, 9957], "avg_logprob": -0.2812499888241291, "compression_ratio": 1.8516483516483517, "no_speech_prob": 0.0, "words": [{"start": 2154.06, "end": 2154.8, "word": "وقلنا", "probability": 0.72650146484375}, {"start": 2154.8, "end": 2155.22, "word": " عندها", "probability": 0.949951171875}, {"start": 2155.22, "end": 2155.5, "word": " ان", "probability": 0.326171875}, {"start": 2155.5, "end": 2156.1, "word": " اتنين", "probability": 0.63616943359375}, {"start": 2156.1, "end": 2156.82, "word": " والتلاتة", "probability": 0.81416015625}, {"start": 2156.82, "end": 2156.92, "word": " و", "probability": 0.6162109375}, {"start": 2156.92, "end": 2157.04, "word": " ال", "probability": 0.73681640625}, {"start": 2157.04, "end": 2157.54, "word": " principle", "probability": 0.65185546875}, {"start": 2157.54, "end": 2158.14, "word": " ideal", "probability": 0.45458984375}, {"start": 2158.14, "end": 2158.8, "word": " generated", "probability": 0.8583984375}, {"start": 2158.8, "end": 2159.18, "word": " by", "probability": 0.9306640625}, {"start": 2159.18, "end": 2159.64, "word": " اتنين", "probability": 0.9525146484375}, {"start": 2159.64, "end": 2159.76, "word": " و", "probability": 0.693359375}, {"start": 2159.76, "end": 2159.88, "word": " ال", "probability": 0.9130859375}, {"start": 2159.88, "end": 2160.32, "word": " principle", "probability": 0.8935546875}, {"start": 2160.32, "end": 2160.9, "word": " ideal", "probability": 0.91845703125}, {"start": 2160.9, "end": 2161.52, "word": " generated", "probability": 0.86962890625}, {"start": 2161.52, "end": 2161.94, "word": " by", "probability": 0.9775390625}, {"start": 2161.94, "end": 2162.78, "word": " التلاتة", "probability": 0.8572998046875}, {"start": 2162.78, "end": 2163.48, "word": " are", "probability": 0.810546875}, {"start": 2163.48, "end": 2164.36, "word": " maximal", "probability": 0.83203125}, {"start": 2164.36, "end": 2165.48, "word": " ideals", "probability": 0.9716796875}, {"start": 2165.48, "end": 2166.04, "word": " in", "probability": 0.33349609375}, {"start": 2166.04, "end": 2166.84, "word": " Z12", "probability": 0.24407958984375}, {"start": 2166.84, "end": 2167.94, "word": " مظبوط", "probability": 0.7736328125}, {"start": 2167.94, "end": 2168.36, "word": " لقيته", "probability": 0.70880126953125}, {"start": 2168.36, "end": 2168.5, "word": " في", "probability": 0.90283203125}, {"start": 2168.5, "end": 2169.32, "word": " الدفاتر", "probability": 0.95458984375}, {"start": 2169.32, "end": 2170.74, "word": " ممتاز", "probability": 0.83837890625}, {"start": 2170.74, "end": 2171.68, "word": " يبقى", "probability": 0.82666015625}, {"start": 2171.68, "end": 2172.0, "word": " هذا", "probability": 0.580078125}, {"start": 2172.0, "end": 2172.24, "word": " يا", "probability": 0.9228515625}, {"start": 2172.24, "end": 2172.78, "word": " بنات", "probability": 0.7884114583333334}, {"start": 2172.78, "end": 2173.68, "word": " بياننا", "probability": 0.6861572265625}, {"start": 2173.68, "end": 2174.78, "word": " سابقا", "probability": 0.84967041015625}, {"start": 2174.78, "end": 2175.46, "word": " ان", "probability": 0.7978515625}, {"start": 2175.46, "end": 2175.7, "word": " ال", "probability": 0.98388671875}, {"start": 2175.7, "end": 2176.3, "word": " principle", "probability": 0.88525390625}, {"start": 2176.3, "end": 2177.02, "word": " ideal", "probability": 0.91650390625}, {"start": 2177.02, "end": 2177.8, "word": " generated", "probability": 0.892578125}, {"start": 2177.8, "end": 2178.28, "word": " by", "probability": 0.98876953125}, {"start": 2178.28, "end": 2178.88, "word": " اتنين", "probability": 0.977783203125}], "temperature": 1.0}, {"id": 77, "seek": 220688, "start": 2179.12, "end": 2206.88, "text": "و ال principle ideals generated by ثلاثة هدول are maximum ideals هدول الأتنين هما ال maximum خلّي هالمعلومة عندك هذه لزمان طيب نيجي لزيد تمانية لزيد تمانية بدي أدور على ال ideals تبعتها الان لو جيت على ال principle ideals generated by one", "tokens": [2407, 2423, 8665, 30956, 10833, 538, 38637, 1211, 5718, 104, 3660, 8032, 3215, 12610, 366, 6674, 30956, 8032, 3215, 12610, 16247, 2655, 1863, 9957, 8032, 15042, 2423, 6674, 16490, 1211, 11703, 1829, 8032, 45340, 30241, 20498, 3660, 43242, 4117, 29538, 5296, 11622, 2304, 7649, 23032, 1829, 3555, 8717, 1829, 7435, 1829, 5296, 11622, 25708, 46811, 7649, 10632, 5296, 11622, 25708, 46811, 7649, 10632, 4724, 16254, 5551, 3215, 13063, 15844, 2423, 30956, 6055, 3555, 34268, 11296, 2423, 7649, 45164, 10874, 36081, 15844, 2423, 8665, 30956, 10833, 538, 472], "avg_logprob": -0.21768466230820527, "compression_ratio": 1.7587939698492463, "no_speech_prob": 0.0, "words": [{"start": 2179.12, "end": 2179.36, "word": "و", "probability": 0.5068359375}, {"start": 2179.36, "end": 2179.54, "word": " ال", "probability": 0.611328125}, {"start": 2179.54, "end": 2180.02, "word": " principle", "probability": 0.58935546875}, {"start": 2180.02, "end": 2180.62, "word": " ideals", "probability": 0.69677734375}, {"start": 2180.62, "end": 2181.22, "word": " generated", "probability": 0.8623046875}, {"start": 2181.22, "end": 2181.56, "word": " by", "probability": 0.95166015625}, {"start": 2181.56, "end": 2182.14, "word": " ثلاثة", "probability": 0.803466796875}, {"start": 2182.14, "end": 2182.62, "word": " هدول", "probability": 0.8885091145833334}, {"start": 2182.62, "end": 2182.98, "word": " are", "probability": 0.79052734375}, {"start": 2182.98, "end": 2183.78, "word": " maximum", "probability": 0.75390625}, {"start": 2183.78, "end": 2185.0, "word": " ideals", "probability": 0.96240234375}, {"start": 2185.0, "end": 2186.3, "word": " هدول", "probability": 0.892578125}, {"start": 2186.3, "end": 2187.12, "word": " الأتنين", "probability": 0.74853515625}, {"start": 2187.12, "end": 2187.68, "word": " هما", "probability": 0.74658203125}, {"start": 2187.68, "end": 2187.96, "word": " ال", "probability": 0.89599609375}, {"start": 2187.96, "end": 2188.66, "word": " maximum", "probability": 0.92041015625}, {"start": 2188.66, "end": 2189.92, "word": " خلّي", "probability": 0.7764892578125}, {"start": 2189.92, "end": 2190.78, "word": " هالمعلومة", "probability": 0.81181640625}, {"start": 2190.78, "end": 2191.4, "word": " عندك", "probability": 0.987548828125}, {"start": 2191.4, "end": 2191.8, "word": " هذه", "probability": 0.611328125}, {"start": 2191.8, "end": 2192.66, "word": " لزمان", "probability": 0.934326171875}, {"start": 2192.66, "end": 2193.72, "word": " طيب", "probability": 0.93798828125}, {"start": 2193.72, "end": 2194.12, "word": " نيجي", "probability": 0.878662109375}, {"start": 2194.12, "end": 2194.72, "word": " لزيد", "probability": 0.5514322916666666}, {"start": 2194.72, "end": 2196.14, "word": " تمانية", "probability": 0.9353841145833334}, {"start": 2196.14, "end": 2196.94, "word": " لزيد", "probability": 0.9479166666666666}, {"start": 2196.94, "end": 2197.46, "word": " تمانية", "probability": 0.9794921875}, {"start": 2197.46, "end": 2197.78, "word": " بدي", "probability": 0.727783203125}, {"start": 2197.78, "end": 2198.36, "word": " أدور", "probability": 0.9283854166666666}, {"start": 2198.36, "end": 2198.74, "word": " على", "probability": 0.71923828125}, {"start": 2198.74, "end": 2198.96, "word": " ال", "probability": 0.9462890625}, {"start": 2198.96, "end": 2199.92, "word": " ideals", "probability": 0.978515625}, {"start": 2199.92, "end": 2202.02, "word": " تبعتها", "probability": 0.9169921875}, {"start": 2202.02, "end": 2202.52, "word": " الان", "probability": 0.472412109375}, {"start": 2202.52, "end": 2202.76, "word": " لو", "probability": 0.98193359375}, {"start": 2202.76, "end": 2203.26, "word": " جيت", "probability": 0.975341796875}, {"start": 2203.26, "end": 2203.52, "word": " على", "probability": 0.7783203125}, {"start": 2203.52, "end": 2203.74, "word": " ال", "probability": 0.9189453125}, {"start": 2203.74, "end": 2204.36, "word": " principle", "probability": 0.90673828125}, {"start": 2204.36, "end": 2205.02, "word": " ideals", "probability": 0.84228515625}, {"start": 2205.02, "end": 2205.78, "word": " generated", "probability": 0.908203125}, {"start": 2205.78, "end": 2206.48, "word": " by", "probability": 0.98486328125}, {"start": 2206.48, "end": 2206.88, "word": " one", "probability": 0.953125}], "temperature": 1.0}, {"id": 78, "seek": 223575, "start": 2207.27, "end": 2235.75, "text": "بتلاقيها هي ال principle ideal generated by تلاتة بتلاقيها هي ال principle ideal generated by خمسة بتلاقيها هي ال principle ideal generated by سبعة يعني كل primes من واحد إلى تمانية بيعطوني مين؟ بيعطوني نفس ال ring الأصلية ليه Z تمانية كل هذا بيساوي Z تمانية", "tokens": [3555, 2655, 15040, 38436, 11296, 39896, 2423, 8665, 7157, 10833, 538, 6055, 1211, 9307, 3660, 39894, 15040, 38436, 11296, 39896, 2423, 8665, 7157, 10833, 538, 16490, 2304, 3794, 3660, 39894, 15040, 38436, 11296, 39896, 2423, 8665, 7157, 10833, 538, 8608, 3555, 27884, 37495, 22653, 28242, 2886, 279, 9154, 36764, 24401, 30731, 46811, 7649, 10632, 4724, 40228, 9566, 11536, 1829, 3714, 9957, 22807, 4724, 40228, 9566, 11536, 1829, 8717, 36178, 2423, 4875, 16247, 36520, 10632, 32239, 3224, 1176, 46811, 7649, 10632, 28242, 23758, 4724, 1829, 3794, 995, 45865, 1176, 46811, 7649, 10632], "avg_logprob": -0.1745923919522244, 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2236.58, "end": 2258.12, "text": "طيب تمام راح الواحد والتلات والخمسة والسبعة بقى اللي عندي اتنين واربعة وستة وبس مظبوط وال zero صح؟ طيب عندك ال principle ideal generated by zero اللي هو zero itself", "tokens": [9566, 1829, 3555, 46811, 10943, 12602, 39319, 2423, 14407, 24401, 16070, 2655, 1211, 9307, 16070, 9778, 2304, 3794, 3660, 16070, 35457, 27884, 4724, 4587, 7578, 13672, 1829, 18871, 16254, 1975, 2655, 1863, 9957, 4032, 9640, 3555, 27884, 4032, 14851, 3660, 46599, 3794, 3714, 19913, 3555, 2407, 9566, 16070, 4018, 20328, 5016, 22807, 23032, 1829, 3555, 43242, 4117, 2423, 8665, 7157, 10833, 538, 4018, 13672, 1829, 31439, 4018, 2564], "avg_logprob": -0.2712862336117288, "compression_ratio": 1.532934131736527, "no_speech_prob": 0.0, "words": [{"start": 2236.58, "end": 2237.06, "word": "طيب", "probability": 0.9724934895833334}, {"start": 2237.06, "end": 2237.66, "word": " تمام", "probability": 0.97412109375}, {"start": 2237.66, "end": 2238.3, "word": " راح", "probability": 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ليه الاتنين طيب هنا هنا بنات اتنين وثلاثة prime numbers وكل واحد فيهم بجسم نهار هذه طلعت اتنين هو prime number بجسم التمانية بناء عليه هذه من هم ال maximum اتنين وخمسة اتنين وخمسة ممتازة", "tokens": [6027, 9307, 1863, 9957, 23032, 1829, 3555, 3714, 2304, 2655, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 29538, 23032, 1211, 34268, 32239, 3224, 2423, 9307, 1863, 9957, 23032, 1829, 3555, 34105, 34105, 4724, 8315, 2655, 1975, 2655, 1863, 9957, 4032, 12984, 1211, 5718, 104, 3660, 5835, 3547, 4032, 28820, 36764, 24401, 8978, 16095, 4724, 7435, 38251, 8717, 3224, 9640, 29538, 23032, 1211, 34268, 1975, 2655, 1863, 9957, 31439, 5835, 1230, 4724, 7435, 38251, 16712, 2304, 7649, 10632, 44945, 16606, 47356, 29538, 9154, 8032, 2304, 2423, 6674, 1975, 2655, 1863, 9957, 4032, 9778, 2304, 3794, 3660, 1975, 2655, 1863, 9957, 4032, 9778, 2304, 3794, 3660, 3714, 2304, 2655, 31377, 3660], "avg_logprob": -0.1788352302529595, "compression_ratio": 1.9528795811518325, "no_speech_prob": 0.0, "words": 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{"start": 2923.41, "end": 2924.29, "word": " تساوي", "probability": 0.9700927734375}, {"start": 2924.29, "end": 2924.47, "word": " ال", "probability": 0.82763671875}, {"start": 2924.47, "end": 2924.79, "word": " X", "probability": 0.97607421875}, {"start": 2924.79, "end": 2925.35, "word": " الواحد", "probability": 0.9072265625}, {"start": 2925.35, "end": 2925.67, "word": " عندى", "probability": 0.677734375}, {"start": 2925.67, "end": 2926.95, "word": " بقدرش", "probability": 0.48870849609375}, {"start": 2926.95, "end": 2927.31, "word": " ب", "probability": 0.453857421875}, {"start": 2927.31, "end": 2927.95, "word": " A", "probability": 0.3310546875}, {"start": 2927.95, "end": 2929.13, "word": " زائد", "probability": 0.80908203125}, {"start": 2929.13, "end": 2929.39, "word": " ال", "probability": 0.65380859375}, {"start": 2929.39, "end": 2929.75, "word": " B", "probability": 0.86279296875}, {"start": 2929.75, "end": 2931.17, "word": " هذا", "probability": 0.86376953125}, {"start": 2931.17, "end": 2931.97, "word": " الكلام", "probability": 0.95849609375}, {"start": 2931.97, "end": 2932.39, "word": " بده", "probability": 0.775146484375}, {"start": 2932.39, "end": 2932.91, "word": " يساوي", "probability": 0.9544677734375}, {"start": 2932.91, "end": 2933.17, "word": " ال", "probability": 0.46484375}, {"start": 2933.17, "end": 2933.53, "word": " X", "probability": 0.935546875}, {"start": 2933.53, "end": 2934.13, "word": " A", "probability": 0.728515625}, {"start": 2934.13, "end": 2934.93, "word": " زائد", "probability": 0.9775390625}, {"start": 2934.93, "end": 2935.27, "word": " ال", "probability": 0.9208984375}, {"start": 2935.27, "end": 2935.75, "word": " X", "probability": 0.96240234375}, {"start": 2935.75, "end": 2936.45, "word": " B", "probability": 0.83984375}, {"start": 2936.45, "end": 2937.33, "word": " ال", "probability": 0.88232421875}, {"start": 2937.33, "end": 2937.69, "word": " R", "probability": 0.63232421875}, {"start": 2937.69, "end": 2938.95, "word": " commutative", "probability": 0.8338216145833334}, {"start": 2938.95, "end": 2940.07, "word": " يبقى", "probability": 0.9869384765625}, {"start": 2940.07, "end": 2940.59, "word": " هذا", "probability": 0.68212890625}, {"start": 2940.59, "end": 2940.87, "word": " ب", "probability": 0.8486328125}, {"start": 2940.87, "end": 2941.29, "word": " A", "probability": 0.51416015625}, {"start": 2941.29, "end": 2941.93, "word": " X", "probability": 0.77001953125}, {"start": 2941.93, "end": 2942.91, "word": " زائد", "probability": 0.9814453125}, {"start": 2942.91, "end": 2943.15, "word": " ال", "probability": 0.900390625}, {"start": 2943.15, "end": 2943.51, "word": " X", "probability": 0.90234375}, {"start": 2943.51, "end": 2944.05, "word": " B", "probability": 0.82568359375}, {"start": 2944.05, "end": 2945.43, "word": " خلّالي", "probability": 0.6127197265625}, {"start": 2945.43, "end": 2945.89, "word": " هنا", "probability": 0.802734375}, {"start": 2945.89, "end": 2946.53, "word": " هذا", "probability": 0.7822265625}, {"start": 2946.53, "end": 2947.05, "word": " موجود", "probability": 0.9884440104166666}, {"start": 2947.05, "end": 2947.49, "word": " وين", "probability": 0.6591796875}], "temperature": 1.0}, {"id": 104, "seek": 297700, "start": 2947.96, "end": 2977.0, "text": "فى ال A و هذا موجود وين فى B هذا موجود فى A و هذا موجود فى B إذا هذا ال A X موجود فى ال A B بنفس الطريقة هذا موجود فى B و هذا موجود وين فى A إذا هذا كله موجود وين فى ال A B", "tokens": [5172, 7578, 2423, 316, 4032, 23758, 3714, 29245, 23328, 4032, 9957, 6156, 7578, 363, 23758, 3714, 29245, 23328, 6156, 7578, 316, 4032, 23758, 3714, 29245, 23328, 6156, 7578, 363, 11933, 15730, 23758, 2423, 316, 1783, 3714, 29245, 23328, 6156, 7578, 2423, 316, 363, 44945, 36178, 41950, 16572, 28671, 23758, 3714, 29245, 23328, 6156, 7578, 363, 4032, 23758, 3714, 29245, 23328, 4032, 9957, 6156, 7578, 316, 11933, 15730, 23758, 28242, 3224, 3714, 29245, 23328, 4032, 9957, 6156, 7578, 2423, 316, 363], "avg_logprob": 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"word": " هذا", "probability": 0.98388671875}, {"start": 2969.54, "end": 2970.28, "word": " موجود", "probability": 0.9908854166666666}, {"start": 2970.28, "end": 2970.82, "word": " وين", "probability": 0.97216796875}, {"start": 2970.82, "end": 2971.32, "word": " فى", "probability": 0.93408203125}, {"start": 2971.32, "end": 2971.74, "word": " A", "probability": 0.98583984375}, {"start": 2971.74, "end": 2972.82, "word": " إذا", "probability": 0.968017578125}, {"start": 2972.82, "end": 2973.34, "word": " هذا", "probability": 0.96826171875}, {"start": 2973.34, "end": 2973.88, "word": " كله", "probability": 0.982177734375}, {"start": 2973.88, "end": 2974.5, "word": " موجود", "probability": 0.9939778645833334}, {"start": 2974.5, "end": 2975.04, "word": " وين", "probability": 0.9892578125}, {"start": 2975.04, "end": 2975.82, "word": " فى", "probability": 0.922607421875}, {"start": 2975.82, "end": 2976.02, "word": " ال", "probability": 0.9599609375}, {"start": 2976.02, "end": 2976.6, "word": " A", "probability": 0.97509765625}, {"start": 2976.6, "end": 2977.0, "word": " B", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 105, "seek": 300570, "start": 2977.54, "end": 3005.7, "text": "يبقى X اللى خدتها في ال intersection اللى جيتها موجودة وين في حاصل الدورة يبقى هنا ساعة ال intersection بيه ساعة ست من مين من ال A بيه هذه العلاقة رقم اتنين يبقى from واحد and اتنين we have", "tokens": [1829, 3555, 4587, 7578, 1783, 13672, 7578, 16490, 3215, 2655, 11296, 8978, 2423, 15236, 13672, 7578, 10874, 36081, 11296, 3714, 29245, 23328, 3660, 4032, 9957, 8978, 11331, 33546, 1211, 32748, 13063, 3660, 7251, 3555, 4587, 7578, 34105, 8608, 995, 27884, 2423, 15236, 4724, 1829, 3224, 8608, 995, 27884, 8608, 2655, 9154, 3714, 9957, 9154, 2423, 316, 4724, 1829, 3224, 29538, 18863, 15040, 28671, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 490, 36764, 24401, 293, 1975, 2655, 1863, 9957, 321, 362], "avg_logprob": -0.2020220539149116, "compression_ratio": 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2983.7, "word": " في", "probability": 0.5810546875}, {"start": 2983.7, "end": 2984.42, "word": " حاصل", "probability": 0.8302408854166666}, {"start": 2984.42, "end": 2985.32, "word": " الدورة", "probability": 0.6210123697916666}, {"start": 2985.32, "end": 2986.12, "word": " يبقى", "probability": 0.9825439453125}, {"start": 2986.12, "end": 2986.56, "word": " هنا", "probability": 0.9833984375}, {"start": 2986.56, "end": 2987.76, "word": " ساعة", "probability": 0.5697428385416666}, {"start": 2987.76, "end": 2989.36, "word": " ال", "probability": 0.98681640625}, {"start": 2989.36, "end": 2990.42, "word": " intersection", "probability": 0.9287109375}, {"start": 2990.42, "end": 2991.9, "word": " بيه", "probability": 0.8253580729166666}, {"start": 2991.9, "end": 2992.42, "word": " ساعة", "probability": 0.8986002604166666}, {"start": 2992.42, "end": 2992.78, "word": " ست", "probability": 0.655517578125}, {"start": 2992.78, "end": 2993.06, "word": " من", "probability": 0.861328125}, {"start": 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3001.32, "end": 3002.38, "word": " and", "probability": 0.84521484375}, {"start": 3002.38, "end": 3003.88, "word": " اتنين", "probability": 0.9827880859375}, {"start": 3003.88, "end": 3004.66, "word": " we", "probability": 0.453857421875}, {"start": 3004.66, "end": 3005.7, "word": " have", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 106, "seek": 303097, "start": 3006.47, "end": 3030.97, "text": "إن الـ A intersection B يساوي الـ A في B يلا صدلوا عندكم exercises ليوم السبت خدوا لسؤال 17 سؤال 22", "tokens": [28814, 1863, 2423, 39184, 316, 15236, 363, 7251, 3794, 995, 45865, 2423, 39184, 316, 8978, 363, 7251, 15040, 20328, 3215, 1211, 14407, 43242, 24793, 11900, 5296, 1829, 20498, 21136, 3555, 2655, 16490, 3215, 14407, 5296, 3794, 33604, 6027, 3282, 8608, 33604, 6027, 5853], "avg_logprob": -0.3430397761139003, "compression_ratio": 1.221311475409836, "no_speech_prob": 0.0, "words": [{"start": 3006.47, "end": 3006.89, "word": "إن", "probability": 0.6776123046875}, {"start": 3006.89, "end": 3007.33, "word": " الـ", "probability": 0.698974609375}, {"start": 3007.33, "end": 3007.67, "word": " A", "probability": 0.5498046875}, {"start": 3007.67, "end": 3008.93, "word": " intersection", "probability": 0.51904296875}, {"start": 3008.93, "end": 3010.23, "word": " B", "probability": 0.89599609375}, {"start": 3010.23, "end": 3011.97, "word": " يساوي", "probability": 0.451446533203125}, {"start": 3011.97, "end": 3012.29, "word": " الـ", "probability": 0.80078125}, {"start": 3012.29, "end": 3012.65, "word": " A", "probability": 0.73583984375}, {"start": 3012.65, "end": 3013.05, "word": " في", "probability": 0.61376953125}, {"start": 3013.05, "end": 3013.49, "word": " B", "probability": 0.90576171875}, {"start": 3013.49, "end": 3014.65, "word": " يلا", "probability": 0.572265625}, {"start": 3014.65, "end": 3015.21, "word": " صدلوا", "probability": 0.70758056640625}, {"start": 3015.21, "end": 3015.81, "word": " عندكم", "probability": 0.870361328125}, {"start": 3015.81, "end": 3017.37, "word": " exercises", "probability": 0.58837890625}, {"start": 3017.37, "end": 3018.15, "word": " ليوم", "probability": 0.8079427083333334}, {"start": 3018.15, "end": 3018.91, "word": " السبت", "probability": 0.8987630208333334}, {"start": 3018.91, "end": 3025.99, "word": " خدوا", "probability": 0.7998046875}, {"start": 3025.99, "end": 3026.43, "word": " لسؤال", "probability": 0.830322265625}, {"start": 3026.43, "end": 3027.55, "word": " 17", "probability": 0.697265625}, {"start": 3027.55, "end": 3030.33, "word": " سؤال", "probability": 0.9695638020833334}, {"start": 3030.33, "end": 3030.97, "word": " 22", "probability": 0.93994140625}], "temperature": 1.0}, {"id": 107, "seek": 306326, "start": 3036.22, "end": 3063.26, "text": "أسئلة أربعة و عشرين سؤال تلاتين تمانية و تلاتين واحد و أربعين نين و أربعين خمسة و أربعين ستة و أربعين تمانية و أربعين", "tokens": [10721, 3794, 19986, 37977, 5551, 25513, 27884, 4032, 6225, 46309, 9957, 8608, 33604, 6027, 6055, 1211, 9307, 9957, 46811, 7649, 10632, 4032, 6055, 1211, 9307, 9957, 36764, 24401, 4032, 5551, 25513, 3615, 9957, 8717, 9957, 4032, 5551, 25513, 3615, 9957, 16490, 2304, 3794, 3660, 4032, 5551, 25513, 3615, 9957, 8608, 2655, 3660, 4032, 5551, 25513, 3615, 9957, 46811, 7649, 10632, 4032, 5551, 25513, 3615, 9957], "avg_logprob": -0.11345880670529424, "compression_ratio": 2.089108910891089, "no_speech_prob": 0.0, "words": [{"start": 3036.22, "end": 3036.78, "word": "أسئلة", "probability": 0.8475341796875}, {"start": 3036.78, "end": 3037.22, "word": " أربعة", "probability": 0.7264811197916666}, {"start": 3037.22, "end": 3037.38, "word": " و", "probability": 0.837890625}, {"start": 3037.38, "end": 3038.1, "word": " عشرين", "probability": 0.8502604166666666}, {"start": 3038.1, "end": 3040.7, "word": " سؤال", "probability": 0.92041015625}, {"start": 3040.7, "end": 3041.74, "word": " تلاتين", "probability": 0.9697265625}, {"start": 3041.74, "end": 3044.22, "word": " تمانية", "probability": 0.84033203125}, {"start": 3044.22, "end": 3044.4, "word": " و", "probability": 0.6181640625}, {"start": 3044.4, "end": 3045.4, "word": " تلاتين", "probability": 0.98681640625}, {"start": 3045.4, "end": 3047.6, "word": " واحد", "probability": 0.9765625}, {"start": 3047.6, "end": 3047.8, "word": " و", "probability": 0.5498046875}, {"start": 3047.8, "end": 3048.92, "word": " أربعين", "probability": 0.9200439453125}, {"start": 3048.92, "end": 3051.44, "word": " نين", "probability": 0.5712890625}, {"start": 3051.44, "end": 3051.6, "word": " و", "probability": 0.95263671875}, {"start": 3051.6, "end": 3052.64, "word": " أربعين", "probability": 0.96435546875}, {"start": 3052.64, "end": 3055.28, "word": " خمسة", "probability": 0.9737548828125}, {"start": 3055.28, "end": 3055.38, "word": " و", "probability": 0.99755859375}, {"start": 3055.38, "end": 3056.42, "word": " أربعين", "probability": 0.9654541015625}, {"start": 3056.42, "end": 3058.62, "word": " ستة", "probability": 0.9873046875}, {"start": 3058.62, "end": 3058.76, "word": " و", "probability": 0.99658203125}, {"start": 3058.76, "end": 3059.76, "word": " أربعين", "probability": 0.973388671875}, {"start": 3059.76, "end": 3062.08, "word": " تمانية", "probability": 0.9861653645833334}, {"start": 3062.08, "end": 3062.3, "word": " و", "probability": 0.99755859375}, {"start": 3062.3, "end": 3063.26, "word": " أربعين", "probability": 0.9735107421875}], "temperature": 1.0}, {"id": 108, "seek": 307230, "start": 3065.4, "end": 3072.3, "text": "خمسين واحد وخمسين ستة وخمسين", "tokens": [9778, 2304, 3794, 9957, 36764, 24401, 4032, 9778, 2304, 3794, 9957, 8608, 2655, 3660, 4032, 9778, 2304, 3794, 9957], "avg_logprob": -0.12734374552965164, "compression_ratio": 1.2682926829268293, "no_speech_prob": 0.0, "words": [{"start": 3065.3999999999996, "end": 3066.7999999999997, "word": "خمسين", "probability": 0.9193115234375}, {"start": 3066.7999999999997, "end": 3068.2, "word": " واحد", "probability": 0.6533203125}, {"start": 3068.2, "end": 3069.4, "word": " وخمسين", "probability": 0.91865234375}, {"start": 3069.4, "end": 3071.36, "word": " ستة", "probability": 0.89111328125}, {"start": 3071.36, "end": 3072.3, "word": " وخمسين", "probability": 0.979296875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3073.4860625, "duration_after_vad": 2980.639999999986}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a182dcc814a5c6a14f028d5033d0fd6a9e14c82d
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/NuxXCXL8BVc_raw.srt
@@ -0,0 +1,1776 @@
+1
+00:00:20,640 --> 00:00:25,720
+بسم الله الرحمن الرحيم عوض على بدء نذكر بما
+
+2
+00:00:25,720 --> 00:00:31,160
+أعطيناه المرة الماضية لأن هذه الكترولري تعتمد على
+
+3
+00:00:31,160 --> 00:00:35,500
+ما درسناه في المحاضرة الماضية المحاضرة الماضية
+
+4
+00:00:35,500 --> 00:00:39,860
+كانت عمود شقري هو نظري تاني النظرية الأولى بتقول
+
+5
+00:00:39,860 --> 00:00:44,370
+لو كانت ال R is commutative ring with unityيبقى من
+
+6
+00:00:44,370 --> 00:00:48,390
+الـ R modulo A is an integral domain if and only
+
+7
+00:00:48,390 --> 00:00:53,630
+if الـ ID الـ A is a prime والنظرية التانية برضه
+
+8
+00:00:53,630 --> 00:00:58,990
+نفس الموطنة تبع النظرية الأولى اللي هو الـ R
+
+9
+00:00:58,990 --> 00:01:02,310
+committed to bring with unity لكن القلاف عند
+
+10
+00:01:02,310 --> 00:01:07,930
+المطلوب فبنقول الـ R modulo A is a field if and
+
+11
+00:01:07,930 --> 00:01:14,040
+only if الـ A is a maximal IDهذا آخر حاجة أثبتناها
+
+12
+00:01:14,040 --> 00:01:18,000
+المرة الماضية الكرولري عبارة عن نتيجة على
+
+13
+00:01:18,000 --> 00:01:22,240
+النظريتين بتقول لو كانت ال R commutative ring with
+
+14
+00:01:22,240 --> 00:01:29,880
+unity يبقى every maximal ideal is prime يبقى ال
+
+15
+00:01:29,880 --> 00:01:39,840
+proof كالتالي ال R is commutative ring with unity
+
+16
+00:01:44,120 --> 00:01:50,080
+طبعا يبقى بدي افترض انه عندي ideal و ال ideal is
+
+17
+00:01:50,080 --> 00:02:01,580
+maximum let ال a be a maximal ideal
+
+18
+00:02:01,580 --> 00:02:11,880
+of R بالنظرية الثانية يبقى ال R modulo a is a
+
+19
+00:02:11,880 --> 00:02:20,600
+fieldيبقى بروح بقوله by the second theorem
+
+20
+00:02:20,600 --> 00:02:32,860
+بالنظرية الثانية ال a modulo a is a field طبعا
+
+21
+00:02:32,860 --> 00:02:40,680
+احنا قلنا قبل ذلك any field is an integral domain
+
+22
+00:02:41,190 --> 00:02:48,770
+هذا بدي يعطينا ان ال R موديول A is an integral
+
+23
+00:02:48,770 --> 00:02:54,070
+domain يبقى
+
+24
+00:02:54,070 --> 00:03:04,290
+بروحنا نقوله by the first theorem النظرية
+
+25
+00:03:04,290 --> 00:03:13,960
+الأولى ال A is a prime IDيبقى أثبتنا إن الـ
+
+26
+00:03:13,960 --> 00:03:20,420
+maximal ideal عبارة عن prime ideal إذا كانت الـR
+
+27
+00:03:20,420 --> 00:03:26,620
+is commutative with unity وصلنا إلى آخر مثال في
+
+28
+00:03:26,620 --> 00:03:34,840
+هذا ال section وهو الاردن يقول
+
+29
+00:03:34,840 --> 00:03:35,960
+the ideal
+
+30
+00:03:39,630 --> 00:03:46,970
+أو الـ principal ideal generated by X is a prime
+
+31
+00:03:46,970 --> 00:03:55,510
+ideal in Z of X but not maximum
+
+32
+00:04:18,540 --> 00:04:24,720
+هذا المثال مشان نحله بيعتمد على سؤالين موجودين في
+
+33
+00:04:24,720 --> 00:04:29,980
+الكتاب مثل ما ذكر الكتاب احنا هنحل السؤالين وانتوا
+
+34
+00:04:29,980 --> 00:04:36,200
+مش دارين من خلال اثباتنا أو خلال حلنا لهذا السؤال
+
+35
+00:04:36,200 --> 00:04:40,840
+أول شي بقوللي ال principle id generated by X هو
+
+36
+00:04:40,840 --> 00:04:45,340
+عبارة عن ال prime ideal في هذه ال ring لكنه ليس
+
+37
+00:04:45,340 --> 00:04:49,720
+maximumيبقى بدي أثبت شغل تاني ان ال principle
+
+38
+00:04:49,720 --> 00:04:54,260
+ideal generated by X هو prime ideal وفي نفس الوقت
+
+39
+00:04:54,260 --> 00:05:00,380
+ليس maximum ideal كمان في Z of X علشان هيك بدنا
+
+40
+00:05:00,380 --> 00:05:04,300
+نبدأ نثبت ال maximum لإن بدنا نثبت اللي هو يفتقر
+
+41
+00:05:04,300 --> 00:05:09,460
+انه prime ideal لكن قبل ذلك خلينا نرجع لتعريف ال
+
+42
+00:05:09,460 --> 00:05:16,210
+principle ideal generated by X قلنا سابقاكل ال
+
+43
+00:05:16,210 --> 00:05:23,070
+elements ال X في R بحيث ال R موجودة في R X R والله
+
+44
+00:05:23,070 --> 00:05:26,290
+R X الاتنين R ده similar لإن ال ring commuted
+
+45
+00:05:26,290 --> 00:05:32,510
+تمام؟ يبقى كل ال X في R بحيث ال R موجودة في R هذا
+
+46
+00:05:32,510 --> 00:05:36,930
+ال general definition لمين؟ لل principle ideal
+
+47
+00:05:36,930 --> 00:05:42,050
+generated by X بدي أروح أطبق هذا التعريف عالميا
+
+48
+00:05:42,050 --> 00:05:47,270
+على ال ring اللي عندنايبقى بقدر أقول هذا كل ال
+
+49
+00:05:47,270 --> 00:05:59,870
+element x كل ال element f of x اللي موجودة في ال z
+
+50
+00:05:59,870 --> 00:06:10,110
+of x such that ان ال x في ال g ان ال f of xشو
+
+51
+00:06:10,110 --> 00:06:16,930
+شكلها .. شو شكل سبعها بحيث ال F of X يساوي ال X في
+
+52
+00:06:16,930 --> 00:06:25,650
+ال G of X وال G of X هذه موجودة في Z of X الشكل
+
+53
+00:06:25,650 --> 00:06:32,290
+اللي عندنا إذا أنا قاعد تعريف اللي هو ال principle
+
+54
+00:06:32,290 --> 00:06:37,510
+ideal generated by X بما يناسب طبيعة المسألة اللي
+
+55
+00:06:37,510 --> 00:06:42,850
+عندنايبقى كل الـ Functions أو الـ Polynomials اللي
+
+56
+00:06:42,850 --> 00:06:47,830
+المعاملات تبعتها أعداد صحيحة اللي بتكون على الشكل
+
+57
+00:06:47,830 --> 00:06:53,990
+التالي X في G of X أنا قولنا X في R بدي أخد R من
+
+58
+00:06:53,990 --> 00:06:58,890
+الـ Z يعني بدي أخد الـ G of X من الـ Z of X مضروبة
+
+59
+00:06:58,890 --> 00:07:06,010
+في المين في الـ F X الآن بدي أفترض أن عندنا ستانية
+
+60
+00:07:06,510 --> 00:07:18,130
+يبقى باجي بقوله consider the ideal I ال
+
+61
+00:07:18,130 --> 00:07:22,490
+I هذا أثبتناه قبل ذلك أنه ideal كل ال polynomials
+
+62
+00:07:22,490 --> 00:07:27,750
+اللي المقدار الثابت فيها يساوي الصفر تذكروا المرة
+
+63
+00:07:27,750 --> 00:07:33,630
+علينا و أثبتناه أنه ideal يبقى ال ideal I كل ال F
+
+64
+00:07:33,630 --> 00:07:40,740
+of Xsuch that ال F of Zero بده يساوي مين؟ Zero طب
+
+65
+00:07:40,740 --> 00:07:44,480
+إيش علاقة هذا بالموضوع؟ آه دلوقت بنريك إيش علاقة
+
+66
+00:07:44,480 --> 00:07:54,360
+هذا الموضوع الان يا عزيزي اننا ندعي
+
+67
+00:07:54,360 --> 00:07:59,810
+ان ال principle ID generated by X بده يساوي Iأنا
+
+68
+00:07:59,810 --> 00:08:05,230
+أدّعي أن هذا ال ideal هو هذا ال ideal مضبط تماما
+
+69
+00:08:05,230 --> 00:08:09,630
+شكله مش مبين هذا في شجه و هذا في شجه لكن احنا
+
+70
+00:08:09,630 --> 00:08:15,150
+بنشتغل شغل رياضي بحيث فعلا نثبت أن هذا يساوي هذا
+
+71
+00:08:15,150 --> 00:08:24,230
+إذا مشان هيك أفترض أن F of X موجود في ال principle
+
+72
+00:08:24,230 --> 00:08:30,760
+ideal generated by Xيبقى في هذه الحالة ال F of X
+
+73
+00:08:30,760 --> 00:08:36,080
+بدها تساوي هاي يبقى ال F of X بدها تساوي مين؟ ال X
+
+74
+00:08:36,080 --> 00:08:43,520
+في G of X يبقى ال X في G of X طيب لو جيت و قلت بدي
+
+75
+00:08:43,520 --> 00:08:49,180
+أشوف قداشي ال F of Zero بدها تساوي يبقى بدها تساوي
+
+76
+00:08:49,180 --> 00:08:56,230
+Zero في G of ZeroD of Zero Zero والله اي رقم اخر
+
+77
+00:08:56,230 --> 00:09:01,270
+اضربه في Zero بده يعطيني Zero element ايش تفسيرك
+
+78
+00:09:01,270 --> 00:09:07,210
+لهذا الكلام ان ال F of X موجودة وين في ال I ده في
+
+79
+00:09:07,210 --> 00:09:13,710
+ال I مظبوط يبقى هذا بده يعطينا مين ان ال F of X
+
+80
+00:09:13,710 --> 00:09:20,200
+موجودة وين في ال I دي ال Iهذا بدّه يعطينا ان ال
+
+81
+00:09:20,200 --> 00:09:24,660
+principle ideal generated by X subset من مين؟
+
+82
+00:09:24,660 --> 00:09:31,120
+subset من I وهذه الخطوات الأولى on the other hand
+
+83
+00:09:31,120 --> 00:09:34,980
+يبقى
+
+84
+00:09:34,980 --> 00:09:42,880
+on the other hand من الناحية الأخرى بدّه اجي أقوله
+
+85
+00:09:42,880 --> 00:09:49,770
+افترضي ان ال F of X موجودة وين؟موجودة في الـ I دي
+
+86
+00:09:49,770 --> 00:09:53,930
+الـ I بدي أحاول أثبت أن ال F of X موجودة في ال X
+
+87
+00:09:53,930 --> 00:10:04,950
+موجودة في ال X then ال F of X بدي أثبت أن F of X
+
+88
+00:10:04,950 --> 00:10:05,170
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+89
+00:10:05,170 --> 00:10:07,410
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+90
+00:10:07,410 --> 00:10:08,310
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+91
+00:10:08,310 --> 00:10:08,390
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+92
+00:10:08,390 --> 00:10:08,430
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+93
+00:10:08,430 --> 00:10:08,430
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+94
+00:10:08,430 --> 00:10:08,430
+موجودة في ال X موجودة في ال X موجودة في ال X
+
+95
+00:10:08,430 --> 00:10:13,450
+موجودة في ال X موجودة في ال X موجودة في ال
+
+96
+00:10:17,070 --> 00:10:23,150
+ليش؟ لإن ال I عندها فيه ال term الأخير ب zero
+
+97
+00:10:23,150 --> 00:10:26,990
+تمام؟ يبقى طيارة ال term الأخير اللي هو ال
+
+98
+00:10:26,990 --> 00:10:31,790
+constant and ال mean zero لإن F of zero زيرو زيرو
+
+99
+00:10:31,790 --> 00:10:37,170
+زيرو كلهم زيرو مضلش إلا ال term الأخير تمام؟ طيب
+
+100
+00:10:37,170 --> 00:10:42,150
+كويس يبقى ال F of X سوى الشكل اللي عندها ده أليس
+
+101
+00:10:42,150 --> 00:10:51,720
+كذلك؟ هذه عبارة عن X ب A Mx in minus one زائد a in
+
+102
+00:10:51,720 --> 00:10:59,700
+minus one x in minus two زائد a one يعني أخدنا x
+
+103
+00:10:59,700 --> 00:11:07,420
+عامل مشترك هذه كلها function موجودة في z of x ولا
+
+104
+00:11:07,420 --> 00:11:15,060
+لا صح إذا بقدر أقول هذه x وشكلها على الشكل التالي
+
+105
+00:11:15,390 --> 00:11:19,490
+هذه موجودة في الـ Principle ID الـ generated by X
+
+106
+00:11:19,490 --> 00:11:26,330
+طبعاً للتعريف تبعه، مظبوط؟ يعني إيش استفدنا؟ أخدنا
+
+107
+00:11:26,330 --> 00:11:33,610
+F of X موجودة في I، دجينا الـ F of X موجودة في الـ
+
+108
+00:11:33,610 --> 00:11:37,850
+Principle ID الـ generated by X، يبقى بجيب أقول له
+
+109
+00:11:37,850 --> 00:11:42,830
+الـ Principle ID الـ generated by X يساوي الـ I
+
+110
+00:11:42,830 --> 00:11:51,520
+كما زعمناقبل قليل، إذا صار عندنا هذا معناه هو هذا
+
+111
+00:11:51,520 --> 00:11:57,460
+يبقى ال principle ideal generated by X هو الـ I،
+
+112
+00:11:57,460 --> 00:12:03,460
+الـ I بالضبط تماماً. طيب، إحنا حتى الآن ما سوناش
+
+113
+00:12:03,460 --> 00:12:09,180
+شيء، سونا مقدمة، المقدمة هذه لزمان، ديرا بالكم
+
+114
+00:12:09,180 --> 00:12:13,640
+مثلها ده في الكتاب، وبيعتمد على سؤالين من الكتاب.
+
+115
+00:12:13,980 --> 00:12:17,800
+هنحل السؤالين و احنا مش دارين ان احنا حلناهم و
+
+116
+00:12:17,800 --> 00:12:24,120
+احنا بنبرهن في السؤال طيب ندل الان للمعلومات اللي
+
+117
+00:12:24,120 --> 00:12:29,860
+احنا عارفينها و مقمنين اليها ال ideal هذا بدي اثبت
+
+118
+00:12:29,860 --> 00:12:34,500
+انه prime ideal يبقى بدي اخد two functions هنا
+
+119
+00:12:34,500 --> 00:12:41,860
+بحيث يكون حصل ضربهم موجود هنا وبالتالي اثبت يا اما
+
+120
+00:12:41,860 --> 00:12:45,680
+الدالة الأولىموجودة في ال principle I D generated
+
+121
+00:12:45,680 --> 00:12:52,900
+I X يا إما دلّه الثاني بقوله كويسة يبقى لان بتاجي
+
+122
+00:12:52,900 --> 00:13:01,820
+اقوله افترض ان عندي دالتين G وH موجودة تمين في Z
+
+123
+00:13:01,820 --> 00:13:12,010
+of X such that بحيث ان الـ G H موجودةموجودة في ال
+
+124
+00:13:12,010 --> 00:13:16,870
+principle ideal generated by X مش هو هذا اللي بثبت
+
+125
+00:13:16,870 --> 00:13:22,910
+انه prime يبقى أخد two elements من ال ring الأصلية
+
+126
+00:13:22,910 --> 00:13:29,050
+بحيث حصل ضربهما موجود هنا بيقولوا كويس يبقى بناء
+
+127
+00:13:29,050 --> 00:13:34,350
+ان عليه بدي أحاول أثبت يا إما ال G موجودة في ال
+
+128
+00:13:34,350 --> 00:13:38,130
+principle ideal generated by X يا إما ال H اللي
+
+129
+00:13:38,130 --> 00:13:47,310
+موجودة مظبوططيب كويس then لو أخدت يا بنات gh
+
+130
+00:13:47,310 --> 00:13:54,710
+تأثيرها على ال zero الشكل دي عندنا هنا طبقا
+
+131
+00:13:54,710 --> 00:14:01,410
+للكلكورات أليس هذا هو g of zero في ال h of zero
+
+132
+00:14:01,410 --> 00:14:08,210
+نعم احنا أخدنا حاصل ضرب موجود هنا اللي هو في ال x
+
+133
+00:14:08,210 --> 00:14:14,750
+طيب من ال x؟مش هي ال I صح؟ يعني بتقدر تقول
+
+134
+00:14:14,750 --> 00:14:20,890
+الموجودة في ال H اللي هي بدها تساوي ال I هي
+
+135
+00:14:20,890 --> 00:14:24,110
+أخدناها الموجودة في ال X اللي هي بدها تساوي ال I
+
+136
+00:14:24,110 --> 00:14:29,690
+يبقى تأثيرها على ال Zero بده يساوي قداش؟ بده يساوي
+
+137
+00:14:29,690 --> 00:14:35,710
+ال Zero itself طب ال G of Zero و ال H of Zero انت
+
+138
+00:14:35,710 --> 00:14:42,070
+جارز ولا لا؟ انت جارز؟هل يُعقل إن حاصل ضربهما يكون
+
+139
+00:14:42,070 --> 00:14:49,270
+بـ0 إلا إذا كان حضرهما بـ0 يبقى فادي بيقول لهم but
+
+140
+00:14:49,270 --> 00:15:01,650
+ولكن الـG of 0 and الـH of 0 are integers يبقى
+
+141
+00:15:01,650 --> 00:15:11,270
+so الـG of 0 الـH of 0 بدي سوى 0imply ان الـG of 0
+
+142
+00:15:11,270 --> 00:15:18,810
+بتساوي 0 او الـH of 0 هو اللي بتساوي 0 طيب اذا G
+
+143
+00:15:18,810 --> 00:15:24,770
+of 0 تساوي 0 يبقى موجودة في X ولا لا يعني في I
+
+144
+00:15:24,770 --> 00:15:31,710
+يبقى هذا بيدي يعطينا ان الـG of X موجودة في
+
+145
+00:15:31,710 --> 00:15:38,660
+الـprinciple ID generated by X او الـH of Xموجودة
+
+146
+00:15:38,660 --> 00:15:43,980
+في من في ال principle ideal generated by X فمش
+
+147
+00:15:43,980 --> 00:15:49,840
+معناه هذا الكلام؟ prime ideal يبقى هذا بده يعطينا
+
+148
+00:15:49,840 --> 00:15:57,360
+ان ال principle ideal generated by X is a prime
+
+149
+00:15:57,360 --> 00:16:05,330
+ideal يبقى أثبتنا الشطر الأول من هذا المثالبدا
+
+150
+00:16:05,330 --> 00:16:09,250
+نيجي للشطر الثاني نثبت ان ال principle ideal
+
+151
+00:16:09,250 --> 00:16:16,430
+generated by X is not maximum نرجع بالذاكرة الى
+
+152
+00:16:16,430 --> 00:16:21,400
+الوراقالـ Maximum Ideal كيف بثبت انه Maximum؟ نجيب
+
+153
+00:16:21,400 --> 00:16:28,100
+Ideal تاني هات ال Ideal اللي عندنا يكون subset منه
+
+154
+00:16:28,100 --> 00:16:32,660
+و ال Ideal الثاني هذا subset من R وبالتالي ال
+
+155
+00:16:32,660 --> 00:16:37,100
+Ideal اللي عندنا يا إما بدي يسوى ال Ideal الجديد
+
+156
+00:16:37,100 --> 00:16:41,960
+يا ال Ideal الجديد بدي يسوى Ring R صح ولا ده؟ طيب
+
+157
+00:16:41,960 --> 00:16:47,530
+تعالوا نشوف هالست هانيبقى بالداخل اقول consider
+
+158
+00:16:47,530 --> 00:16:56,710
+the set ال set بالدرموز اللي هي x و 2 جديد
+
+159
+00:16:56,710 --> 00:17:04,530
+هذا علينا صح نشوف مين هي هذه يبدو هذه كل العناصر f
+
+160
+00:17:04,530 --> 00:17:12,180
+of x اللي موجودة في z of x such thatالـ F of X
+
+161
+00:17:12,180 --> 00:17:23,880
+بيتساور X الـ G of X زائد 2H of X إيش
+
+162
+00:17:23,880 --> 00:17:30,900
+يعني؟ يعني كل ال functions اللي المقدار الثابت هنا
+
+163
+00:17:30,900 --> 00:17:37,260
+تبعها بيكون عدد زوجي H of X جد ما تقطع تظهر بيها
+
+164
+00:17:37,260 --> 00:17:43,200
+في 2 بيصير عدد زوجي صحيح ولا لأ؟يعني بالبلد زي ما
+
+165
+00:17:43,200 --> 00:17:47,600
+عرفنا اتنين هدول بيقول كل ال F of X في حيث F of
+
+166
+00:17:47,600 --> 00:17:52,740
+Zero بده يساوي اتنين K اتنين K اللي هو على زوجيك
+
+167
+00:17:52,740 --> 00:17:57,260
+بيه اتنين في H of X هذا ما يعني ايه الست اللي
+
+168
+00:17:57,260 --> 00:18:02,840
+عندنا هل هي ايدين اذا أثبتنا انها ايدين خلاص هنحلت
+
+169
+00:18:02,840 --> 00:18:09,320
+مشكلتنا نهائيا يبقى انا ازعم ان هذه ايدين بس
+
+170
+00:18:09,320 --> 00:18:24,430
+بتكتسبيبقى now ال X والإتنين is an ID because ليش؟
+
+171
+00:18:24,430 --> 00:18:31,950
+بتدل النقطة الأولة ال X والإتنين is من M
+
+172
+00:18:35,820 --> 00:18:40,620
+يبقى هذه المهنية الشفرة فيها على الأقل ولو عمصر
+
+173
+00:18:40,620 --> 00:18:48,240
+واحد لإيش؟ since لو أخدت ال F of Zero هناك كدهش
+
+174
+00:18:48,240 --> 00:18:55,100
+بده يساوي؟ Zero زائد اتنين H of Zero يبقى Zero
+
+175
+00:18:55,100 --> 00:19:03,240
+زائد اتنين H of Zero يبقى موجودة هنا ولا هناك صح؟
+
+176
+00:19:03,520 --> 00:19:08,820
+يبقى هذه موجودة في الـ principle في الـ 6 اللي
+
+177
+00:19:08,820 --> 00:19:15,240
+عندناها طيب النقطة الثانية إذا أخدت elements مثلًا
+
+178
+00:19:15,240 --> 00:19:27,100
+F1 و F2 موجودة في الـ 6 اللي عندناها ثاني ال F1 of
+
+179
+00:19:27,100 --> 00:19:32,860
+X تساوي خطة موجودة يبقى اش بده تساوي بده تساوي ال
+
+180
+00:19:32,860 --> 00:19:46,180
+Xالـ G1 of X زائد 2H1 of X والـ F2 of X بتساوي الـ
+
+181
+00:19:46,180 --> 00:19:55,960
+X في الـ G2 of X زائد 2H2 of X هي أحتياط عمصرين
+
+182
+00:19:55,960 --> 00:20:02,500
+موجودات في هذه الستة بتشوف الفرق في ما بينهماقداش
+
+183
+00:20:02,500 --> 00:20:10,560
+بده يساوي يبقى هادي بدي أقوله بده ال F1 ناقص F2 as
+
+184
+00:20:10,560 --> 00:20:16,540
+a function of X طبقا لمعلوماتنا في ال calculus F1
+
+185
+00:20:16,540 --> 00:20:24,200
+of X ناقص F2 of X بده أطرح هدول من بعض يبقى لو
+
+186
+00:20:24,200 --> 00:20:34,330
+طرحته من هناك بده يصير X في G1 of X-G2 of X زائد
+
+187
+00:20:34,330 --> 00:20:47,250
+اتنين في H1 of X ناقص H2 of X ويسافر هذه بقدر
+
+188
+00:20:47,250 --> 00:20:57,150
+اكتبها على الشكل X في G1 ناقص G2 of X وهذه زائد
+
+189
+00:20:57,150 --> 00:21:04,200
+اللي هو الاتنينفمين في H واحد ناقص H اتنين كل هذا
+
+190
+00:21:04,200 --> 00:21:09,980
+a function of X أليس تهالي على الصيغة اللي فوق هذه
+
+191
+00:21:09,980 --> 00:21:18,340
+صح يبقى صار الفرق فيما بينهما موجود وين موجود يبقى
+
+192
+00:21:18,340 --> 00:21:25,940
+هذا بدي يعطينا ان ال F واحد ناقص F اتنين موجودةفي
+
+193
+00:21:25,940 --> 00:21:32,360
+الـ 6 اللي هو الـ X و 2 ضايل علينا مين؟ النقطة
+
+194
+00:21:32,360 --> 00:21:42,140
+الأخيرة يبقى النقطة الثالثة بقول مافي خدلي ال F of
+
+195
+00:21:42,140 --> 00:21:54,820
+X موجودة في مين؟ في ال ring الأساسية أن ال F1 of X
+
+196
+00:21:55,080 --> 00:22:03,660
+و من F1 هاجر اللي هي باتنية موجودة و موجودة في
+
+197
+00:22:03,660 --> 00:22:11,120
+الست اللي عندناها then بتاخد حاصل الطرق إلها then
+
+198
+00:22:11,120 --> 00:22:23,500
+if F1 of X بدل ساول F of X فالـ F1 of X بدل ساول F
+
+199
+00:22:23,500 --> 00:22:38,180
+of Xالـ F1 هي جازة يبقى X G1 يبقى X G1 of X زائد 2
+
+200
+00:22:38,180 --> 00:22:52,640
+H1 of X شكل اللي عندنا هذا طيب هذه صارت الـ F F1
+
+201
+00:22:52,640 --> 00:22:58,450
+of Xيساوى هذي بقدر .. طبعا ال ring قبلنا
+
+202
+00:22:58,450 --> 00:23:06,510
+commutative يبقى هذي X في ال F of X في ال G1 of X
+
+203
+00:23:06,510 --> 00:23:16,830
+زائد اتنين F of X في ال H1 of X اللي بقدر اكتبها
+
+204
+00:23:16,830 --> 00:23:28,420
+على الشكل التالي X اللي هي LXفي ال FG1 as a
+
+205
+00:23:28,420 --> 00:23:38,740
+function of X زائد اتنين F F1 F F1 كله as a
+
+206
+00:23:38,740 --> 00:23:44,720
+function of X يبقى هذه هنا كتبتها على صيغة هذه
+
+207
+00:23:44,720 --> 00:23:49,260
+أليست الصيغة هذه هي الصيغة اللي عندنا؟ أستاذ اتنين
+
+208
+00:23:49,260 --> 00:24:00,720
+F H واحد مش F واحدH1 اتنين F H1 و هذه G1 مظبوط
+
+209
+00:24:00,720 --> 00:24:04,660
+كلامكوا صحيح مظبوطي بصرت على الصيغة اللي قدامنا
+
+210
+00:24:04,660 --> 00:24:08,840
+هذه ولا لا على الصيغة اللي قدامنا هذه ولا لا تمام
+
+211
+00:24:08,840 --> 00:24:14,920
+اذا الهدف اللي بده يعطينا انه مين ال F ال F1
+
+212
+00:24:14,920 --> 00:24:24,620
+موجودة في ال principal ideal generatedby x و 2 by
+
+213
+00:24:24,620 --> 00:24:32,300
+x و 2 يا ابنها أنا عليه هذا صار أيديل ولا لا يا
+
+214
+00:24:32,300 --> 00:24:37,900
+ابنها؟ كويس طب استاذ أنا سامحت سامحت ال g of x ولا
+
+215
+00:24:37,900 --> 00:24:43,120
+h of x موجودين برضه في ال ring الأصلية؟ أه بالضبط
+
+216
+00:24:43,120 --> 00:24:50,250
+سؤال تاني أيضا ال g of x ولا h of x في الأصلية؟هذه
+
+217
+00:24:50,250 --> 00:25:00,830
+وهذه يظهر في التعريف الـ G of X والـ H of X عبارة
+
+218
+00:25:00,830 --> 00:25:06,390
+عن كثيرات حدود في Z of X ليس من خلق جايبينها كل
+
+219
+00:25:06,390 --> 00:25:11,430
+شغل لداخل ال ring Z of X ماخلة ذلك ماليش علاقة فيه
+
+220
+00:25:11,430 --> 00:25:16,410
+يعني المعاملات كلها أعداد صحيحة من ال set of
+
+221
+00:25:16,410 --> 00:25:21,870
+integersطيب، لغاية هنا إيش اللي أثبتناها؟ أثبتناها
+
+222
+00:25:21,870 --> 00:25:30,910
+ده عبارة عن IE يبقى هنا بقولوا بص و هكذا ال X و 2
+
+223
+00:25:30,910 --> 00:25:38,270
+is an ideal أو is a principle، ideal generated by
+
+224
+00:25:38,270 --> 00:25:45,830
+X و 2 طيب، احنا إيش بدنا نثبت؟ Maximality، يبقى
+
+225
+00:25:45,830 --> 00:25:53,890
+احنا جيبنا ideal جديدال ID للجديد شو علاقته بال ID
+
+226
+00:25:53,890 --> 00:25:59,110
+للأصلي تمام
+
+227
+00:25:59,110 --> 00:26:09,170
+سبست منه ولا يساوي أكيد هاي ال ID للأصلي هاي X في
+
+228
+00:26:09,170 --> 00:26:15,430
+G of X وهذا لأ عضفنا عليه كمان ال term اللي عندنا
+
+229
+00:26:15,430 --> 00:26:23,230
+مش Zeroأضفنا عليه اللي هو عدد صحيح زوجي، تمام؟ طيب
+
+230
+00:26:23,230 --> 00:26:31,210
+كويس، إذن واضح إن هذا معنى سبسي من هذا، تمام؟ بس و
+
+231
+00:26:31,210 --> 00:26:39,630
+لأن هل ال principle ideal generated by X و 2 بده
+
+232
+00:26:39,630 --> 00:26:46,060
+يساوي Z of X؟يعني هل كل ال elements اللي في ال Z و
+
+233
+00:26:46,060 --> 00:26:51,040
+X بقدر أكتبهم على الشكل هذا؟ لأ، هذا ممكن يكون
+
+234
+00:26:51,040 --> 00:26:55,480
+الزوج و ممكن يكون الفرد و ممكن يكون الصفر، صحيح؟
+
+235
+00:26:55,480 --> 00:27:02,120
+إذا لا يمكن لهذا ال ID أنه يسوى مين؟ أنه يسوى ال
+
+236
+00:27:02,120 --> 00:27:07,820
+ring الأصلية، يبقى هذا لا يمكن أن يسوى ال ring
+
+237
+00:27:07,820 --> 00:27:12,760
+الأصلية من خلال ال definition اللي عندنايبقى أنا
+
+238
+00:27:12,760 --> 00:27:19,200
+جبت ID الآخر ال ID اللي عندي subset منه ولا يسوي
+
+239
+00:27:19,200 --> 00:27:24,480
+يعني proper subset وهذا في نفس الوقت ضال proper
+
+240
+00:27:24,480 --> 00:27:30,360
+ولا يسوي ال ring الأصلية يبقى بناء عليه لا يمكن
+
+241
+00:27:30,360 --> 00:27:36,880
+لهذا أن يكون maximal ID يبقى بصر ال principle
+
+242
+00:27:36,880 --> 00:27:40,340
+ideal generated by X is
+
+243
+00:27:44,440 --> 00:27:50,300
+maximal ممكن يكون maximum أبداً هيك يكون أجابنا
+
+244
+00:27:50,300 --> 00:27:54,140
+على سؤالين من التمرين ما بعرف سبعة و تلاتين اظن و
+
+245
+00:27:54,140 --> 00:27:59,400
+تسعة و عشرين او شغل رجل من أسئلات الكتاب لأنه
+
+246
+00:27:59,400 --> 00:28:05,020
+مدخلهم في من في الحل اللعنى طيب احنا هيك انتهينا
+
+247
+00:28:05,020 --> 00:28:09,720
+من هذا ال section و الآن بنتقل إلى مناقشة بعض
+
+248
+00:28:09,720 --> 00:28:17,160
+المسائل منهمونحدد بعض المسائل للمحاضرة القادمة إن
+
+249
+00:28:17,160 --> 00:28:18,300
+شاء الله
+
+250
+00:28:40,070 --> 00:28:45,970
+بنرجل ال exercises على شبتر اربعتاشر ب exercises
+
+251
+00:28:45,970 --> 00:28:54,470
+of شبتر اربعتاشر سؤال
+
+252
+00:28:54,470 --> 00:29:04,690
+رابع سؤال رابع بقول find a suffering find a
+
+253
+00:29:04,690 --> 00:29:15,160
+suffering of theplus z direct sum that is not an
+
+254
+00:29:15,160 --> 00:29:32,860
+id so bring that is not an id solution
+
+255
+00:29:32,860 --> 00:29:37,580
+طبعا
+
+256
+00:29:38,560 --> 00:29:42,940
+direct sum الـ element اللي هنا بيكون على شكل
+
+257
+00:29:42,940 --> 00:29:49,420
+order pair يعني ذكر تذكير بس الـ Z direct sum مع Z
+
+258
+00:29:49,420 --> 00:29:56,100
+يعني كل العناصر A و B بحيث الـ A و الـ B موجودة و
+
+259
+00:29:56,100 --> 00:30:01,780
+يعني موجودة في Z أي العناصر اللي عليها والجمع
+
+260
+00:30:01,780 --> 00:30:07,160
+component twice والضغط component twice طيب بقول
+
+261
+00:30:07,660 --> 00:30:16,060
+أثبتلي إنه هذه الـ Subring بدك تاخدلي set S مثلا
+
+262
+00:30:16,060 --> 00:30:21,560
+subset من هذه و تحاول تثبتها إنها الـ Subring يبقى
+
+263
+00:30:21,560 --> 00:30:29,900
+هذه بيكون عليها شكل قوس مُركّب من عنصرين يلّا مين
+
+264
+00:30:29,900 --> 00:30:36,460
+أخد عنصرين أبدا؟ عنصرين منزل؟ يلّا، بيحتفل على الـ
+
+265
+00:30:36,460 --> 00:30:45,180
+Subringوفي نفس الوقت مش ideal يالا
+
+266
+00:30:45,180 --> 00:30:50,340
+ذكر ايش
+
+267
+00:30:50,340 --> 00:30:55,000
+ممكن يجي في بارك اه او اتنين او اتنين او اتنين
+
+268
+00:30:55,000 --> 00:31:02,240
+مثلا اخدت ا و اتنين كعنصر يعني ال ا موجود في زي
+
+269
+00:31:02,240 --> 00:31:08,220
+مين مكان يكون و اتنين صار ثابت تمامبنشوف هالصبرينج
+
+270
+00:31:08,220 --> 00:31:14,400
+و لا لأ طبعا الجامعة و .. و لإنه non-empty صحيح
+
+271
+00:31:14,400 --> 00:31:19,280
+موجود و الجامعة ناخد عنصرين و نطرحهم من بعض حتى
+
+272
+00:31:19,280 --> 00:31:23,580
+يكون موجود لإن اتنين ممكن ناخدها عامل مشترك و الله
+
+273
+00:31:23,580 --> 00:31:32,620
+يطلع صفر لو طرحناهم من بعض بيطلع صفر صح يبقى بطلة
+
+274
+00:31:32,620 --> 00:31:39,200
+الصير بطلت صبركصح ولا لا؟ عادي عندنا طرح سقط اللي
+
+275
+00:31:39,200 --> 00:31:43,920
+هو الشرط الثاني يبقى غيريها اه اتنين A و اتنين B
+
+276
+00:31:43,920 --> 00:31:50,920
+اتنين A و اتنين B طب ما تخليها A و B خلاص طب
+
+277
+00:31:50,920 --> 00:31:55,360
+و يتساوي شو المشكلة؟ بتاخدها A و A شو المشكلة؟
+
+278
+00:31:55,360 --> 00:32:04,000
+يبقى من داخل A و A و بحيث ال A موجودة في ذلك شفوي
+
+279
+00:32:04,000 --> 00:32:10,900
+شفويzero و zero موجودة في S ولا لا؟ طيب الشرط
+
+280
+00:32:10,900 --> 00:32:18,320
+الأول صحيح نجي للثاني بتاخد a و a و b و b موجودة
+
+281
+00:32:18,320 --> 00:32:22,120
+في S يبقى a ناقص بي و a ناقص بي موجودة في S الشرط
+
+282
+00:32:22,120 --> 00:32:27,500
+التاني مظبوط تاني بارك هنا a و a و خدي الرقم اللي
+
+283
+00:32:27,500 --> 00:32:34,760
+يعجبك بعد ذلك من مين؟ من ال S بي و بي يبقى وصير
+
+284
+00:32:34,760 --> 00:32:41,320
+من؟ABAB نفس الرقم موجود في اس و لا يوجد اس اس ليه
+
+285
+00:32:41,320 --> 00:32:53,860
+subring يبقى هنا اس هذه is a sub ring يبقى check
+
+286
+00:32:53,860 --> 00:32:57,820
+بدك تروح تعمليها في الدار انا بقول سهل كده اي شفوي
+
+287
+00:32:57,820 --> 00:33:03,100
+و انت بده تروح تعمليها تحريري انا بهمن انها ماهياش
+
+288
+00:33:03,100 --> 00:33:03,540
+ID
+
+289
+00:33:13,130 --> 00:33:18,970
+مش هنجي في S إذا ما نجتوش في S يبقى بطلة suffering
+
+290
+00:33:18,970 --> 00:33:25,370
+اللي جاته في S يبقى صارت main suffering أو صارت
+
+291
+00:33:25,370 --> 00:33:35,380
+ideal طيب بدأت أقول let X موجودة في S and مثلاواحد
+
+292
+00:33:35,380 --> 00:33:43,660
+و تلاتة موجودة في direct sum عزيزي عنصر هنا من ال
+
+293
+00:33:43,660 --> 00:33:51,720
+ring الأصلية وعنصر من ال S ثاني ال
+
+294
+00:33:51,720 --> 00:34:03,710
+X في واحد و تلاتة بالدرسة ال A و ال Aمضربة في واحد
+
+295
+00:34:03,710 --> 00:34:11,110
+و تلاتة هذي بدها تساوي مين؟ ايه؟ و تلاتة ايه؟
+
+296
+00:34:11,110 --> 00:34:17,390
+موجودة في S؟ لأ يبقى the is not belonging to S
+
+297
+00:34:17,390 --> 00:34:24,990
+يبقى هنا س ال S is not ID
+
+298
+00:34:26,390 --> 00:34:30,490
+انت ممكن تاخد اتنين وثلاثة، ممكن تاخد اتنين وخمسة،
+
+299
+00:34:30,490 --> 00:34:34,950
+المهم الرقمين مايكونوش زي بعض، وعندي جداش مالة
+
+300
+00:34:34,950 --> 00:34:39,510
+ليها من الأرقام، يبقى هذا مثال بسيط على ان ال
+
+301
+00:34:39,510 --> 00:34:44,630
+subset اللي أخدتها هي ال sub ring، لكنها ليست
+
+302
+00:34:44,630 --> 00:34:55,830
+عادية. طيب سؤال آخر مثلا زي سؤال ستة، سؤال ستة،
+
+303
+00:34:56,620 --> 00:35:02,560
+بيقولّي اهدّي كل ال maximum ideas و اعين ال
+
+304
+00:35:02,560 --> 00:35:06,780
+maximum ideas
+
+305
+00:35:06,780 --> 00:35:23,060
+ان جالس زت تمانى و زد عشرة و زد اتناشر و زد ان
+
+306
+00:35:25,670 --> 00:35:33,010
+نبدأ شكل الـ maximal ideal فيهم احنا
+
+307
+00:35:33,010 --> 00:35:37,910
+خدنا مثال زبدة 12 و جبنا ال maximum ideal فيهم
+
+308
+00:35:37,910 --> 00:35:44,870
+كمثال تذكروا و الله راحت أدراجي الرياح و طبعا
+
+309
+00:35:44,870 --> 00:35:49,550
+بيرنا و عملنا لها ال lattice و المثال الوحيد اللي
+
+310
+00:35:49,550 --> 00:35:55,220
+عمله الشبكية تبعته خلال هذا ال sectionوقلنا عندها
+
+311
+00:35:55,220 --> 00:35:58,800
+ان اتنين والتلاتة و ال principle ideal generated
+
+312
+00:35:58,800 --> 00:36:02,780
+by اتنين و ال principle ideal generated by التلاتة
+
+313
+00:36:02,780 --> 00:36:09,320
+are maximal ideals in Z12 مظبوط لقيته في الدفاتر
+
+314
+00:36:09,320 --> 00:36:15,700
+ممتاز يبقى هذا يا بنات بياننا سابقا ان ال
+
+315
+00:36:15,700 --> 00:36:20,020
+principle ideal generated by اتنينو ال principle
+
+316
+00:36:20,020 --> 00:36:25,000
+ideals generated by ثلاثة هدول are maximum ideals
+
+317
+00:36:25,000 --> 00:36:31,400
+هدول الأتنين هما ال maximum خلّي هالمعلومة عندك
+
+318
+00:36:31,400 --> 00:36:37,780
+هذه لزمان طيب نيجي لزيد تمانية لزيد تمانية بدي
+
+319
+00:36:37,780 --> 00:36:43,740
+أدور على ال ideals تبعتها الان لو جيت على ال
+
+320
+00:36:43,740 --> 00:36:48,570
+principle ideals generated by oneبتلاقيها هي ال
+
+321
+00:36:48,570 --> 00:36:53,790
+principle ideal generated by تلاتة بتلاقيها هي ال
+
+322
+00:36:53,790 --> 00:36:58,510
+principle ideal generated by خمسة بتلاقيها هي ال
+
+323
+00:36:58,510 --> 00:37:03,270
+principle ideal generated by سبعة يعني كل primes
+
+324
+00:37:03,270 --> 00:37:09,290
+من واحد إلى تمانية بيعطوني مين؟ بيعطوني نفس ال
+
+325
+00:37:09,290 --> 00:37:15,750
+ring الأصلية ليه Z تمانية كل هذا بيساوي Z تمانية
+
+326
+00:37:16,580 --> 00:37:22,960
+طيب تمام راح الواحد والتلات والخمسة والسبعة بقى
+
+327
+00:37:22,960 --> 00:37:32,520
+اللي عندي اتنين واربعة وستة وبس مظبوط وال zero صح؟
+
+328
+00:37:32,520 --> 00:37:36,920
+طيب عندك ال principle ideal generated by zero اللي
+
+329
+00:37:36,920 --> 00:37:42,880
+هو zero itselfعندك ال principle ideal generated by
+
+330
+00:37:42,880 --> 00:37:49,560
+اتنين اللي هو Zero اتنين اربعة ستة تمام؟ عندك ال
+
+331
+00:37:49,560 --> 00:37:54,200
+principle ideal generated by اربعة اللي هو Zero
+
+332
+00:37:54,200 --> 00:38:01,660
+اربعة في الشريرة خلصنا؟ لأ ما خلصناش By ال
+
+333
+00:38:01,660 --> 00:38:05,680
+principle ideal generated by ستة بيكون كله عندي
+
+334
+00:38:05,680 --> 00:38:13,630
+بيصير عندي واحدوهي اتنين وهي تلاتة وهي أربعة وهي
+
+335
+00:38:13,630 --> 00:38:17,790
+خمسة وهي سبعة بيظل ال principle ideal generated by
+
+336
+00:38:17,790 --> 00:38:22,910
+ستة بدي أعرفه من هنا يبقى ال principle ideal
+
+337
+00:38:22,910 --> 00:38:28,510
+generated by ستة هو Zero والستة ستة وستة اتناش من
+
+338
+00:38:28,510 --> 00:38:35,030
+تمانية بيظل أربعة ستة في تلاتة بتمنتاش من ستاش
+
+339
+00:38:35,030 --> 00:38:40,830
+بيظلوا اتنين6 في 4 بـ 24 اللي هو مضاعفاتها Zero
+
+340
+00:38:40,830 --> 00:38:48,430
+يبقى طالع هذه هي مين؟ يا زد اتنين يا زد ستة يبقى
+
+341
+00:38:48,430 --> 00:38:53,530
+انا اقول ده ليه اعمل ال lattice الشباكية تبعت هذه
+
+342
+00:38:53,530 --> 00:39:01,710
+ال race مظبوط يبقى بعدين بقول الأولاني يا زد
+
+343
+00:39:01,710 --> 00:39:09,550
+تمانية اوهدى أو هدى أو هدى أو هدى كل واحد طلع
+
+344
+00:39:09,550 --> 00:39:16,370
+عندنا مين؟ principle ideal generated by اتنين وطلع
+
+345
+00:39:16,370 --> 00:39:21,610
+منه ال principle ideal generated by اربعة وطلع ال
+
+346
+00:39:21,610 --> 00:39:25,470
+principle ideal generated by zero اللي هو تساوي
+
+347
+00:39:25,470 --> 00:39:31,530
+Zero في غيرهم من ال maximum اللي هو ال proper ولا
+
+348
+00:39:31,530 --> 00:39:38,160
+يسوى ال ring الأصلي منهمالاتنين طيب ممتاز جدا يبقى
+
+349
+00:39:38,160 --> 00:39:44,980
+هذه طلعت ليه الاتنين طيب هنا هنا بنات اتنين وثلاثة
+
+350
+00:39:44,980 --> 00:39:51,880
+prime numbers وكل واحد فيهم بجسم نهار هذه طلعت
+
+351
+00:39:51,880 --> 00:39:58,180
+اتنين هو prime number بجسم التمانية بناء عليه هذه
+
+352
+00:39:58,180 --> 00:40:03,580
+من هم ال maximum اتنين وخمسة اتنين وخمسة ممتازة
+
+353
+00:40:03,670 --> 00:40:08,210
+تبقى ال principle ideal generated by اتنين و ال
+
+354
+00:40:08,210 --> 00:40:12,850
+principle ideal generated by خمسة لو جيتي حسب تهم
+
+355
+00:40:12,850 --> 00:40:18,230
+هيطلع الكلام اللي عندك هنا طبعا طيب لو جيت اعمل
+
+356
+00:40:18,230 --> 00:40:24,450
+انها الشبكية تبعتها فبقى اللي بقول ايه زاد عشرة في
+
+357
+00:40:24,450 --> 00:40:28,910
+عند ال principle ideal generated by اتنين و في ال
+
+358
+00:40:28,910 --> 00:40:34,690
+principle ideal generated by خمسةبعد هيك في ال
+
+359
+00:40:34,690 --> 00:40:40,010
+principle id generated by 0 و هذا ال principle id
+
+360
+00:40:40,010 --> 00:40:48,410
+generated by 0 هذه خمسة و هذه اتنين طبعا يبقى هذه
+
+361
+00:40:48,410 --> 00:40:54,790
+الشبكية تبعت ال z عشرة ال باقي كل الأرقام الأخرى
+
+362
+00:40:54,790 --> 00:40:59,110
+مثلا z عشرة عزيزي ال principle هذه generated by
+
+363
+00:40:59,110 --> 00:41:04,340
+oneprincipal ideal generated by three ,principal
+
+364
+00:41:04,340 --> 00:41:08,640
+ideal generated by seven ,principal ideal
+
+365
+00:41:08,640 --> 00:41:13,140
+generated by nine ,by تسعة كلهم هذول بيسووا بعض
+
+366
+00:41:13,140 --> 00:41:17,460
+يبقى كله هي ال ring هذول و الباقى هتلاقي واحدة
+
+367
+00:41:17,460 --> 00:41:21,460
+بتساوي تانية وماضنش عندى إلا مين إلا الأربعة اللي
+
+368
+00:41:21,460 --> 00:41:26,660
+بيبقى ال maximal ideals هم مين الاثنين وخمسة مثل
+
+369
+00:41:26,660 --> 00:41:32,240
+ما زعمنا بناءً عليهبدي الـ maximal ID اللي هذه بيه
+
+370
+00:41:32,240 --> 00:41:39,180
+هم كل الـprimes بحيث هذه الـprimes بتقسم الـN تقسم
+
+371
+00:41:39,180 --> 00:41:47,100
+الـL يبقى هذه كل الـprinciple ID generated by P
+
+372
+00:41:47,100 --> 00:41:58,550
+والـP is prime divisor of Nيعني اللي بيكون
+
+373
+00:41:58,550 --> 00:42:03,450
+relatively primal in itself، جداش جد ما يكون، ان
+
+374
+00:42:03,450 --> 00:42:07,950
+شاء الله تكون الـResult خمسمية، ماعناش مشكلة فيها،
+
+375
+00:42:07,950 --> 00:42:12,530
+يفجأ هاي حلناها، طبعا هذا حلناها السابقة، وهي حل
+
+376
+00:42:12,530 --> 00:42:19,290
+ذلك التلاتة، الأخيرة ستنتج بناء على مين؟ بناء على
+
+377
+00:42:19,290 --> 00:42:21,810
+ال rings التلاتة اللي عندنا
+
+378
+00:42:24,920 --> 00:42:33,640
+طيب نروح لأننا سؤال اربعة عشر مثلا نفجر سؤال اربعة
+
+379
+00:42:33,640 --> 00:42:39,640
+عشر سؤال اربعة عشر بيقول ما يتخذ ال A و ال B ايديل
+
+380
+00:42:39,640 --> 00:42:50,980
+ال A و ال B ايديل اثبت ان ال A بيستخدم ال A
+
+381
+00:42:50,980 --> 00:42:52,920
+intersection B
+
+382
+00:43:17,180 --> 00:43:21,780
+الان اتعلمنا من ال set theory لكي نثبت ان set هي
+
+383
+00:43:21,780 --> 00:43:25,480
+subset من setبدي أخد element في الست الأولى و أثبت
+
+384
+00:43:25,480 --> 00:43:28,900
+إنه موجود في الست التانية و الأعلى أبسط اللي أشاء
+
+385
+00:43:28,900 --> 00:43:33,680
+في مبادئ رياضية على كل المعلومات اللي عندنا اتنين
+
+386
+00:43:33,680 --> 00:43:38,680
+هذول ID بس حصل ضرب ال A في D ماشوفتاش له تعريف
+
+387
+00:43:38,680 --> 00:43:42,520
+جدليك طب
+
+388
+00:43:42,520 --> 00:43:46,260
+إذا بدنا نروح و نحط التعريف اللي حطه الكتاب من
+
+389
+00:43:46,260 --> 00:43:53,310
+خلال التمرين يبقى solutionفي سؤال 12 اللي جابله
+
+390
+00:43:53,310 --> 00:44:00,250
+راح حطني حاصن الضرب فقرفلي حاصن الضرب A في B وكل
+
+391
+00:44:00,250 --> 00:44:11,610
+العموظة A1 B1 B2 B2 plus ANBN بحيث أن ال AI موجودة
+
+392
+00:44:11,610 --> 00:44:20,350
+في I و أنكوا كمان منه و ال BI موجودة في Bالـ I
+
+393
+00:44:20,350 --> 00:44:27,270
+تأخذ من واحد لغاية الـ M والـ I تساوي واحد واتنين
+
+394
+00:44:27,270 --> 00:44:33,730
+لغاية الـ M هذا هو تعريف حاصل الضرر لـ Two Ideas
+
+395
+00:44:33,730 --> 00:44:40,630
+يبقى أنا بتروح اقول افترض ان ال X موجود في ال A في
+
+396
+00:44:40,630 --> 00:44:50,980
+B يبقى بلاء ان علي شكل ال Xالـ X متساوي A1 B1 زائد
+
+397
+00:44:50,980 --> 00:45:01,160
+ال A2 B2 زائد زائد ال A M B M بحيث ال AI موجودة في
+
+398
+00:45:01,160 --> 00:45:10,280
+A و ال BI موجودة في B و ال AI موجودة في ال A و ال
+
+399
+00:45:10,280 --> 00:45:16,360
+BI موجودة غير في ال B طيب
+
+400
+00:45:17,410 --> 00:45:25,850
+تعالى نشوف وين هذا بدها تصير هذا يا بنات ال A1
+
+401
+00:45:25,850 --> 00:45:34,470
+موجودة وين؟ فى ال A مظبوط و ال AID و ال B1 element
+
+402
+00:45:34,470 --> 00:45:38,870
+موجود فى B يعني موجود فى ال ring لما نقرأ ال B1
+
+403
+00:45:38,870 --> 00:45:45,790
+موجود فى A من زاوية أخرى ال B1 موجودة وين؟في الـB
+
+404
+00:45:45,790 --> 00:45:55,090
+والـA والموجودة في الـR في الـA
+
+405
+00:45:55,090 --> 00:46:00,590
+والموجودة في الـB بالمثل هذا موجود في A وB موجود
+
+406
+00:46:00,590 --> 00:46:08,050
+في AB وهذا كله موجود في AB يبقى هذا يقين إن الـX
+
+407
+00:46:08,050 --> 00:46:20,920
+موجودة في الـAو and ال X موجودة في ال B هذا موجودة
+
+408
+00:46:20,920 --> 00:46:26,180
+في ال اتنين موجودة وين ال intersection لهم يبقى
+
+409
+00:46:26,180 --> 00:46:32,840
+هذا يعطينا ان ال X موجودة في ال A intersection B
+
+410
+00:46:32,840 --> 00:46:39,140
+طبعا ستسأل واحدة فيكم ممكن يكون ال intersection
+
+411
+00:46:39,140 --> 00:46:46,780
+subset من أعصر الدارممكن بس في شوق بدنا نحطه زيادة
+
+412
+00:46:46,780 --> 00:46:53,820
+وهذا هو موضوع سؤال ستاشر سؤال ستاشر بيقول ال a و
+
+413
+00:46:53,820 --> 00:47:03,440
+ال b ideally commutative ال a و ال b ideals where
+
+414
+00:47:03,440 --> 00:47:06,020
+are commutative
+
+415
+00:47:09,550 --> 00:47:18,210
+و .. و كذلك ان ال A زائد ال B متساوي ال R كونها
+
+416
+00:47:18,210 --> 00:47:27,010
+اثبت ان ال intersection A intersection B بتساوي ال
+
+417
+00:47:27,010 --> 00:47:35,710
+A في B أول شيء ال A بيسلسل من ال A intersection B
+
+418
+00:47:35,710 --> 00:47:41,340
+هذا واحد هيه قدامك مظبوط؟يبقى الاتجاه الأول جاهز
+
+419
+00:47:41,340 --> 00:47:49,660
+الاتجاه الثاني فيه عندي معلومة ال R commutative
+
+420
+00:47:49,660 --> 00:47:55,700
+with unity فيها ال unity يبقى باجي بقوله الواحد
+
+421
+00:47:55,700 --> 00:48:00,740
+موجود في ال R اللي يبدأ تساوي A زائد ال B يبقى
+
+422
+00:48:00,740 --> 00:48:05,840
+معنى هذا الكلام ان الواحد بدي يساوي A زائد ال B
+
+423
+00:48:05,840 --> 00:48:16,380
+for someA موجود في A والـ B موجود في B الان بدأ
+
+424
+00:48:16,380 --> 00:48:24,440
+يقول خد ال X موجود في A intersection B then ال X
+
+425
+00:48:24,440 --> 00:48:32,280
+موجود في A and ال X موجود في B طيب
+
+426
+00:48:32,280 --> 00:48:39,530
+بدأ ياخد الآن ال X هذه أضربها في واحديبقى ال X
+
+427
+00:48:39,530 --> 00:48:45,670
+تساوي X في واحد يعني بدها تساوي ال X الواحد عندى
+
+428
+00:48:45,670 --> 00:48:54,130
+بقدرش ب A زائد ال B هذا الكلام بده يساوي ال X A
+
+429
+00:48:54,130 --> 00:49:02,910
+زائد ال X B ال R commutative يبقى هذا ب A X زائد
+
+430
+00:49:02,910 --> 00:49:10,780
+ال X B خلّالي هنا هذا موجود وينفى ال A و هذا موجود
+
+431
+00:49:10,780 --> 00:49:20,820
+وين فى B هذا موجود فى A و هذا موجود فى B إذا هذا
+
+432
+00:49:20,820 --> 00:49:28,440
+ال A X موجود فى ال A B بنفس الطريقة هذا موجود فى B
+
+433
+00:49:28,440 --> 00:49:36,600
+و هذا موجود وين فى A إذا هذا كله موجود وين فى ال A
+
+434
+00:49:36,600 --> 00:49:42,400
+Bيبقى X اللى خدتها في ال intersection اللى جيتها
+
+435
+00:49:42,400 --> 00:49:49,360
+موجودة وين في حاصل الدورة يبقى هنا ساعة ال
+
+436
+00:49:49,360 --> 00:49:56,260
+intersection بيه ساعة ست من مين من ال A بيه هذه
+
+437
+00:49:56,260 --> 00:50:05,700
+العلاقة رقم اتنين يبقى from واحد and اتنين we have
+
+438
+00:50:06,470 --> 00:50:15,210
+إن الـ A intersection B يساوي الـ A في B يلا صدلوا
+
+439
+00:50:15,210 --> 00:50:25,990
+عندكم exercises ليوم السبت خدوا
+
+440
+00:50:25,990 --> 00:50:30,970
+لسؤال 17 سؤال 22
+
+441
+00:50:36,220 --> 00:50:45,400
+أسئلة أربعة و عشرين سؤال تلاتين تمانية و تلاتين
+
+442
+00:50:45,400 --> 00:50:58,760
+واحد و أربعين نين و أربعين خمسة و أربعين ستة و
+
+443
+00:50:58,760 --> 00:51:03,260
+أربعين تمانية و أربعين
+
+444
+00:51:05,400 --> 00:51:12,300
+خمسين واحد وخمسين ستة وخمسين
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a4b89067db2eed90935da476ba382a905b1cbbda
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I.srt
@@ -0,0 +1,1369 @@
+1
+00:00:21,280 --> 00:00:25,160
+بسم الله الرحمن الرحيم. المرة اللي فاتت بدأنا
+
+2
+00:00:25,160 --> 00:00:29,260
+بموضوع الـ integral domain اللي هو chapter 14
+
+3
+00:00:29,260 --> 00:00:34,340
+chapter 13 وعطينا تعريف الـ integral domain وقلنا
+
+4
+00:00:34,340 --> 00:00:38,440
+الـ integral domain هو عبارة عن commutative ring
+
+5
+00:00:38,440 --> 00:00:44,500
+with unity وهذه الـ ring مافيهاش zero divisors
+
+6
+00:00:44,500 --> 00:00:49,340
+تمام؟ يبقى هذا كان تعريف الـ integral domain وعطينا
+
+7
+00:00:49,340 --> 00:00:55,480
+على ذلك مثالين، وهذا هو المثال الثالث. إذا نقول للرمز
+
+8
+00:00:55,480 --> 00:01:01,540
+Z[X] of polynomial with integer coefficients is
+
+9
+00:01:01,540 --> 00:01:09,500
+an integral domain because يبقى مجموعة الدوال كل
+
+10
+00:01:09,500 --> 00:01:16,700
+كلها على شكل كثيرة حدود والمعاملات هي أعداد صحيحة
+
+11
+00:01:16,700 --> 00:01:22,770
+هو عبارة عن integral domain. ليش؟ طبعا الـ Z[X]
+
+12
+00:01:22,770 --> 00:01:29,190
+أثبتناها قبل ذلك أنها ring with unity، والـ unity
+
+13
+00:01:29,190 --> 00:01:34,410
+تبعها f(x) يساوي واحد، وكنا commutative لأن كل
+
+14
+00:01:34,410 --> 00:01:39,370
+واحدة عند التعويض بتعطيني real number. يبقى
+
+15
+00:01:39,370 --> 00:01:53,860
+because we know that بنعرف أن الـ Z[X] is a
+
+16
+00:01:53,860 --> 00:01:59,860
+commutative ring
+
+17
+00:01:59,860 --> 00:02:11,400
+with unity اللي هو f(x) يساوي واحد. ضايل
+
+18
+00:02:11,400 --> 00:02:17,180
+علينا نثبت أن هذه الـ ring مافيهاش zero divisors
+
+19
+00:02:17,180 --> 00:02:24,600
+طبعا يبقى بدنا نفترض أن فيها zero divisor ونحاول
+
+20
+00:02:24,600 --> 00:02:29,500
+نثبت أن هذا الكلام خاطئ. zero divisor أو الرقم اللي يجعل
+
+21
+00:02:29,500 --> 00:02:35,680
+النتيجة تساوي صفر. إن أحد العناصر يساوي صفر. يبقى هنا
+
+22
+00:02:35,680 --> 00:02:47,600
+بعدين بقول assume that إن الـ f(x) في الـ g(x)
+
+23
+00:02:47,600 --> 00:02:58,800
+بده يساوي صفر، والـ f والـ g موجودة في Z[X]. أما
+
+24
+00:02:58,800 --> 00:03:06,640
+ذلك، مادام حاصل ضرب عنصرين يساوي صفر، يبقى
+
+25
+00:03:06,640 --> 00:03:14,700
+ذلك الـ f(x) بتساوي صفر أو الـ g(x) بتساوي صفر
+
+26
+00:03:14,700 --> 00:03:24,280
+دائما وأبدا. for example، توضيحا لذلك بدي أعطيك أبسط
+
+27
+00:03:24,280 --> 00:03:28,540
+الأشياء. بدي أعطيك two linear functions، يعني two
+
+28
+00:03:28,540 --> 00:03:37,360
+polynomials من الدرجة الأولى. يبقى باجي بقول الـ f
+
+29
+00:03:37,360 --> 00:03:47,700
+(x) بدي تساوي ax + b، والـ g(x) بدي تساوي cx
+
+30
+00:03:47,700 --> 00:03:55,440
++ d، والـ a والـ b والـ c والـ d كلها موجودة في Z
+
+31
+00:03:55,440 --> 00:04:06,720
+then الـ ax + b في الـ cx + d بده يساوي صفر
+
+32
+00:04:06,720 --> 00:04:15,120
+implies بتروح تضربها هذه، يبقى هذه بتعطيني ac في x
+
+33
+00:04:15,120 --> 00:04:28,390
+تربيع زائد ac في x تربيع زائد ad في الـ x زائد bc في الـ x
+
+34
+00:04:28,390 --> 00:04:36,130
+زائد bd كله بده يساوي صفر. صار
+
+35
+00:04:36,130 --> 00:04:41,790
+عندي polynomial من الدرجة الثانية تساوي صفر. مدام
+
+36
+00:04:41,790 --> 00:04:47,530
+تساوي صفر، إذا المعاملات هي اللي خلتها لي تساوي
+
+37
+00:04:47,530 --> 00:04:54,030
+صفر. يبقى بناء عليه الـ ac يبقى يساوي صفر، معامل x
+
+38
+00:04:54,030 --> 00:05:01,410
+تربيع. معامل x اللي هو ad + bc يبقى
+
+39
+00:05:01,410 --> 00:05:09,990
+يساوي صفر. الآن bd يبقى يساوي صفر. طيب هذول الـ a والـ b والـ c
+
+40
+00:05:09,990 --> 00:05:16,810
+والـ d هم عناصر، حاصل ضربهم يساوي صفر. يبدو على الأقل واحد
+
+41
+00:05:16,810 --> 00:05:22,810
+فيهم يساوي صفر. هذا معناه أن الـ a بده يساوي صفر
+
+42
+00:05:22,810 --> 00:05:31,210
+أو الـ c بده يساوي صفر. وهذا معناه أن الـ b تساوي
+
+43
+00:05:31,210 --> 00:05:41,770
+صفر أو الـ d بدها تساوي صفر. طب لو كانت الـ a تساوي
+
+44
+00:05:41,770 --> 00:05:47,700
+صفر من هنا، يبقى إيش بده يكون عندنا؟ بصير المعادلة
+
+45
+00:05:47,700 --> 00:05:56,600
+هذه ما يلي. يبقى الـ a تساوي صفر، then تحطها صفر
+
+46
+00:05:56,600 --> 00:06:05,640
+بصير الـ bc تساوي صفر. هذا معناه أن الـ b تساوي
+
+47
+00:06:05,640 --> 00:06:13,840
+صفر أو الـ c تساوي صفر. تمام. إذا صار الـ a تساوي
+
+48
+00:06:13,840 --> 00:06:22,400
+صفر والـ b تساوي صفر، معناته الـ ax + b، الـ ax
+
+49
+00:06:22,400 --> 00:06:30,200
++ b بده يساوي صفر. يبقى هنا الـ a تساوي صفر
+
+50
+00:06:30,200 --> 00:06:37,220
+والـ b تساوي صفر. implies أن الـ ax + b تساوي
+
+51
+00:06:37,220 --> 00:06:45,630
+صفر، or الـ c تساوي صفر وd
+
+52
+00:06:45,630 --> 00:06:54,690
+تساوي صفر. implies أن cx + d تساوي صفر. وبناء عليه،
+
+53
+00:06:54,690 --> 00:07:00,790
+لذلك Z[X] is an integral domain لأن أخدت
+
+54
+00:07:00,790 --> 00:07:06,410
+حاصل ضرب عنصرين يساوي صفر، لقيت إما الأول يساوي صفر
+
+55
+00:07:06,410 --> 00:07:18,930
+أو الثاني يساوي صفر. يبقى صراحة Z[x] has
+
+56
+00:07:18,930 --> 00:07:28,510
+no zero divisors. مش فيها zero divisors. هذا معناته
+
+57
+00:07:28,510 --> 00:07:38,710
+أن Z[x] is an integral domain.
+
+58
+00:07:47,370 --> 00:07:51,330
+ما أخدناه على المعادلة من الدرجة الأولى، ممكن
+
+59
+00:07:51,330 --> 00:07:55,890
+تاخده الدرجة الثانية، الثالثة، الرابعة. ممكن واحد من
+
+60
+00:07:55,890 --> 00:07:59,130
+الدرجة الأولى، وممكن واحد من الدرجة الثانية، وممكن
+
+61
+00:07:59,130 --> 00:08:03,150
+معادلة من الأولى ومعادلة من الثالثة، زي ما بدك. مافي
+
+62
+00:08:03,150 --> 00:08:08,290
+مشكلة في هذه الحالة. أروح لمثال اللي بعده اللي هو
+
+63
+00:08:08,290 --> 00:08:17,440
+مثال أربعة، example four، بيقول لي that Z
+
+64
+00:08:17,440 --> 00:08:25,340
+[√2]، Z[√2]، اللي عناصرها بتتكون على
+
+65
+00:08:25,340 --> 00:08:32,160
+الصورة a + b√2 بحيث الـ a والـ b موجودة
+
+66
+00:08:32,160 --> 00:08:43,820
+في الـ set of integers is an integral domain. يبقى
+
+67
+00:08:43,820 --> 00:08:45,940
+هذه integral domain
+
+68
+00:08:50,580 --> 00:08:55,620
+طبعا احنا قبل قليل قلنا الـ integral domain عبارة
+
+69
+00:08:55,620 --> 00:09:05,120
+عبارة عن إيش؟ ring وcommutative ومافيش فيها zero
+
+70
+00:09:05,120 --> 00:09:10,740
+divisors. لو حصل أن حصل ضرب عنصرين بده يساوي صفر، هذا
+
+71
+00:09:10,740 --> 00:09:16,560
+الكلام بده يحصل إذا كان أحدهم يساوي صفر، يعني
+
+72
+00:09:16,560 --> 00:09:23,410
+مافيهاش zero divisors. على كل الأحوال، طيب الآن بيقول
+
+73
+00:09:23,410 --> 00:09:27,930
+يُثبت أن الـ set هذه عبارة عن integral domain. هل
+
+74
+00:09:27,930 --> 00:09:32,530
+أثبتناها سابقا أن هذه commutative ring with
+
+75
+00:09:32,530 --> 00:09:38,770
+unity؟ طبعا لأ، أول مرة بنشوفها. يبقى الآن بدنا نثبت
+
+76
+00:09:38,770 --> 00:09:43,330
+أولا أنها عبارة عن commutative ring
+
+77
+00:09:43,330 --> 00:09:50,550
+with unity. يبقى هنا النقطة الأولى هي أن
+
+78
+00:09:50,550 --> 00:10:08,670
+Z[√2] is a commutative ring with unity
+
+79
+00:10:08,670 --> 00:10:15,550
+one اللي هو بده يكون واحد زائد صفر في √2
+
+80
+00:10:18,330 --> 00:10:21,130
+مكافئ. بقى أنت بتقولي أن هو sub ring، ولا أعطيكم
+
+81
+00:10:21,130 --> 00:10:26,110
+العافية؟ طبعا فيها الـ zero element، أن الـ zero
+
+82
+00:10:26,110 --> 00:10:30,350
+بكل بساطة، والـ zero زائد صفر في √2. يبقى هنا
+
+83
+00:10:30,350 --> 00:10:35,810
+non empty. نطرح عنصرين من بعض، مينهم في √2
+
+84
+00:10:35,810 --> 00:10:40,910
+الموجودات في الـ ring. هنا نأخذ عنصرين، ونضربهم في
+
+85
+00:10:40,910 --> 00:10:47,150
+بعض. والآن هنضرب وإحنا بنحل، وبالتالي بكون شبه جاهز
+
+86
+00:10:47,150 --> 00:10:51,560
+عندك. يبقى هذه a commutative ring with unity. غير a
+
+87
+00:10:51,560 --> 00:10:55,940
+زي b√2، لو ضربتها في c + d√2 من
+
+88
+00:10:55,940 --> 00:11:01,200
+الأول، والمهم بيعطيني نفس النتيجة على كلا الأمرين.
+
+89
+00:11:01,200 --> 00:11:07,720
+المهم بدي أثبت أنه مافيش فيها zero divisor. يبقى
+
+90
+00:11:07,720 --> 00:11:11,680
+هنا check that there is a commutative ring with
+
+91
+00:11:11,680 --> 00:11:23,330
+unity. يبقى it remains that يبقى أن الـ Z[√2]
+
+92
+00:11:23,330 --> 00:11:37,610
+has no zero divisors. فوراً، ولذلك بدي أفترض أن
+
+93
+00:11:37,610 --> 00:11:43,490
+عندي عنصرين موجودتين في الـ ring هذه، وحاصل ضربهما
+
+94
+00:11:43,490 --> 00:11:48,940
+يساوي صفر، وأشوف إيش بدي أتوجه الدنيا معه. يبقى for
+
+95
+00:11:48,940 --> 00:11:57,340
+f = a + b√2، والـ g = c + d√2
+
+96
+00:11:57,340 --> 00:12:07,500
+موجودة في الـ Z[√2]. هنا اللي هو الـ a
+
+97
+00:12:07,500 --> 00:12:15,100
++ b√2 في الـ c + d√2 بده
+
+98
+00:12:15,100 --> 00:12:22,730
+يساوي صفر. يبقى افتراض في عندي عنصرين، والعنصرين هدول
+
+99
+00:12:22,730 --> 00:12:31,910
+حاصل ضربهما يساوي صفر. إذا قلت أثبت أن الـ a + b
+
+100
+00:12:31,910 --> 00:12:38,210
+√2 يساوي صفر أو الـ c + d√2
+
+101
+00:12:38,210 --> 00:12:44,940
+يساوي صفر، وتم المطلوب مظبوط. يبقى then بدي أروح
+
+102
+00:12:44,940 --> 00:12:49,540
+أضرب هذول، وأشوف إيش بده يعطيني. لأن هذا بدنا
+
+103
+00:12:49,540 --> 00:12:58,580
+يعطيني ac + 2bd +
+
+104
+00:12:58,580 --> 00:13:07,140
+(ad + bc)√2. هذول كلهم بدي آخذهم مع بعض زائد لأن أضرب
+
+105
+00:13:07,140 --> 00:13:16,410
+هذا بيصير ad√2 وهذا bc√2. يبقى
+
+106
+00:13:16,410 --> 00:13:24,230
+بالاختصار ac + 2bd + (ad + bc)√2 يساوي صفر. هاي
+
+107
+00:13:24,230 --> 00:13:31,210
+ضاعفنا مرة ثانية. a في c، هاي الجذر مع الجذر بيطلع
+
+108
+00:13:31,210 --> 00:13:36,930
+اثنين. 2bd، هاي 2bd، هدول مش فيهم جذر اثنين
+
+109
+00:13:36,930 --> 00:13:42,470
+اللي فيهم جذر اثنين بدي أخليهم مع بعض. يبقى ad√2
+
+110
+00:13:42,470 --> 00:13:48,140
+و bc√2، بدي آخذ عامل مشترك √2
+
+111
+00:13:48,140 --> 00:13:51,920
+كما بيطلع المقدار هذا يساوي صفر. طب هذا هو ال
+
+112
+00:13:51,920 --> 00:13:56,700
+number. متى إيش بيطلع صفر؟ إذا كان الجُزء الأول في
+
+113
+00:13:56,700 --> 00:14:02,000
+صفر والجُزء الثاني في صفر، بصير كلامنا صحيح. يبقى
+
+114
+00:14:02,000 --> 00:14:10,640
+هذا معناه معناه إيش؟ أن الـ ac + 2bd بده
+
+115
+00:14:10,640 --> 00:14:18,090
+يساوي صفر، وهذا معناه أن الـ ad + الـ bc بده
+
+116
+00:14:18,090 --> 00:14:23,630
+يساوي صفر. أغلبت المعادلة الأولى هذه، سميها للمعادلة
+
+117
+00:14:23,630 --> 00:14:32,470
+رقم 1. طبعاً من هذه المعادلة إيش بقدر أستنتج؟ بدي
+
+118
+00:14:32,470 --> 00:14:41,150
+أجيب d. يبقى من هذه المعادلة d يساوي سالب bc / a
+
+119
+00:14:41,890 --> 00:14:49,090
+وسمي لهذه المعادلة كمان رقم واحد. الآن بدي آخذ من
+
+120
+00:14:49,090 --> 00:14:53,810
+المعادلة رقم واحد، وأعوض في المعادلة الأولى
+
+121
+00:14:53,810 --> 00:14:58,470
+المعادلة الأولى لسه ما اشتغلتش عليها. يبقى بدي أعوض
+
+122
+00:14:58,470 --> 00:15:03,910
+أشيل d وأحط بدلها سالب bc / a، بيصير
+
+123
+00:15:03,910 --> 00:15:12,490
+عندنا هنا بيصير ac + 2b (-bc / a) = 0. بدي أضرب
+
+124
+00:15:12,490 --> 00:15:20,030
+الطرفين في a. لو ضربت
+
+125
+00:15:20,030 --> 00:15:29,890
+الطرفين في a بيصير a تربيع c - 2b تربيع c
+
+126
+00:15:29,890 --> 00:15:31,490
+يساوي صفر.
+
+127
+00:15:34,420 --> 00:15:41,940
+بدي يعطينا أن الـ a تربيع - 2b تربيع في c
+
+128
+00:15:41,940 --> 00:15:48,920
+بده يساوي صفر. هذا إيش بده يعطينا؟ يا إما الـ c بدها
+
+129
+00:15:48,920 --> 00:15:57,280
+تساوي صفر، يا إما or الـ a تربيع - 2b تربيع
+
+130
+00:15:57,280 --> 00:16:03,430
+يساوي صفر. هذا بده يعطينا ما يأتي: يا إما الـ
+
+131
+00:16:03,430 --> 00:16:09,250
+c بدها تساوي صفر، أو بدي أنقل هذه على الجهة التالية
+
+132
+00:16:09,250 --> 00:16:16,130
+وأخذ الـ جذر التربيعي للطرفين، أو الـ a بدها تساوي
+
+133
+00:16:16,130 --> 00:16:24,490
+زائد أو ناقص b في جذر 2، نقلنا، تمام؟
+
+134
+00:16:24,490 --> 00:16:45,220
+يبقى بدي آخذ الحالة، الـ c تساوي صفر. من المعادلة
+
+135
+00:16:45,220 --> 00:16:54,260
+يبقى d تساوي صفر. هذا يجب أن يعطيكم أن c + d جذر
+
+136
+00:16:54,260 --> 00:17:00,920
+اثنين يساوي صفر. يبقى صار عندنا حاصل الضرب هذا يساوي
+
+137
+00:17:00,920 --> 00:17:06,380
+صفر. أثبت أن هذا يساوي صفر، إذا الـ ring عبارة عن
+
+138
+00:17:06,380 --> 00:17:10,080
+integral domain، أو الـ Z[√2] عبارة عن
+
+139
+00:17:10,080 --> 00:17:17,640
+integral domain. لو كانت c تساوي صفر. طيب أفرض
+
+140
+00:17:17,640 --> 00:17:23,100
+أنه كانت الـ a تساوي زائد أو ناقص b جذر اثنين، يبقى
+
+141
+00:17:23,100 --> 00:17:32,840
+هذول حالتين. يبقى الحالة الأولى، f اللي هو الـ a تساوي
+
+142
+00:17:32,840 --> 00:17:40,720
+bجذر 2. خلاصة، لو كانت c تساوي صفر، لأن لو كانت الـ a
+
+143
+00:17:40,720 --> 00:17:51,900
+تساوي b جذر 2، then from (1) we have من المعادلة
+
+144
+00:17:51,900 --> 00:17:57,480
+(1) اللي فوق، يبقى بدي أشيل الـ a وأحط مكانها b
+
+145
+00:17:57,480 --> 00:18:05,300
+جذر اثنين، يبقى بيصير bجذر اثنين + bجذر اثنين
+
+146
+00:18:05,300 --> 00:18:12,420
+في c + dجذر اثنين يساوي صفر. هذا معناته 2
+
+147
+00:18:12,420 --> 00:18:21,380
+ب جذر اثنين في c + dجذر اثنين، كل هذا الكلام
+
+148
+00:18:21,380 --> 00:18:31,340
+بده يساوي صفر. هذا معناه أن إما الـ b يساوي صفر، أو الـ c
+
+149
+00:18:31,340 --> 00:18:42,420
++ dجذر اثنين يساوي صفر. لو كانت الـ b تساوي صفر، بده
+
+150
+00:18:42,420 --> 00:18:48,660
+أشوف إيش اللي بده يحصل عندك. يبقى هنا بروح بقوله if
+
+151
+00:18:48,660 --> 00:19:00,610
+الـ b تساوي صفر، then equation (1) is بدي أشيل الـ b وأ
+
+152
+00:19:00,610 --> 00:19:06,390
+ضع مكانها صفر. إيش بيصير؟ أن أضع مكانها الـ a في c
+
+153
+00:19:06,390 --> 00:19:13,770
++ dجذر اثنين بدي يساوي صفر. هذا معناته أن a
+
+154
+00:19:13,770 --> 00:19:22,650
+تساوي صفر أو c + dجذر اثنين يساوي صفر. طيب
+
+155
+00:19:22,650 --> 00:19:30,010
+يكون صار عندنا b تساوي صفر و a تساوي صفر. تمام.
+
+156
+00:19:30,010 --> 00:19:38,850
+يبقى هنا صار a تساوي صفر و b تساوي صفر. هذا يتطلب
+
+157
+00:19:38,850 --> 00:19:47,390
+أن الـ a + b جذر اثنين يساوي صفر، أو الـ c +
+
+158
+00:19:47,390 --> 00:19:53,560
+dجذر اثنين يساوي صفر. هذه بالصفر وهذه بالصفر.
+
+159
+00:19:53,560 --> 00:19:56,760
+إذا المجموعة بتساوي صفر، أو الثانية اللي ضايلة
+
+160
+00:19:56,760 --> 00:20:05,980
+عندنا بتساوي صفر، أمامكم. خلصنا هكذا؟ خلصنا ولا
+
+161
+00:20:05,980 --> 00:20:10,900
+لسة؟ لحظة.
+
+162
+00:20:10,900 --> 00:20:19,140
+إن لو كانت الـ a تساوي b جذر اثنين أو لو كانت بالسالب.
+
+163
+00:20:20,420 --> 00:20:25,140
+وتعالى نشوف f
+
+164
+00:20:25,140 --> 00:20:28,540
+ال
+
+165
+00:20:28,540 --> 00:20:39,640
+a تساوي سالب bجذر اثنين، then equation (1) is اللي
+
+166
+00:20:39,640 --> 00:20:48,450
+هو a + bجذر اثنين في c + dجذر اثنين
+
+167
+00:20:48,450 --> 00:20:55,470
+يساوي صفر. implies a صارت سالب bجذر اثنين. يبقى
+
+168
+00:20:55,470 --> 00:21:04,590
+بضل قد إيش هنا صفر؟ يبقى صفر في c + d جذر
+
+169
+00:21:04,590 --> 00:21:12,330
+
+223
+00:27:54,700 --> 00:27:58,980
+Zero أقل من P؟ تمام، إذا هذا ممكن. يقول ليش؟ لأنه
+
+224
+00:27:58,980 --> 00:28:03,720
+بصير Zero × P بده يساوي Zero، يبقى بتاعته اسمه
+
+225
+00:28:03,720 --> 00:28:11,180
+ولا لا؟ يبقى هذا، هذا بقول this is a
+
+226
+00:28:11,180 --> 00:28:24,950
+true only when الـ M تساوي Zero or الـ N تساوي Zero
+
+227
+00:28:24,950 --> 00:28:36,910
+إيه السبب؟ لأن الـ M أقل من P and الـ N أقل من P
+
+228
+00:28:36,910 --> 00:28:50,130
+كذلك، يبقى هنا الـ M تساوي Zero or الـ N تساوي Zero
+
+229
+00:28:50,830 --> 00:29:02,930
+معنى هذا الكلام أن ZP has no zero divisors مادام
+
+230
+00:29:02,930 --> 00:29:07,710
+مافيهاش zero divisors، مافيهاش، تصير integral domain
+
+231
+00:29:07,710 --> 00:29:12,290
+Therefore، ولهذا
+
+232
+00:29:12,290 --> 00:29:19,610
+الـ ZP is an integral domain
+
+233
+00:29:26,090 --> 00:29:32,490
+integral domain، طيب
+
+234
+00:29:32,490 --> 00:29:40,170
+احنا خدنا الآن المثال الخامس على الـ integral
+
+235
+00:29:40,170 --> 00:29:48,710
+domain، فبنحاول ناخد بعض الأمثلة على الـ rings اللي
+
+236
+00:29:48,710 --> 00:29:57,440
+بتنفعش تكون integral domain، يعني بندور على الـ ring
+
+237
+00:29:57,440 --> 00:30:03,120
+الـ ring هذا مثلاً ما تكونش commutative، تبقى تصير
+
+238
+00:30:03,120 --> 00:30:07,860
+ماهيش integral domain، مافيش فيها الـ unity، يبقى
+
+239
+00:30:07,860 --> 00:30:13,580
+ماهيش integral domain، مافيش فيها، مافيش فيها الـ
+
+240
+00:30:13,580 --> 00:30:18,880
+unity، مافيش فيها الـ unity، مافيش فيها الـ unity
+
+241
+00:30:18,880 --> 00:30:19,280
+الـ unity، مافيش فيها الـ unity، مافيش فيها الـ unity
+
+242
+00:30:19,280 --> 00:30:20,960
+الـ unity، مافيش فيها الـ unity، مافيش فيها الـ unity
+
+243
+00:30:20,960 --> 00:30:29,270
+مافيش فيها الـ unity. The ring هو M2 of Z
+
+244
+00:30:29,270 --> 00:30:37,070
+مين هذه يا بنات؟ مجموعة المصفوفات اللي نظامها اتنين
+
+245
+00:30:37,070 --> 00:30:42,170
+في اتنين، والمحدد تبعها يا بده يساوي واحد يا بده
+
+246
+00:30:42,170 --> 00:30:52,450
+يساوي سالب واحد، تمام. هذه is not an integral
+
+247
+00:30:53,550 --> 00:30:58,270
+دو مين؟
+
+248
+00:30:58,270 --> 00:31:04,970
+because مش commutative، هه commutative؟ لأ، يبقى step
+
+249
+00:31:04,970 --> 00:31:10,730
+one is two، على شكل commutative، because M two of اه
+
+250
+00:31:10,730 --> 00:31:21,650
+because M two of Z is not commutative
+
+251
+00:31:22,590 --> 00:31:28,750
+يعني سقط أحد شروط الـ Integral domain، أن الـ ring
+
+252
+00:31:28,750 --> 00:31:33,070
+تكون commutative، بدأ يسقط شرط، تصبح الـ
+
+253
+00:31:33,070 --> 00:31:42,570
+Integral domain. سابعاً، الـ ring هو Z، هو ring
+
+254
+00:31:42,570 --> 00:31:49,190
+ولا sub ring؟ sub ring هي ring، لأنه قلنا الـ sub
+
+255
+00:31:49,190 --> 00:31:55,010
+ring هي subset من الـ ring الأصلية، بس إيه الشرط؟ الـ
+
+256
+00:31:55,010 --> 00:31:58,650
+ring تحت نفس الـ two operations، يبقى هي في الحقيقة
+
+257
+00:31:58,650 --> 00:32:04,390
+ring. طب هي sub ring من مين؟ من Z itself، يبقى هذه
+
+258
+00:32:04,390 --> 00:32:10,170
+الـ sub ring، لكنها ليست integral domain لأنها تحتوي
+
+259
+00:32:10,170 --> 00:32:14,490
+على الـ unity اللي هو واحد صحيح، هذا الواحد مش
+
+260
+00:32:14,490 --> 00:32:20,770
+موجود فيها. يبقى هذه الـ .. the ring is not a
+
+261
+00:32:20,770 --> 00:32:35,690
+integral domain، السبب because 2Z has no
+
+262
+00:32:35,690 --> 00:32:44,150
+unity.  سمّينا واحدة zero divisors
+
+263
+00:33:10,510 --> 00:33:17,520
+طبعاً هذه commutative، with unity، 1، 1، طبعاً طيب، بس
+
+264
+00:33:17,520 --> 00:33:22,880
+بدنا نثبت أن فيها على الأقل ولو zero divisors
+
+265
+00:33:22,880 --> 00:33:28,080
+واحد، لكن بعد ما أثبت هقول لك فيها مالهاش نهاية من الـ
+
+266
+00:33:28,080 --> 00:33:32,260
+zero divisors، طبعاً because it is not an integral
+
+267
+00:33:32,260 --> 00:33:40,490
+domain، because مثلاً تلاتة و Zero و Zero أربعة موجودة
+
+268
+00:33:40,490 --> 00:33:48,690
+في الـ direct sum، موجود صحيح أو لا؟ ولا صح؟ and لو
+
+269
+00:33:48,690 --> 00:33:57,010
+ضربناهم في بعض كده، إيش بتظهر؟ Zero و Zero، كل عنصر
+
+270
+00:33:57,010 --> 00:34:02,330
+مع  العنصر  اللي  بنضربه  فيه  في  direct sum  يبقى  طالع  Zero  و Zero
+
+271
+00:34:02,330 --> 00:34:08,590
+كويس؟ حصل ضرب two elements لا يساوي كل واحد منهم الـ
+
+272
+00:34:08,590 --> 00:34:14,170
+Zero، وطلع بـ Zero، يبقى هذا معناه zero divisors هنا
+
+273
+00:34:14,170 --> 00:34:24,630
+بدي أعطيك إنه تلاتة و Zero and Zero أربعة are zero
+
+274
+00:34:24,630 --> 00:34:29,710
+divisors، يبقى هنا
+
+275
+00:34:32,550 --> 00:34:45,590
+plus the direct sum is not an integral domain، لو
+
+276
+00:34:45,590 --> 00:34:52,430
+واحدة ثانية، أخدت رقمين تانية، أخدت واحد و Zero و
+
+277
+00:34:52,430 --> 00:35:03,910
+اتنين، in general، بدي أخد M و Zero و N، طبعاً، و الـ
+
+278
+00:35:03,910 --> 00:35:07,450
+M مين ما كان يكون، و الـ N مين ما كان يكون، يبقى يزيدش
+
+279
+00:35:07,450 --> 00:35:13,190
+تصير عدد الـ zero divisors تصير infinite zero
+
+280
+00:35:13,190 --> 00:35:16,810
+divisors، يبقى عندي عدد لانهائي من الـ zero divisors
+
+281
+00:35:16,810 --> 00:35:24,210
+إذا لا يمكن لهذا أن يكون integral domain، طبعاً طيب
+
+282
+00:35:24,210 --> 00:35:28,570
+بدنا نيجي لأول نظرية لهذا الدرس
+
+283
+00:35:46,290 --> 00:35:49,190
+النظرية بتقول ما يأتي:
+
+284
+00:36:04,180 --> 00:36:10,980
+Integral domain. Let
+
+285
+00:36:10,980 --> 00:36:21,160
+الـ A والـ B والـ C موجودات من Integral domain A، if الـ
+
+286
+00:36:21,160 --> 00:36:29,900
+A لا يساوي Zero، and الـ A × B بده يساوي الـ A ×
+
+287
+00:36:29,900 --> 00:36:49,330
+الـ C، then الـ B تساوي مين؟ تساوي الـ C
+
+288
+00:36:49,330 --> 00:36:55,910
+ثانية، بقول أخذنا الـ R Integral Domain، تمام؟ و
+
+289
+00:36:55,910 --> 00:36:59,530
+أخذنا ثلاث عناصر موجودة في الـ Integral Domain الـ
+
+290
+00:36:59,530 --> 00:37:04,300
+A والـ B والـ C، لو كان الـ A لا يساوي Zero، وعندي
+
+291
+00:37:04,300 --> 00:37:09,880
+معادلة A × B بده يساوي الـ A × C، يبقى بدنا نثبت
+
+292
+00:37:09,880 --> 00:37:14,100
+أن الـ B بده تساوي الـ C.  عظمنا أخذنا هذه
+
+293
+00:37:14,100 --> 00:37:18,500
+النظرية في الـ ring أخذناها
+
+294
+00:37:18,500 --> 00:37:24,980
+بس قلنا B لا تساوي C، يبقى في حالة الـ ring النظرية
+
+295
+00:37:24,980 --> 00:37:29,230
+كانت غير متحققة، لكن في حالة الـ Integral domain
+
+296
+00:37:29,230 --> 00:37:35,530
+النظرية محققة، تمام؟ طيب، إذا بدنا نروح نثبت صحة
+
+297
+00:37:35,530 --> 00:37:40,330
+هذا الكلام. يبقى احنا عندنا R Integral domain
+
+298
+00:37:40,330 --> 00:37:50,330
+وأخذنا ثلاث عناصر موجودة فيه. بداية، أقول في الـ R الـ
+
+299
+00:37:50,330 --> 00:37:54,110
+Integral
+
+300
+00:37:54,110 --> 00:37:54,910
+domain
+
+301
+00:37:58,930 --> 00:38:12,270
+الـ A لا يساوي Zero، و الـ A × B بيساوي الـ A × C
+
+302
+00:38:12,270 --> 00:38:23,350
+و الـ A و الـ B و الـ C موجودات في R. الـ A
+
+303
+00:38:23,350 --> 00:38:29,760
+بتساويش Zero. هذا معقول. هذه ممكن أعملها معادلة صفرية
+
+304
+00:38:29,760 --> 00:38:39,300
+يبقى، and A × B ناقص A × C بده يساوي Zero. هذا بده
+
+305
+00:38:39,300 --> 00:38:45,820
+يعطينا أن الـ A بتساويش الـ Zero، وممكن ناخد الـ A عامل مشترك
+
+306
+00:38:45,820 --> 00:38:53,800
+الـ B ناقص الـ C اللي تساوي Zero. إذا حصل ضرب two
+
+307
+00:38:53,800 --> 00:39:00,330
+elements بده يساوي Zero، واحد فيهم لا يساوي Zero، إذا
+
+308
+00:39:00,330 --> 00:39:09,390
+الثاني هو اللي بده يساوي Zero. ليش؟ أيوة، then الـ A
+
+309
+00:39:09,390 --> 00:39:15,930
+لا تساوي Zero implies أن الـ B ناقص الـ C هي اللي
+
+310
+00:39:15,930 --> 00:39:24,690
+بدها تساوي Zero. ليش؟ لأن الـ R is an integral
+
+311
+00:39:27,580 --> 00:39:33,500
+domain. لأن هذا لا يمكن أن يكون zero divisor. ليش؟
+
+312
+00:39:33,500 --> 00:39:38,760
+إمكانية؟ لأن هذا integral domain، مافيش فيه zero
+
+313
+00:39:38,760 --> 00:39:43,300
+divisors.  مدى ما فيش فيه zero divisors، و الـ A لا يساوي
+
+314
+00:39:43,300 --> 00:39:48,140
+Zero. إذا، إجباري  العنصر  اللي  بقي  بده  يكون  الـ B ناقص
+
+315
+00:39:48,140 --> 00:39:54,320
+الـ C هو اللي بده يساوي Zero. هذا بده يعطينا أن B
+
+316
+00:39:54,320 --> 00:40:03,760
+تساوي C، وهو المطلوب. وعدناكم بيه. الـ ring والـ
+
+317
+00:40:03,760 --> 00:40:09,040
+integral domain والـ field.  بظبط، تعرضنا للـ rings
+
+318
+00:40:09,040 --> 00:40:12,560
+تعرضنا للـ integral domain، والآن بدنا نعطي تعريف
+
+319
+00:40:12,560 --> 00:40:17,520
+للـ field وبعض الأمثلة البسيطة عليه. جبنا
+
+320
+00:40:17,520 --> 00:40:18,400
+definition
+
+321
+00:40:21,860 --> 00:40:31,780
+بيقول a commutative ring، a commutative ring with
+
+322
+00:40:31,780 --> 00:40:39,180
+unity، with unity is
+
+323
+00:40:39,180 --> 00:40:43,320
+called a
+
+324
+00:40:43,320 --> 00:40:51,200
+field. is called a field if every
+
+325
+00:40:52,270 --> 00:41:06,570
+non-zero element، non-zero element is
+
+326
+00:41:06,570 --> 00:41:07,510
+a unit.
+
+327
+00:41:35,420 --> 00:41:40,960
+فعلاً، نقف لحظة بسيطة أمام الـ integral domain والـ
+
+328
+00:41:40,960 --> 00:41:47,400
+field، مشان نقدر نميز بينهم. المرة اللي فاتت قلنا الـ
+
+329
+00:41:47,400 --> 00:41:51,500
+.. الـ .. الـ integral domain هو commutative ring
+
+330
+00:41:51,500 --> 00:41:56,960
+with unity، تمام؟ الـ field هو commutative ring with
+
+331
+00:41:56,960 --> 00:42:02,880
+unity، يبقى أول خاصيتين زي بعض تماماً. الخلاف وين؟
+
+332
+00:42:02,880 --> 00:42:06,990
+الخاصية الثالثة. في حالة الـ Integral domain قلنا
+
+333
+00:42:06,990 --> 00:42:12,370
+الـ R مافيش فيها Zero divisors. لو بقدر الله طلع
+
+334
+00:42:12,370 --> 00:42:17,010
+حصل ضرب عنصرين بده يساوي Zero، لازم على الأقل
+
+335
+00:42:17,010 --> 00:42:20,570
+أحدهما يساوي Zero. في الـ Integral domain هذا، بيقول
+
+336
+00:42:20,570 --> 00:42:26,450
+ليش؟ الشرط الثالث.  حطّ Zero divisor على جنب. كل عنصر
+
+337
+00:42:26,450 --> 00:42:31,370
+غير صفري بده يكون unit. يعني إيش unit؟ يعني هو بيمتلك
+
+338
+00:42:31,370 --> 00:42:38,460
+multiplicative Inverse. يعني بده يكون معكوس تحت عملية
+
+339
+00:42:38,460 --> 00:42:45,120
+الضرب. والله، لو رجعنا بالذاكرة إلى  حديثنا واحد
+
+340
+00:42:45,120 --> 00:42:50,840
+بجينا نقول في عندنا abelian group، والـ group اللي
+
+341
+00:42:50,840 --> 00:42:56,440
+قبلها تبقى commutative وفيها الـ identity element
+
+342
+00:42:56,440 --> 00:43:02,540
+وكل عنصر له معكوس، صح ولا لا؟ يبقى كل field هو
+
+343
+00:43:02,540 --> 00:43:07,200
+abelian group، ولا كل abelian group هي field؟ كل
+
+344
+00:43:07,200 --> 00:43:13,280
+abelian group هي field؟ تمام؟ مظبوط هيك يا بنات؟
+
+345
+00:43:13,280 --> 00:43:17,540
+لأ. ليش؟ لأن الـ group عليها عملية واحدة،
+
+346
+00:43:17,540 --> 00:43:23,160
+يبقى لا يمكن للـ abelian group أن تكون field،
+
+347
+00:43:23,160 --> 00:43:27,770
+ليش؟ لأن الـ field عليها two binary operations، بس الـ
+
+348
+00:43:27,770 --> 00:43:31,870
+group عليها one binary operation، يبقى الـ group
+
+349
+00:43:31,870 --> 00:43:36,270
+يقول آه ممكن تعمل  كذا وكذا، يبقى الـ field لا
+
+350
+00:43:36,270 --> 00:43:42,150
+يمكن أن يكون abelian group. هذا الكلام صحيح، لأن الـ
+
+351
+00:43:42,150 --> 00:43:46,070
+abelian group عليها عملية واحدة، لكن الـ field عليها
+
+352
+00:43:46,070 --> 00:43:50,330
+two binary operations. يبقى هذا الفرق في ما بينهم
+
+353
+00:43:52,480 --> 00:43:58,520
+ممكن يكون الـ integral domain هو field، وممكن الـ
+
+354
+00:43:58,520 --> 00:44:04,260
+field يكون integral domain. هذا الكلام ما رح نجيب
+
+355
+00:44:04,260 --> 00:44:08,400
+عليه في المحاضرة القادمة إن شاء الله. هنا في عندنا
+
+356
+00:44:08,400 --> 00:44:13,500
+نظرية: every finite integral domain is a field، طبعاً
+
+357
+00:44:13,500 --> 00:44:19,450
+نظرية في المحاضرة القادمة إن شاء الله. بالبسيط،  تفهمي
+
+358
+00:44:19,450 --> 00:44:24,530
+إنه إذا كان عندي كلمة field، يبقى كل عنصر له معكوس، على
+
+359
+00:44:24,530 --> 00:44:31,690
+الصفر، تمام؟ آه، في الـ integral domain ما عنديش zero
+
+360
+00:44:31,690 --> 00:44:37,230
+divisors، لكن عندي units، وغير الـ units لأنه في حاجة
+
+361
+00:44:37,230 --> 00:44:42,630
+اسمه nilpotent element، وفي idempotent element
+
+362
+00:44:42,630 --> 00:44:46,950
+فرحنا نعرفهم  ما كناش نعرفهم في الـ group، تمام؟
+
+363
+00:44:47,120 --> 00:44:51,280
+يبقى في عناصر لها مسميات أخرى. كل اللي بدي أؤكد
+
+364
+00:44:51,280 --> 00:44:58,340
+عليه إنه في الـ field، كل عنصر غير صفري يكون له معكوس
+
+365
+00:44:58,340 --> 00:45:02,100
+بالنسبة لعملية الضرب، بالنسبة لعملية الضرب، خلاص
+
+366
+00:45:02,100 --> 00:45:13,000
+نعطي بعض الأمثلة البسيطة. Examples، examples
+
+367
+00:45:13,000 --> 00:45:20,010
+له، the set of rational numbers، والـ set of real numbers
+
+368
+00:45:20,010 --> 00:45:26,110
+والـ set of complex numbers، تمام؟ الـ set of
+
+369
+00:45:26,110 --> 00:45:31,850
+complex numbers، الثلاثة commutative، والثلاثة فيهم
+
+370
+00:45:31,850 --> 00:45:37,510
+unity، تمام؟ اللي هو الواحد الصحيح.  اللي الثلاثة بأيش
+
+371
+00:45:37,510 --> 00:45:43,860
+فيه الشرطين اتحققوا؟ كل عنصر له معكوس؟ واحد على كل
+
+372
+00:45:43,860 --> 00:45:46,080
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+373
+00:45:46,080 --> 00:45:46,840
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+374
+00:45:46,840 --> 00:45:47,760
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+375
+00:45:47,760 --> 00:45:53,220
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+376
+00:45:53,220 --> 00:45:54,760
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+377
+00:45:54,760 --> 00:45:54,800
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+378
+00:45:54,800 --> 00:45:55,080
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+379
+00:45:55,080 --> 00:45:55,120
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+380
+00:45:55,120 --> 00:45:56,760
+واحد، على كل واحد، على كل واحد، على كل واحد، على كل
+
+381
+00:45:56,760 --> 00:46:03,260
+واحد، على كل واحد، على كل واحد
+
+382
+00:46:03,260 --> 00:46:06,880
+على
+
+383
+00:46:35,250 --> 00:46:43,810
+لو أخذنا sub ring من أحدهم مثلاً، هل ضروري الـ sub
+
+384
+00:46:43,810 --> 00:46:51,230
+ring تبقى field؟ لأ، زي إيش مثلاً؟ الـ Z، الـ Z هذه
+
+385
+00:46:51,230 --> 00:46:56,270
+commutative ring with unity، صحيح ولا لأ؟ لكن هل الـ
+
+386
+00:46:56,270 --> 00:47:02,330
+Z integral domain؟ لأ، ولا حتى field، لأن كل عنصر ما لهوش
+
+387
+00:47:02,330 --> 00:47:06,530
+معكوس، المعكوس المقلوب تبعه، الرقم مش
+
+388
+00:47:06,530 --> 00:47:15,600
+موجود في Z. يبقى، باقي بقول، هدول عارفين فقط، ولكن الـ
+
+389
+00:47:15,600 --> 00:47:28,840
+Z is a sub ring، sub ring of R. الـ Z is a sub ring
+
+390
+00:47:28,840 --> 00:47:39,710
+of R. فعلاً، الـ Z is not a field، بس هي انتقال دماغي
+
+391
+00:47:39,710 --> 00:47:49,430
+بس هي انتقال
+
+392
+00:47:49,430 --> 00:47:51,370
+دماغي، بس هي انتقال دماغي، بس هي انتقال دماغي، بس هي
+
+393
+00:47:51,370 --> 00:47:51,490
+انتقال دماغي، بس هي انتقال دماغي، بس هي انتقال دماغي
+
+394
+00:47:51,490 --> 00:47:52,430
+انتقال دماغي، بس هي انتقال دماغي، بس هي انتقال دماغي
+
+395
+00:47:52,430 --> 00:48:01,890
+بس هي انتقال دماغي، بس هي انتقال دماغي، بس هي انتقال
+
+396
+00
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..86034acf1ba75a042e836f7ab75938dd5895fb03
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I_raw.json
@@ -0,0 +1 @@
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"end": 56.72, "word": " X", "probability": 0.96875}, {"start": 56.72, "end": 57.14, "word": " of", "probability": 0.8955078125}, {"start": 57.14, "end": 57.94, "word": " polynomial", "probability": 0.47119140625}, {"start": 57.94, "end": 59.28, "word": " with", "probability": 0.74169921875}, {"start": 59.28, "end": 60.06, "word": " integer", "probability": 0.869140625}, {"start": 60.06, "end": 61.1, "word": " coefficients", "probability": 0.68017578125}, {"start": 61.1, "end": 61.54, "word": " is", "probability": 0.83447265625}, {"start": 61.54, "end": 61.92, "word": " an", "probability": 0.88427734375}, {"start": 61.92, "end": 62.4, "word": " integral", "probability": 0.791015625}, {"start": 62.4, "end": 63.1, "word": " domain", "probability": 0.97998046875}, {"start": 63.1, "end": 63.86, "word": " because", "probability": 0.431884765625}, {"start": 63.86, "end": 65.4, "word": " يبقى", "probability": 0.9560546875}, {"start": 65.4, "end": 66.74, "word": " مجموعة", "probability": 0.95283203125}, {"start": 66.74, "end": 68.08, "word": " الدوال", "probability": 0.7861328125}, {"start": 68.08, "end": 69.5, "word": " كل", "probability": 0.5341796875}, {"start": 69.5, "end": 70.24, "word": " كلده", "probability": 0.4630533854166667}, {"start": 70.24, "end": 70.58, "word": " على", "probability": 0.8310546875}, {"start": 70.58, "end": 71.12, "word": " شكل", "probability": 0.97900390625}, {"start": 71.12, "end": 71.94, "word": " كثيرة", "probability": 0.9461263020833334}, {"start": 71.94, "end": 72.72, "word": " حدود", "probability": 0.9833984375}, {"start": 72.72, "end": 74.82, "word": " والمعاملات", "probability": 0.8906656901041666}, {"start": 74.82, "end": 75.22, "word": " هي", "probability": 0.80224609375}, {"start": 75.22, "end": 75.84, "word": " أعداد", "probability": 0.9580078125}, {"start": 75.84, "end": 76.7, "word": " صحيحة", "probability": 0.96328125}, {"start": 76.7, "end": 77.14, "word": " هو", "probability": 0.544921875}, {"start": 77.14, "end": 77.66, "word": " عبارة", "probability": 0.989013671875}, {"start": 77.66, "end": 78.12, "word": " عن", "probability": 0.9921875}, {"start": 78.12, "end": 78.82, "word": " integral", "probability": 0.80078125}, {"start": 78.82, "end": 79.84, "word": " domain", "probability": 0.98486328125}, {"start": 79.84, "end": 80.72, "word": " ليش؟", "probability": 0.5765787760416666}], "temperature": 1.0}, {"id": 3, "seek": 11067, "start": 81.27, "end": 110.67, "text": "طبعا ال Z of X هدفناها قبل ذلك أنها ring with unity و ال unity تبعها F of X مسا واحد و كنا commutative لإن كل واحدة عند التعويض تبتعطيني real number يبقى because we know that نبتعرف أن ال Z of X", "tokens": [9566, 3555, 3615, 995, 2423, 1176, 295, 1783, 8032, 3215, 5172, 8315, 11296, 12174, 36150, 29910, 23275, 14739, 11296, 4875, 365, 18205, 4032, 2423, 18205, 6055, 3555, 3615, 11296, 479, 295, 1783, 47524, 995, 36764, 24401, 4032, 9122, 8315, 800, 325, 1166, 5296, 28814, 1863, 28242, 36764, 24401, 3660, 43242, 16712, 3615, 45865, 11242, 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ring", "probability": 0.46826171875}, {"start": 86.19, "end": 87.57, "word": " with", "probability": 0.517578125}, {"start": 87.57, "end": 88.33, "word": " unity", "probability": 0.95703125}, {"start": 88.33, "end": 88.69, "word": " و", "probability": 0.48828125}, {"start": 88.69, "end": 88.83, "word": " ال", "probability": 0.90966796875}, {"start": 88.83, "end": 89.19, "word": " unity", "probability": 0.9833984375}, {"start": 89.19, "end": 90.01, "word": " تبعها", "probability": 0.95849609375}, {"start": 90.01, "end": 90.41, "word": " F", "probability": 0.748046875}, {"start": 90.41, "end": 90.71, "word": " of", "probability": 0.951171875}, {"start": 90.71, "end": 90.95, "word": " X", "probability": 0.99267578125}, {"start": 90.95, "end": 91.41, "word": " مسا", "probability": 0.4413909912109375}, {"start": 91.41, "end": 91.85, "word": " واحد", "probability": 0.871337890625}, {"start": 91.85, "end": 92.37, "word": " و", "probability": 0.8603515625}, {"start": 92.37, "end": 92.67, "word": " كنا", "probability": 0.598388671875}, {"start": 92.67, "end": 93.67, "word": " commutative", "probability": 0.7688802083333334}, {"start": 93.67, "end": 93.97, "word": " لإن", "probability": 0.8243815104166666}, {"start": 93.97, "end": 94.41, "word": " كل", "probability": 0.8974609375}, {"start": 94.41, "end": 94.99, "word": " واحدة", "probability": 0.9261067708333334}, {"start": 94.99, "end": 95.21, "word": " عند", "probability": 0.9892578125}, {"start": 95.21, "end": 95.77, "word": " التعويض", "probability": 0.7459716796875}, {"start": 95.77, "end": 96.67, "word": " تبتعطيني", "probability": 0.7212262834821429}, {"start": 96.67, "end": 97.15, "word": " real", "probability": 0.77392578125}, {"start": 97.15, "end": 98.37, "word": " number", "probability": 0.98486328125}, {"start": 98.37, "end": 99.37, "word": " يبقى", "probability": 0.907470703125}, {"start": 99.37, "end": 100.21, "word": " because", "probability": 0.84423828125}, {"start": 100.21, "end": 101.43, "word": " we", "probability": 0.8583984375}, {"start": 101.43, "end": 103.31, "word": " know", "probability": 0.89111328125}, {"start": 103.31, "end": 105.55, "word": " that", "probability": 0.9150390625}, {"start": 105.55, "end": 107.09, "word": " نبتعرف", "probability": 0.66328125}, {"start": 107.09, "end": 107.49, "word": " أن", "probability": 0.51025390625}, {"start": 107.49, "end": 108.55, "word": " ال", "probability": 0.53662109375}, {"start": 108.55, "end": 108.99, "word": " Z", "probability": 0.96826171875}, {"start": 108.99, "end": 110.11, "word": " of", "probability": 0.96533203125}, {"start": 110.11, "end": 110.67, "word": " X", "probability": 0.9970703125}], "temperature": 1.0}, {"id": 4, "seek": 14082, "start": 111.1, "end": 140.82, "text": "is a commutative ring with unity اللي هو f of x تساوي 100 تساوي 1 ضايل علينا نثبت ان هذه ال ring مافيهاش zero divisors طبعا يبقى بدنا نفترض", "tokens": [271, 257, 800, 325, 1166, 4875, 365, 18205, 13672, 1829, 31439, 283, 295, 2031, 6055, 3794, 995, 45865, 2319, 6055, 3794, 995, 45865, 502, 48812, 995, 26895, 25894, 8315, 8717, 12984, 3555, 2655, 16472, 29538, 2423, 4875, 19446, 41185, 3224, 33599, 4018, 25974, 830, 23032, 3555, 3615, 995, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 5172, 2655, 43042], "avg_logprob": -0.27171610371541166, "compression_ratio": 1.2756410256410255, "no_speech_prob": 0.0, "words": [{"start": 111.1, "end": 111.96, "word": "is", "probability": 0.3486328125}, {"start": 111.96, "end": 113.86, "word": " a", "probability": 0.87939453125}, {"start": 113.86, "end": 116.76, "word": " commutative", "probability": 0.9283854166666666}, {"start": 116.76, "end": 119.86, "word": " ring", "probability": 0.951171875}, {"start": 119.86, "end": 122.32, "word": " with", "probability": 0.857421875}, {"start": 122.32, "end": 124.44, "word": " unity", "probability": 0.90185546875}, {"start": 124.44, "end": 126.48, "word": " اللي", "probability": 0.509613037109375}, {"start": 126.48, "end": 126.64, "word": " هو", "probability": 0.90966796875}, {"start": 126.64, "end": 127.16, "word": " f", "probability": 0.3505859375}, {"start": 127.16, "end": 127.64, "word": " of", "probability": 0.5927734375}, {"start": 127.64, "end": 128.1, "word": " x", "probability": 0.830078125}, {"start": 128.1, "end": 128.72, "word": " تساوي", "probability": 0.8619384765625}, {"start": 128.72, "end": 129.1, "word": " 100", "probability": 0.226806640625}, {"start": 129.1, "end": 130.0, "word": " تساوي", "probability": 0.9427490234375}, {"start": 130.0, "end": 130.26, "word": " 1", "probability": 0.83740234375}, {"start": 130.26, "end": 131.4, "word": " ضايل", "probability": 0.72802734375}, {"start": 131.4, "end": 131.78, "word": " علينا", "probability": 0.906494140625}, {"start": 131.78, "end": 132.46, "word": " نثبت", "probability": 0.9451904296875}, {"start": 132.46, "end": 133.04, "word": " ان", "probability": 0.60400390625}, {"start": 133.04, "end": 133.54, "word": " هذه", "probability": 0.5810546875}, {"start": 133.54, "end": 133.78, "word": " ال", "probability": 0.90283203125}, {"start": 133.78, "end": 134.1, "word": " ring", "probability": 0.93603515625}, {"start": 134.1, "end": 135.4, "word": " مافيهاش", "probability": 0.9525146484375}, {"start": 135.4, "end": 136.06, "word": " zero", "probability": 0.576171875}, {"start": 136.06, "end": 137.18, "word": " divisors", "probability": 0.966796875}, {"start": 137.18, "end": 137.98, "word": " طبعا", "probability": 0.76556396484375}, {"start": 137.98, "end": 138.82, "word": " يبقى", "probability": 0.79931640625}, {"start": 138.82, "end": 139.12, "word": " بدنا", "probability": 0.7481689453125}, {"start": 139.12, "end": 140.82, "word": " نفترض", "probability": 0.87060546875}], "temperature": 1.0}, {"id": 5, "seek": 16984, "start": 141.34, "end": 169.84, "text": "إن فيها Zero divisor ونحاول نثبت إن هذا الكلام Zero divisor أو الرقم اللي يجعل نتيجة يسوى صفر إن أحد العناصر يساوي صفر يبقى هنا بعدين بقول assume that إن ال F of X في ال G of X بده يساوي Zero", "tokens": [28814, 1863, 8978, 11296, 17182, 25974, 284, 4032, 1863, 5016, 995, 12610, 8717, 12984, 3555, 2655, 36145, 23758, 2423, 28820, 10943, 17182, 25974, 284, 34051, 34892, 4587, 2304, 13672, 1829, 7251, 7435, 30241, 8717, 31371, 7435, 3660, 7251, 3794, 2407, 7578, 20328, 5172, 2288, 36145, 5551, 24401, 18863, 1863, 33546, 2288, 7251, 3794, 995, 45865, 20328, 5172, 2288, 7251, 3555, 4587, 7578, 34105, 39182, 9957, 4724, 39648, 6552, 300, 36145, 2423, 479, 295, 1783, 8978, 2423, 460, 295, 1783, 47525, 3224, 7251, 3794, 995, 45865, 17182], "avg_logprob": -0.257183912841753, "compression_ratio": 1.5797872340425532, "no_speech_prob": 0.0, "words": [{"start": 141.34, "end": 141.7, "word": "إن", "probability": 0.5819091796875}, {"start": 141.7, "end": 142.22, "word": " فيها", "probability": 0.7666015625}, {"start": 142.22, "end": 142.6, "word": " Zero", "probability": 0.459228515625}, {"start": 142.6, "end": 143.62, "word": " divisor", "probability": 0.814208984375}, {"start": 143.62, "end": 144.6, "word": " ونحاول", "probability": 0.854296875}, {"start": 144.6, "end": 145.24, "word": " نثبت", "probability": 0.951416015625}, {"start": 145.24, "end": 145.5, "word": " إن", "probability": 0.48876953125}, {"start": 145.5, "end": 145.86, "word": " هذا", "probability": 0.8642578125}, {"start": 145.86, "end": 146.58, "word": " الكلام", "probability": 0.9690755208333334}, {"start": 146.58, "end": 147.36, "word": " Zero", "probability": 0.58349609375}, {"start": 147.36, "end": 148.08, "word": " divisor", "probability": 0.899169921875}, {"start": 148.08, "end": 148.36, "word": " أو", "probability": 0.81494140625}, {"start": 148.36, "end": 148.94, "word": " الرقم", "probability": 0.9763997395833334}, {"start": 148.94, "end": 149.12, "word": " اللي", "probability": 0.8662109375}, {"start": 149.12, "end": 149.5, "word": " يجعل", "probability": 0.7939453125}, {"start": 149.5, "end": 150.06, "word": " نتيجة", "probability": 0.80731201171875}, {"start": 150.06, "end": 150.44, "word": " يسوى", "probability": 0.6781005859375}, {"start": 150.44, "end": 150.9, "word": " صفر", "probability": 0.93017578125}, {"start": 150.9, "end": 151.5, "word": " إن", "probability": 0.400146484375}, {"start": 151.5, "end": 151.94, "word": " أحد", "probability": 0.873779296875}, {"start": 151.94, "end": 152.78, "word": " العناصر", "probability": 0.83721923828125}, {"start": 152.78, "end": 153.38, "word": " يساوي", "probability": 0.67755126953125}, {"start": 153.38, "end": 153.94, "word": " صفر", "probability": 0.9659830729166666}, {"start": 153.94, "end": 155.18, "word": " يبقى", "probability": 0.93115234375}, {"start": 155.18, "end": 155.68, "word": " هنا", "probability": 0.98681640625}, {"start": 155.68, "end": 156.82, "word": " بعدين", "probability": 0.55810546875}, {"start": 156.82, "end": 157.52, "word": " بقول", "probability": 0.88720703125}, {"start": 157.52, "end": 158.82, "word": " assume", "probability": 0.72021484375}, {"start": 158.82, "end": 161.06, "word": " that", "probability": 0.8466796875}, {"start": 161.06, "end": 162.54, "word": " إن", "probability": 0.418212890625}, {"start": 162.54, "end": 162.88, "word": " ال", "probability": 0.7900390625}, {"start": 162.88, "end": 163.44, "word": " F", "probability": 0.58056640625}, {"start": 163.44, "end": 164.66, "word": " of", "probability": 0.82275390625}, {"start": 164.66, "end": 165.32, "word": " X", "probability": 0.9521484375}, {"start": 165.32, "end": 165.92, "word": " في", "probability": 0.8095703125}, {"start": 165.92, "end": 166.16, "word": " ال", "probability": 0.59326171875}, {"start": 166.16, "end": 166.48, "word": " G", "probability": 0.806640625}, {"start": 166.48, "end": 167.06, "word": " of", "probability": 0.91357421875}, {"start": 167.06, "end": 167.6, "word": " X", "probability": 0.99560546875}, {"start": 167.6, "end": 168.42, "word": " بده", "probability": 0.562255859375}, {"start": 168.42, "end": 169.2, "word": " يساوي", "probability": 0.859375}, {"start": 169.2, "end": 169.84, "word": " Zero", "probability": 0.53466796875}], "temperature": 1.0}, {"id": 6, "seek": 19898, "start": 170.84, "end": 198.98, "text": "و ال F و ال G موجودة في Z of X اما ذلك مادام حاصل ضرب Two Pronouns بتسوي Zero يبقى ذلك ال F of X بتسوي Zero او ال G of X بتسوي Zero دائما و أبدا For example", "tokens": [2407, 2423, 479, 4032, 2423, 460, 3714, 29245, 23328, 3660, 8978, 1176, 295, 1783, 1975, 15042, 29910, 23275, 3714, 18513, 10943, 11331, 33546, 1211, 48812, 25513, 4453, 27723, 1733, 82, 39894, 3794, 45865, 17182, 7251, 3555, 4587, 7578, 29910, 23275, 2423, 479, 295, 1783, 39894, 3794, 45865, 17182, 1975, 2407, 2423, 460, 295, 1783, 39894, 3794, 45865, 17182, 11778, 16373, 15042, 4032, 5551, 3555, 28259, 1171, 1365], "avg_logprob": -0.31043198134969263, "compression_ratio": 1.516778523489933, "no_speech_prob": 0.0, "words": [{"start": 170.84, "end": 171.2, "word": "و", "probability": 0.88134765625}, {"start": 171.2, "end": 171.44, "word": " ال", "probability": 0.2236328125}, 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لو كانت C تساوي 0 لأن لو كانت الـ A تساوي B جاذب 2 then from start we have من المعادلة star اللي فوق", "tokens": [1829, 3555, 4587, 7578, 21542, 6027, 3660, 16247, 12610, 7578, 479, 13672, 1829, 31439, 2423, 39184, 316, 6055, 3794, 995, 45865, 363, 10874, 45636, 3555, 568, 16490, 1211, 33546, 3660, 45164, 25961, 2655, 383, 6055, 3794, 995, 45865, 1958, 5296, 33456, 45164, 25961, 2655, 2423, 39184, 316, 6055, 3794, 995, 45865, 363, 10874, 45636, 3555, 568, 550, 490, 722, 321, 362, 9154, 9673, 3615, 18513, 37977, 3543, 13672, 1829, 6156, 30543], "avg_logprob": -0.2133246591935555, "compression_ratio": 1.5844155844155845, "no_speech_prob": 0.0, "words": [{"start": 1045.64, "end": 1046.2, "word": "يبقى", "probability": 0.912109375}, {"start": 1046.2, "end": 1046.88, "word": " الحالة", "probability": 0.9856770833333334}, {"start": 1046.88, "end": 1047.94, "word": " الأولى", "probability": 0.9866536458333334}, {"start": 1047.94, "end": 1048.64, "word": " F", "probability": 0.80419921875}, 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زائد", "probability": 0.9679361979166666}, {"start": 1271.01, "end": 1271.51, "word": " B", "probability": 0.97998046875}, {"start": 1271.51, "end": 1272.33, "word": " جذر", "probability": 0.9959309895833334}, {"start": 1272.33, "end": 1273.07, "word": " اتنين", "probability": 0.98828125}, {"start": 1273.07, "end": 1273.63, "word": " هو", "probability": 0.9765625}, {"start": 1273.63, "end": 1273.91, "word": " اللي", "probability": 0.927490234375}, {"start": 1273.91, "end": 1274.27, "word": " بده", "probability": 0.6689453125}, {"start": 1274.27, "end": 1274.77, "word": " يساوي", "probability": 0.9842529296875}, {"start": 1274.77, "end": 1275.23, "word": " Zero", "probability": 0.9501953125}, {"start": 1275.23, "end": 1276.19, "word": " تمام؟", "probability": 0.8517252604166666}], "temperature": 1.0}, {"id": 44, "seek": 130520, "start": 1276.36, "end": 1305.2, "text": "معنى كلام ال ring هذه فيها zero divisors على كل الاحتمالات مافيش يبقى بروح و بقول له بص و هكذا ال z of جدر اتنين has no 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1370.31, "end": 1371.35, "word": " يبقى", "probability": 0.94677734375}, {"start": 1371.35, "end": 1372.01, "word": " ZP", "probability": 0.708251953125}, {"start": 1372.01, "end": 1372.31, "word": " وال", "probability": 0.3603515625}, {"start": 1372.31, "end": 1372.59, "word": " P", "probability": 0.51513671875}, {"start": 1372.59, "end": 1372.95, "word": " is", "probability": 0.73046875}, {"start": 1372.95, "end": 1373.15, "word": " a", "probability": 0.77392578125}, {"start": 1373.15, "end": 1373.65, "word": " prime", "probability": 0.9150390625}, {"start": 1373.65, "end": 1374.25, "word": " number", "probability": 0.98095703125}, {"start": 1374.25, "end": 1375.21, "word": " هذي", "probability": 0.624755859375}, {"start": 1375.21, "end": 1375.91, "word": " is", "probability": 0.763671875}, {"start": 1375.91, "end": 1377.63, "word": " an", "probability": 0.5537109375}, {"start": 1377.63, "end": 1379.57, "word": " integral", "probability": 0.75}, {"start": 1379.57, "end": 1381.57, "word": " domain", "probability": 0.96533203125}, {"start": 1381.57, "end": 1385.43, "word": " يجب", "probability": 0.6192220052083334}, {"start": 1385.43, "end": 1391.73, "word": " أن", "probability": 0.60302734375}, {"start": 1391.73, "end": 1392.27, "word": " نخبط", "probability": 0.7705078125}, {"start": 1392.27, "end": 1392.53, "word": " له", "probability": 0.69287109375}], "temperature": 1.0}, {"id": 48, "seek": 142031, "start": 1393.11, "end": 1420.31, "text": "إن ال ZP اللي هي كل الأعداد الصحية integers modulo P is an integral domain طبعا احنا بنعرف سابقا من الأمثلة اللي أخدناها سابقا that ان ال ZP is a commutative ring", "tokens": [28814, 1863, 2423, 1176, 47, 13672, 1829, 39896, 28242, 16247, 22488, 18513, 31767, 5016, 10632, 41674, 1072, 13455, 430, 307, 364, 11573, 9274, 23032, 3555, 3615, 995, 1975, 5016, 8315, 44945, 3615, 28480, 8608, 16758, 4587, 995, 9154, 16247, 2304, 12984, 37977, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 8608, 16758, 4587, 995, 300, 16472, 2423, 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{"start": 1406.87, "end": 1407.81, "word": " أخدناها", "probability": 0.9548828125}, {"start": 1407.81, "end": 1408.71, "word": " سابقا", "probability": 0.9879150390625}, {"start": 1408.71, "end": 1409.89, "word": " that", "probability": 0.53466796875}, {"start": 1409.89, "end": 1410.73, "word": " ان", "probability": 0.484619140625}, {"start": 1410.73, "end": 1411.05, "word": " ال", "probability": 0.5908203125}, {"start": 1411.05, "end": 1412.09, "word": " ZP", "probability": 0.963134765625}, {"start": 1412.09, "end": 1413.55, "word": " is", "probability": 0.9453125}, {"start": 1413.55, "end": 1414.55, "word": " a", "probability": 0.98291015625}, {"start": 1414.55, "end": 1417.03, "word": " commutative", "probability": 0.9666341145833334}, {"start": 1417.03, "end": 1420.31, "word": " ring", "probability": 0.80126953125}], "temperature": 1.0}, {"id": 49, "seek": 144907, "start": 1421.89, "end": 1449.07, "text": "community bring with unity اللي هو 1 modulo P هذا ال unity تبع ال ring هذا إيش بيضل علينا community bring with unity إيش ضالع نثبت هذه؟ مافيش فيها zero divisor يعني بدنا نحاول نثبت", "tokens": [25451, 507, 1565, 365, 18205, 13672, 1829, 31439, 502, 1072, 13455, 430, 23758, 2423, 18205, 6055, 3555, 3615, 2423, 4875, 23758, 11933, 1829, 8592, 4724, 1829, 11242, 1211, 25894, 8315, 1768, 1565, 365, 18205, 11933, 1829, 8592, 48812, 6027, 3615, 8717, 12984, 3555, 2655, 29538, 22807, 19446, 41185, 8592, 8978, 11296, 4018, 25974, 284, 37495, 22653, 47525, 8315, 8717, 5016, 995, 12610, 8717, 12984, 3555, 2655], "avg_logprob": -0.29034514391600197, "compression_ratio": 1.5365853658536586, "no_speech_prob": 0.0, "words": [{"start": 1421.89, "end": 1422.71, "word": "community", "probability": 0.46734619140625}, {"start": 1422.71, "end": 1423.29, "word": " bring", "probability": 0.384033203125}, {"start": 1423.29, "end": 1424.15, "word": " with", "probability": 0.84228515625}, {"start": 1424.15, "end": 1426.51, "word": " unity", "probability": 0.95947265625}, {"start": 1426.51, "end": 1429.45, "word": " اللي", "probability": 0.588134765625}, {"start": 1429.45, "end": 1429.81, "word": " هو", "probability": 0.98291015625}, {"start": 1429.81, "end": 1430.85, "word": " 1", "probability": 0.4365234375}, {"start": 1430.85, "end": 1431.83, "word": " modulo", "probability": 0.862060546875}, {"start": 1431.83, "end": 1432.49, "word": " P", "probability": 0.7314453125}, {"start": 1432.49, "end": 1434.55, "word": " هذا", "probability": 0.302734375}, {"start": 1434.55, "end": 1434.77, "word": " ال", "probability": 0.89404296875}, {"start": 1434.77, "end": 1435.11, "word": " unity", "probability": 0.88134765625}, {"start": 1435.11, "end": 1435.61, "word": " تبع", "probability": 0.88232421875}, {"start": 1435.61, "end": 1435.81, "word": " ال", "probability": 0.9150390625}, {"start": 1435.81, "end": 1436.07, "word": " ring", "probability": 0.640625}, {"start": 1436.07, "end": 1436.31, "word": " هذا", "probability": 0.345703125}, {"start": 1436.31, "end": 1436.61, "word": " إيش", "probability": 0.705078125}, {"start": 1436.61, "end": 1436.97, "word": " بيضل", "probability": 0.68048095703125}, {"start": 1436.97, "end": 1437.65, "word": " علينا", "probability": 0.93408203125}, {"start": 1437.65, "end": 1438.75, "word": " community", "probability": 0.165283203125}, {"start": 1438.75, "end": 1439.55, "word": " bring", "probability": 0.87744140625}, {"start": 1439.55, "end": 1439.83, "word": " with", "probability": 0.9130859375}, {"start": 1439.83, "end": 1440.11, "word": " unity", "probability": 0.96875}, {"start": 1440.11, "end": 1440.33, "word": " إيش", "probability": 0.84619140625}, {"start": 1440.33, "end": 1440.67, "word": " ضالع", "probability": 0.6822916666666666}, {"start": 1440.67, "end": 1441.13, "word": " نثبت", "probability": 0.968017578125}, {"start": 1441.13, "end": 1442.39, "word": " هذه؟", "probability": 0.6065673828125}, {"start": 1442.39, "end": 1443.89, "word": " مافيش", "probability": 0.8948567708333334}, {"start": 1443.89, "end": 1444.59, "word": " فيها", "probability": 0.99267578125}, {"start": 1444.59, "end": 1445.85, "word": " zero", "probability": 0.44775390625}, {"start": 1445.85, "end": 1446.93, "word": " divisor", "probability": 0.9521484375}, {"start": 1446.93, "end": 1447.47, "word": " يعني", "probability": 0.89697265625}, {"start": 1447.47, "end": 1447.85, "word": " بدنا", "probability": 0.828857421875}, {"start": 1447.85, "end": 1448.37, "word": " نحاول", "probability": 0.9945068359375}, {"start": 1448.37, "end": 1449.07, "word": " نثبت", "probability": 0.9915771484375}], "temperature": 1.0}, {"id": 50, "seek": 147836, "start": 1449.36, "end": 1478.36, "text": "إنه ماعنديش zero divisors على الإطلاق تمام نقول كويس يبقى هنا well to show that بنحاول نثبت ان ال zp has no zero divisors بنثبت بالعكس", "tokens": [28814, 1863, 3224, 19446, 3615, 1863, 16254, 8592, 4018, 25974, 830, 15844, 33688, 9566, 15040, 4587, 46811, 10943, 8717, 39648, 9122, 45865, 3794, 7251, 3555, 4587, 7578, 34105, 731, 281, 855, 300, 44945, 5016, 995, 12610, 8717, 12984, 3555, 2655, 16472, 2423, 710, 79, 575, 572, 4018, 25974, 830, 44945, 12984, 3555, 2655, 20666, 3615, 4117, 3794], "avg_logprob": -0.24474677083821134, "compression_ratio": 1.356164383561644, "no_speech_prob": 0.0, "words": [{"start": 1449.36, "end": 1450.3, "word": "إنه", "probability": 0.6734212239583334}, {"start": 1450.3, "end": 1451.12, "word": " ماعنديش", "probability": 0.9501953125}, {"start": 1451.12, "end": 1451.52, "word": " zero", "probability": 0.335205078125}, {"start": 1451.52, "end": 1452.5, "word": " divisors", "probability": 0.96533203125}, {"start": 1452.5, "end": 1452.94, "word": " على", "probability": 0.76611328125}, {"start": 1452.94, "end": 1454.02, "word": " الإطلاق", "probability": 0.927490234375}, {"start": 1454.02, "end": 1454.84, "word": " تمام", "probability": 0.8515625}, {"start": 1454.84, "end": 1455.86, "word": " نقول", "probability": 0.59588623046875}, {"start": 1455.86, "end": 1456.54, "word": " كويس", "probability": 0.9241536458333334}, {"start": 1456.54, "end": 1457.96, "word": " يبقى", "probability": 0.9385986328125}, {"start": 1457.96, "end": 1458.54, "word": " هنا", "probability": 0.98876953125}, {"start": 1458.54, "end": 1458.92, "word": " well", "probability": 0.150146484375}, {"start": 1458.92, "end": 1459.4, "word": " to", "probability": 0.9345703125}, {"start": 1459.4, "end": 1460.4, "word": " show", "probability": 0.8984375}, {"start": 1460.4, "end": 1463.76, "word": " that", "probability": 0.8203125}, {"start": 1463.76, "end": 1464.68, "word": " بنحاول", "probability": 0.84716796875}, {"start": 1464.68, "end": 1465.72, "word": " نثبت", "probability": 0.970703125}, {"start": 1465.72, "end": 1466.22, "word": " ان", "probability": 0.470458984375}, {"start": 1466.22, "end": 1466.56, "word": " ال", "probability": 0.79638671875}, {"start": 1466.56, "end": 1467.94, "word": " zp", "probability": 0.515625}, {"start": 1467.94, "end": 1469.24, "word": " has", "probability": 0.68212890625}, {"start": 1469.24, "end": 1470.46, "word": " no", "probability": 0.7138671875}, {"start": 1470.46, "end": 1472.0, "word": " zero", "probability": 0.85693359375}, {"start": 1472.0, "end": 1473.62, "word": " divisors", "probability": 0.978271484375}, {"start": 1473.62, "end": 1477.72, "word": " بنثبت", "probability": 0.790130615234375}, {"start": 1477.72, "end": 1478.36, "word": " بالعكس", "probability": 0.9940185546875}], "temperature": 1.0}, {"id": 51, "seek": 150732, "start": 1479.06, "end": 1507.32, "text": "بدي افترض ان عندي zero divisor بمعنى اخر بدي افترض ان عندي رقمين موجودات في ZP وحاصل ضربهما يساوي Zero فبتروح اقول assume that افترض ان ال M و ال N موجودات في ZP and", "tokens": [3555, 16254, 1975, 5172, 2655, 43042, 16472, 18871, 16254, 4018, 25974, 284, 4724, 2304, 3615, 1863, 7578, 1975, 34740, 4724, 16254, 1975, 5172, 2655, 43042, 16472, 18871, 16254, 12602, 4587, 2304, 9957, 3714, 29245, 23328, 9307, 8978, 1176, 47, 4032, 5016, 33546, 1211, 48812, 25513, 3224, 15042, 7251, 3794, 995, 45865, 17182, 6156, 3555, 2655, 32887, 5016, 1975, 39648, 6552, 300, 1975, 5172, 2655, 43042, 16472, 2423, 376, 4032, 2423, 426, 3714, 29245, 23328, 9307, 8978, 1176, 47, 293], "avg_logprob": -0.23769531771540642, "compression_ratio": 1.6273291925465838, "no_speech_prob": 0.0, "words": [{"start": 1479.06, "end": 1479.42, "word": "بدي", "probability": 0.27459716796875}, {"start": 1479.42, "end": 1479.8, "word": " افترض", "probability": 0.894775390625}, {"start": 1479.8, "end": 1480.06, "word": " ان", "probability": 0.9150390625}, {"start": 1480.06, "end": 1480.7, "word": " عندي", "probability": 0.7822265625}, {"start": 1480.7, "end": 1481.66, "word": " zero", "probability": 0.2265625}, {"start": 1481.66, "end": 1482.66, "word": " divisor", "probability": 0.848876953125}, {"start": 1482.66, "end": 1483.34, "word": " بمعنى", "probability": 0.95908203125}, {"start": 1483.34, "end": 1483.78, "word": " اخر", "probability": 0.696044921875}, {"start": 1483.78, "end": 1484.48, "word": " بدي", "probability": 0.805419921875}, {"start": 1484.48, "end": 1485.08, "word": " افترض", "probability": 0.9893798828125}, {"start": 1485.08, "end": 1485.44, "word": " ان", "probability": 0.94921875}, {"start": 1485.44, "end": 1485.96, "word": " عندي", "probability": 0.931396484375}, {"start": 1485.96, "end": 1487.32, "word": " رقمين", "probability": 0.872314453125}, {"start": 1487.32, "end": 1488.72, "word": " موجودات", "probability": 0.9007568359375}, {"start": 1488.72, "end": 1488.96, "word": " في", "probability": 0.943359375}, {"start": 1488.96, "end": 1489.66, "word": " ZP", "probability": 0.5462646484375}, {"start": 1489.66, "end": 1490.4, "word": " وحاصل", "probability": 0.84375}, {"start": 1490.4, "end": 1491.34, "word": " ضربهما", "probability": 0.958984375}, {"start": 1491.34, "end": 1492.34, "word": " يساوي", "probability": 0.943115234375}, {"start": 1492.34, "end": 1492.84, "word": " Zero", "probability": 0.345458984375}, {"start": 1492.84, "end": 1493.86, "word": " فبتروح", "probability": 0.79638671875}, {"start": 1493.86, "end": 1494.3, "word": " اقول", "probability": 0.83544921875}, {"start": 1494.3, "end": 1495.64, "word": " assume", "probability": 0.323486328125}, {"start": 1495.64, "end": 1497.9, "word": " that", "probability": 0.6328125}, {"start": 1497.9, "end": 1498.84, "word": " افترض", "probability": 0.944091796875}, {"start": 1498.84, "end": 1499.36, "word": " ان", "probability": 0.9443359375}, {"start": 1499.36, "end": 1500.88, "word": " ال", "probability": 0.291259765625}, {"start": 1500.88, "end": 1501.86, "word": " M", "probability": 0.7880859375}, {"start": 1501.86, "end": 1502.48, "word": " و", "probability": 0.8759765625}, {"start": 1502.48, "end": 1502.76, "word": " ال", "probability": 0.76513671875}, {"start": 1502.76, "end": 1503.2, "word": " N", "probability": 0.9580078125}, {"start": 1503.2, "end": 1504.86, "word": " موجودات", "probability": 0.908935546875}, {"start": 1504.86, "end": 1505.12, "word": " في", "probability": 0.9814453125}, {"start": 1505.12, "end": 1506.22, "word": " ZP", "probability": 0.969482421875}, {"start": 1506.22, "end": 1507.32, "word": " and", "probability": 0.8642578125}], "temperature": 1.0}, {"id": 52, "seek": 153193, "start": 1507.81, "end": 1531.93, "text": "حاصل ضربهما بده يساوي Zero modulo P ال degree تثبت انه اما ال M بزيرو او ال N بزيرو بكون ايه خلصنا من السؤال التابع عندي طيب نفترض ان في عندي رقمين فينزلتي قبل ما اكمل", "tokens": [5016, 33546, 1211, 48812, 25513, 3224, 15042, 47525, 3224, 7251, 3794, 995, 45865, 17182, 1072, 13455, 430, 2423, 4314, 6055, 12984, 3555, 2655, 16472, 3224, 1975, 15042, 2423, 376, 4724, 11622, 13546, 2407, 1975, 2407, 2423, 426, 4724, 11622, 13546, 2407, 4724, 30544, 1975, 1829, 3224, 16490, 1211, 9381, 8315, 9154, 21136, 33604, 6027, 16712, 16758, 3615, 18871, 16254, 23032, 1829, 3555, 8717, 5172, 2655, 43042, 16472, 8978, 18871, 16254, 12602, 4587, 2304, 9957, 8978, 1863, 11622, 1211, 31371, 12174, 36150, 19446, 1975, 24793, 1211], "avg_logprob": -0.36482558174188745, "compression_ratio": 1.5384615384615385, "no_speech_prob": 0.0, "words": [{"start": 1507.81, "end": 1508.59, "word": "حاصل", "probability": 0.6066080729166666}, {"start": 1508.59, "end": 1509.63, "word": " ضربهما", "probability": 0.7728271484375}, {"start": 1509.63, "end": 1510.37, "word": " بده", "probability": 0.3656005859375}, {"start": 1510.37, "end": 1511.01, "word": " يساوي", "probability": 0.8525390625}, {"start": 1511.01, "end": 1511.81, "word": " Zero", "probability": 0.1431884765625}, {"start": 1511.81, "end": 1512.65, "word": " modulo", "probability": 0.42578125}, {"start": 1512.65, "end": 1513.13, "word": " P", "probability": 0.8447265625}, {"start": 1513.13, "end": 1516.63, "word": " ال", "probability": 0.0848388671875}, {"start": 1516.63, "end": 1516.85, "word": " degree", "probability": 0.8466796875}, {"start": 1516.85, "end": 1517.51, "word": " تثبت", "probability": 0.8798828125}, {"start": 1517.51, "end": 1518.59, "word": " انه", "probability": 0.4873046875}, {"start": 1518.59, "end": 1519.13, "word": " اما", "probability": 0.697021484375}, {"start": 1519.13, "end": 1519.35, "word": " ال", "probability": 0.7783203125}, {"start": 1519.35, "end": 1519.65, "word": " M", "probability": 0.59716796875}, {"start": 1519.65, "end": 1520.35, "word": " بزيرو", "probability": 0.619384765625}, {"start": 1520.35, "end": 1520.93, "word": " او", "probability": 0.899169921875}, {"start": 1520.93, "end": 1521.17, "word": " ال", "probability": 0.86865234375}, {"start": 1521.17, "end": 1521.53, "word": " N", "probability": 0.9130859375}, {"start": 1521.53, "end": 1522.33, "word": " بزيرو", "probability": 0.9813232421875}, {"start": 1522.33, "end": 1523.17, "word": " بكون", "probability": 0.56689453125}, {"start": 1523.17, "end": 1523.45, "word": " ايه", "probability": 0.6460774739583334}, {"start": 1523.45, "end": 1524.61, "word": " خلصنا", "probability": 0.8944091796875}, {"start": 1524.61, "end": 1524.77, "word": " من", "probability": 0.62109375}, {"start": 1524.77, "end": 1525.33, "word": " السؤال", "probability": 0.9920247395833334}, {"start": 1525.33, "end": 1525.95, "word": " التابع", "probability": 0.7869466145833334}, {"start": 1525.95, "end": 1526.33, "word": " عندي", "probability": 0.45257568359375}, {"start": 1526.33, "end": 1527.23, "word": " طيب", "probability": 0.91259765625}, {"start": 1527.23, "end": 1528.41, "word": " نفترض", "probability": 0.84698486328125}, {"start": 1528.41, "end": 1528.87, "word": " ان", "probability": 0.90576171875}, {"start": 1528.87, "end": 1529.07, "word": " في", "probability": 0.62744140625}, {"start": 1529.07, "end": 1529.37, "word": " عندي", "probability": 0.705322265625}, {"start": 1529.37, "end": 1530.11, "word": " رقمين", "probability": 0.9566650390625}, {"start": 1530.11, "end": 1530.77, "word": " فينزلتي", "probability": 0.6756591796875}, {"start": 1530.77, "end": 1531.17, "word": " قبل", "probability": 0.882080078125}, {"start": 1531.17, "end": 1531.35, "word": " ما", "probability": 0.9501953125}, {"start": 1531.35, "end": 1531.93, "word": " اكمل", "probability": 0.92578125}], "temperature": 1.0}, {"id": 53, "seek": 155791, "start": 1532.25, "end": 1557.91, "text": "يطر ال M و ال N أكبر من P ولا أصغر من P كل واحد فيهم؟ أقل من P صح ولا لأ؟ يبقى هذ الأرقام أقل من P لأن علاصر ZP ببدأ 0 1 2 3 لغاية P minus 1 تمام، إذن هذول دايما وابدا M و N أقل من P", "tokens": [1829, 9566, 2288, 2423, 376, 4032, 2423, 426, 5551, 4117, 26890, 9154, 430, 49429, 5551, 9381, 17082, 2288, 9154, 430, 28242, 36764, 24401, 8978, 16095, 22807, 5551, 4587, 1211, 9154, 430, 20328, 5016, 49429, 5296, 10721, 22807, 7251, 3555, 4587, 7578, 8032, 8848, 16247, 2288, 4587, 10943, 5551, 4587, 1211, 9154, 430, 5296, 33456, 6225, 15040, 9381, 2288, 1176, 47, 4724, 44510, 10721, 1958, 502, 568, 805, 5296, 17082, 995, 10632, 430, 3175, 502, 46811, 10943, 12399, 11933, 8848, 1863, 8032, 8848, 12610, 11778, 47302, 15042, 4032, 16758, 28259, 376, 4032, 426, 5551, 4587, 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"seek": 173013, "start": 1701.69, "end": 1730.13, "text": "or ال N تساوي Zero ايه السبب؟ لأن ال M أقل من P and ال N أقل من P كذلك يبقى هنا ال M تساوي Zero or ال N تساوي Zero", "tokens": [284, 2423, 426, 6055, 3794, 995, 45865, 17182, 1975, 1829, 3224, 21136, 3555, 3555, 22807, 5296, 33456, 2423, 376, 5551, 4587, 1211, 9154, 430, 293, 2423, 426, 5551, 4587, 1211, 9154, 430, 9122, 8848, 23275, 7251, 3555, 4587, 7578, 34105, 2423, 376, 6055, 3794, 995, 45865, 17182, 420, 2423, 426, 6055, 3794, 995, 45865, 17182], "avg_logprob": -0.17912946907537325, "compression_ratio": 1.638095238095238, "no_speech_prob": 0.0, "words": [{"start": 1701.69, "end": 1702.73, "word": "or", "probability": 0.418701171875}, {"start": 1702.73, "end": 1703.35, "word": " ال", "probability": 0.8974609375}, {"start": 1703.35, "end": 1703.75, "word": " N", "probability": 0.36669921875}, {"start": 1703.75, "end": 1704.61, "word": " تساوي", "probability": 0.9500732421875}, {"start": 1704.61, "end": 1704.95, "word": " 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because اتنين زيه has no unity five سمن واحدة zero divisors", "tokens": [1829, 3555, 4587, 7578, 29538, 2423, 4386, 264, 4875, 307, 406, 257, 11573, 9274, 21136, 3555, 3555, 570, 1975, 2655, 1863, 9957, 30767, 1829, 3224, 575, 572, 18205, 1732, 8608, 27842, 36764, 24401, 3660, 4018, 25974, 830], "avg_logprob": -0.37808387295195933, "compression_ratio": 1.1162790697674418, "no_speech_prob": 0.0, "words": [{"start": 1935.65, "end": 1936.19, "word": "يبقى", "probability": 0.869873046875}, {"start": 1936.19, "end": 1936.59, "word": " هذه", "probability": 0.77099609375}, {"start": 1936.59, "end": 1937.23, "word": " ال", "probability": 0.56884765625}, {"start": 1937.23, "end": 1937.23, "word": " ..", "probability": 0.1265869140625}, {"start": 1937.23, "end": 1937.53, "word": " the", "probability": 0.460693359375}, {"start": 1937.53, "end": 1937.87, "word": " ring", "probability": 0.9697265625}, {"start": 1937.87, "end": 1938.57, "word": " is", "probability": 0.8671875}, {"start": 1938.57, "end": 1939.71, "word": " not", "probability": 0.89453125}, {"start": 1939.71, "end": 1940.77, "word": " a", "probability": 0.50537109375}, {"start": 1940.77, "end": 1942.49, "word": " integral", "probability": 0.77880859375}, {"start": 1942.49, "end": 1944.83, "word": " domain", "probability": 0.9677734375}, {"start": 1944.83, "end": 1947.43, "word": " السبب", "probability": 0.8798828125}, {"start": 1947.43, "end": 1949.41, "word": " because", "probability": 0.67626953125}, {"start": 1949.41, "end": 1951.67, "word": " اتنين", "probability": 0.854736328125}, {"start": 1951.67, "end": 1952.73, "word": " زيه", "probability": 0.4498697916666667}, {"start": 1952.73, "end": 1954.17, "word": " has", "probability": 0.7353515625}, {"start": 1954.17, "end": 1955.69, "word": " no", "probability": 0.89697265625}, {"start": 1955.69, "end": 1957.07, "word": " unity", "probability": 0.974609375}, {"start": 1957.07, "end": 1959.59, "word": " five", "probability": 0.30615234375}, {"start": 1959.59, "end": 1960.61, "word": " سمن", "probability": 0.5029296875}, {"start": 1960.61, "end": 1963.11, "word": " واحدة", "probability": 0.8310546875}, {"start": 1963.11, "end": 1963.35, "word": " zero", "probability": 0.40087890625}, {"start": 1963.35, "end": 1964.15, "word": " divisors", "probability": 0.941650390625}], "temperature": 1.0}, {"id": 68, "seek": 199407, "start": 1990.51, "end": 1994.07, "text": "طبعا هذه الكميوتر تتبنق with unity 1 1", "tokens": [9566, 3555, 3615, 995, 29538, 2423, 24793, 1829, 35473, 2288, 6055, 2655, 3555, 1863, 4587, 365, 18205, 502, 502], "avg_logprob": -0.6312500268220902, "compression_ratio": 0.8405797101449275, "no_speech_prob": 0.0, "words": [{"start": 1990.51, "end": 1991.39, "word": "طبعا", "probability": 0.75848388671875}, {"start": 1991.39, "end": 1991.63, "word": " هذه", "probability": 0.79248046875}, {"start": 1991.63, "end": 1992.07, "word": " الكميوتر", "probability": 0.71845703125}, {"start": 1992.07, "end": 1992.59, "word": " تتبنق", "probability": 0.53505859375}, {"start": 1992.59, "end": 1992.75, "word": " with", "probability": 0.1549072265625}, {"start": 1992.75, "end": 1993.13, "word": " unity", "probability": 0.5185546875}, {"start": 1993.13, "end": 1993.57, "word": " 1", "probability": 0.5166015625}, {"start": 1993.57, "end": 1994.07, "word": " 1", "probability": 0.4013671875}], "temperature": 1.0}, {"id": 69, "seek": 201712, "start": 1994.62, "end": 2017.12, "text": "طبعا طيب بس بدنا نثبت ان فيها على الأقل و لو zero divisors واحد لكن بعد ما أثبت هقولك فيها مالة نهاية من ال zero divisors طبعا because it is not an integral domain because مثلا تلاتة و Zero", "tokens": [9566, 3555, 3615, 995, 23032, 1829, 3555, 4724, 3794, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 8978, 11296, 15844, 16247, 4587, 1211, 4032, 45164, 4018, 25974, 830, 36764, 24401, 44381, 39182, 19446, 5551, 12984, 3555, 2655, 8032, 39648, 4117, 8978, 11296, 3714, 6027, 3660, 8717, 11296, 10632, 9154, 2423, 4018, 25974, 830, 23032, 3555, 3615, 995, 570, 309, 307, 406, 364, 11573, 9274, 570, 50113, 15040, 6055, 1211, 9307, 3660, 4032, 17182], "avg_logprob": -0.26455478472252414, "compression_ratio": 1.4945652173913044, "no_speech_prob": 0.0, "words": [{"start": 1994.62, "end": 1995.26, "word": "طبعا", "probability": 0.86865234375}, {"start": 1995.26, "end": 1996.92, "word": " طيب", "probability": 0.8826497395833334}, {"start": 1996.92, "end": 1997.52, "word": " بس", "probability": 0.848876953125}, {"start": 1997.52, "end": 1998.1, "word": " بدنا", "probability": 0.60296630859375}, {"start": 1998.1, "end": 1998.92, "word": " نثبت", "probability": 0.98486328125}, {"start": 1998.92, "end": 1999.1, "word": " ان", "probability": 0.49658203125}, {"start": 1999.1, "end": 1999.54, "word": " فيها", "probability": 0.91552734375}, {"start": 1999.54, "end": 1999.82, "word": " على", "probability": 0.38671875}, {"start": 1999.82, "end": 2000.98, "word": " الأقل", "probability": 0.9532877604166666}, {"start": 2000.98, "end": 2001.38, "word": " و", "probability": 0.406005859375}, {"start": 2001.38, "end": 2001.62, "word": " لو", "probability": 0.9638671875}, {"start": 2001.62, "end": 2002.0, "word": " zero", "probability": 0.461669921875}, {"start": 2002.0, "end": 2002.88, "word": " divisors", "probability": 0.773681640625}, {"start": 2002.88, "end": 2003.42, "word": " واحد", "probability": 0.98388671875}, {"start": 2003.42, "end": 2004.5, "word": " لكن", "probability": 0.62939453125}, {"start": 2004.5, "end": 2004.98, "word": " بعد", "probability": 0.85791015625}, {"start": 2004.98, "end": 2005.16, "word": " ما", "probability": 0.466064453125}, {"start": 2005.16, "end": 2005.54, "word": " أثبت", "probability": 0.8885498046875}, {"start": 2005.54, "end": 2006.02, "word": " هقولك", "probability": 0.6769205729166666}, {"start": 2006.02, "end": 2006.4, "word": " فيها", "probability": 0.9375}, {"start": 2006.4, "end": 2007.06, "word": " مالة", "probability": 0.6875}, {"start": 2007.06, "end": 2007.6, "word": " نهاية", "probability": 0.9036458333333334}, {"start": 2007.6, "end": 2007.88, "word": " من", "probability": 0.984375}, {"start": 2007.88, "end": 2008.08, "word": " ال", "probability": 0.8935546875}, {"start": 2008.08, "end": 2008.4, "word": " zero", "probability": 0.68115234375}, {"start": 2008.4, "end": 2009.5, "word": " divisors", "probability": 0.980224609375}, {"start": 2009.5, "end": 2010.52, "word": " طبعا", "probability": 0.80279541015625}, {"start": 2010.52, "end": 2011.02, "word": " because", "probability": 0.394287109375}, {"start": 2011.02, "end": 2011.02, "word": " it", "probability": 0.43701171875}, {"start": 2011.02, "end": 2011.26, "word": " is", "probability": 0.5546875}, {"start": 2011.26, "end": 2011.54, "word": " not", "probability": 0.9560546875}, {"start": 2011.54, "end": 2011.86, "word": " an", "probability": 0.81298828125}, {"start": 2011.86, "end": 2012.26, "word": " integral", "probability": 0.7958984375}, {"start": 2012.26, "end": 2012.88, "word": " domain", "probability": 0.9775390625}, {"start": 2012.88, "end": 2013.34, "word": " because", "probability": 0.77197265625}, {"start": 2013.34, "end": 2014.62, "word": " مثلا", "probability": 0.964111328125}, {"start": 2014.62, "end": 2016.16, "word": " تلاتة", "probability": 0.9136962890625}, {"start": 2016.16, "end": 2016.54, "word": " و", "probability": 0.6845703125}, {"start": 2016.54, "end": 2017.12, "word": " Zero", "probability": 0.40380859375}], "temperature": 1.0}, {"id": 70, "seek": 204343, "start": 2017.69, "end": 2043.43, "text": "و zero اربع موجودة في ال direct sum موجود صحيح او لا و لا صح؟ and لو ضربناهم في بعض كده ايش بتظهر؟ zero و zero كل عنصر معنى غير ضرب فيه direct sum يبقى طالع zero و zero كويس؟", "tokens": [2407, 4018, 1975, 25513, 3615, 3714, 29245, 23328, 3660, 8978, 2423, 2047, 2408, 3714, 29245, 23328, 20328, 5016, 1829, 5016, 1975, 2407, 20193, 4032, 20193, 20328, 5016, 22807, 293, 45164, 48812, 25513, 8315, 16095, 8978, 45030, 11242, 9122, 3215, 3224, 1975, 1829, 8592, 39894, 19913, 3224, 2288, 22807, 4018, 4032, 4018, 28242, 18871, 9381, 2288, 20449, 1863, 7578, 32771, 13546, 48812, 25513, 8978, 3224, 2047, 2408, 7251, 3555, 4587, 7578, 23032, 6027, 3615, 4018, 4032, 4018, 9122, 45865, 3794, 22807], "avg_logprob": -0.3433641975308642, "compression_ratio": 1.567251461988304, "no_speech_prob": 0.0, "words": [{"start": 2017.69, "end": 2018.17, "word": "و", "probability": 0.68017578125}, {"start": 2018.17, "end": 2019.11, "word": " zero", "probability": 0.10546875}, {"start": 2019.11, "end": 2019.89, "word": " اربع", "probability": 0.6556803385416666}, {"start": 2019.89, "end": 2020.49, "word": " موجودة", "probability": 0.9635009765625}, {"start": 2020.49, "end": 2020.59, "word": " في", "probability": 0.8935546875}, {"start": 2020.59, "end": 2020.73, "word": " ال", "probability": 0.61279296875}, {"start": 2020.73, "end": 2021.03, "word": " direct", "probability": 0.57080078125}, {"start": 2021.03, "end": 2021.51, "word": " sum", "probability": 0.86083984375}, {"start": 2021.51, "end": 2022.67, "word": " موجود", "probability": 0.764404296875}, {"start": 2022.67, "end": 2023.15, "word": " صحيح", "probability": 0.9410400390625}, {"start": 2023.15, "end": 2023.29, "word": " او", "probability": 0.473388671875}, {"start": 2023.29, "end": 2023.47, "word": " لا", "probability": 0.83544921875}, {"start": 2023.47, "end": 2023.59, "word": " و", "probability": 0.427490234375}, {"start": 2023.59, "end": 2023.85, "word": " لا", "probability": 0.8994140625}, {"start": 2023.85, "end": 2025.95, "word": " صح؟", "probability": 0.6142578125}, {"start": 2025.95, "end": 2026.75, "word": " and", "probability": 0.326171875}, {"start": 2026.75, "end": 2028.69, "word": " لو", "probability": 0.91357421875}, {"start": 2028.69, "end": 2029.57, "word": " ضربناهم", "probability": 0.9227294921875}, {"start": 2029.57, "end": 2029.85, "word": " في", "probability": 0.97705078125}, {"start": 2029.85, "end": 2030.73, "word": " بعض", "probability": 0.996337890625}, {"start": 2030.73, "end": 2032.21, "word": " كده", "probability": 0.87060546875}, {"start": 2032.21, "end": 2032.27, "word": " ايش", "probability": 0.715087890625}, {"start": 2032.27, "end": 2033.25, "word": " بتظهر؟", "probability": 0.7681640625}, {"start": 2033.25, "end": 2034.75, "word": " zero", "probability": 0.319091796875}, {"start": 2034.75, "end": 2035.11, "word": " و", "probability": 0.5751953125}, {"start": 2035.11, "end": 2035.59, "word": " zero", "probability": 0.86083984375}, {"start": 2035.59, "end": 2036.41, "word": " كل", "probability": 0.82275390625}, {"start": 2036.41, "end": 2037.01, "word": " عنصر", "probability": 0.9249674479166666}, {"start": 2037.01, "end": 2037.59, "word": " معنى", "probability": 0.7933756510416666}, {"start": 2037.59, "end": 2038.03, "word": " غير", "probability": 0.995361328125}, {"start": 2038.03, "end": 2038.55, "word": " ضرب", "probability": 0.732666015625}, {"start": 2038.55, "end": 2039.01, "word": " فيه", "probability": 0.6295166015625}, {"start": 2039.01, "end": 2039.39, "word": " direct", "probability": 0.58984375}, {"start": 2039.39, "end": 2039.85, "word": " sum", "probability": 0.9609375}, {"start": 2039.85, "end": 2040.61, "word": " يبقى", "probability": 0.7850341796875}, {"start": 2040.61, "end": 2040.97, "word": " طالع", "probability": 0.6791178385416666}, {"start": 2040.97, "end": 2041.45, "word": " zero", "probability": 0.39697265625}, {"start": 2041.45, "end": 2041.81, "word": " و", "probability": 0.94189453125}, {"start": 2041.81, "end": 2042.33, "word": " zero", "probability": 0.908203125}, {"start": 2042.33, "end": 2043.43, "word": " كويس؟", "probability": 0.7952880859375}], "temperature": 1.0}, {"id": 71, "seek": 206971, "start": 2043.51, "end": 2069.71, "text": "حصل ضرف two elements لا يساوي كل واحد يوم الـ zero وطلع بـ zero يبقى هذا معناه zero divisors هنا بدي أعطيك انه تلاتة و zero and zero أربعة are zero divisors يبقى هنا", "tokens": [5016, 36520, 48812, 28480, 732, 4959, 20193, 7251, 3794, 995, 45865, 28242, 36764, 24401, 7251, 20498, 2423, 39184, 4018, 4032, 9566, 1211, 3615, 4724, 39184, 4018, 7251, 3555, 4587, 7578, 23758, 3714, 3615, 8315, 3224, 4018, 25974, 830, 34105, 4724, 16254, 5551, 3615, 9566, 1829, 4117, 16472, 3224, 6055, 1211, 9307, 3660, 4032, 4018, 293, 4018, 5551, 25513, 27884, 366, 4018, 25974, 830, 7251, 3555, 4587, 7578, 34105], "avg_logprob": -0.37115036750185315, "compression_ratio": 1.4814814814814814, "no_speech_prob": 0.0, "words": [{"start": 2043.51, "end": 2044.19, "word": "حصل", "probability": 0.590087890625}, {"start": 2044.19, "end": 2044.63, "word": " ضرف", "probability": 0.706787109375}, {"start": 2044.63, "end": 2044.99, "word": " two", "probability": 0.135498046875}, {"start": 2044.99, "end": 2045.91, "word": " elements", "probability": 0.87890625}, {"start": 2045.91, "end": 2046.29, "word": " لا", "probability": 0.5634765625}, {"start": 2046.29, "end": 2047.15, "word": " يساوي", "probability": 0.9100341796875}, {"start": 2047.15, "end": 2047.57, "word": " كل", "probability": 0.7216796875}, {"start": 2047.57, "end": 2047.95, "word": " واحد", "probability": 0.994140625}, {"start": 2047.95, "end": 2048.33, "word": " يوم", "probability": 0.77587890625}, {"start": 2048.33, "end": 2048.59, "word": " الـ", "probability": 0.5626220703125}, {"start": 2048.59, "end": 2048.71, "word": " zero", "probability": 0.437255859375}, {"start": 2048.71, "end": 2049.23, "word": " وطلع", "probability": 0.67303466796875}, {"start": 2049.23, "end": 2049.53, "word": " بـ", "probability": 0.680908203125}, {"start": 2049.53, "end": 2049.77, "word": " zero", "probability": 0.80419921875}, {"start": 2049.77, "end": 2050.53, "word": " يبقى", "probability": 0.9058837890625}, {"start": 2050.53, "end": 2050.81, "word": " هذا", "probability": 0.8447265625}, {"start": 2050.81, "end": 2051.27, "word": " معناه", "probability": 0.7431640625}, {"start": 2051.27, "end": 2051.77, "word": " zero", "probability": 0.4560546875}, {"start": 2051.77, "end": 2053.29, "word": " divisors", "probability": 0.9208984375}, {"start": 2053.29, "end": 2054.17, "word": " هنا", "probability": 0.58935546875}, {"start": 2054.17, "end": 2054.69, "word": " بدي", "probability": 0.6094970703125}, {"start": 2054.69, "end": 2055.41, "word": " أعطيك", "probability": 0.70712890625}, {"start": 2055.41, "end": 2056.57, "word": " انه", "probability": 0.427978515625}, {"start": 2056.57, "end": 2057.25, "word": " تلاتة", "probability": 0.81304931640625}, {"start": 2057.25, "end": 2057.47, "word": " و", "probability": 0.931640625}, {"start": 2057.47, "end": 2058.05, "word": " zero", "probability": 0.5009765625}, {"start": 2058.05, "end": 2059.09, "word": " and", "probability": 0.91357421875}, {"start": 2059.09, "end": 2060.31, "word": " zero", "probability": 0.37353515625}, {"start": 2060.31, "end": 2061.37, "word": " أربعة", "probability": 0.7666015625}, {"start": 2061.37, "end": 2062.35, "word": " are", "probability": 0.84521484375}, {"start": 2062.35, "end": 2064.63, "word": " zero", "probability": 0.71435546875}, {"start": 2064.63, "end": 2066.53, "word": " divisors", "probability": 0.970458984375}, {"start": 2066.53, "end": 2069.11, "word": " يبقى", "probability": 0.982177734375}, {"start": 2069.11, "end": 2069.71, "word": " هنا", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 72, "seek": 210183, "start": 2072.55, "end": 2101.83, "text": "plus the direct sum is not an integral domain لو واحدة ثانية أخدت رقمين تانية أخدت واحد وزير وزير واتنين in general بدي أخد M وزير وزير وN", "tokens": [18954, 264, 2047, 2408, 307, 406, 364, 11573, 9274, 45164, 36764, 24401, 3660, 38637, 7649, 10632, 5551, 9778, 3215, 2655, 12602, 4587, 2304, 9957, 6055, 7649, 10632, 5551, 9778, 3215, 2655, 36764, 24401, 4032, 11622, 13546, 4032, 11622, 13546, 4032, 9307, 1863, 9957, 294, 2674, 4724, 16254, 5551, 9778, 3215, 376, 4032, 11622, 13546, 4032, 11622, 13546, 4032, 45], "avg_logprob": -0.4127604136864344, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 2072.55, "end": 2073.13, "word": "plus", "probability": 0.051422119140625}, {"start": 2073.13, "end": 2073.63, "word": " the", "probability": 0.3681640625}, {"start": 2073.63, "end": 2074.21, "word": " direct", "probability": 0.8076171875}, {"start": 2074.21, "end": 2074.69, "word": " sum", "probability": 0.9697265625}, {"start": 2074.69, "end": 2075.67, "word": " is", "probability": 0.73388671875}, {"start": 2075.67, "end": 2076.95, "word": " not", "probability": 0.91552734375}, {"start": 2076.95, "end": 2078.49, "word": " an", "probability": 0.72998046875}, {"start": 2078.49, "end": 2079.93, "word": " integral", "probability": 0.84619140625}, {"start": 2079.93, "end": 2081.57, "word": " domain", "probability": 0.89404296875}, {"start": 2081.57, "end": 2085.59, "word": " لو", "probability": 0.0965576171875}, {"start": 2085.59, "end": 2086.99, "word": " واحدة", "probability": 0.694091796875}, {"start": 2086.99, "end": 2087.33, "word": " 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{"start": 2679.65, "end": 2680.15, "word": " وفي", "probability": 0.8046875}, {"start": 2680.15, "end": 2681.03, "word": " idem", "probability": 0.4273681640625}, {"start": 2681.03, "end": 2681.65, "word": " potent", "probability": 0.87255859375}, {"start": 2681.65, "end": 2682.63, "word": " element", "probability": 0.96484375}, {"start": 2682.63, "end": 2683.95, "word": " فأرناكوا", "probability": 0.5310465494791666}, {"start": 2683.95, "end": 2684.11, "word": " هذا", "probability": 0.67724609375}, {"start": 2684.11, "end": 2684.23, "word": " اللي", "probability": 0.7841796875}, {"start": 2684.23, "end": 2684.69, "word": " ماكناش", "probability": 0.8229166666666666}, {"start": 2684.69, "end": 2685.19, "word": " نعرفهم", "probability": 0.9041748046875}, {"start": 2685.19, "end": 2685.37, "word": " في", "probability": 0.8974609375}, {"start": 2685.37, "end": 2685.51, "word": " ال", "probability": 0.79541015625}, {"start": 2685.51, "end": 2686.01, "word": " group", "probability": 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واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل واحد على كل", "tokens": [14407, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 36764, 24401, 15844, 28242, 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"temperature": 1.0}, {"id": 102, "seek": 297385, "start": 2947.17, "end": 2973.85, "text": "زد سكس زد سكس is not a field because اتنين unit يا بنات يعني بقدر الاقي رقم في زد ستة اضربه في اتنين يعطيني الواحد الصحيح", "tokens": [11622, 3215, 8608, 4117, 3794, 30767, 3215, 8608, 4117, 3794, 307, 406, 257, 2519, 570, 1975, 2655, 1863, 9957, 4985, 35186, 4724, 8315, 2655, 37495, 22653, 4724, 28543, 2288, 1975, 15040, 38436, 12602, 4587, 2304, 8978, 30767, 3215, 8608, 2655, 3660, 1975, 11242, 25513, 3224, 8978, 1975, 2655, 1863, 9957, 37495, 9566, 1829, 22653, 2423, 14407, 24401, 31767, 5016, 1829, 5016], "avg_logprob": -0.26058466732501984, "compression_ratio": 1.4338235294117647, "no_speech_prob": 0.0, "words": [{"start": 2947.17, "end": 2948.15, "word": "زد", "probability": 0.3341064453125}, {"start": 2948.15, "end": 2949.15, "word": " سكس", "probability": 0.5956217447916666}, {"start": 2949.15, "end": 2951.05, "word": " زد", "probability": 0.60235595703125}, {"start": 2951.05, "end": 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ستة طبعا لأ لأن اتنية في التلاتة في ستة Zero Divisor و Zero Divisor منفعش يكون له معاكس خاصة في ZN لأن في ZN اي element يا اما unit يا اما Zero Divisor يبقى هنا اتنية موجودة في Z6 and اتنية is a", "tokens": [10721, 2407, 2423, 14407, 24401, 3714, 2407, 16254, 43761, 8608, 2655, 3660, 23032, 3555, 3615, 995, 5296, 10721, 5296, 33456, 1975, 2655, 1863, 10632, 8978, 16712, 1211, 9307, 3660, 8978, 8608, 2655, 3660, 17182, 9886, 271, 284, 4032, 17182, 9886, 271, 284, 3714, 1863, 5172, 3615, 8592, 7251, 30544, 46740, 20449, 995, 4117, 3794, 16490, 33546, 3660, 8978, 1176, 45, 5296, 33456, 8978, 1176, 45, 1975, 1829, 4478, 35186, 1975, 15042, 4985, 35186, 1975, 15042, 17182, 9886, 271, 284, 7251, 3555, 4587, 7578, 34105, 1975, 2655, 1863, 10632, 3714, 29245, 23328, 3660, 8978, 1176, 21, 293, 1975, 2655, 1863, 10632, 307, 257], "avg_logprob": -0.33191748730187276, "compression_ratio": 1.6806282722513088, "no_speech_prob": 0.0, "words": [{"start": 2974.91, "end": 2975.21, "word": "أو", 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field", "tokens": [32226, 25974, 284, 1670, 1975, 2655, 1863, 9957, 8978, 6055, 1211, 9307, 3660, 4724, 1829, 3794, 45865, 4018, 1072, 13455, 430, 37495, 22653, 23758, 19446, 31439, 6225, 8592, 7649, 8978, 3224, 611, 1176, 1072, 13455, 286, 307, 406, 257, 2519], "avg_logprob": -0.32679115853658536, "compression_ratio": 1.153225806451613, "no_speech_prob": 0.0, "words": [{"start": 3004.15, "end": 3005.09, "word": "zero", "probability": 0.47265625}, {"start": 3005.09, "end": 3008.29, "word": " divisor", "probability": 0.927490234375}, {"start": 3008.29, "end": 3010.63, "word": " since", "probability": 0.625}, {"start": 3010.63, "end": 3012.79, "word": " اتنين", "probability": 0.879638671875}, {"start": 3012.79, "end": 3013.47, "word": " في", "probability": 0.91552734375}, {"start": 3013.47, "end": 3014.65, "word": " تلاتة", "probability": 0.907958984375}, {"start": 3014.65, "end": 3015.71, "word": " بيسوي", "probability": 0.822021484375}, {"start": 3015.71, "end": 3016.67, "word": " 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{"start": 3076.05, "end": 3076.63, "word": " a", "probability": 0.822265625}, {"start": 3076.63, "end": 3077.15, "word": " field", "probability": 0.822265625}, {"start": 3077.15, "end": 3078.97, "word": " لو", "probability": 0.465087890625}, {"start": 3078.97, "end": 3079.29, "word": " كان", "probability": 0.990234375}, {"start": 3079.29, "end": 3079.49, "word": " ال", "probability": 0.96630859375}, {"start": 3079.49, "end": 3079.75, "word": " R", "probability": 0.9541015625}, {"start": 3079.75, "end": 3079.99, "word": " is", "probability": 0.89990234375}, {"start": 3079.99, "end": 3080.27, "word": " a", "probability": 0.978515625}, {"start": 3080.27, "end": 3080.93, "word": " field", "probability": 0.95556640625}, {"start": 3080.93, "end": 3081.65, "word": " and", "probability": 0.9189453125}, {"start": 3081.65, "end": 3083.27, "word": " ال", "probability": 0.6708984375}, {"start": 3083.27, "end": 3083.77, "word": " S", "probability": 0.9814453125}, {"start": 3083.77, "end": 3085.01, 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"probability": 0.1639404296875}, {"start": 3091.33, "end": 3091.57, "word": " it", "probability": 0.95947265625}, {"start": 3091.57, "end": 3091.79, "word": " is", "probability": 0.95654296875}, {"start": 3091.79, "end": 3092.31, "word": " not", "probability": 0.958984375}, {"start": 3092.31, "end": 3093.33, "word": " then", "probability": 0.70166015625}, {"start": 3093.33, "end": 3094.81, "word": " it", "probability": 0.9609375}, {"start": 3094.81, "end": 3095.81, "word": " is", "probability": 0.96484375}, {"start": 3095.81, "end": 3096.99, "word": " not", "probability": 0.9423828125}, {"start": 3096.99, "end": 3098.77, "word": " necessarily", "probability": 0.83251953125}, {"start": 3098.77, "end": 3102.07, "word": " it", "probability": 0.84765625}, {"start": 3102.07, "end": 3104.37, "word": " is", "probability": 0.96240234375}, {"start": 3104.37, "end": 3104.75, "word": " not", "probability": 0.95703125}, {"start": 3104.75, "end": 3105.73, "word": " necessarily", "probability": 0.85791015625}, {"start": 3105.73, "end": 3106.73, "word": " ال", "probability": 0.8701171875}, {"start": 3106.73, "end": 3107.23, "word": " S", "probability": 0.69775390625}, {"start": 3107.23, "end": 3108.99, "word": " is", "probability": 0.896484375}, {"start": 3108.99, "end": 3109.63, "word": " a", "probability": 0.69140625}, {"start": 3109.63, "end": 3110.03, "word": " theme", "probability": 0.311767578125}, {"start": 3110.03, "end": 3112.37, "word": " for", "probability": 0.865234375}, {"start": 3112.37, "end": 3113.15, "word": " example", "probability": 0.970703125}, {"start": 3113.15, "end": 3115.43, "word": " for", "probability": 0.440673828125}, {"start": 3115.43, "end": 3117.29, "word": " example", "probability": 0.9560546875}, {"start": 3117.29, "end": 3118.87, "word": " كان", "probability": 0.30859375}, {"start": 3118.87, "end": 3119.41, "word": " يخال", "probability": 0.7146809895833334}, {"start": 3119.41, "end": 3119.73, "word": " على", "probability": 0.78515625}, {"start": 3119.73, "end": 3120.29, "word": " ذلك", "probability": 0.982421875}], "temperature": 1.0}, {"id": 108, "seek": 314940, "start": 3121.9, "end": 3149.4, "text": "sc set of complex number is a field but ولكن is a field but z of I is a sub ring of", "tokens": [4417, 992, 295, 3997, 1230, 307, 257, 2519, 457, 35525, 19452, 307, 257, 2519, 457, 710, 295, 286, 307, 257, 1422, 4875, 295], "avg_logprob": -0.3759765674670537, "compression_ratio": 1.1756756756756757, "no_speech_prob": 0.0, "words": [{"start": 3121.9, "end": 3123.3, "word": "sc", "probability": 0.1060791015625}, {"start": 3123.3, "end": 3124.26, "word": " set", "probability": 0.214599609375}, {"start": 3124.26, "end": 3124.56, "word": " of", "probability": 0.77685546875}, {"start": 3124.56, "end": 3125.16, "word": " complex", "probability": 0.89794921875}, {"start": 3125.16, "end": 3125.76, "word": " number", "probability": 0.47900390625}, {"start": 3125.76, "end": 3127.06, "word": " is", "probability": 0.8447265625}, {"start": 3127.06, "end": 3128.68, "word": " a", "probability": 0.919921875}, {"start": 3128.68, "end": 3129.56, "word": " field", "probability": 0.90576171875}, {"start": 3129.56, "end": 3132.46, "word": " but", "probability": 0.76611328125}, {"start": 3132.46, "end": 3134.48, "word": " ولكن", "probability": 0.62353515625}, {"start": 3134.48, "end": 3135.6, "word": " is", "probability": 0.66650390625}, {"start": 3135.6, "end": 3136.1, "word": " a", "probability": 0.9736328125}, {"start": 3136.1, "end": 3136.54, "word": " field", "probability": 0.95458984375}, {"start": 3136.54, "end": 3137.98, "word": " but", "probability": 0.900390625}, {"start": 3137.98, "end": 3139.44, "word": " z", "probability": 0.88916015625}, {"start": 3139.44, "end": 3140.8, "word": " of", "probability": 0.9013671875}, {"start": 3140.8, "end": 3141.56, "word": " I", "probability": 0.57275390625}, {"start": 3141.56, "end": 3144.4, "word": " is", "probability": 0.8857421875}, {"start": 3144.4, "end": 3145.92, "word": " a", "probability": 0.9423828125}, {"start": 3145.92, "end": 3146.7, "word": " sub", "probability": 0.814453125}, {"start": 3146.7, "end": 3148.12, "word": " ring", "probability": 0.791015625}, {"start": 3148.12, "end": 3149.4, "word": " of", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 109, "seek": 317161, "start": 3149.85, "end": 3171.61, "text": "الـ Z of I برنامج قبل قليل is ما .. يعني مالجيش عنصر يلو ما كوز", "tokens": [6027, 39184, 1176, 295, 286, 4724, 2288, 8315, 2304, 7435, 12174, 36150, 12174, 20292, 1211, 307, 19446, 4386, 37495, 22653, 3714, 6027, 7435, 1829, 8592, 18871, 9381, 2288, 7251, 1211, 2407, 19446, 9122, 2407, 11622], "avg_logprob": -0.7139756944444444, "compression_ratio": 1.10752688172043, "no_speech_prob": 0.0, "words": [{"start": 3149.85, "end": 3150.41, "word": "الـ", "probability": 0.256927490234375}, {"start": 3150.41, "end": 3150.69, "word": " Z", "probability": 0.2822265625}, {"start": 3150.69, "end": 3157.61, "word": " of", "probability": 0.2763671875}, {"start": 3157.61, "end": 3158.27, "word": " I", "probability": 0.802734375}, {"start": 3158.27, "end": 3159.55, "word": " برنامج", "probability": 0.742724609375}, {"start": 3159.55, "end": 3159.87, "word": " قبل", "probability": 0.389617919921875}, {"start": 3159.87, "end": 3161.21, "word": " قليل", "probability": 0.7632649739583334}, {"start": 3161.21, "end": 3161.81, "word": " is", "probability": 0.2166748046875}, {"start": 3161.81, "end": 3162.85, "word": " ما", "probability": 0.32763671875}, {"start": 3162.85, "end": 3164.57, "word": " ..", "probability": 0.225341796875}, {"start": 3164.57, "end": 3168.27, "word": " يعني", "probability": 0.813232421875}, {"start": 3168.27, "end": 3168.97, "word": " مالجيش", "probability": 0.686328125}, {"start": 3168.97, "end": 3169.69, "word": " عنصر", "probability": 0.7872721354166666}, {"start": 3169.69, "end": 3170.55, "word": " يلو", "probability": 0.554443359375}, {"start": 3170.55, "end": 3170.79, "word": " ما", "probability": 0.325927734375}, {"start": 3170.79, "end": 3171.61, "word": " كوز", "probability": 0.50732421875}], "temperature": 1.0}, {"id": 110, "seek": 318902, "start": 3178.12, "end": 3189.02, "text": "على هيك انتهينا من المحاضرة و بنكمل ان شاء الله المرة الماضية، المرة القادمة ان شاء الله بنكمل نفس الموضوع", "tokens": [3615, 23942, 39896, 4117, 16472, 47395, 1829, 8315, 9154, 9673, 5016, 46958, 25720, 4032, 44945, 24793, 1211, 16472, 13412, 16606, 21984, 9673, 25720, 9673, 46958, 10632, 12399, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 8717, 36178, 9673, 2407, 11242, 45367], "avg_logprob": -0.11480978487626366, "compression_ratio": 1.7706422018348624, "no_speech_prob": 0.0, "words": [{"start": 3178.12, "end": 3178.48, "word": "على", "probability": 0.5638427734375}, {"start": 3178.48, "end": 3178.76, "word": " هيك", "probability": 0.874267578125}, {"start": 3178.76, "end": 3179.32, "word": " انتهينا", "probability": 0.9293212890625}, {"start": 3179.32, "end": 3179.46, "word": " من", "probability": 0.97900390625}, {"start": 3179.46, "end": 3180.22, "word": " المحاضرة", "probability": 0.9879150390625}, {"start": 3180.22, "end": 3180.72, "word": " و", "probability": 0.50390625}, {"start": 3180.72, "end": 3181.54, "word": " بنكمل", "probability": 0.9152018229166666}, {"start": 3181.54, "end": 3181.84, "word": " ان", "probability": 0.78564453125}, {"start": 3181.84, "end": 3182.16, "word": " شاء", "probability": 0.970703125}, {"start": 3182.16, "end": 3182.64, "word": " الله", "probability": 0.9541015625}, {"start": 3182.64, "end": 3183.8, "word": " المرة", "probability": 0.969970703125}, {"start": 3183.8, "end": 3185.42, "word": " الماضية،", "probability": 0.8857421875}, {"start": 3185.42, "end": 3185.86, "word": " المرة", "probability": 0.982666015625}, {"start": 3185.86, "end": 3186.6, "word": " القادمة", "probability": 0.92822265625}, {"start": 3186.6, "end": 3187.1, "word": " ان", "probability": 0.44775390625}, {"start": 3187.1, "end": 3187.32, "word": " شاء", "probability": 0.98291015625}, {"start": 3187.32, "end": 3187.4, "word": " الله", "probability": 0.94970703125}, {"start": 3187.4, "end": 3187.94, "word": " بنكمل", "probability": 0.96875}, {"start": 3187.94, "end": 3188.4, "word": " نفس", "probability": 0.996337890625}, {"start": 3188.4, "end": 3189.02, "word": " الموضوع", "probability": 0.9942626953125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3189.167875, "duration_after_vad": 3075.084374999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QpvkLUWn3LA.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QpvkLUWn3LA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1d5c655f1408d321d806243ece5b3dee91b33c34
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QpvkLUWn3LA.srt
@@ -0,0 +1,1361 @@
+1
+00:00:21,210 --> 00:00:24,870
+بسم الله الرحمن الرحيم. المرة اللي فاتت أنهينا
+
+2
+00:00:24,870 --> 00:00:29,270
+chapter. أتناشى وطلبتوا كم من سؤال، تتعرفوا عليهم
+
+3
+00:00:29,270 --> 00:00:36,070
+بالبيت، مشان يعرف هل يعني الفهم  ثبت عندكوا والله
+
+4
+00:00:36,070 --> 00:00:40,190
+كيف يعني؟ صرتوا بتعرفوا تشتغلوا في الـ things ولا لأ؟
+
+5
+00:00:40,190 --> 00:00:46,570
+طلبتوا أول سؤال من هذه الأسئلة، اللي هو سؤال اثنين.
+
+6
+00:00:46,570 --> 00:00:56,990
+يبقى اليوم عندنا exercises on chapter 12. أول سؤال
+
+7
+00:00:56,990 --> 00:01:05,310
+هناك، وسؤال اتنين. سؤال اتنين بيقول لي: الـ ring الـ
+
+8
+00:01:05,310 --> 00:01:15,610
+ring اللي هو صفر، اتنين، أربعة، ستة، ثمانية، under اللي
+
+9
+00:01:15,610 --> 00:01:17,450
+هو addition
+
+10
+00:01:20,780 --> 00:01:30,160
+and multiplication. multiplication
+
+11
+00:01:30,160 --> 00:01:44,100
+modulo كده modulo عشرة. modulo عشرة has a unit. has
+
+12
+00:01:44,100 --> 00:01:54,180
+a unit. You gonna find it. fine. إيه؟ حسب فيها يا
+
+13
+00:01:54,180 --> 00:01:59,680
+بنان؟ جدعاش طالع؟ ستة. ممتاز. يبقى الستة هو الـ unity
+
+14
+00:01:59,680 --> 00:02:04,400
+لأن الستة لو ضربته في أي عنصر من العناصر اللي
+
+15
+00:02:04,400 --> 00:02:10,320
+قدامي هذي، بطلع نفس إيه؟ بطلع نفس الـ .. بطلع نفس الـ ..
+
+16
+00:02:10,320 --> 00:02:14,920
+نفس العنصر اللي موجود في الـ ring. يبقى بروح بقوله
+
+17
+00:02:14,920 --> 00:02:19,040
+هي الحل. الـ unity
+
+18
+00:02:20,620 --> 00:02:30,280
+is ستة. Because for example, for example، لو جيت قول
+
+19
+00:02:30,280 --> 00:02:39,040
+ستة في أربعة. ستة في أربعة، بـ ٢٠ بنشيل منهم
+
+20
+00:02:39,040 --> 00:02:46,040
+عشرة، وعشرة بيظل كده؟ بيظل أربعة. نفس العنصر. وهنا
+
+21
+00:02:46,040 --> 00:02:53,720
+and so on، وهكذا بالنسبة لبقية العناصر. ستة في
+
+22
+00:02:53,720 --> 00:02:59,280
+ثمانية، بستة. ستة في اتنين، بستة. ستة في أربعة، بستة. وهكذا.
+
+23
+00:02:59,280 --> 00:03:03,900
+هذا كان السؤال رقم اتنين. بعدين قلنا بأن
+
+24
+00:03:03,900 --> 00:03:09,820
+السؤال تلاتة، بيقول: الوصول الـ sub ring من رجعه بانتهاء
+
+25
+00:03:09,820 --> 00:03:20,310
+يرجع. السؤال تلاتة، بدنا sub rings of مجموعة الأعداد
+
+26
+00:03:20,310 --> 00:03:26,570
+الصحية. يبقى أي sub ring من مجموعة الأعداد الصحية
+
+27
+00:03:26,570 --> 00:03:31,230
+بتقدر تجيبولي sub ring واحدة، نفسها. نفسها. دي الـ
+
+28
+00:03:31,230 --> 00:03:38,110
+trivial case. نفسها.
+
+29
+00:03:38,110 --> 00:03:39,890
+دي الـ trivial case. نفسها نفسها نفسها نفسها نفسها
+
+30
+00:03:39,890 --> 00:03:40,730
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها
+
+31
+00:03:40,730 --> 00:03:42,250
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها
+
+32
+00:03:42,250 --> 00:03:44,150
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها
+
+33
+00:03:44,150 --> 00:03:46,810
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها. نـ
+
+34
+00:03:47,000 --> 00:03:57,240
+subring of Z is in the form في الشكل التالي in Z، و
+
+35
+00:03:57,240 --> 00:04:10,400
+Z is a positive integer. يبقى هذا الشكل العام لـ الـ
+
+36
+00:04:10,400 --> 00:04:17,880
+in Z. بنقدر نثبتها بكل بساطة، والبساطة اللي نقدر
+
+37
+00:04:17,880 --> 00:04:24,700
+نشتغلها. حط الـ .. كيف؟ أخدناها قبل ذلك، صحيح؟ أخدناها
+
+38
+00:04:24,700 --> 00:04:31,780
+كمي ذلك. تمام. يبقى ده سؤال تلاتة. سؤال تسعة عشر سؤال
+
+39
+00:04:31,780 --> 00:04:36,540
+تسعة عشر اللي هو بتتكلم عن الـ center تبع الـ ring.
+
+40
+00:04:36,540 --> 00:04:46,150
+يبقى سؤال تسعة عشر بيقول: الـ R ring، والـ center تبع الـ
+
+41
+00:04:46,150 --> 00:04:55,890
+ring هو عبارة عن مجموعة ليه كل العناصر، كل
+
+42
+00:04:55,890 --> 00:05:04,250
+العناصر X اللي موجودة في الـ ring R، بحيث أن الـ AX
+
+43
+00:05:04,250 --> 00:05:12,390
+بده يساوي XA، لكل الـ A اللي موجودة في الـ ring R.
+
+44
+00:05:12,660 --> 00:05:19,080
+بنثبت إن الـ Center هذا عبارة عن sub-group. طيب
+
+45
+00:05:19,080 --> 00:05:24,360
+السؤال هذا شبيه بالـ Center تبع الـ group، كان معانا
+
+46
+00:05:24,360 --> 00:05:29,380
+سؤال بيقول: اثبت إن الـ Center تبع الـ group هو
+
+47
+00:05:29,380 --> 00:05:32,540
+عبارة
+
+48
+00:05:32,540 --> 00:05:38,300
+عن sub-group من الـ group itself. وهذا أثبتناه في جبر
+
+49
+00:05:38,300 --> 00:05:42,800
+حديث واحد، نفس الكلام في جبر حديث اتنين، بس هنا
+
+50
+00:05:42,800 --> 00:05:48,040
+كانت two conditions، هنا بنخليهم جديد، بنخليهم
+
+51
+00:05:48,040 --> 00:05:54,860
+تلاتة، يبقى مشان نثبت هذا solution،
+
+52
+00:05:54,860 --> 00:05:58,560
+في حد فيكوا أثبت هذا الكلام يا بنات؟ هي واحدة، في
+
+53
+00:05:58,560 --> 00:06:02,780
+غير تنتين، تلاتة، اه كويس، يعني على كل اتحال،
+
+54
+00:06:02,780 --> 00:06:07,740
+خمسين في المئة. مليعطيب، لكن لو رجعتي للـ group كان
+
+55
+00:06:07,740 --> 00:06:12,580
+صارت النتيجة مائة بالمائة، وليس خمسين بالمائة. خمسين
+
+56
+00:06:12,580 --> 00:06:17,460
+بالمائة، بعتبرها نتيجة مش نافعة إلا تتعدى الستين
+
+57
+00:06:17,460 --> 00:06:23,820
+على الأقل. طيب هي التعريف قدامي قبل ما نبدأ. التعريف
+
+58
+00:06:23,820 --> 00:06:29,520
+بدي أعرف مين هم بالضبط عناصر الـ center. بقول: أه
+
+59
+00:06:29,520 --> 00:06:35,010
+الآن، جيت على الـ ring فيها عناصر، جد عددكوا مثلا. كويس.
+
+60
+00:06:35,010 --> 00:06:40,250
+عشرين طالبة، تمام؟ بتعتبر عند رنق بعشرين أنصار
+
+61
+00:06:40,250 --> 00:06:45,510
+ماسكت الأنصار الأول من اليمين، والله من الشمال
+
+62
+00:06:45,510 --> 00:06:50,730
+أعطاني نفسي النتيجة عند ما ضربته في جميع عناصر الـ
+
+63
+00:06:50,730 --> 00:06:55,530
+ring. تمام؟ لقيته إيش؟ commutative مع جميع العنصر
+
+64
+00:06:55,530 --> 00:06:58,890
+قلت له: أيه وأنت كويس، اقعد عشرة جامعة. ماسكت
+
+65
+00:06:58,890 --> 00:07:03,660
+الأنصار التاني، لقيته ما هوش commutative مع جميع
+
+66
+00:07:03,660 --> 00:07:08,480
+العناصر، قلت له: أنت صفّع، شجع، ما أنت مش لازم. جينا للي
+
+67
+00:07:08,480 --> 00:07:13,080
+بعده، إزاي؟ ولي بعده، اللي بعده. لقيته commutative مع
+
+68
+00:07:13,080 --> 00:07:16,500
+جميع عناصر الـ ring. قلنا له: أنت كويس، صفّع أنصافك
+
+69
+00:07:16,500 --> 00:07:22,880
+الأولان. وهكذا. لقيت مثلاً خمس ست عناصر commutes مع
+
+70
+00:07:22,880 --> 00:07:29,360
+جميع عناصر من الـ ring. بالاستثناء، يبقى إن حدث ذلك
+
+71
+00:07:29,360 --> 00:07:34,660
+بقول الستة عناصر هدول، بيكونوا لي من؟ بيكونوا لي الـ sub
+
+72
+00:07:34,660 --> 00:07:39,180
+ring؟ هذا اللي عايزينه بتفتح. إذا الـ synth of the
+
+73
+00:07:39,180 --> 00:07:47,940
+ring are كل العناصر X اللي موجودة في R، بحيث أن AX
+
+74
+00:07:47,940 --> 00:07:56,320
+يساوي XA، لجميع الـ A اللي موجودة في R. يبقى العنصر X
+
+75
+00:07:56,320 --> 00:08:03,560
+اللي commutes مع جميع عناصر R بلا استثناء. كويس.
+
+76
+00:08:03,560 --> 00:08:09,960
+يبقى أنا هدعي أن الـ center هذا is non-empty. ليش؟
+
+77
+00:08:09,960 --> 00:08:16,260
+إن على الأقل الـ zero موجود فيه. يبقى هنا الـ center
+
+78
+00:08:16,260 --> 00:08:21,660
+تبع الـ R is non-empty.
+
+79
+00:08:24,870 --> 00:08:31,530
+because إن zero في الـ .. الـ zero في الـ .. أو الـ
+
+80
+00:08:31,530 --> 00:08:38,970
+الـ .. الـ A مين ما كان يكون. لأن الـ A في الـ zero بتساوي
+
+81
+00:08:38,970 --> 00:08:44,870
+الـ zero في A بتساوي الـ zero. هذا معناه أن الـ zero
+
+82
+00:08:44,870 --> 00:08:51,830
+موجود في الـ center تبع الـ ring. بعد إيه؟ بدي أفترض
+
+83
+00:08:51,830 --> 00:08:57,090
+أن عندي عنصرين موجودات في الـ Center. النقطة
+
+84
+00:08:57,090 --> 00:09:01,930
+الثانية، هذه كانت النقطة الأولى. النقطة الثانية، بدي
+
+85
+00:09:01,930 --> 00:09:09,290
+آخذ عنصرين X و Y موجودات في الـ Center تبع الـ ring.
+
+86
+00:09:09,290 --> 00:09:19,070
+الآن، معنى هذا الكلام أن الـ AX بده يساوي XA. وفي نفس
+
+87
+00:09:19,070 --> 00:09:25,510
+الوقت، الـ A و الـ Y بده يساوي الـ YA. إذا والله
+
+88
+00:09:25,510 --> 00:09:32,150
+قدرنا نثبت إن الـ X ناقص الـ Y موجودة في الـ center.
+
+89
+00:09:32,150 --> 00:09:38,530
+بيكون خلاص. القضية هذه، طبقناها. الـ X ناقص الـ Y بمعنى
+
+90
+00:09:38,530 --> 00:09:45,190
+أن الـ A في الـ X ناقص الـ Y بده يساوي الـ X ناقص الـ
+
+91
+00:09:45,190 --> 00:09:53,050
+Y في الـ A. بصير الـ X ناقص الـ Y مع كل الـ A الموجودة في
+
+92
+00:09:53,050 --> 00:10:00,590
+الـ R. إذا خليني آخذ الـ A في X ناقص الـ Y، أنطيع
+
+93
+00:10:00,590 --> 00:10:06,670
+الناتج X ناقص الـ Y مضروباً في A، بتم المطلوب. يبقى
+
+94
+00:10:06,670 --> 00:10:14,110
+بناء عليه، هذا سيكون X ناقص الـ AY. الـ distributive
+
+95
+00:10:14,110 --> 00:10:21,760
+law. أنا عندي هنا الـ AX يساوي مين؟ الـ XA. يبقى بدي
+
+96
+00:10:21,760 --> 00:10:30,160
+أستبدلها بالـ XA. هذا الكلام يساوي XA. وهذه الـ YA
+
+97
+00:10:30,160 --> 00:10:36,020
+من مين؟ من التانية اللي عندناها برضه. بتدرج على الـ
+
+98
+00:10:36,020 --> 00:10:41,120
+distributive. من الـ distributive اللي هو هذا. الـ X
+
+99
+00:10:41,120 --> 00:10:49,210
+ناقص الـ Y مضروباً في الـ A. صار الآن A في الـ X ناقص الـ
+
+100
+00:10:49,210 --> 00:10:56,010
+Y يساوي الـ X ناقص الـ Y في الـ A، لكل الـ A اللي موجودة
+
+101
+00:10:56,010 --> 00:11:02,570
+في الـ R بلا استثناء. معنى هذا الكلام أن الـ X ناقص
+
+102
+00:11:02,570 --> 00:11:09,610
+الـ Y commutes with all elements of the ring. يبقى
+
+103
+00:11:09,610 --> 00:11:16,840
+الـ X ناقص الـ Y موجودة في الـ Center تبع الـ R. طيب
+
+104
+00:11:16,840 --> 00:11:24,780
+باقية النقطة هي الأخيرة. علامة: X و Y موجود كذلك في
+
+105
+00:11:24,780 --> 00:11:34,900
+R. لأن X و Y موجود في الـ Center تبع الـ R، then إذا
+
+106
+00:11:34,900 --> 00:11:42,400
+قدرت تثبت إن الـ A في XY بيساوي الـ XY في A، لكل الـ A
+
+107
+00:11:42,400 --> 00:11:49,760
+الموجودة في R. بتم المطلوب. يبقى بدي آخذ A مضروبة في
+
+108
+00:11:49,760 --> 00:11:56,200
+الـ XY. الآن، هدول العناصر الموجودة في
+
+109
+00:11:56,200 --> 00:12:00,120
+الـ ring. وخاصية الـ associativity بالنسبة للضرب
+
+110
+00:12:00,120 --> 00:12:07,980
+صحيحة على الـ ring. إذا بقدر أقول: هذا AX في Y.
+
+111
+00:12:07,980 --> 00:12:15,010
+الـ Y. طب أنا عندي AX بده يساوي من الـ XA، لأن
+
+112
+00:12:15,010 --> 00:12:20,310
+الـ X و Y موجودة في الـ center. يبقى هذا الكلام بده
+
+113
+00:12:20,310 --> 00:12:27,290
+يساوي الـ XA في الـ Y. نظراً لأن الـ X موجودة في الـ
+
+114
+00:12:27,290 --> 00:12:31,790
+center تبع الـ group. خاصية الـ associativity كمان
+
+115
+00:12:31,790 --> 00:12:41,490
+مرة. يبقى هذا X في AY. تمام. الآن عندنا الـ AY هي man
+
+116
+00:12:41,490 --> 00:12:47,830
+و YA، نظراً لأن Y موجودة في الـ center تبع الـ ring.
+
+117
+00:12:47,830 --> 00:12:55,950
+يبقى هذا الكلام يساوي X في YA. نرجع لخاصية الـ
+
+118
+00:12:55,950 --> 00:13:02,910
+associativity كمان مرة. يبقى هذا يساوي الـ XYA.
+
+119
+00:13:02,910 --> 00:13:09,880
+يبقى إيش الاستفادة هنا؟ ضربنا A في XY، جينا الناتج
+
+120
+00:13:09,880 --> 00:13:16,820
+يساوي XY في A. معنى هذا الكلام أن الـ XY موجودة في
+
+121
+00:13:16,820 --> 00:13:26,360
+الـ center. يبقى this means that هذا يعني أن الـ X في
+
+122
+00:13:26,360 --> 00:13:31,740
+الـ Y موجودة في الـ center تبع الـ ring. بناء عليه
+
+123
+00:13:31,740 --> 00:13:36,450
+تحققت الشروط التلاتة تبعت النظرية. يبقى الـ center
+
+124
+00:13:36,450 --> 00:13:44,510
+صار ماله؟ sub ring. يبقى بروح بقوله: باص. وهكذا اللي
+
+125
+00:13:44,510 --> 00:13:54,490
+هو الـ center تبع الـ ring R is a sub ring of R.
+
+126
+00:13:54,490 --> 00:13:55,550
+الأصمين.
+
+127
+00:14:02,700 --> 00:14:09,100
+هذا كان السؤال رقم تسعة عشر من الكتاب. الآن، سؤال
+
+128
+00:14:09,100 --> 00:14:19,240
+تلاتة وعشرين، بيقول: يونيت من الـ ZI. سؤال تلاتة
+
+129
+00:14:19,240 --> 00:14:27,400
+وعشرين، اتنين وعشرين، اتنين وعشرين، إيش بيقول
+
+130
+00:14:27,400 --> 00:14:33,090
+اتنين وعشرين؟ اتنين وعشرين بيقول: تلقاه بـ
+
+131
+00:14:33,090 --> 00:14:39,310
+commutative ring with unity. الـ R ring أو
+
+132
+00:14:39,310 --> 00:14:50,210
+commutative .. commutative ring with unity. تمام؟
+
+133
+00:14:50,210 --> 00:14:56,890
+commutative ring with unity. الـ UR denotes the set
+
+134
+00:14:56,890 --> 00:15:10,480
+of units of R. والـ UR اللي هو set of units of R. set
+
+135
+00:15:10,480 --> 00:15:14,100
+of units of R. فهو الـ UR is a group under
+
+136
+00:15:14,100 --> 00:15:23,900
+multiplication of R. هذا بدي يعطينا إن الـ UR is a
+
+137
+00:15:23,900 --> 00:15:27,620
+group تحت نفس عملية الضرب.
+
+138
+00:15:30,350 --> 00:15:35,370
+طيب، سؤال مرة تانية. احنا عندنا commutative ring
+
+139
+00:15:35,370 --> 00:15:42,450
+with unity. تمام؟ وزيادة على ذلك، الـ six units اللي
+
+140
+00:15:42,450 --> 00:15:49,170
+موجودة في الـ ring، الـ data runs U of R. بدي أثبت إن
+
+141
+00:15:49,170 --> 00:15:54,110
+الـ U of R is a group. طب لو أثبتنا إنها sub group
+
+142
+00:15:54,110 --> 00:16:00,730
+بص الصدق ولا لأ؟ لأن any sub group is a group. لأن هي
+
+143
+00:16:00,730 --> 00:16:04,910
+group تحت الـ operation اللي موجودة على الـ set
+
+144
+00:16:04,910 --> 00:16:09,010
+الأصلية. طب كيف بنثبت أن الـ set هذه، أو الـ subset
+
+145
+00:16:09,010 --> 00:16:13,010
+اللي بناخدها، الـ sub group من الـ group الأصلية؟ two
+
+146
+00:16:13,010 --> 00:16:18,490
+conditions. مظبوط. أول شيء: non empty. اتنين: أخدت
+
+147
+00:16:18,490 --> 00:16:21,990
+عنصرين فيها، أثبتت إن الأول فيه معكوس التاني
+
+148
+00:16:21,990 --> 00:16:27,360
+موجود. إن تم ذلك، بنقوله خلاص. نقال لي: تحت عملية
+
+149
+00:16:27,360 --> 00:16:33,960
+الضرب، والله تحت عملية الجمع. تحت
+
+150
+00:16:33,960 --> 00:16:38,720
+عملية
+
+151
+00:16:38,720 --> 00:16:44,060
+الضرب تبع الـ R. ممتازة. يعني الأول في معكوسي التاني
+
+152
+00:16:44,060 --> 00:16:52,160
+بدي يكون موجود. الآن، هنا الـ solution. هل
+
+153
+00:16:52,160 --> 00:17:01,220
+الـ U of R is non-empty؟ نقدر نجيب، وهو لو عنصر واحد
+
+154
+00:17:01,220 --> 00:17:12,440
+فيه، الـ unity. ممتاز جداً. موجود في الـ U of A. يفجر هنا
+
+155
+00:17:12,440 --> 00:17:19,960
+بدي بيقوله: sense الـ unity، لأن ما حددتش مين هو
+
+156
+00:17:19,960 --> 00:17:21,880
+sense الـ unity.
+
+157
+00:17:26,050 --> 00:17:41,170
+belong to الـ U of R. الـ U of R is من إيه؟ كويس.
+
+158
+00:17:41,170 --> 00:17:48,390
+بدراج. آخذ الآن عنصرين بالـ units. يبقى little a و
+
+159
+00:17:48,390 --> 00:17:58,420
+الـ b موجودة في set of units. السؤال: هل بقدر أثبت
+
+160
+00:17:58,420 --> 00:18:03,740
+إن الأول في معكوسي الثاني موجود هنا ولا لا؟ إن
+
+161
+00:18:03,740 --> 00:18:12,760
+أثبتنا بكون خلصنا. صح؟ يالا شوف كيف. الـ B ده هي a
+
+162
+00:18:12,760 --> 00:18:17,220
+ring with unity. كيف؟ a ring with unity. اه و بحكي
+
+163
+00:18:17,220 --> 00:18:22,950
+إن الـ B لا يساوي صفر. الـ B؟ ماشي. الهال. احنا أخدنا a
+
+164
+00:18:22,950 --> 00:18:31,270
+و b أي عنصرين يعني units، يعني ليسوا أصفار. إلها
+
+165
+00:18:31,270 --> 00:18:35,490
+إلها صحيح، و الـ inverse ينتمي للـ UR. و حسب درس أي
+
+166
+00:18:35,490 --> 00:18:41,770
+عددين في الـ UR ينتمي للـ UR. إيه بيخلصنا؟ طيب، تقدر
+
+167
+00:18:41,770 --> 00:18:48,700
+تلخص اللي قلتيه مرة تانية؟ مش a, b تنتمي للـ UR، يعني
+
+168
+00:18:48,700 --> 00:18:52,500
+P inverse تنتمي لـ UI، يعني حصل ضرب two units هو
+
+169
+00:18:5
+
+223
+00:25:12,290 --> 00:25:19,720
+أشياء بسيطة. بنقول أما القصاص بتقول إن الـ units تبع
+
+224
+00:25:19,720 --> 00:25:25,260
+الـ ZI هي واحد، و سالب واحد، و I، و سالب I. نريد نشوف
+
+225
+00:25:25,260 --> 00:25:30,980
+هل هدول units ولا لا، و هل هناك غيرهم ولا لا. أول
+
+226
+00:25:30,980 --> 00:25:34,960
+واحد ماشي الـ only three. يعني واحد في واحد يساوي
+
+227
+00:25:34,960 --> 00:25:39,260
+واحد. الثاني سالب واحد في سالب واحد يساوي الـ unit
+
+228
+00:25:39,260 --> 00:25:46,950
+اللي هو الواحد. الثالث I في سالب I لإنه بصير سالب واحد.
+
+229
+00:25:46,950 --> 00:25:51,530
+تربيعه I تربيع بسالب واحد لأن الجذر التربيعي ليه
+
+230
+00:25:51,530 --> 00:25:57,790
+سالب واحد. يبقى بيعطيني كمان واحد. يبقى الواحد هو الـ
+
+231
+00:25:57,790 --> 00:26:05,740
+unit ومقلوبه، مش مقلوبة، معكوسه هو سالب I. يبقى الـ I و
+
+232
+00:26:05,740 --> 00:26:10,880
+سالب I كلهم نفس الشيء لأن كل واحد فيهم معكوس للآخر. لكن
+
+233
+00:26:10,880 --> 00:26:17,480
+الواحد و السالب واحد، كل واحد معكوس لنفسه طبعاً. يبقى
+
+234
+00:26:17,480 --> 00:26:23,840
+هدول الأرقام، في غيرهم؟ إذا بتلاقوا من هنا لنهاية
+
+235
+00:26:23,840 --> 00:26:28,220
+الفصل، قصد السنة الجاية، قصد لما تتخرج من الجامعة،
+
+236
+00:26:28,220 --> 00:26:33,940
+تبقوا تبلغوني. يبقى لا يوجد units غير هذه الأربعة
+
+237
+00:26:33,940 --> 00:26:40,800
+عناصر فقط لا غير. طيب هذا سؤال ثلاثة و عشرين، ثمانية
+
+238
+00:26:40,800 --> 00:26:50,920
+و عشرين، ثمانية و عشرين. بيقول لي إن زد سكس، إن زد
+
+239
+00:26:50,920 --> 00:26:59,440
+سكس. أثبتولنا إن الأربعة بتقسم الاتنين، وكذلك في ذكر
+
+240
+00:26:59,660 --> 00:27:10,160
+ثمانية. بدنا نثبت إن التلاتة تقسم السبعة، وكذلك في زد
+
+241
+00:27:10,160 --> 00:27:19,000
+خمسة عشر. بدنا نثبت إن التسعة تقسم الإثناشر.
+
+242
+00:27:25,260 --> 00:27:31,660
+أول شيء، ماذا يعني أن عدد يقسم عدد آخر؟ معناه أنه
+
+243
+00:27:31,660 --> 00:27:37,320
+ممكن ألاقي عدد أضرب فيه يعطيني العدد الآخر. صح ولا
+
+244
+00:27:37,320 --> 00:27:42,660
+لا؟ إن حدث ذلك يبقى العدد اللي عندي بيقسم العدد
+
+245
+00:27:42,660 --> 00:27:49,240
+الآخر. هذا في الأعداد العادية. نفس الفكرة، بدنا نروح
+
+246
+00:27:49,240 --> 00:27:54,670
+نطبقها على الأعداد في أي ring أخرى، من الـ rings اللي
+
+247
+00:27:54,670 --> 00:28:00,890
+بيكونوا عارفين شكل الأعداد فيها. فمثلاً لو جينا لـ Z6،
+
+248
+00:28:00,890 --> 00:28:07,370
+عناصرها من صفر لغاية خمسة. يبقى الأربعة و الاتنين من
+
+249
+00:28:07,370 --> 00:28:13,770
+ضمن العناصر. السؤال هو: هل بقدر ألاقي رقم أضربه في
+
+250
+00:28:13,770 --> 00:28:20,830
+أربعة يطلع ناتج اتنين؟ له مين؟ اتنين. اتنين. طيب لو
+
+251
+00:28:20,830 --> 00:28:26,950
+جيت قلت هنا أربعة في اتنين، الثمانية. أشيل منهم ستة،
+
+252
+00:28:26,950 --> 00:28:32,170
+بيظل اتنين. صحيح. يبقى اتنين في أربعة بدي يعطيني
+
+253
+00:28:32,170 --> 00:28:38,170
+ثمانية. يبقى الأربعة تقسم الاتنين، أو الاتنين بيقسم الاتنين،
+
+254
+00:28:38,170 --> 00:28:44,510
+صح؟ آه، بس هذه بتلخطك. اتنين و اتنين، هذه لا، صح مية و
+
+255
+00:28:44,510 --> 00:28:52,890
+المئة هي، لكن يمكن نقدر نجيب كمًّا طبعاً. كمًّا. فـ أربعة
+
+256
+00:28:52,890 --> 00:29:01,550
+في خمسة قداش؟ أربعة في خمسة، عشرين. صح ولا لا؟ مش أربعة
+
+257
+00:29:01,550 --> 00:29:06,490
+في خمسة، خمسة وعشرين. شيل منه ثلاثة ستات، بيضل اتنين. يبقى
+
+258
+00:29:06,490 --> 00:29:14,970
+هنا أربعة تقسم اتنين. هنا ليش؟ لأنه أربعة في خمسة بده
+
+259
+00:29:14,970 --> 00:29:20,540
+يساوي قداش؟ بده يساوي اتنين. أربعة في خمسة، خمسة وعشرين. شيله
+
+260
+00:29:20,540 --> 00:29:25,080
+ثلاثة ستات، بتنطرح من العشرين، بيضل اتنين. هيك إذا
+
+261
+00:29:25,080 --> 00:29:31,180
+الأربعة بتقسم الاتنين. يبقى هذا بيعطيك إن الأربعة
+
+262
+00:29:31,180 --> 00:29:41,580
+بتقسم الاتنين. و بيجي على Z ثمانية. آه. بدنا نضمن إنه
+
+263
+00:29:41,580 --> 00:29:47,760
+ثلاثة بتقسم سبعة. خمسة؟ خمسة في ثلاثة، خمسة عشر. بيضل
+
+264
+00:29:47,760 --> 00:29:57,910
+سبعة صحيح. الآن ثلاثة ضرب خمسة ويساوي الخمسة عشر. ثلاثة
+
+265
+00:29:57,910 --> 00:30:02,970
+في الخمسة، خمسة عشر. شيل الثمانية منهم، بيبقى سبعة.
+
+266
+00:30:02,970 --> 00:30:10,450
+إذا الثلاثة بتقسم، بتقسم السبعة. زي ما هو جد اللي
+
+267
+00:30:10,450 --> 00:30:15,530
+بعدها، بزيد خمسة عشر. بدي أثبت أن التسعة بتقسم الـ
+
+268
+00:30:15,530 --> 00:30:16,490
+إثناشر.
+
+269
+00:30:18,580 --> 00:30:26,700
+تسعة في ثلاثة، سبعة وعشرين. شيل خمسة عشر، بيظل
+
+270
+00:30:26,700 --> 00:30:34,580
+إثناشر. بيظل إثناشر. هذا معناه أن التس... أن الثلاثة
+
+271
+00:30:34,580 --> 00:30:46,300
+أن التسعة بتقسم الإثناشر. هذا، أنزل خمسة عشر. وهذا
+
+272
+00:30:46,300 --> 00:31:01,680
+الكلام صحيح. في زد ثمانية. هذا الكلام صحيح في زد ستة.
+
+273
+00:31:40,540 --> 00:31:47,360
+طيب هذا كان سؤال ثمانية و عشرين. بدنا نروح لسؤال
+
+274
+00:31:47,360 --> 00:31:53,400
+ثلاثين. بقول: يفترض أنه عندي عدد N أكبر من واحد بحيث
+
+275
+00:31:53,400 --> 00:32:01,620
+الـ XM بتكون ساوي الـ X لكل الـ X for all element X
+
+276
+00:32:01,620 --> 00:32:08,620
+of some ring. يبقى هنا سؤال ثلاثين، في عندي X to the
+
+277
+00:32:08,620 --> 00:32:17,880
+power بتساوي X لكل X الموجودة في ring R. وكذلك F
+
+278
+00:32:17,880 --> 00:32:25,700
+لهم is a positive integer و AM بتساوي Zero for
+
+279
+00:32:25,700 --> 00:32:36,020
+some A. يبقى for some، اللي هو العنصر A. show that أن
+
+280
+00:32:36,020 --> 00:32:43,480
+الـ A بده يساوي مين؟ بده يساوي Zero. يبقى show أن الـ A
+
+281
+00:32:43,480 --> 00:32:51,560
+هذا بده يساوي مين؟ بده يساوي Zero. solution. المعطيات
+
+282
+00:32:51,560 --> 00:32:58,620
+في المسألة كمان مرة بيقول لي: لو أخدت أي element من R
+
+283
+00:32:58,620 --> 00:33:04,080
+ورفعته للأس N، بده يعطينا الـ element نفسه. X to the
+
+284
+00:33:04,080 --> 00:33:10,260
+power N بده يساوي X لحاله. كمان لو أخدت
+
+285
+00:33:10,260 --> 00:33:16,760
+عنصر A، مش أي عنصر، هي اللي ممكن ينطبق على عنصر أو
+
+286
+00:33:16,760 --> 00:33:22,790
+اثنين أو ثلاثة، مش الكل. لأن A to the power of M بدها
+
+287
+00:33:22,790 --> 00:33:27,990
+تساوي 0 for some A الموجودة في الـ ring R. بيقول لي
+
+288
+00:33:27,990 --> 00:33:34,610
+بيقول لي إن الـ A هذه تساوي، بتساوي 0. تمام، تمام. أنا
+
+289
+00:33:34,610 --> 00:33:41,350
+عندها بنات إن X to the power of N بدها تساوي X for
+
+290
+00:33:41,350 --> 00:33:46,070
+all x اللي موجودة في ring. السؤال هو: A موجودة في ring ولا
+
+291
+00:33:46,070 --> 00:33:53,110
+لا؟ يبقى ينطبق عليه هذا الكلام. يبقى A to the power
+
+292
+00:33:53,110 --> 00:34:00,750
+N بده يساوي مين؟ بده يساوي الـ A. طيب، حضروا لو أحد فيكم
+
+293
+00:34:00,750 --> 00:34:05,030
+حل السؤال، والله في حل، حلّت إيه، قالوا بيه، أنا
+
+294
+00:34:05,030 --> 00:34:09,070
+حكيت إن الـ A مفروضة في المسألة، فممكن تكون يا واحد يا
+
+295
+00:34:09,070 --> 00:34:14,490
+أكبر من الواحد. إذا كانت أكبر من الواحد، هم تبقى
+
+296
+00:34:14,490 --> 00:34:19,070
+عليها الموضوع، المعطى. إذا كانت، بس هو ال... أن AM
+
+297
+00:34:19,070 --> 00:34:23,770
+تساوي AM، بس هو معطى أن AM تساوي صفر. فالـ AM حتساوي
+
+298
+00:34:23,770 --> 00:34:31,570
+واحد، و AM حتساوي صفر. أنا حكيت في عينيا إن AM، A أس
+
+299
+00:34:31,570 --> 00:34:35,350
+M بتساوي A، و A أس M بتساوي Zero. يعني عيني، هدولنتين
+
+300
+00:34:35,350 --> 00:34:41,020
+متناقضتين. بيجي منا هنجي، ابنينا نعمل علاقة بين N و M. حكيت
+
+301
+00:34:41,020 --> 00:34:45,840
+أن N ممكن نكتبها على صورة M في Q زائد R. بس خلاص، سمعت
+
+302
+00:34:45,840 --> 00:34:50,600
+بالـ division algorithm. طبعاً أعطاكم يا دكتورة محمد
+
+303
+00:34:50,600 --> 00:34:56,040
+في بداية الكورس، واللي أخذت نظرية الأعداد، أخذت
+
+304
+00:34:56,040 --> 00:35:02,160
+division algorithm، خوارزمية القسمة. إذا باجي بقول
+
+305
+00:35:02,160 --> 00:35:11,900
+إن اللي عندها الـ N تساوي M في Q زائد R. يعني الـ N
+
+306
+00:35:11,900 --> 00:35:17,980
+بدها تساوي مضاعفات الـ M، ويمكن أن تنتهي أو يظل
+
+307
+00:35:17,980 --> 00:35:21,780
+الباقي، الـ remainder، اللي ودّيته الرمز R.
+
+308
+00:35:21,780 --> 00:35:29,150
+إحنا عندنا الـ A تساوي الـ A to the power N. هذا
+
+309
+00:35:29,150 --> 00:35:37,870
+الكلام بده يساوي A to the power M في Q زائد R، حسب
+
+310
+00:35:37,870 --> 00:35:46,710
+خواص الأسس. يبقى AMQ مضروبة في A أس R. أو إن شئتم
+
+311
+00:35:46,710 --> 00:35:55,510
+فقولوا هذا الكلام AM أس Q في A أس R. من المعطى
+
+312
+00:35:55,510 --> 00:36:04,450
+AM بقداش؟ بـ Zero. يبقى هذا Zero مرفوع للقوة Q مضروب
+
+313
+00:36:04,450 --> 00:36:11,090
+في الـ AR. ناتج قداش؟ Zero. أظن هو المطلوب. يبقى هي
+
+314
+00:36:11,090 --> 00:36:17,650
+الـ A تساوي Zero. طيب، ما بعدناش عن الفكرة، لازلنا في
+
+315
+00:36:17,650 --> 00:36:24,810
+نفس الفكرة في سؤال تالي. هذا كان سؤال ثلاثين. سؤال
+
+316
+00:36:24,810 --> 00:36:32,880
+اثنين و ثلاثين. سؤال اثنين و ثلاثين بيقول: خد الـ N
+
+317
+00:36:32,880 --> 00:36:39,060
+integer أكبر من واحد in a ring in which الـ X to the
+
+318
+00:36:39,060 --> 00:36:44,320
+power N بده يساوي الـ X لكل الـ X اللي موجودة وين؟ في
+
+319
+00:36:44,320 --> 00:36:54,500
+الـ ring R. قال لي show that، show إن الـ، الـ A في الـ
+
+320
+00:36:54,500 --> 00:37:04,270
+B بده يساوي Zero، then B في A بده يساوي، بده
+
+321
+00:37:04,270 --> 00:37:16,510
+يساوي Zero. يبقى
+
+322
+00:37:16,510 --> 00:37:19,430
+الخاصية اللي كانت في السؤال ثلاثين، في السؤال اثنين
+
+323
+00:37:19,430 --> 00:37:25,650
+و ثلاثين هي هي، لم تتغير. الخاصية الأولى، لكن شأن هذا
+
+324
+00:37:25,650 --> 00:37:32,410
+وقال: لو كان حاصل ضرب الـ A في B من جهة اليسار يساوي
+
+325
+00:37:32,410 --> 00:37:36,870
+Zero، يبقى حاصل الضرب من جهة اليمين، A في B بدك
+
+326
+00:37:36,870 --> 00:37:42,410
+تكونه يساوي مين؟ بدك تكونه يساوي Zero. وقال: الله
+
+327
+00:37:42,410 --> 00:37:50,290
+كويس. إحنا عندنا الـ X to the power N بدها تساوي الـ X
+
+328
+00:37:50,290 --> 00:37:57,670
+لكل الـ X اللي موجودة في R. سؤال هو: هل الـ BA
+
+329
+00:37:57,670 --> 00:38:03,470
+المطلوبة هذه موجودة في R ولا لا؟ إذا ينطبق عليها
+
+330
+00:38:03,470 --> 00:38:13,590
+هذا الشرط. يبقى هذا يعني أن الـ BA هي الـ BA
+
+331
+00:38:13,590 --> 00:38:19,730
+to the power N. طبقاً للـ condition اللي عندك. ليش هذا؟
+
+332
+00:38:19,730 --> 00:38:29,150
+because إن الـ BA موجودة في الـ ring R. طيب، تمام.
+
+333
+00:38:29,150 --> 00:38:35,490
+هذا لو بدأنا نكتب، بنات، بقدر أقول B أس N في A أس N.
+
+334
+00:38:35,490 --> 00:38:40,690
+نقُدر؟ نقدرش.
+
+335
+00:38:40,690 --> 00:38:46,560
+لأن هذه مش commutative. لو commutative بحط دوري B أس N
+
+336
+00:38:46,560 --> 00:38:52,260
+A أس N، وخلاصنا. لكن كونها ماهي commutative، هذه فكرة
+
+337
+00:38:52,260 --> 00:38:59,600
+بقول BA، BA، BA، وضل لغاية BA كم
+
+338
+00:38:59,600 --> 00:39:08,500
+مرة؟ N من المرات. يبقى N times، يبقى N من المرات. هذا
+
+339
+00:39:08,500 --> 00:39:13,970
+الكلام يساوي، بدي أستخدم خاصية الـ associativity. يبقى
+
+340
+00:39:13,970 --> 00:39:20,830
+خاصية الـ associativity. يبقى هي الـ BA، BA، B
+
+341
+00:39:20,830 --> 00:39:31,610
+ونضل ماشيين A، B، آخر حاجة A. هدول كلهم، كل واحدة فيهم
+
+342
+00:39:31,610 --> 00:39:39,170
+بـ Zero. صح؟ يبقى هذا بده يساوي B في Zero في Zero
+
+343
+00:39:39,170 --> 00:39:46,610
+ونضل ماشيين في Zero في A. يعني هذا الكلام بده يساوي
+
+344
+00:39:46,610 --> 00:39:53,770
+B في Zero في إيه؟ يبقى هذا بده يعطيني Zero في إيه؟
+
+345
+00:39:53,770 --> 00:40:00,530
+اللي يبقى داك؟ بـ Zero، أظن وهو المطلوب. يبقى هذا بده
+
+346
+00:40:00,530 --> 00:40:07,290
+يعطيك إنه B في A تساوي Zero. الآن السؤال اللي
+
+347
+00:40:07,290 --> 00:40:15,720
+بعده بنفس الفكرة، بس راح يعطاني إن رقم محدد، مخلّوش
+
+348
+00:40:15,720 --> 00:40:23,140
+سائق. يبقى هذا كان سؤال اثنين و ثلاثين. سؤال ثلاثة و
+
+349
+00:40:23,140 --> 00:40:28,260
+ثلاثين، سؤال
+
+350
+00:40:28,260 --> 00:40:34,640
+ثلاثة و ثلاثين. قال: افترض الـ R هي ring بحيث إن الـ
+
+351
+00:40:34,640 --> 00:40:41,840
+X تكعيب بتساوي X لكل الـ X اللي موجودة في الـ ring R.
+
+352
+00:40:41,840 --> 00:40:53,080
+قال لي: أثبت أن 6X، هذا بيعطيك إن 6X يساوي 0 لكل الـ X
+
+353
+00:40:53,080 --> 00:40:57,920
+اللي موجودة في الـ R. هذا اللي عايزين نذكره.
+
+354
+00:41:11,440 --> 00:41:17,540
+مرة ثانية، الـ condition هذا هو هو، بس أعطاني رقم
+
+355
+00:41:17,540 --> 00:41:24,980
+محدد، مش على إطلاقه. أعطاني إن لو أخدت أي X موجودة في
+
+356
+00:41:24,980 --> 00:41:30,400
+الـ ring R ورفعتها للأس ثلاثة بتعطيني نفس الـ X. تحت
+
+357
+00:41:30,400 --> 00:41:35,060
+هذا الـ condition. قال لي: أثبت إنه ستة في X يساوي
+
+358
+00:41:35,060 --> 00:41:42,790
+جديد، يساوي صفر. يساوي ستة. تمام. بقوله: كويس، الآن كنت
+
+359
+00:41:42,790 --> 00:41:49,650
+أجي وأقوله: افترض إن في عندنا X موجودة في الـ ring
+
+360
+00:41:49,650 --> 00:41:58,250
+R. السؤال هو: then، هل اثنين X موجودة في R ولا لا؟
+
+361
+00:41:58,250 --> 00:42:04,690
+لأن R is closed under addition. اثنين X يعني X زائد
+
+362
+00:42:04,690 --> 00:42:15,310
+X. طيب، معطى أن 2X موجودة في R. إذن 2X، بقدر أقوله: هي 2X
+
+363
+00:42:15,310 --> 00:42:21,850
+تكعيب. سكت، الشعر، مظلوم؟ يبقى الـ condition هذا
+
+364
+00:42:21,850 --> 00:42:28,830
+بيخلي 2X هي 2X تكعيب. هذه عبارة عن مين؟ عبارة عن
+
+365
+00:42:28,830 --> 00:42:37,420
+2X في 2X في 2X. طبعاً للخواص، اثنينات هذه بتطلع وين؟
+
+366
+00:42:37,420 --> 00:42:43,220
+بره. يبقى اثنين في اثنين في اثنين، بصير ثمانية في X
+
+367
+00:42:43,220 --> 00:42:50,600
+في X في X، بـ X تكعيب. تمام. يبقى صارت إنّ الطرف
+
+368
+00:42:50,600 --> 00:42:58,880
+الـ أيْسر 2X، الطرف الـ أيمن يساوي ثمانية X تكعيب. طَب
+
+369
+00:42:58,880 --> 00:43:07,020
+X تكعيب بقد ايه؟ X. يبقى هذا الكلام بده يساوي ثمانية X.
+
+370
+00:43:07,020 --> 00:43:14,820
+لأن X تكعيب هي بـ X. يعني هذه بالضبط هي ثمانية X.
+
+371
+00:43:14,820 --> 00:43:20,740
+يبقى صار 2X يساوي ثمانية X. نجيب هذه على الجهة
+
+372
+00:43:20,740 --> 00:43:25,420
+الثانية، أو نضيف المعكوس الجمعي للطرفين. الحساب بـ
+
+373
+00:43:25,420 --> 00:43:31,940
+2X. Automatically، هذا بيعطيك 6X تساوي جدّاك Zero.
+
+374
+00:43:31,940 --> 00:43:40,920
+وهو المطلوب. سؤال فكرة بسيطة لكن بده تفكير شوية.
+
+375
+00:43:40,920 --> 00:43:47,720
+يعني كيف نستخدم المعطيات اللي عندنا في الوصول إلى
+
+376
+00:43:47,720 --> 00:43:51,760
+الإجابة على المطلوب تبع السؤال.
+
+377
+00:44:07,620 --> 00:44:14,860
+هذا كان... عندنا سؤال اللي هو قداش؟ سؤال ثلاثة و
+
+378
+00:44:14,860 --> 00:44:23,260
+ثلاثين. طيب، نروح لسؤال تسعة و ثلاثين. سؤال تسعة و
+
+379
+00:44:23,260 --> 00:44:29,060
+ثلاثين. سؤال تسعة و ثلاثين بيقول: افترض R هي ring
+
+380
+00:44:29,060 --> 00:44:35,140
+with unity اللي فيه، الـ ring with
+
+381
+00:44:35,140 --> 00:44:43,470
+unity. هذه المعلومة الأولى. و A is an element
+
+382
+00:44:43,470 --> 00:44:53,470
+of R، و الـ A موجود في R such that... such that أن
+
+383
+00:44:53,470 --> 0
+
+445
+00:52:41,050 --> 00:52:46,470
+ها دي ها ها بدليلي فوق و بنخنفش احنا وياه طب لما
+
+446
+00:52:46,470 --> 00:52:50,010
+الواحد .. خلاص؟ لأ طيب بده اللي هو الواحد بتبقى
+
+447
+00:52:50,010 --> 00:52:56,680
+لها ولا كأنه طيب ماشي هل الواحد بيحققها ولا لا؟
+
+448
+00:52:56,680 --> 00:53:03,940
+بيسأل سؤال هل الواحد موجود في S ولا لا؟ بنقوله
+
+449
+00:53:03,940 --> 00:53:12,840
+موجود والسبب أه ليش السبب بيبرأك؟
+
+450
+00:53:12,840 --> 00:53:27,170
+لأن الـ A في واحد، الـ A يساوي مين؟ يساوي a في a، تمام؟
+
+451
+00:53:27,170 --> 00:53:32,970
+يساوي a تربيع، يساوي واحد، يبقى صار هذا الـ element
+
+452
+00:53:32,970 --> 00:53:41,170
+موجود في S، هذا بدي أقول لك إن الـ a، واحد a، موجود في S
+
+453
+00:53:41,170 --> 00:53:48,880
+يعني الـ واحد موجود وين؟ موجود في S، أول مرة جايب إن
+
+454
+00:53:48,880 --> 00:53:54,760
+نكمل الأسئلة قبل أن ندخل الـ Integral domain اللي
+
+455
+00:53:54,760 --> 00:53:59,120
+هو الشبطر اللي بعده إن شاء الله تعالى
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QpvkLUWn3LA_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QpvkLUWn3LA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d9392967c440a3e8a337d9d3764ecbeaf2688ee2
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QpvkLUWn3LA_raw.srt
@@ -0,0 +1,1828 @@
+1
+00:00:21,210 --> 00:00:24,870
+بسم الله الرحمن الرحيم المرة اللى فاتت أنهينا
+
+2
+00:00:24,870 --> 00:00:29,270
+chapter أتناشى واطلبتوا كم من سؤال تتعرف عليهم
+
+3
+00:00:29,270 --> 00:00:36,070
+بالبيت مشان يعرف هل يعني الفهم تنام عندكوا و الله
+
+4
+00:00:36,070 --> 00:00:40,190
+كيف يعني صرتوا بتعرفوا تشتغلوا في ال things ولا لأ
+
+5
+00:00:40,190 --> 00:00:46,570
+اطلبتوا أول سؤال من هذه الأسئلة اللى هو سؤال اثنين
+
+6
+00:00:46,570 --> 00:00:56,990
+يبقى اليوم عندنا exerciseson chapter 12 أول سؤال
+
+7
+00:00:56,990 --> 00:01:05,310
+هناك و سؤال اتنين سؤال اتنين بيقول لي ال ring ال
+
+8
+00:01:05,310 --> 00:01:15,610
+ring اللي هو zero اتنين اربع ستة تمانية under اللي
+
+9
+00:01:15,610 --> 00:01:17,450
+هو addition
+
+10
+00:01:20,780 --> 00:01:30,160
+and multiplication multiplication
+
+11
+00:01:30,160 --> 00:01:44,100
+modulo كدهش modulo عشرة modulo عشرة has a unit has
+
+12
+00:01:44,100 --> 00:01:54,180
+a unit you gonna find itfine ايه؟ حسب فيها يا
+
+13
+00:01:54,180 --> 00:01:59,680
+بنان؟ جداش طالع؟ ستة ممتاز يبقى الستة هو ال unity
+
+14
+00:01:59,680 --> 00:02:04,400
+لإن الستة لو ضربته في أي عنصر من العناصر اللي
+
+15
+00:02:04,400 --> 00:02:10,320
+قدامي هذي بطلع نفس ايه؟ بطلع نفس ال .. بطلع نفس ..
+
+16
+00:02:10,320 --> 00:02:14,920
+نفس العنصر اللي موجود في ال ring يبقى بروح بقوله
+
+17
+00:02:14,920 --> 00:02:19,040
+هي للحل ال unity
+
+18
+00:02:20,620 --> 00:02:30,280
+is ستة because for example for example لو جيت قول
+
+19
+00:02:30,280 --> 00:02:39,040
+ستة في أربع ستة في أربع بأربع هو عشرين بنشيل منهم
+
+20
+00:02:39,040 --> 00:02:46,040
+عشرة وعشرة بيظل كده؟ بيظل أربعة نفس العنصر وهنا
+
+21
+00:02:46,040 --> 00:02:53,720
+andSo on و هكذا بالنسبة لبقية العناصر ستة في
+
+22
+00:02:53,720 --> 00:02:59,280
+تمانية بستة ستة في اتنين بستة ستة في اربعة بستة و
+
+23
+00:02:59,280 --> 00:03:03,900
+هكذا هذا كان السؤال رقم اتنين بعدين قلنا بأن
+
+24
+00:03:03,900 --> 00:03:09,820
+السؤال تلتاشة وصول ال sub ring من رجعه بانتهاء
+
+25
+00:03:09,820 --> 00:03:20,310
+يرجع السؤال تلتاشة بدنا sub ringsof مجموعة الأعداد
+
+26
+00:03:20,310 --> 00:03:26,570
+الصحية يبقى أي sub ring من مجموعة الأعداد الصحية
+
+27
+00:03:26,570 --> 00:03:31,230
+بتقدر تجيبولي sub ring واحدة نفسها نفسها دي ال
+
+28
+00:03:31,230 --> 00:03:38,110
+trivial case نفسها
+
+29
+00:03:38,110 --> 00:03:39,890
+دي ال trivial case نفسها نفسها نفسها نفسها نفسها
+
+30
+00:03:39,890 --> 00:03:40,730
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها نفسها
+
+31
+00:03:40,730 --> 00:03:42,250
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها نفسها
+
+32
+00:03:42,250 --> 00:03:44,150
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها نفسها
+
+33
+00:03:44,150 --> 00:03:44,150
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها نفسها
+
+34
+00:03:44,150 --> 00:03:44,150
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها نفسها
+
+35
+00:03:44,150 --> 00:03:46,810
+نفسها نفسها نفسها نفسها نفسها نفسها نفسها نفسها ن
+
+36
+00:03:47,000 --> 00:03:57,240
+subring of z is in the form في الشكل التالي in z و
+
+37
+00:03:57,240 --> 00:04:10,400
+z is a positive integer يبقى هذا الشكل العام ل ال
+
+38
+00:04:10,400 --> 00:04:17,880
+in z بنقدر نثبتها بكل بساطةوالبساطة اللي نقدر
+
+39
+00:04:17,880 --> 00:04:24,700
+نشتغلها حط ال .. كيف؟ أخدناها قبل ذلك صحيح أخدناها
+
+40
+00:04:24,700 --> 00:04:31,780
+كمي ذلك تمام يبقى ده سؤال تلتاش سؤال تسعتاش سؤال
+
+41
+00:04:31,780 --> 00:04:36,540
+تسعتاش اللي هو بتتكلم عن ال center تبع ال ring
+
+42
+00:04:36,540 --> 00:04:46,150
+يبقى سؤال تسعتاش بيقول ال R ring و ال centerتبع ال
+
+43
+00:04:46,150 --> 00:04:55,890
+ring هو عبارة عن معرف ليه كل العناصر كل
+
+44
+00:04:55,890 --> 00:05:04,250
+العناصر X اللي موجود في ال ring R بحيث ان ال A X
+
+45
+00:05:04,250 --> 00:05:12,390
+بده يساوي X A لكل ال A اللي موجود في ال ring R
+
+46
+00:05:12,660 --> 00:05:19,080
+بنثبت إن الـ Center هذا عبارة عن sub-group طيب
+
+47
+00:05:19,080 --> 00:05:24,360
+السؤال هذا شبيه بالـ Center تبع ال group كان معانا
+
+48
+00:05:24,360 --> 00:05:29,380
+سؤال بيقول اثبت إن الـ Center تبع ال group هو
+
+49
+00:05:29,380 --> 00:05:32,540
+عبارة
+
+50
+00:05:32,540 --> 00:05:38,300
+عن sub-group من ال group itselfوهذا أثبتناه في جبر
+
+51
+00:05:38,300 --> 00:05:42,800
+حديث واحد، نفس الكلام في جبر حديث اتنين، بس هنا
+
+52
+00:05:42,800 --> 00:05:48,040
+كانت two conditions، هنا بنخليهم جديد، بنخليهم
+
+53
+00:05:48,040 --> 00:05:54,860
+تلاتة، يبقى مشان نثبت هذا solution،
+
+54
+00:05:54,860 --> 00:05:58,560
+في حد فيكوا أثبتت هذا كلام يا بنات؟ هي واحدة، في
+
+55
+00:05:58,560 --> 00:06:02,780
+غير تنتين، تلاتة، اه كويس، يعني على كل اتحال،
+
+56
+00:06:02,780 --> 00:06:07,740
+خمسين في المية مليعطيب لكن لو رجعتي لل group كان
+
+57
+00:06:07,740 --> 00:06:12,580
+صارت النتيجة مائة بالمائة وليس خمسين بالمائة خمسين
+
+58
+00:06:12,580 --> 00:06:17,460
+بالمائة بعتبرها نتيجة مش نافعة إلا تتعدى الستين
+
+59
+00:06:17,460 --> 00:06:23,820
+على الأقل طيب هي التعريف قدامي قبل ما نبدأ التعريف
+
+60
+00:06:23,820 --> 00:06:29,520
+بدي أعرف مين هم بالضبط عناصر ال center بقول أه
+
+61
+00:06:29,520 --> 00:06:35,010
+الأن جيت على ال ring فيها عناصر جد عددكوا مثلاكويس
+
+62
+00:06:35,010 --> 00:06:40,250
+عشرين طالبة تمام؟ بتعتبر عند رنق بعشرين أنصار
+
+63
+00:06:40,250 --> 00:06:45,510
+ماسكت الأنصار الأول من اليامين والله من الشمال
+
+64
+00:06:45,510 --> 00:06:50,730
+أعطاني نفسي النتيجة عند ما ضرقته في جميع عناصر ال
+
+65
+00:06:50,730 --> 00:06:55,530
+ring تمام؟ لجيته ايش؟ commutative مع جميع العنصر
+
+66
+00:06:55,530 --> 00:06:58,890
+اقول له أيه وانت كويس اقعد عشرة جامعه ماسكت
+
+67
+00:06:58,890 --> 00:07:03,660
+الأنصار التانيلقيته ما هوش commutative مع جميع
+
+68
+00:07:03,660 --> 00:07:08,480
+العناصر قلت له انت صفع شجع ماانتش لازم جينا للي
+
+69
+00:07:08,480 --> 00:07:13,080
+بعده ازاي ولي بعده اللي بعده لقيته commutative مع
+
+70
+00:07:13,080 --> 00:07:16,500
+جميع عناصر ال ring قلنا له انت كويس صفع انصافك
+
+71
+00:07:16,500 --> 00:07:22,880
+الأولان وهكذا لقيت مثلا خمس ست عناصر commutes مع
+
+72
+00:07:22,880 --> 00:07:29,360
+جميع عناصر من ال ring بالاستثناءيبقى إن حدث ذلك
+
+73
+00:07:29,360 --> 00:07:34,660
+بقول الستة عناصر هدول بيكونولي من؟ بيكونولي ال sub
+
+74
+00:07:34,660 --> 00:07:39,180
+ring؟ هذا اللي عايزين بتفتح، إذا ال synth of the
+
+75
+00:07:39,180 --> 00:07:47,940
+ring are كل العناصر X اللي موجودة في R بحيث أن AX
+
+76
+00:07:47,940 --> 00:07:56,320
+يسوى XA لجميع ال A اللي موجودة في Rيبقى العنصر X
+
+77
+00:07:56,320 --> 00:08:03,560
+اللي commutes مع جميع عناصر R بلا استثناء كويس
+
+78
+00:08:03,560 --> 00:08:09,960
+يبقى انا هدعي ان ال center هذا is non-empty ليش؟
+
+79
+00:08:09,960 --> 00:08:16,260
+ان على الأقل ال zero موجود فيه يبقى هنا ال center
+
+80
+00:08:16,260 --> 00:08:21,660
+تبع ال R is non-empty
+
+81
+00:08:24,870 --> 00:08:31,530
+because انه zero في ال .. ال zero في ال .. او ال
+
+82
+00:08:31,530 --> 00:08:38,970
+.. ال a مين ماكان يكون لإن ال a في ال zero بتساوي
+
+83
+00:08:38,970 --> 00:08:44,870
+ال zero في a بتساوي ال zero هذا معناته ان ال zero
+
+84
+00:08:44,870 --> 00:08:51,830
+موجود في ال center تبع ال ring بعد ايه؟بدي افترض
+
+85
+00:08:51,830 --> 00:08:57,090
+ان عندي عمصرين موجودات في الـ Center النقطة
+
+86
+00:08:57,090 --> 00:09:01,930
+الثانية هذه كانت النقطة الأولى النقطة الثانية بدي
+
+87
+00:09:01,930 --> 00:09:09,290
+اخد عمصرين X وY موجودات في الـ Center تبعي الرنجل
+
+88
+00:09:09,290 --> 00:09:19,070
+الان معناه هذا الكلام ان ال AX بده يساوي XAوفي نفس
+
+89
+00:09:19,070 --> 00:09:25,510
+الوقت ال a و ال y يبدو يساوي ال y a إذا و الله
+
+90
+00:09:25,510 --> 00:09:32,150
+جدرنا نثبت إن ال x ناقص ال y موجودة في ال center
+
+91
+00:09:32,150 --> 00:09:38,530
+بيكون خلاص القصية هذه طبقناها ال x ناقص ال y بمعنى
+
+92
+00:09:38,530 --> 00:09:45,190
+إن ال a في ال x ناقص ال y يبدو يساوي ال x ناقص ال
+
+93
+00:09:45,190 --> 00:09:53,050
+y في ال aبصير ال X ناقص ال Y مع كل ال L موجود في
+
+94
+00:09:53,050 --> 00:10:00,590
+ال R إذا خليني أخد ال A في X ناقص ال Y انطيع
+
+95
+00:10:00,590 --> 00:10:06,670
+الناتج X ناقص ال Y مضروبا في A بتم المطلوب يبقى
+
+96
+00:10:06,670 --> 00:10:14,110
+بناء عليه هذا سيكون X ناقص ال A Y ال distributive
+
+97
+00:10:14,110 --> 00:10:21,760
+lawانا عندى هنا ال a x يساوي مين؟ ال x a يبقى بدى
+
+98
+00:10:21,760 --> 00:10:30,160
+استبدلها بال x a هذا الكلام يساوي x a وهذه ال y a
+
+99
+00:10:30,160 --> 00:10:36,020
+من مين؟ من التانية اللى عندناها برضه بتدرج على ال
+
+100
+00:10:36,020 --> 00:10:41,120
+distributive من ال distributive اللى هو هذا ال x
+
+101
+00:10:41,120 --> 00:10:49,210
+ناقص ال yمضغوبا في ال a صار الآن a في ال x ناقص ال
+
+102
+00:10:49,210 --> 00:10:56,010
+y يسوى ال x ناقص ال y في ال a لكل ال a اللي موجود
+
+103
+00:10:56,010 --> 00:11:02,570
+في ال R بلا استثناء معناه هذا الكلام ان ال x ناقص
+
+104
+00:11:02,570 --> 00:11:09,610
+ال y commutes with all elements of the ring يبقى
+
+105
+00:11:09,610 --> 00:11:16,840
+ال x ناقص ال y موجودةفي الـ Center تبع الـ R طيب
+
+106
+00:11:16,840 --> 00:11:24,780
+بقيت النقطة هي الأخيرة علامات X و Y موجود كذلك في
+
+107
+00:11:24,780 --> 00:11:34,900
+R لأن X و Y موجود في الـ Center تبع الـ R then إذا
+
+108
+00:11:34,900 --> 00:11:42,400
+كدت تثبت إن الـ A في XY بسوء الـ XY في Aلكل الـ A
+
+109
+00:11:42,400 --> 00:11:49,760
+الموجود في R بتم المطموع يبقى بدي أخد A مضروبة في
+
+110
+00:11:49,760 --> 00:11:56,200
+ال main في ال X وY الآن هدول العناص الموجودات في
+
+111
+00:11:56,200 --> 00:12:00,120
+ال ring وخاصية ال associativity بالنسبة للضرب
+
+112
+00:12:00,120 --> 00:12:07,980
+صحيحة على ال ring إذا بقدر أقول هذا A X في main في
+
+113
+00:12:07,980 --> 00:12:15,010
+ال Yطب أنا عند ال A X بده تساوي من ال X في A لإن
+
+114
+00:12:15,010 --> 00:12:20,310
+ال X و Y موجودة في ال center يبقى هذا الكلام بده
+
+115
+00:12:20,310 --> 00:12:27,290
+يساوي ال X A في ال Y نظرا لإن ال X موجودة في ال
+
+116
+00:12:27,290 --> 00:12:31,790
+center تبع ال group خاصية ال associativity كمان
+
+117
+00:12:31,790 --> 00:12:41,490
+مرة يبقى هذا X في A Y تمامالآن عندنا ال a y هي man
+
+118
+00:12:41,490 --> 00:12:47,830
+و y a نظرا لأن y موجودة في ال center تبع ال ring
+
+119
+00:12:47,830 --> 00:12:55,950
+يبقى هذا الكلام يساوي x في y a نرجع لخاصية ال
+
+120
+00:12:55,950 --> 00:13:02,910
+associativity كمان مرة يبقى هذا يساوي ال x y a
+
+121
+00:13:02,910 --> 00:13:09,880
+يبقى ايش الاستفادة هنا ضلبنا aفي XY لجينا النتج
+
+122
+00:13:09,880 --> 00:13:16,820
+يساوي XY في X معناه هذا الكلام ان ال XY موجودة في
+
+123
+00:13:16,820 --> 00:13:26,360
+ال center يبقى this means that هذا يعني ان ال X في
+
+124
+00:13:26,360 --> 00:13:31,740
+ال Y موجودة في ال center تبع ال ring بناء عليه
+
+125
+00:13:31,740 --> 00:13:36,450
+تحققت الشروط التلاتة تبعت النظريةيبقى ال center
+
+126
+00:13:36,450 --> 00:13:44,510
+صار ماله sub ring يبقى بروح بقوله باص و هكذا اللي
+
+127
+00:13:44,510 --> 00:13:54,490
+هو ال center تبع ال ring R is a sub ring of R
+
+128
+00:13:54,490 --> 00:13:55,550
+الأصمين
+
+129
+00:14:02,700 --> 00:14:09,100
+هذا كان السؤال لرقم تسعة عشر من الكتاب، الآن سؤال
+
+130
+00:14:09,100 --> 00:14:19,240
+تلاتة وعشرين بالمل يونيت من الـ ZI. سؤال تلاتة
+
+131
+00:14:19,240 --> 00:14:27,400
+وعشرين، اتنين وعشرين، اتنين وعشرين، ايش بيقول
+
+132
+00:14:27,400 --> 00:14:33,090
+اتنين وعشرين؟إتنين و عشرين بيقول تلقاه بـ
+
+133
+00:14:33,090 --> 00:14:39,310
+commutative ring with unity ال R ring أو
+
+134
+00:14:39,310 --> 00:14:50,210
+commutative .. commutative ring with unity تمام؟
+
+135
+00:14:50,210 --> 00:14:56,890
+commutative ring with unity ال UR denotes the set
+
+136
+00:14:56,890 --> 00:15:10,480
+of units of Rو ال UR اللي هو set of units of R set
+
+137
+00:15:10,480 --> 00:15:14,100
+of units of R فهو ال UR is a group under
+
+138
+00:15:14,100 --> 00:15:23,900
+multiplication of R هذا بدي يعطينا ان ال UR is a
+
+139
+00:15:23,900 --> 00:15:27,620
+group تحت نفس عملية تضبط
+
+140
+00:15:30,350 --> 00:15:35,370
+طيب سؤال مرة تانية احنا عندنا competitive ring
+
+141
+00:15:35,370 --> 00:15:42,450
+with unity تمام؟ وزيادة على ذلك ال 6 units اللي
+
+142
+00:15:42,450 --> 00:15:49,170
+موجودة في ال ring ال data runs U of R بدي اثبت ان
+
+143
+00:15:49,170 --> 00:15:54,110
+ال U of R is a group طب لو اثبتنا انها sub group
+
+144
+00:15:54,110 --> 00:16:00,730
+بصد ولا لأ؟ لأن any sub group is a groupلأن هى
+
+145
+00:16:00,730 --> 00:16:04,910
+group تحت ال operation اللى موجودة على ال set
+
+146
+00:16:04,910 --> 00:16:09,010
+الاصلية طب كيف بنثبت أن ال set هذه أو ال subset
+
+147
+00:16:09,010 --> 00:16:13,010
+اللى بناخدها ال sub group من ال group الأصلية؟ two
+
+148
+00:16:13,010 --> 00:16:18,490
+conditions مظبوط أول شي non empty اتنين أخدت
+
+149
+00:16:18,490 --> 00:16:21,990
+عنصرين فيها بدأتبت أن الأول فيه معاكوس التاني
+
+150
+00:16:21,990 --> 00:16:27,360
+موجود إن تم ذلك بنقوله خلاصناقال لي تحت عملية
+
+151
+00:16:27,360 --> 00:16:33,960
+الضرب والله تحت عملية الجامعة تحت
+
+152
+00:16:33,960 --> 00:16:38,720
+عملية
+
+153
+00:16:38,720 --> 00:16:44,060
+الضرب تبع الـ R ممتازة يعني الأول في معكوسي التاني
+
+154
+00:16:44,060 --> 00:16:52,160
+بدي يكون موجود الآن هنا ال solution هل
+
+155
+00:16:52,160 --> 00:17:01,220
+ال U of R isnon-empty نقدر نجيب و هو لو عنصر واحد
+
+156
+00:17:01,220 --> 00:17:12,440
+فيه ال unity ممتاز جدا موجود في ال U of A يفجر هنا
+
+157
+00:17:12,440 --> 00:17:19,960
+بدي بيقوله sense ال unity لأن ما حددتش مين هو
+
+158
+00:17:19,960 --> 00:17:21,880
+sense ال unity
+
+159
+00:17:26,050 --> 00:17:41,170
+belong to ال U of R ال U of R is من إيه؟ كويس
+
+160
+00:17:41,170 --> 00:17:48,390
+بدراجة أخد الآن عنصرين بال units يبقى little a و
+
+161
+00:17:48,390 --> 00:17:58,420
+ال b موجودة في set of units السؤال هوهل بقدر أثبت
+
+162
+00:17:58,420 --> 00:18:03,740
+إن الأول في معكوسي الثاني موجود هنا ولا لا؟ إن
+
+163
+00:18:03,740 --> 00:18:12,760
+أثبتنا بك ونخلصنا صح؟ يالا شوف كيف ال B ده هي a
+
+164
+00:18:12,760 --> 00:18:17,220
+ring with unity كيف؟ a ring with unity اه و بحكي
+
+165
+00:18:17,220 --> 00:18:22,950
+إن ال B لا يساوي صفر ال B؟ماشي الهال احنا أخدنا a
+
+166
+00:18:22,950 --> 00:18:31,270
+و b أي عنصرين يعني units يعني ليسوا أسفارا إلها
+
+167
+00:18:31,270 --> 00:18:35,490
+إلها صحيح و ال inverse ينتمي لل UR و حسب درس أي
+
+168
+00:18:35,490 --> 00:18:41,770
+عددان في ال UR ينتمي لل UR إيه بيخلصنا؟ طيب تقدر
+
+169
+00:18:41,770 --> 00:18:48,700
+تلخص اللي قلتيه مرة تانية؟ مش a, b تنتمي لل URيعني
+
+170
+00:18:48,700 --> 00:18:52,500
+P inverse تنتمي ل UI يعني حصل ضرب two units هو
+
+171
+00:18:52,500 --> 00:18:57,300
+unit نفهم
+
+172
+00:18:57,300 --> 00:19:03,880
+إذا كان هكذا يكون خلصنا أبقى
+
+173
+00:19:03,880 --> 00:19:08,520
+احنا اخدنا هاي A وB مفيدين يبقى A وB are units
+
+174
+00:19:08,520 --> 00:19:16,840
+يعني هذا بدي يعطينا ان ال A andالـ B has
+
+175
+00:19:16,840 --> 00:19:22,260
+multiplicative
+
+176
+00:19:22,260 --> 00:19:31,780
+inverse يعني كل واحد من ال A و ال B له معكوس مظبوط
+
+177
+00:19:31,780 --> 00:19:37,840
+يعني A inverse exist و B inverse كذلك مالها exist
+
+178
+00:19:37,840 --> 00:19:45,250
+صح؟طيب، هل الأول في معكوس الثاني موجود ولا لأ؟
+
+179
+00:19:45,250 --> 00:19:49,210
+يالا نشوف،
+
+180
+00:19:49,210 --> 00:19:53,030
+ها الأول
+
+181
+00:19:53,030 --> 00:19:59,170
+في معكوس الثاني، هل موجود ولا لأ؟ بأي طريقة إن
+
+182
+00:19:59,170 --> 00:20:04,290
+شئتي، باللي بدكي هي من اللي اتعلمتي في جبرح حديث
+
+183
+00:20:04,290 --> 00:20:08,050
+واحد، سياسي، جبرح حديث واحد، هذا مش جبرح حديث
+
+184
+00:20:08,050 --> 00:20:14,390
+اتنين،هيوك كيف كنتوا تتبتوا؟
+
+185
+00:20:14,390 --> 00:20:19,390
+و ده واحدة أثبتت؟ لأ أخده هنا إنه إيه بدأ تسوى X
+
+186
+00:20:19,390 --> 00:20:23,770
+مثلا هيك؟ مش فاكرها لأ بقى هو قال لي هيك ال
+
+187
+00:20:23,770 --> 00:20:28,010
+computer ت bring و ال unity ال unity موجود ماعندي
+
+188
+00:20:28,010 --> 00:20:31,770
+مشكلة فيه وبالتالي مدى ماعندي unity يبقى فيه عندي
+
+189
+00:20:31,770 --> 00:20:38,230
+unitsلأنه فيه ولو الواحد الصحي هو يعتبر unit كذلك
+
+190
+00:20:38,230 --> 00:20:42,450
+لإن لو ضربت منه سبعتين لل unit يبقى على الأقل في
+
+191
+00:20:42,450 --> 00:20:46,150
+عندي unit واحدة استخدام الغضبية تتعرق الواحدة في
+
+192
+00:20:46,150 --> 00:20:50,230
+حياتك سابقة بدي واحدة تحكي بس ممكن إحنا نجرب نضرب
+
+193
+00:20:50,230 --> 00:20:54,510
+ال A B inverse لماعكوس تبعها تخدي المعكوس ال A B
+
+194
+00:20:54,510 --> 00:21:03,970
+inverse بصير B A inverse تضربي مين؟اللي هي المقوسة
+
+195
+00:21:03,970 --> 00:21:09,850
+اه وبالتالي انت تبتعد انه unit اه كويس؟ اه اه
+
+196
+00:21:09,850 --> 00:21:18,410
+انجرب؟ انجرب؟ ممتاز يبقى انا بدى اجرب a b inverse
+
+197
+00:21:18,410 --> 00:21:25,870
+اذا طلع هذا unit يبقى موجود في ال U of R بيكون
+
+198
+00:21:25,870 --> 00:21:32,800
+خلصنا مظبوط ولا لا؟يبقى لو جيت ضرابته في ال B A
+
+199
+00:21:32,800 --> 00:21:38,360
+inverse بالفعل بي انفرس انا ضارب بهكد افتراضي
+
+200
+00:21:38,360 --> 00:21:44,100
+ماعرفش تمام يبقى هذا الكلام دي يساوي حسب خاصية ال
+
+201
+00:21:44,100 --> 00:21:54,560
+associativity A B inverse B في ال A inverse تمام
+
+202
+00:21:54,560 --> 00:22:02,590
+هذا يعتبر مين؟يعتبر ال unity يبقى هذا بده يساوي A
+
+203
+00:22:02,590 --> 00:22:13,070
+في E في ال A inverse where ال E is the unity مين
+
+204
+00:22:13,070 --> 00:22:17,610
+مكان يكون اعطيته رمز انا يمكن يكون واحد يمكن يكون
+
+205
+00:22:17,610 --> 00:22:23,630
+غير الواحد الله أعلم يبقى هذا A في ال A inverse شو
+
+206
+00:22:23,630 --> 00:22:30,470
+بده يعطينيال unity معناه هذا الكلام ان ال a b
+
+207
+00:22:30,470 --> 00:22:37,950
+inverse is a unit يعني معناه هذا الكلام ان ال a b
+
+208
+00:22:37,950 --> 00:22:46,350
+inverse موجود في ال U of R يبقى صار في group ولا
+
+209
+00:22:46,350 --> 00:23:01,870
+لا يبقى هنا ال U of R isa subgroup of R هذا يعني
+
+210
+00:23:01,870 --> 00:23:18,290
+ان ال U of R is a group تمام هذا 22 23 23 قال لي
+
+211
+00:23:18,290 --> 00:23:28,140
+في 23 بده نحدد ال units سبعة ال Z ofI فعند او جدلي
+
+212
+00:23:28,140 --> 00:23:44,400
+ال units ال units of Z of I بدنيا Z of I مجموعة
+
+213
+00:23:44,400 --> 00:23:54,670
+الاعداد المركبةاللي على صورة a زائد ib وبحيث ال a
+
+214
+00:23:54,670 --> 00:23:59,610
+و ال b موجودة وين؟ موجودة في z يعني بد ال a و ال b
+
+215
+00:23:59,610 --> 00:24:07,010
+أعداد صحيحة تمام يالا تقدر أجيبولي ال units كلهم و
+
+216
+00:24:07,010 --> 00:24:13,750
+لبعضهم اه مين حلت السؤال طيب أيوة ذكرلي الواحد
+
+217
+00:24:13,750 --> 00:24:23,150
+والسلب واحد وال I والسلب I أكيدفي غيرهم؟ متأكدين؟
+
+218
+00:24:23,150 --> 00:24:34,450
+طيب هدول لو جيت بدي بقولهم ال units of Z of I بدها
+
+219
+00:24:34,450 --> 00:24:42,030
+تساوي واحد و سالف واحد و I و سالف I كما زعمت
+
+220
+00:24:42,030 --> 00:24:44,570
+زميلتك وش اسمك؟
+
+221
+00:24:46,670 --> 00:24:53,930
+أماني إيش؟ اسم والدك القصاص أماني مازل القصاص
+
+222
+00:24:53,930 --> 00:25:00,570
+أماني مازل من السنة أن يذكر الإنسان اسم أبيه لإن
+
+223
+00:25:00,570 --> 00:25:07,710
+هذا يعتبر من بر الوالدين فإن ذكرتي اسم والدك بنيت
+
+224
+00:25:07,710 --> 00:25:12,290
+بر الوالدين تأخذ أجر من الله سبحانه وتعالى من
+
+225
+00:25:12,290 --> 00:25:19,720
+أشياء بسيطةبنقول اما القصاص بتقول ان ال units تبع
+
+226
+00:25:19,720 --> 00:25:25,260
+ال ZI هي واحد و سالب واحد و I و سالب I نريد نشوف
+
+227
+00:25:25,260 --> 00:25:30,980
+هل هدول units ولا لا و هل هناك في غيرهم ولا لا اول
+
+228
+00:25:30,980 --> 00:25:34,960
+واحد ماشي ال only three يعني واحد في واحد يساوي
+
+229
+00:25:34,960 --> 00:25:39,260
+واحد التاني سالب واحد في سالب واحد يساوي ال unit
+
+230
+00:25:39,260 --> 00:25:46,950
+اللي هو الواحد التالتI في سالف I لإنه بصير سالف I
+
+231
+00:25:46,950 --> 00:25:51,530
+تربيعه I تربية بسالف واحد لإن الجدرق التربيعي ليه
+
+232
+00:25:51,530 --> 00:25:57,790
+سالف واحد يبقى بيعطيني كمان واحد يبقى الواحد هو ال
+
+233
+00:25:57,790 --> 00:26:05,740
+unit ومقلبه مش مقلبه معكوسه هو سالف Iيبقى ال I و
+
+234
+00:26:05,740 --> 00:26:10,880
+سلب I كلهم نفسه لإن كل واحد فيهم معكوس للآخر لكن
+
+235
+00:26:10,880 --> 00:26:17,480
+الواحد و السلب واحد كل واحد معكوس لنفسه طبعا يبقى
+
+236
+00:26:17,480 --> 00:26:23,840
+هدول الأرقام في غيرهم إذا بتلاقوا من هنا لنهاية
+
+237
+00:26:23,840 --> 00:26:28,220
+الفصل القصدي لسنة الجاية قصد لما تتخرج من الجامعة
+
+238
+00:26:28,220 --> 00:26:33,940
+تبقوا تبلغونييبقى لا يوجد units غير هذه الأربعة
+
+239
+00:26:33,940 --> 00:26:40,800
+عناصر فقط لا غير طيب هذا سؤال تلاتة و عشرين تمانية
+
+240
+00:26:40,800 --> 00:26:50,920
+و عشرين تمانية و عشرين بيقول لي ان زد ساكس ان زد
+
+241
+00:26:50,920 --> 00:26:59,440
+ساكس اثبتولنا ان الأربعة بتقسم اتنين و كذلك في ذكر
+
+242
+00:26:59,660 --> 00:27:10,160
+تمنية بدنا نثبت ان التلاتة تقسم السبعة وكذلك في زد
+
+243
+00:27:10,160 --> 00:27:19,000
+خمستاش بدنا نثبت ان التسعة تقسم الاطناش
+
+244
+00:27:25,260 --> 00:27:31,660
+أول شيء ما يعني أن عدد يقسم عدد آخر؟ معناه أنه
+
+245
+00:27:31,660 --> 00:27:37,320
+ممكن ألاقي عدد أضرب فيه يعطيني العدد الآخر صح ولا
+
+246
+00:27:37,320 --> 00:27:42,660
+لأ؟ إن حدث ذلك يبقى العدد اللي عندي بيقسم من العدد
+
+247
+00:27:42,660 --> 00:27:49,240
+الآخر هذا في الأعداد العادية نفس الفكرة بدنا نروح
+
+248
+00:27:49,240 --> 00:27:54,670
+نطبقها على الأعداد في أي ring أخرىمن ال rings اللي
+
+249
+00:27:54,670 --> 00:28:00,890
+بيكونوا عارفين شكل الأعداد فيها فمثلا لو جينا ل Z6
+
+250
+00:28:00,890 --> 00:28:07,370
+عناصرها من صفر لغاية خمسة يبقى الأربعة و اتنين من
+
+251
+00:28:07,370 --> 00:28:13,770
+ضمن العناصر السؤال هو هل بقدر ألاقي رقم أضربه في
+
+252
+00:28:13,770 --> 00:28:20,830
+أربعة يطلع ناتج اتنين له مين اتنين اتنين طيب لو
+
+253
+00:28:20,830 --> 00:28:26,950
+جيت قلت هنا أربعة في اتنينالتمانية اشيل منهم ستة
+
+254
+00:28:26,950 --> 00:28:32,170
+بيظل اتنين صحيح يبقى اتنين في اربع بدي اعطيهم
+
+255
+00:28:32,170 --> 00:28:38,170
+تمانية يبقى الاربع تقسم اتنين او اتنين بيقسم اتنين
+
+256
+00:28:38,170 --> 00:28:44,510
+صح؟ اه بس هذي بتلخطك اتنين و اتنين هذي لأ صح مية و
+
+257
+00:28:44,510 --> 00:28:52,890
+المية هي لكن يمكن نقدر نجيب كمرة طبعا كمرةفباربع
+
+258
+00:28:52,890 --> 00:29:01,550
+في خمسة قداش؟ اربع في خمسة اتنس صح ولا لا؟ مش اربع
+
+259
+00:29:01,550 --> 00:29:06,490
+في خمسة بعشرين شيل منه تلت ستات مضال اتنين يبقى
+
+260
+00:29:06,490 --> 00:29:14,970
+هنا اربع تقسم اتنين هنا ليش؟ لأنه اربع في خمسة بده
+
+261
+00:29:14,970 --> 00:29:20,540
+يساوي قداش بده يساوي اتنين اربع في خمسة بعشرينشيله
+
+262
+00:29:20,540 --> 00:29:25,080
+تلت ستات بتمنتعش من العشرين بيضل اتنين هيئة إذا
+
+263
+00:29:25,080 --> 00:29:31,180
+الأربعة بتقسم اتنين. يبقى هذا بيعطيك ان الأربعة
+
+264
+00:29:31,180 --> 00:29:41,580
+بتقسم اتنين. وبيجي على Z تمانية. اه. بدنا نضمن انه
+
+265
+00:29:41,580 --> 00:29:47,760
+تلاتة بتقسم سبعة. خمسة؟ خمسة في تلاتة وخمساش بيضل
+
+266
+00:29:47,760 --> 00:29:57,910
+سبعة صحيح.الان تلاتة ضرب خمسة ويساوي السبعة تلاتة
+
+267
+00:29:57,910 --> 00:30:02,970
+في الخمسة بخمستاش شيري التمانية منهم بيبقى لسبعة
+
+268
+00:30:02,970 --> 00:30:10,450
+إذا التلاتة بتقسم من تقسم السبعة زي ما هو جد اللي
+
+269
+00:30:10,450 --> 00:30:15,530
+بعدها بيزد خمستاش بدي أثبت أن التسعة بتقسم إلى
+
+270
+00:30:15,530 --> 00:30:16,490
+اتناشر
+
+271
+00:30:18,580 --> 00:30:26,700
+تسعة في تلاتة بقدر تبعة وعشرين شيل خمستاشر بظل
+
+272
+00:30:26,700 --> 00:30:34,580
+اتناشر بظل اتناشر هذا معناته ان التس .. ان التلاتة
+
+273
+00:30:34,580 --> 00:30:46,300
+ان التسعة بتقسم اتناشر هذا انزل خمستاشر وهذا
+
+274
+00:30:46,300 --> 00:31:01,680
+الكلامصحيح ان زد تمانى هذا الكلام صحيح ان زد ستة
+
+275
+00:31:40,540 --> 00:31:47,360
+طيب هذا كان سؤال تمانية وعشرين بدنا نروح لسؤال
+
+276
+00:31:47,360 --> 00:31:53,400
+تلاتين بقول يفترض انه عندي عدد N أكبر من واحد بحيث
+
+277
+00:31:53,400 --> 00:32:01,620
+ال X M بتكون ساوي ال X لكل ال X for all element X
+
+278
+00:32:01,620 --> 00:32:08,620
+of some ringيبقى هنا سؤال تلاتين في عندي X to the
+
+279
+00:32:08,620 --> 00:32:17,880
+power بتساوي X لكل X الموجودة في ring R وكذلك F
+
+280
+00:32:17,880 --> 00:32:25,700
+لهم is a positive integer و AM بتساوي Zero for
+
+281
+00:32:25,700 --> 00:32:36,020
+some A يبقى for someاللي هو العنصر A show that أن
+
+282
+00:32:36,020 --> 00:32:43,480
+ال A بده يساوي مين بده يساوي Z يبقى show أن ال A
+
+283
+00:32:43,480 --> 00:32:51,560
+هذا بده يساوي مين بده يساوي Z solution المعطيات
+
+284
+00:32:51,560 --> 00:32:58,620
+في المثلة كمان مرة بيقولينلو أخدت أي element من R
+
+285
+00:32:58,620 --> 00:33:04,080
+ورفعته للأس ان بده يعطينا ال element نفسه X to the
+
+286
+00:33:04,080 --> 00:33:10,260
+power ان بده يسوى X to the X لحاله كمان لو أخدت
+
+287
+00:33:10,260 --> 00:33:16,760
+عنصر A مش أي عنصر هي اللي ممكن ينطبق على عنصر او
+
+288
+00:33:16,760 --> 00:33:22,790
+اتنين او تلاتة ميشي الكلإن A to the power of M بدي
+
+289
+00:33:22,790 --> 00:33:27,990
+تساوي 0 for some A الموجودة في ال ring R بيقول لي
+
+290
+00:33:27,990 --> 00:33:34,610
+بييلي إن ال A هذي تساوي 100 تساوي 0 تمام تمام أنا
+
+291
+00:33:34,610 --> 00:33:41,350
+عندها بنات إن X to the power of N بدي تساوي Xfor
+
+292
+00:33:41,350 --> 00:33:46,070
+all x اللي موجود في عر السؤال هو a موجود في عر ولا
+
+293
+00:33:46,070 --> 00:33:53,110
+لا يبقى ينطقق عليه هذا الكلام يبقى a to the power
+
+294
+00:33:53,110 --> 00:34:00,750
+n بده ساوي مين بده ساوي ال a طيب حضروا لو حد فيكوا
+
+295
+00:34:00,750 --> 00:34:05,030
+حلة السؤال و الله في حلة حلت ايه قالوا بيه انا
+
+296
+00:34:05,030 --> 00:34:09,070
+حكيت ان ال a مفوزة في التجارةفممكن تكون يا واحد يا
+
+297
+00:34:09,070 --> 00:34:14,490
+أكبر من الواحد إذا كانت أكبر من الواحد هم تبقى
+
+298
+00:34:14,490 --> 00:34:19,070
+عليها الموضوع المعطنية إذا كانت بس هو ال .. أن AM
+
+299
+00:34:19,070 --> 00:34:23,770
+تساوي AM بس هو معطن أن AM تساوي سفر فال AM هتساوي
+
+300
+00:34:23,770 --> 00:34:31,570
+واحد و AM هتساوي سفر أنا حكيت في عيننا أن AM A أس
+
+301
+00:34:31,570 --> 00:34:35,350
+M بتساوي A و A أس M بتساوي Zero يعني عيني هدولتين
+
+302
+00:34:35,350 --> 00:34:41,020
+مضنسة بيج منهاهجيت ابننا نعمل علاقة بين N و M حكيت
+
+303
+00:34:41,020 --> 00:34:45,840
+أن N ممكن نكتب على صورة M في Q plus I بس خلاص سمعت
+
+304
+00:34:45,840 --> 00:34:50,600
+بال division algorithm طبعا أعطاكم يا دكتورة محمد
+
+305
+00:34:50,600 --> 00:34:56,040
+في بداية الجروز و اللي أخدت نظرية الاعداد أخدت
+
+306
+00:34:56,040 --> 00:35:02,160
+division algorithm خوارزمية القسمة إذا باجي بقول
+
+307
+00:35:02,160 --> 00:35:11,900
+إن اللي عندهاالـ N تساوي M E Q ذات R يعني الـ N
+
+308
+00:35:11,900 --> 00:35:17,980
+بدأت تساوي المضاعفات الـ M ويمكن ان تنتهي او يظل
+
+309
+00:35:17,980 --> 00:35:21,780
+الباقي الباقي الـ remainder اللي وديته الرمز R
+
+310
+00:35:21,780 --> 00:35:29,150
+احنا عندنا الـ A تساوي الـ A to the power Nهذا
+
+311
+00:35:29,150 --> 00:35:37,870
+الكلام بده يساوي A to the power N لـ MQ زائد A حسب
+
+312
+00:35:37,870 --> 00:35:46,710
+خواص الأساس يبقى AMQ مضروبة في A أُس A أو انشئتم
+
+313
+00:35:46,710 --> 00:35:55,510
+فقولوا هذا الكلام AM أُس Q في A أُس A من المعطية
+
+314
+00:35:55,510 --> 00:36:04,450
+AM بجداش ب Zeroيبقى هذا Zero مرفوع للقصة Q مضروب
+
+315
+00:36:04,450 --> 00:36:11,090
+في الـAR ناتج جداش Zero أظن هو المطلوب يبقى هي
+
+316
+00:36:11,090 --> 00:36:17,650
+الـA تساوي Zero طيب مابعدناش عن الفكرة لازلنا في
+
+317
+00:36:17,650 --> 00:36:24,810
+نفس الفكرة في سؤال تالي لهذا كان سؤال تلاتين سؤال
+
+318
+00:36:24,810 --> 00:36:32,880
+اتنين وتلاتينسؤال اتنين وثلاثين بيقول خد ال N
+
+319
+00:36:32,880 --> 00:36:39,060
+انتجر اكبر من واحد in a ring in which ال X to the
+
+320
+00:36:39,060 --> 00:36:44,320
+power N بده يساوي ال X لكل ال X اللي موجودة وين في
+
+321
+00:36:44,320 --> 00:36:54,500
+ال ring R قال لي show that show ان ال F ال A في ال
+
+322
+00:36:54,500 --> 00:37:04,270
+B بده يساوي Zerothen B في A بده يساوي مان بده
+
+323
+00:37:04,270 --> 00:37:16,510
+يساوي Zero يبقى
+
+324
+00:37:16,510 --> 00:37:19,430
+الخاصية اللي كانت في السؤال تلاتين في السؤال اتنين
+
+325
+00:37:19,430 --> 00:37:25,650
+و تلاتين هي هي لم تغير الخاصية الأولىلكن شان هذا
+
+326
+00:37:25,650 --> 00:37:32,410
+وقال لو كان حاصل ضرب ال A في B من جهة الشمال يساوي
+
+327
+00:37:32,410 --> 00:37:36,870
+Zero يبقى حاصل الضرب من جهة اليمين A في B بدك
+
+328
+00:37:36,870 --> 00:37:42,410
+تكيبته يساوي مين؟ بدك تكيبته يساوي Zero وقال الله
+
+329
+00:37:42,410 --> 00:37:50,290
+كويس احنا عندنا ال Xto the power n بدي سوى ال X
+
+330
+00:37:50,290 --> 00:37:57,670
+لكل ال X اللي موجود في R سؤال هو هل ال B A
+
+331
+00:37:57,670 --> 00:38:03,470
+المطلوبة هذه موجودة في R ولا لا؟ إذا ينطبق عليها
+
+332
+00:38:03,470 --> 00:38:13,590
+هذا الشرط يبقى هذا يعني أن ال B في A هي ال B في A
+
+333
+00:38:13,590 --> 00:38:19,730
+to the power Nطبقا لل condition اللي عندك ليش هذا
+
+334
+00:38:19,730 --> 00:38:29,150
+because ان ال B في A موجودة في ال ring A طيب تمام
+
+335
+00:38:29,150 --> 00:38:35,490
+هذا لو بدأ كتابة بنات بقدر أقول B أُس N في A أُس N
+
+336
+00:38:35,490 --> 00:38:40,690
+نقدر نقدرش
+
+337
+00:38:40,690 --> 00:38:46,560
+لأن هذه مش commutativeلو كميوتاتر بحط دوري B أس N
+
+338
+00:38:46,560 --> 00:38:52,260
+A أس N وخلاصنا لكن كونها ماهياش كميوتاتر هذه فاترة
+
+339
+00:38:52,260 --> 00:38:59,600
+بقول B في A بي في A بي في A وضل لغاية بي في N كم
+
+340
+00:38:59,600 --> 00:39:08,500
+مرة N من المرات يبقى N times يبقى N من المرات هذا
+
+341
+00:39:08,500 --> 00:39:13,970
+الكلام يساوي بدا أستخدم خاصية ال associativityيبقى
+
+342
+00:39:13,970 --> 00:39:20,830
+خاصية ال associativity يبقى هي ال B في A B في A B
+
+343
+00:39:20,830 --> 00:39:31,610
+ونظل ماشيين A B أخر حاجة A هدول كلهم كل واحدة فيهم
+
+344
+00:39:31,610 --> 00:39:39,170
+ب Zero صح؟ يبقى هذا بده ساوي B في Zero في Zero
+
+345
+00:39:39,170 --> 00:39:46,610
+ونظل ماشيين في Zero في Aيعني هذا الكلام بده يساوي
+
+346
+00:39:46,610 --> 00:39:53,770
+بي في Zero في إيه؟ يبقى هذا بده يعطيني Zero في إيه
+
+347
+00:39:53,770 --> 00:40:00,530
+اللي يبقى داك؟ ب Zero أظن وهو المطلوب يبقى هذا بده
+
+348
+00:40:00,530 --> 00:40:07,290
+يعطيلك إنه بي في إيه تساوي Zero الآن السؤال اللي
+
+349
+00:40:07,290 --> 00:40:15,720
+بعده بنفس الفكرة بس راح يعطاني إنرقم محدد مخلوش
+
+350
+00:40:15,720 --> 00:40:23,140
+سائق يبقى هذا كان سؤال اتنين و تلاتين سؤال تلاتة و
+
+351
+00:40:23,140 --> 00:40:28,260
+تلاتين سؤال
+
+352
+00:40:28,260 --> 00:40:34,640
+تلاتة و تلاتين قال افترض ال R هي ring و بحيث ان ال
+
+353
+00:40:34,640 --> 00:40:41,840
+X تكيب بالبساوي Xلكل ال X اللي موجودة في ال ring R
+
+354
+00:40:41,840 --> 00:40:53,080
+قاللي اثبت ان 6X هذا بيعطيك ان 6X يساوي 0 لكل ال X
+
+355
+00:40:53,080 --> 00:40:57,920
+اللي موجود في ال R هذا اللي عايزين تذكره
+
+356
+00:41:11,440 --> 00:41:17,540
+مرة تانية ال condition هذا هو هو بس أعطاني رقم
+
+357
+00:41:17,540 --> 00:41:24,980
+محدد مش على إطلاقه أعطاني إن لو أخدت أي X موجود في
+
+358
+00:41:24,980 --> 00:41:30,400
+ال ring R ورفعت للأس ثلاثة بتعطيني نفس ال X تحت
+
+359
+00:41:30,400 --> 00:41:35,060
+هذا ال condition قاللي اثبت إنه ستة في X يساوي
+
+360
+00:41:35,060 --> 00:41:42,790
+جديد يساوي ثلاثة يساوي ستة تمامبقوله كويس الان كنت
+
+361
+00:41:42,790 --> 00:41:49,650
+أجي و أقوله افترض ان في عندنا X موجودة في ال ring
+
+362
+00:41:49,650 --> 00:41:58,250
+R السؤال هو then هلي اتنين X موجودة في R ولا لا؟
+
+363
+00:41:58,250 --> 00:42:04,690
+لأن R is closed under addition اتنين X يعني X plus
+
+364
+00:42:04,690 --> 00:42:15,310
+Xطيب، مداني 2X موجود في R إذن 2X بقدر أقوله هي 2X
+
+365
+00:42:15,310 --> 00:42:21,850
+تكعيد سكت الشعر، مظلوم؟ يبقى ال condition هذا
+
+366
+00:42:21,850 --> 00:42:28,830
+بيخللي 2X هي 2X تكعيد هذه عبارة عن مين؟ عبارة عن
+
+367
+00:42:28,830 --> 00:42:37,420
+2X في 2X في 2Xطبغى للخواص اتنينات هذه بتطلع وين؟
+
+368
+00:42:37,420 --> 00:42:43,220
+برا يبقى اتنين في اتنين في اتنين بصير تمانية في X
+
+369
+00:42:43,220 --> 00:42:50,600
+في X في X ب X تكيب تمام يبقى صارة ان ابنة الطرف
+
+370
+00:42:50,600 --> 00:42:58,880
+الايسر اتنين X الطرف الايمن يساوي تمانية X تكيب طب
+
+371
+00:42:58,880 --> 00:43:07,020
+X تكيب بجد ايه؟ Xيبقى هذا الكلام بده يسوي تمانية X
+
+372
+00:43:07,020 --> 00:43:14,820
+لأن X تكييب هي ب X يعني هذه بالضبط هي تمانية X
+
+373
+00:43:14,820 --> 00:43:20,740
+يبقى صار اتنين X يسوي تمانية X نجيب هذه على الشجة
+
+374
+00:43:20,740 --> 00:43:25,420
+التانية او نضيف المعكوس الجمعي للطرفين الهسالي ب
+
+375
+00:43:25,420 --> 00:43:31,940
+اتنين XAutomatic هذا بيعطيك 6 X تساوي جدّاك Zero
+
+376
+00:43:31,940 --> 00:43:40,920
+وهو المطلوب سؤال فكرة بسيطة لكن بده تفكير شوية
+
+377
+00:43:40,920 --> 00:43:47,720
+يعني كيف نستخدم المعقيات اللي عندنا في الوصول إلى
+
+378
+00:43:47,720 --> 00:43:51,760
+الإجابة على المطلوب تبع السؤال
+
+379
+00:44:07,620 --> 00:44:14,860
+هذا كان .. عندنا سؤال اللي هو جداش سؤال تلاتة و
+
+380
+00:44:14,860 --> 00:44:23,260
+تلاتين طيب نروح لسؤال تسعة و تلاتين سؤال تسعة و
+
+381
+00:44:23,260 --> 00:44:29,060
+تلاتين سؤال تسعة و تلاتين بيقول افترض الارض a ring
+
+382
+00:44:29,060 --> 00:44:35,140
+with unity اللي يفجر الأعراع بعرع ال ring with
+
+383
+00:44:35,140 --> 00:44:43,470
+unityهذه المعلومة الأولى و Underlay is an element
+
+384
+00:44:43,470 --> 00:44:53,470
+of R و الـ A موجود في R such that .. such that ان
+
+385
+00:44:53,470 --> 00:44:59,890
+الـ A تربيع بده يساوي ال unity itself طيب و بعدين
+
+386
+00:44:59,890 --> 00:45:10,500
+جالي خل ال S هي كل العناصراللي على الشكل ARA بحيث
+
+387
+00:45:10,500 --> 00:45:20,540
+R موجودة في R اثبتلي ان هذه sub ring من R وهل هذه
+
+388
+00:45:20,540 --> 00:45:25,920
+ال 6 بتحتوي على الواحد الصحيح على ال unity ام لا
+
+389
+00:45:25,920 --> 00:45:34,040
+يبقى هنا بقوله sure ال S is a sub ring
+
+390
+00:45:36,480 --> 00:45:41,020
+Solutions في واحدة فيكم يا بنات حلت السؤال حلًا
+
+391
+00:45:41,020 --> 00:45:49,040
+كاملًا؟ اه يعني ذي على بركة الله نيجي انا ماخد set
+
+392
+00:45:49,040 --> 00:45:53,080
+بالشكل اللي عندنا هذي و بدي اشوف ال set هل هي
+
+393
+00:45:53,080 --> 00:45:58,900
+subring ام لا بقول بسيطة بدنا نروح تحت تأثير
+
+394
+00:45:58,900 --> 00:46:03,720
+المعلومات اللي عندنا نحاول نثبت صحة ثلاثة شروط
+
+395
+00:46:03,720 --> 00:46:11,220
+تبعت ال subringللعنصر الأول انا هادعي ان ال S is
+
+396
+00:46:11,220 --> 00:46:19,640
+man entity حدا فيكم تقدر تجيبلي عنصر يا بناد زي
+
+397
+00:46:19,640 --> 00:46:30,640
+ايش مثلا ال zero R is a zero element موجود فيها
+
+398
+00:46:30,640 --> 00:46:38,940
+اذا ال zero Rموجود فيه صح؟ طب لو قلنا واحد R واحد
+
+399
+00:46:38,940 --> 00:46:43,200
+ليش؟
+
+400
+00:46:43,200 --> 00:46:48,080
+مش ال R unity مش ال واحد unity؟ بيستخديني R صح ولا
+
+401
+00:46:48,080 --> 00:46:54,060
+لا؟ اه يبقى لأي element R في R أخدت الواحد في R في
+
+402
+00:46:54,060 --> 00:47:01,000
+واحد بيظل موجود في ال ring مظبوط لكن بس اصبر شوية
+
+403
+00:47:01,000 --> 00:47:09,920
+انا بدي كل عنصرهه شكله ايه ر ايه و الار اي انصر
+
+404
+00:47:09,920 --> 00:47:16,700
+موجود في ايه VR مظبوط يبقى لو قلنا zero ال S ما
+
+405
+00:47:16,700 --> 00:47:29,060
+ممتي because ال zero موجود في S since ال zero are
+
+406
+00:47:29,060 --> 00:47:39,100
+zero بده يساوي zeroثمان يبقى هاي شكل العنصر و zero
+
+407
+00:47:39,100 --> 00:47:45,780
+موجود في ال ring ا يبقى هذه non infinite اتنين بدي
+
+408
+00:47:45,780 --> 00:47:52,120
+اخد عنصريين موجودة في S إذا لو قلت افترض X و Y
+
+409
+00:47:52,120 --> 00:48:05,120
+موجودة في S then شكل ال X بدي يكون A R 1 Aالان شكل
+
+410
+00:48:05,120 --> 00:48:13,380
+ال Y بيكون A R to A الان بدي اشوف الفرق في ما
+
+411
+00:48:13,380 --> 00:48:19,800
+بينهم اذا وضع طلع ال X ناقص Y على الشكل اللي عندنا
+
+412
+00:48:19,800 --> 00:48:25,640
+هذا بيتم المطلوب لذا بدي اخد ال X ناقص Y يبقى A R
+
+413
+00:48:25,640 --> 00:48:34,400
+1 A ناقص A R to Aالان بالـ distributive law بدأ
+
+414
+00:48:34,400 --> 00:48:44,880
+يأخذ الـ a اللي في جهة الشمال بظل r1a ناقص r2a بدأ
+
+415
+00:48:44,880 --> 00:48:49,200
+يأخذ a اللي في جهة اليمين من الـ distributive law
+
+416
+00:48:49,200 --> 00:49:01,590
+يبقى r1 ناقص r2a r1 ناقص r2a أليس عنصراً في rلأن
+
+417
+00:49:01,590 --> 00:49:07,190
+R2 موجود في R والسالب R2 موجود في R إذا لو قلت
+
+418
+00:49:07,190 --> 00:49:13,570
+الفرق من ما هو R ثلاثة مثلا أو R كويس إذا ممكن
+
+419
+00:49:13,570 --> 00:49:24,750
+أشيل هذا و أحط بدل من A R A سميت هذا R هي موجود في
+
+420
+00:49:24,750 --> 00:49:33,090
+S يبقى صار ال X ناقص ال Yموجود في S هذا بدي يعطينا
+
+421
+00:49:33,090 --> 00:49:38,370
+ان ال X ناقص ال Y belongs to S اذا انتحقق الشرط
+
+422
+00:49:38,370 --> 00:49:45,830
+الثاني من شروط ال sub-brane بدي اجي اخد حاصل ضربه
+
+423
+00:49:45,830 --> 00:49:57,250
+معاه يبقى بدي اجي اخد X في Y تمام؟ من ال X؟ ال R1A
+
+424
+00:50:01,860 --> 00:50:15,540
+AR1A وYAR2A يعني هذا AR1A ترابيع R2A يعطيني
+
+425
+00:50:15,540 --> 00:50:21,460
+أن ال A ترابيع سوى ال unity إذا بقدر أشيل وقته بدل
+
+426
+00:50:21,460 --> 00:50:32,380
+ال unity يبقى AR1 ال unityR2A ال unity تضور بيه في
+
+427
+00:50:32,380 --> 00:50:40,720
+أي عنصر بيعطيني نفس العنصر يبقى هذا هو يساوي AR1
+
+428
+00:50:40,720 --> 00:50:49,940
+R2A هذا عنصر موجود في R ولا لا موجود في R يبقى
+
+429
+00:50:49,940 --> 00:50:59,390
+بصير هذا موجود في S since R1 R2موجود في a إذا
+
+430
+00:50:59,390 --> 00:51:05,170
+انتقفت الشروط التلاتة لذلك ال S عندنا أصبحت
+
+431
+00:51:05,170 --> 00:51:13,470
+asubring يبقى ال S asubring
+
+432
+00:51:13,470 --> 00:51:19,050
+of a السؤال
+
+433
+00:51:19,050 --> 00:51:24,350
+اللي بعده ورد أنا بغمض عن الصفر عن القرم اللي عن
+
+434
+00:51:24,350 --> 00:51:29,340
+ال aعوض باللي تقدر عليه قلبهم مصيبة ايه؟ مش احنا
+
+435
+00:51:29,340 --> 00:51:33,740
+بنعوض يعني بدل العدر اللي هو بتغير يعني R موجود في
+
+436
+00:51:33,740 --> 00:51:37,740
+الـR يعني بنعوض بدل .. ماشي شراية تنحط بدل الـR،
+
+437
+00:51:37,740 --> 00:51:44,240
+Zero بصير A في Zero في A بجد S Zero موجود في S ولا
+
+438
+00:51:44,240 --> 00:51:50,780
+لا؟ صحيح يبقى ان قلت هيك و راح ان قلت هيك ماشي
+
+439
+00:51:50,780 --> 00:51:59,280
+حالهوإن قلت a في zero في a هو zero وهذا موجود في S
+
+440
+00:51:59,280 --> 00:52:06,260
+إذا قلت a صح وإذا قلت a صح ال X
+
+441
+00:52:06,260 --> 00:52:09,960
+وY باخد كلمة ال R هي المتغيرة R1R2 .. ماشي ما انت
+
+442
+00:52:09,960 --> 00:52:15,620
+بدك شكل التلت عناصر المضروبات في بعض يطلعوا في S
+
+443
+00:52:15,620 --> 00:52:22,510
+مظبوط؟ واحنا بندور على شكل التلت عناصرA و A ثابت
+
+444
+00:52:22,510 --> 00:52:26,830
+تمام اقولك طب لو اخدت zero في zero في zero بمشي
+
+445
+00:52:26,830 --> 00:52:34,770
+الحال ولا لأ مظبوط يبقى هنا بس مالليش يبقى هنا A
+
+446
+00:52:34,770 --> 00:52:41,050
+في zero في A هنرجع خدنا خدنا zero في A خلاص بدليلي
+
+447
+00:52:41,050 --> 00:52:46,470
+ها دي ها ها بدليلي فوق و بنخنفش احنا وياه طب لما
+
+448
+00:52:46,470 --> 00:52:50,010
+الواحد .. خلاص؟ لأ طيب بده اللي هو الواحد بتبقى
+
+449
+00:52:50,010 --> 00:52:56,680
+لها ولاكأه طيب ماشي هل الواحد بيحققها ولا لا؟
+
+450
+00:52:56,680 --> 00:53:03,940
+بيسأل سؤال هل الواحد موجود في اسم ولا لا؟ بنقوله
+
+451
+00:53:03,940 --> 00:53:12,840
+موجود والسبب أه ليش السبب بيبرأك؟
+
+452
+00:53:12,840 --> 00:53:27,170
+لإن ال A في واحد ال Aيسوى مين؟ يسوى a في a تمام؟
+
+453
+00:53:27,170 --> 00:53:32,970
+يسوى a تربية يسوى واحد يبقى صار هذا ال element
+
+454
+00:53:32,970 --> 00:53:41,170
+موجود في S هذا بدي أقولك إن ال a واحد a موجود في S
+
+455
+00:53:41,170 --> 00:53:48,880
+يعني ال واحد موجود وين؟ موجود في Sأول مرة جايب إن
+
+456
+00:53:48,880 --> 00:53:54,760
+نكمل الأسئلة قبل أن ندخل الـ Integral domain اللي
+
+457
+00:53:54,760 --> 00:53:59,120
+هو الشبطر اللي بعده إن شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..68cbbeefaae01667ceb784082483dc5e480f28dc
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4953, "start": 20.99, "end": 49.53, "text": "بسم الله الرحمن الرحيم نكمل اليوم ما ابتدأنا به في المرة الماضية وهو chapter 16 اللي هو ال polynomial rings المرة اللي فاتت عرفنا ال polynomial ring واخدنا جميع two polynomials وكذلك أصل ضرب two polynomials وعطيناكم مثال على ذلك اليوم ان شاء الله بنكمل هذا الموضوع", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 24793, 1211, 45595, 20498, 19446, 48127, 2655, 3215, 10721, 8315, 39627, 8978, 9673, 25720, 9673, 46958, 10632, 37037, 2407, 7187, 3165, 13672, 1829, 31439, 2423, 26110, 11136, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 6225, 28480, 8315, 2423, 26110, 4875, 4032, 47283, 3215, 8315, 10874, 2304, 40228, 732, 22560, 12356, 4032, 4117, 8848, 23275, 5551, 36520, 48812, 25513, 732, 22560, 12356, 4032, 3615, 9566, 1829, 8315, 4117, 2304, 50113, 6027, 15844, 29910, 23275, 45595, 20498, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 23758, 9673, 2407, 11242, 45367], 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0.97021484375}, {"start": 192.32, "end": 193.52, "word": " بشرط", "probability": 0.9246419270833334}, {"start": 193.52, "end": 193.86, "word": " ان", "probability": 0.6181640625}, {"start": 193.86, "end": 194.16, "word": " ال", "probability": 0.79443359375}, {"start": 194.16, "end": 194.36, "word": " G", "probability": 0.5615234375}, {"start": 194.36, "end": 194.74, "word": " of", "probability": 0.9306640625}, {"start": 194.74, "end": 194.98, "word": " X", "probability": 0.9931640625}, {"start": 194.98, "end": 195.48, "word": " ممنوع", "probability": 0.9143880208333334}, {"start": 195.48, "end": 196.16, "word": " تساوي", "probability": 0.892578125}, {"start": 196.16, "end": 197.2, "word": " Zero", "probability": 0.57568359375}, {"start": 197.2, "end": 197.6, "word": " زي", "probability": 0.92822265625}, {"start": 197.6, "end": 197.78, "word": " ما", "probability": 0.93896484375}, {"start": 197.78, "end": 198.42, "word": " كانت", "probability": 0.654296875}, {"start": 198.42, "end": 198.82, "word": " B", "probability": 0.4345703125}, {"start": 198.82, "end": 199.5, "word": " في", "probability": 0.841796875}, {"start": 199.5, "end": 200.06, "word": " التعريف", "probability": 0.9913330078125}, {"start": 200.06, "end": 200.6, "word": " الأول", "probability": 0.92724609375}, {"start": 200.6, "end": 201.2, "word": " ممنوع", "probability": 0.9295247395833334}, {"start": 201.2, "end": 201.78, "word": " تساوي", "probability": 0.9830322265625}, {"start": 201.78, "end": 203.0, "word": " Zero", "probability": 0.955078125}, {"start": 203.0, "end": 203.52, "word": " Then", "probability": 0.360107421875}, {"start": 203.52, "end": 204.26, "word": " there", "probability": 0.66162109375}, {"start": 204.26, "end": 204.78, "word": " exist", "probability": 0.6044921875}, {"start": 204.78, "end": 205.14, "word": " a", "probability": 0.7177734375}, {"start": 205.14, "end": 205.64, "word": " unique", "probability": 0.83544921875}, {"start": 205.64, "end": 207.22, "word": " pronomials", "probability": 0.7864583333333334}, {"start": 207.22, "end": 208.02, "word": " يبقى", "probability": 0.967041015625}, {"start": 208.02, "end": 208.78, "word": " بنلاقي", "probability": 0.7935384114583334}, {"start": 208.78, "end": 210.48, "word": " كثيرات", "probability": 0.989013671875}, {"start": 210.48, "end": 211.14, "word": " حدود", "probability": 0.9903971354166666}, {"start": 211.14, "end": 212.62, "word": " واحدات", "probability": 0.8421223958333334}], "temperature": 1.0}, {"id": 8, "seek": 23768, "start": 212.88, "end": 237.68, "text": "مافيش غيرهم لل two functions أو ال two polynomials هدول لل Q of X و R of X في نفس ال field اللي هو ال F هذه بس هذه على أعداد صحيحة integers هذه عالمين على polynomials كثيرات حدود يبقى ال polynomial F of X", "tokens": [15042, 41185, 8592, 32771, 13546, 16095, 24976, 732, 6828, 34051, 2423, 732, 22560, 12356, 8032, 3215, 12610, 24976, 1249, 295, 1783, 4032, 497, 295, 1783, 8978, 8717, 36178, 2423, 2519, 13672, 1829, 31439, 2423, 479, 29538, 4724, 3794, 29538, 15844, 5551, 22488, 18513, 20328, 5016, 1829, 5016, 3660, 41674, 29538, 6225, 45340, 9957, 15844, 22560, 12356, 9122, 12984, 13546, 9307, 11331, 3215, 23328, 7251, 3555, 4587, 7578, 2423, 26110, 479, 295, 1783], "avg_logprob": -0.22645548271806273, "compression_ratio": 1.5077720207253886, "no_speech_prob": 0.0, "words": [{"start": 212.88, "end": 213.68, "word": "مافيش", "probability": 0.7091471354166666}, {"start": 213.68, "end": 214.38, "word": " غيرهم", "probability": 0.935546875}, {"start": 214.38, "end": 214.96, "word": " لل", "probability": 0.32470703125}, {"start": 214.96, "end": 215.32, "word": " two", "probability": 0.391357421875}, {"start": 215.32, "end": 216.04, "word": " functions", "probability": 0.8173828125}, {"start": 216.04, "end": 216.3, "word": " أو", "probability": 0.65673828125}, {"start": 216.3, "end": 216.44, "word": " ال", "probability": 0.8427734375}, {"start": 216.44, "end": 216.62, "word": " two", "probability": 0.7490234375}, {"start": 216.62, "end": 217.6, "word": " polynomials", "probability": 0.90966796875}, {"start": 217.6, "end": 218.16, "word": " هدول", "probability": 0.7109375}, {"start": 218.16, "end": 218.92, "word": " لل", "probability": 0.315185546875}, {"start": 218.92, "end": 219.36, "word": " Q", "probability": 0.6337890625}, {"start": 219.36, "end": 219.7, "word": " of", "probability": 0.79833984375}, {"start": 219.7, "end": 220.1, "word": " X", "probability": 0.9638671875}, {"start": 220.1, "end": 220.4, "word": " و", "probability": 0.9658203125}, {"start": 220.4, "end": 220.84, "word": " R", "probability": 0.48876953125}, {"start": 220.84, "end": 221.18, "word": " of", "probability": 0.9775390625}, {"start": 221.18, "end": 221.58, "word": " X", "probability": 0.994140625}, {"start": 221.58, "end": 222.14, "word": " في", "probability": 0.77685546875}, {"start": 222.14, "end": 222.66, "word": " نفس", "probability": 0.989501953125}, {"start": 222.66, "end": 223.12, "word": " ال", "probability": 0.84423828125}, {"start": 223.12, "end": 223.62, "word": " field", "probability": 0.93115234375}, {"start": 223.62, "end": 223.82, "word": " اللي", "probability": 0.843017578125}, {"start": 223.82, "end": 223.94, "word": " هو", "probability": 0.6611328125}, {"start": 223.94, "end": 224.08, "word": " ال", "probability": 0.71337890625}, {"start": 224.08, "end": 224.38, "word": " F", "probability": 0.8876953125}, {"start": 224.38, "end": 224.86, "word": " هذه", "probability": 0.286865234375}, {"start": 224.86, "end": 226.08, "word": " بس", "probability": 0.936767578125}, {"start": 226.08, "end": 226.48, "word": " هذه", "probability": 0.74853515625}, {"start": 226.48, "end": 226.84, "word": " على", "probability": 0.80908203125}, {"start": 226.84, "end": 227.58, "word": " أعداد", "probability": 0.8876953125}, {"start": 227.58, "end": 228.44, "word": " صحيحة", "probability": 0.9482421875}, {"start": 228.44, "end": 229.18, "word": " integers", "probability": 0.86962890625}, {"start": 229.18, "end": 230.3, 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"end": 264.4, "text": "قدرت اكتبها على شكل polynomial في polynomial تانية والباقي قد يكون polynomial وقد يكون constant polynomial جالي قالت ايضا اما R of X تساوي Zero لو كانت R of X تساوي Zero يبقى راحة يبقى صاحي ال F of X يحاصل ضرب لمين", "tokens": [28543, 43500, 1975, 4117, 2655, 3555, 11296, 15844, 13412, 28820, 26110, 8978, 26110, 6055, 7649, 10632, 16070, 3555, 995, 38436, 12174, 3215, 7251, 30544, 26110, 4032, 28543, 7251, 30544, 5754, 26110, 10874, 6027, 1829, 50239, 2655, 1975, 1829, 11242, 995, 1975, 15042, 497, 295, 1783, 6055, 3794, 995, 45865, 17182, 45164, 25961, 2655, 497, 295, 1783, 6055, 3794, 995, 45865, 17182, 7251, 3555, 4587, 7578, 12602, 39319, 3660, 7251, 3555, 4587, 7578, 20328, 39319, 1829, 2423, 479, 295, 1783, 7251, 5016, 33546, 1211, 48812, 25513, 32767, 9957], "avg_logprob": -0.1946022715419531, "compression_ratio": 1.6825396825396826, "no_speech_prob": 0.0, "words": [{"start": 238.04, "end": 238.66, "word": "قدرت", "probability": 0.71484375}, {"start": 238.66, "end": 239.38, "word": " اكتبها", "probability": 0.898046875}, {"start": 239.38, "end": 239.68, "word": " على", "probability": 0.85888671875}, {"start": 239.68, "end": 240.24, "word": " شكل", "probability": 0.97412109375}, {"start": 240.24, "end": 241.18, "word": " polynomial", "probability": 0.49462890625}, {"start": 241.18, "end": 241.46, "word": " في", "probability": 0.6337890625}, {"start": 241.46, "end": 242.3, "word": " polynomial", "probability": 0.91259765625}, {"start": 242.3, "end": 243.36, "word": " تانية", "probability": 0.9560546875}, {"start": 243.36, "end": 244.44, "word": " والباقي", "probability": 0.861083984375}, {"start": 244.44, "end": 244.84, "word": " قد", "probability": 0.952880859375}, {"start": 244.84, "end": 245.58, "word": " يكون", "probability": 0.986572265625}, {"start": 245.58, "end": 246.46, "word": " polynomial", "probability": 0.958984375}, {"start": 246.46, "end": 247.28, "word": " وقد", "probability": 0.876708984375}, {"start": 247.28, "end": 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"probability": 0.84423828125}, {"start": 256.5, "end": 257.14, "word": " كانت", "probability": 0.94921875}, {"start": 257.14, "end": 257.46, "word": " R", "probability": 0.9296875}, {"start": 257.46, "end": 257.8, "word": " of", "probability": 0.94189453125}, {"start": 257.8, "end": 258.08, "word": " X", "probability": 0.99462890625}, {"start": 258.08, "end": 258.6, "word": " تساوي", "probability": 0.97509765625}, {"start": 258.6, "end": 258.9, "word": " Zero", "probability": 0.94677734375}, {"start": 258.9, "end": 259.38, "word": " يبقى", "probability": 0.94189453125}, {"start": 259.38, "end": 260.02, "word": " راحة", "probability": 0.8028971354166666}, {"start": 260.02, "end": 260.86, "word": " يبقى", "probability": 0.966064453125}, {"start": 260.86, "end": 261.42, "word": " صاحي", "probability": 0.4081217447916667}, {"start": 261.42, "end": 261.56, "word": " ال", "probability": 0.443359375}, {"start": 261.56, "end": 261.84, "word": " F", "probability": 0.8642578125}, {"start": 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0.80400390625}, {"start": 473.73, "end": 475.43, "word": " طب", "probability": 0.7685546875}, {"start": 475.43, "end": 475.59, "word": " أنا", "probability": 0.2406005859375}, {"start": 475.59, "end": 475.93, "word": " بدأ", "probability": 0.70166015625}, {"start": 475.93, "end": 476.33, "word": " أسأل", "probability": 0.8795166015625}, {"start": 476.33, "end": 477.33, "word": " Z6", "probability": 0.8447265625}, {"start": 477.33, "end": 477.55, "word": " في", "probability": 0.82080078125}, {"start": 477.55, "end": 481.67, "word": " Z6", "probability": 0.6875}, {"start": 481.67, "end": 481.91, "word": " في", "probability": 0.966796875}, {"start": 481.91, "end": 484.21, "word": " كيف؟", "probability": 0.757568359375}], "temperature": 1.0}, {"id": 18, "seek": 51024, "start": 484.26, "end": 510.24, "text": "فيها Zero وفيها Zero Divisor Z6 فيه؟ لأ طبعا كيف؟ النظرية فيه من اللي اختلف بـ AFL يعني مانفعش اخد في Z6 كلامنا غلط لإن Z6 is not AFL فيه Non Zero Zero Divisor اتنين في تلاتة بستة يبقى اتنين Zero Divisor والتلاتة Zero Divisor ولا واحد فيهم اللي معكوس مصبوط", "tokens": [41185, 11296, 17182, 4032, 41185, 11296, 17182, 9886, 271, 284, 1176, 21, 8978, 3224, 22807, 5296, 10721, 23032, 3555, 3615, 995, 9122, 33911, 22807, 28239, 19913, 2288, 10632, 8978, 3224, 9154, 13672, 1829, 1975, 46456, 46538, 4724, 39184, 20389, 43, 37495, 22653, 3714, 7649, 5172, 3615, 8592, 1975, 9778, 3215, 8978, 1176, 21, 28242, 10943, 8315, 32771, 1211, 9566, 5296, 28814, 1863, 1176, 21, 307, 406, 20389, 43, 8978, 3224, 8774, 17182, 17182, 9886, 271, 284, 1975, 2655, 1863, 9957, 8978, 6055, 1211, 9307, 3660, 4724, 14851, 3660, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 17182, 9886, 271, 284, 16070, 2655, 1211, 9307, 3660, 17182, 9886, 271, 284, 49429, 36764, 24401, 8978, 16095, 13672, 1829, 20449, 4117, 41779, 3714, 9381, 3555, 2407, 9566], "avg_logprob": -0.2984999961853027, "compression_ratio": 1.7647058823529411, "no_speech_prob": 0.0, "words": [{"start": 484.26, "end": 484.64, "word": "فيها", "probability": 0.4510498046875}, {"start": 484.64, "end": 484.78, "word": " Zero", "probability": 0.219482421875}, {"start": 484.78, "end": 485.32, "word": " وفيها", "probability": 0.6434733072916666}, {"start": 485.32, "end": 485.56, "word": " Zero", "probability": 0.85888671875}, {"start": 485.56, "end": 485.92, "word": " Divisor", "probability": 0.773681640625}, {"start": 485.92, "end": 486.78, "word": " Z6", "probability": 0.5631103515625}, {"start": 486.78, "end": 487.42, "word": " فيه؟", "probability": 0.748046875}, {"start": 487.42, "end": 488.12, "word": " لأ", "probability": 0.68115234375}, {"start": 488.12, "end": 489.16, "word": " طبعا", "probability": 0.7481689453125}, {"start": 489.16, "end": 489.54, "word": " كيف؟", "probability": 0.5814615885416666}, {"start": 489.54, "end": 490.02, "word": " النظرية", "probability": 0.896240234375}, {"start": 490.02, "end": 490.3, "word": " فيه", "probability": 0.720947265625}, {"start": 490.3, "end": 490.4, "word": " من", "probability": 0.443603515625}, {"start": 490.4, "end": 490.58, "word": " اللي", "probability": 0.608642578125}, {"start": 490.58, "end": 490.94, "word": " اختلف", "probability": 0.738037109375}, {"start": 490.94, "end": 491.3, "word": " بـ", "probability": 0.52239990234375}, {"start": 491.3, "end": 491.76, "word": " AFL", "probability": 0.7322998046875}, {"start": 491.76, "end": 492.82, "word": " يعني", "probability": 0.759765625}, {"start": 492.82, "end": 493.48, "word": " مانفعش", "probability": 0.748388671875}, {"start": 493.48, "end": 493.84, "word": " اخد", "probability": 0.7755533854166666}, {"start": 493.84, "end": 494.0, "word": " في", "probability": 0.87255859375}, {"start": 494.0, "end": 494.68, "word": " Z6", "probability": 0.941650390625}, {"start": 494.68, "end": 495.36, "word": " كلامنا", "probability": 0.88916015625}, {"start": 495.36, "end": 495.76, "word": " غلط", "probability": 0.9864908854166666}, {"start": 495.76, "end": 496.02, "word": " لإن", "probability": 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"word": " معكوس", "probability": 0.7960611979166666}, {"start": 509.16, "end": 510.24, "word": " مصبوط", "probability": 0.68232421875}], "temperature": 1.0}, {"id": 19, "seek": 53875, "start": 510.43, "end": 538.75, "text": "يبقى Z6 is not a field وإحنا نظريتنا محوطة على مين؟ على ال field يعني بلو استبدل Z5 بZ6 بيكون كلامنا كله خطأ رأسا على عقب ياري بالك، صح، عايز كويس Z5 ماشي الحال، Z7 ماشي الحال، Z11 ماشي الحال، مدام هذا prime ماعناه مشكلة قلص، بيكون هذا ياشفير", "tokens": [1829, 3555, 4587, 7578, 1176, 21, 307, 406, 257, 2519, 4032, 28814, 5016, 8315, 8717, 19913, 16572, 2655, 8315, 3714, 5016, 2407, 9566, 3660, 15844, 3714, 9957, 22807, 15844, 2423, 2519, 37495, 22653, 4724, 1211, 2407, 44713, 44510, 1211, 1176, 20, 4724, 57, 21, 4724, 1829, 30544, 28242, 10943, 8315, 28242, 3224, 16490, 9566, 10721, 12602, 10721, 3794, 995, 15844, 6225, 4587, 3555, 7251, 9640, 1829, 20666, 4117, 12399, 20328, 5016, 12399, 6225, 47302, 11622, 9122, 45865, 3794, 1176, 20, 3714, 33599, 1829, 21542, 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"probability": 0.768798828125}, {"start": 528.47, "end": 528.99, "word": " ماشي", "probability": 0.9427083333333334}, {"start": 528.99, "end": 529.59, "word": " الحال،", "probability": 0.8854166666666666}, {"start": 529.59, "end": 530.43, "word": " Z7", "probability": 0.9931640625}, {"start": 530.43, "end": 530.89, "word": " ماشي", "probability": 0.9661458333333334}, {"start": 530.89, "end": 531.49, "word": " الحال،", "probability": 0.9435221354166666}, {"start": 531.49, "end": 532.71, "word": " Z11", "probability": 0.989013671875}, {"start": 532.71, "end": 533.67, "word": " ماشي", "probability": 0.9484049479166666}, {"start": 533.67, "end": 534.19, "word": " الحال،", "probability": 0.9093424479166666}, {"start": 534.19, "end": 534.53, "word": " مدام", "probability": 0.8624674479166666}, {"start": 534.53, "end": 534.83, "word": " هذا", "probability": 0.8955078125}, {"start": 534.83, "end": 535.41, "word": " prime", "probability": 0.724609375}, {"start": 535.41, "end": 536.39, "word": " ماعناه", "probability": 0.78662109375}, {"start": 536.39, "end": 536.91, "word": " مشكلة", "probability": 0.9689127604166666}, {"start": 536.91, "end": 537.41, "word": " قلص،", "probability": 0.5760498046875}, {"start": 537.41, "end": 537.73, "word": " بيكون", "probability": 0.8976236979166666}, {"start": 537.73, "end": 538.05, "word": " هذا", "probability": 0.9541015625}, {"start": 538.05, "end": 538.75, "word": " ياشفير", "probability": 0.6077880859375}], "temperature": 1.0}, {"id": 20, "seek": 56891, "start": 539.15, "end": 568.91, "text": "Any non-zero element has a multiplicative inverse أي عنصر غير صفري له معكس وبالتالي فهو field إذا إحنا شغولنا على مين؟ على ال field اللي هو حالة خاصة من مين؟ من ال ring تمام؟ هي يبقى هي عندي دالة وهي دالة تانية وتنتين موجودة في z خمسة طب ينفع أقول الأولى مثلا موجودة في z خمسة", "tokens": [29647, 2107, 12, 32226, 4478, 575, 257, 17596, 1166, 17340, 36632, 18871, 9381, 2288, 32771, 13546, 20328, 5172, 16572, 46740, 20449, 4117, 3794, 46599, 6027, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bcb8bac202f88c02d0db6fd66365be4fd3db7de6
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_raw.srt
@@ -0,0 +1,1444 @@
+1
+00:00:20,990 --> 00:00:26,070
+بسم الله الرحمن الرحيم نكمل اليوم ما ابتدأنا به في
+
+2
+00:00:26,070 --> 00:00:32,950
+المرة الماضية وهو chapter 16 اللي هو ال polynomial
+
+3
+00:00:32,950 --> 00:00:37,470
+rings المرة اللي فاتت عرفنا ال polynomial ring
+
+4
+00:00:37,470 --> 00:00:43,190
+واخدنا جميع two polynomials وكذلك أصل ضرب two
+
+5
+00:00:43,190 --> 00:00:48,010
+polynomials وعطيناكم مثال على ذلك اليوم ان شاء
+
+6
+00:00:48,010 --> 00:00:53,140
+الله بنكمل هذا الموضوعالتعريف الأول هو تذكير بما
+
+7
+00:00:53,140 --> 00:00:59,020
+أخدته في كل في تفاضل وتكافي جفر حديث واحد في
+
+8
+00:00:59,020 --> 00:01:04,740
+المقدمة اللي هي خوارزمية القسمة division algorithm
+
+9
+00:01:04,740 --> 00:01:09,660
+على الأعداد بذكر بهذا التذكير لأنه هنتقل من
+
+10
+00:01:09,660 --> 00:01:16,020
+الأعداد إلى ال polynomial فالتعريف كان بيقول افترض
+
+11
+00:01:16,020 --> 00:01:24,240
+يساوي مضعفات ال BP مضغوط في Q زائد ال R ال R هذا
+
+12
+00:01:24,240 --> 00:01:31,260
+قد يكون صفر و قد يكون أقل من P قال لي where ال R
+
+13
+00:01:31,260 --> 00:01:38,480
+أكبر من أو تساوي zero و less than P السبب ان ال R
+
+14
+00:01:38,480 --> 00:01:45,240
+هذا ممكن يكون صفر و ممكن يكون رقم أقل من P السؤال
+
+15
+00:01:45,240 --> 00:01:52,740
+هوممكن يكون اكبر من B؟ لأ لو كان اكبر من D دخل مع
+
+16
+00:01:52,740 --> 00:02:00,980
+الجزء الاول من هذه المعدة يبقى R اقل من B وقد يكون
+
+17
+00:02:00,980 --> 00:02:09,040
+صفر لو كان صفر معناته ال B بيقسم ال A بدون باقي
+
+18
+00:02:09,040 --> 00:02:15,110
+مضلش باقيلكن لو ضال رقم يبقى بيه اسمه و بيضل ايش و
+
+19
+00:02:15,110 --> 00:02:21,790
+بيضل باقي طيب ال this operation هذه العملية هي
+
+20
+00:02:21,790 --> 00:02:27,710
+اللي بده اسميها division algorithm خوارزمية القسمة
+
+21
+00:02:27,710 --> 00:02:36,020
+على الأعداد هذه طبعا في مقدمة جبر حديث واحدهذه
+
+22
+00:02:36,020 --> 00:02:40,920
+خوازمية وقسمة على الـ fields على ال functions اللي
+
+23
+00:02:40,920 --> 00:02:46,160
+موجودة في ال field فجينا قولنا division algorithm
+
+24
+00:02:46,160 --> 00:02:52,820
+for capital F of X يبقى قولنا خد ال F عبارة عن
+
+25
+00:02:52,820 --> 00:02:59,140
+field وخد ال two elements موجودات في capital F of
+
+26
+00:02:59,140 --> 00:03:08,660
+X يعني F of X وG of XPronomials كثيرات حدود موجودة
+
+27
+00:03:08,660 --> 00:03:14,740
+في ال field اللي هو capital F of X بشرط ان ال G of
+
+28
+00:03:14,740 --> 00:03:20,600
+X ممنوع تساوي Zero زي ما كانت B في التعريف الأول
+
+29
+00:03:20,600 --> 00:03:25,640
+ممنوع تساوي Zero Then there exist a unique
+
+30
+00:03:25,640 --> 00:03:33,680
+pronomials يبقى بنلاقي كثيرات حدود واحداتمافيش
+
+31
+00:03:33,680 --> 00:03:38,160
+غيرهم لل two functions أو ال two polynomials هدول
+
+32
+00:03:38,160 --> 00:03:44,380
+لل Q of X و R of X في نفس ال field اللي هو ال F
+
+33
+00:03:44,380 --> 00:03:51,400
+هذه بس هذه على أعداد صحيحة integers هذه عالمين على
+
+34
+00:03:51,400 --> 00:03:57,680
+polynomials كثيرات حدود يبقى ال polynomial F of X
+
+35
+00:03:58,040 --> 00:04:03,360
+قدرت اكتبها على شكل polynomial في polynomial تانية
+
+36
+00:04:03,360 --> 00:04:08,980
+والباقي قد يكون polynomial وقد يكون constant
+
+37
+00:04:08,980 --> 00:04:16,500
+polynomial جالي قالت ايضا اما R of X تساوي Zero لو
+
+38
+00:04:16,500 --> 00:04:22,120
+كانت R of X تساوي Zero يبقى راحة يبقى صاحي ال F of
+
+39
+00:04:22,120 --> 00:04:31,290
+X يحاصل ضرب لمينلتو Polynomials طبعا؟ طيب يا إما
+
+40
+00:04:31,290 --> 00:04:38,390
+درجة ال R of X أقل من درجة ال G of X يبقى درجة ال
+
+41
+00:04:38,390 --> 00:04:45,950
+R of X أقل من درجة ال G of X بنفع تساويها؟ لو سوى
+
+42
+00:04:45,950 --> 00:04:51,390
+التكانصال R of X ب Zero دخلت في مين؟ في خارج القسم
+
+43
+00:04:51,390 --> 00:04:59,130
+هذهأقل من درجة ال U of X يبقى بظل هذا باقي يبقى
+
+44
+00:04:59,130 --> 00:05:05,030
+هذه المعادلة هذا بسميه خارج القسمة وال R of X
+
+45
+00:05:05,030 --> 00:05:11,150
+بسميه مين بسميه الباقي يبقى ال polynomial ال U of
+
+46
+00:05:11,150 --> 00:05:17,750
+X بسميها quotient يعني خارج القسمة يعني خارج قسمة
+
+47
+00:05:17,750 --> 00:05:25,210
+F على G and ال R of Xبسميه الـ remainder الباقي
+
+48
+00:05:25,210 --> 00:05:32,970
+نتيجة لقسم F of X على مين؟ على G of X إذا لما أقسم
+
+49
+00:05:32,970 --> 00:05:40,870
+F of X على G of X ممكن يظهر نتيجة G of X مضروبة في
+
+50
+00:05:40,870 --> 00:05:47,030
+Q of X فقط وفي هذه الحالة يكون R of X بقدرش؟ بزير
+
+51
+00:05:47,610 --> 00:05:52,270
+طيب لو ما طلعش بزير و طلع زائد شغلة يبقى الشغلة دي
+
+52
+00:05:52,270 --> 00:05:59,170
+بسميها الباقي و درجة الباقي أقل من درجة GeoVec
+
+53
+00:05:59,170 --> 00:06:03,810
+يعني لو كان GeoVec من الدرجة الثانية الباقية بدي
+
+54
+00:06:03,810 --> 00:06:08,470
+يكون يا إما من الدرجة الأولى يا إما من الدرجة
+
+55
+00:06:08,470 --> 00:06:14,630
+الصفرية يعني constant تمام؟لكن إن كان بجسمه على
+
+56
+00:06:14,630 --> 00:06:19,310
+بعض بيكون الاروف اكس زيرو على طول الخط واضح
+
+57
+00:06:19,310 --> 00:06:23,430
+كلامنا؟ طبعا البرهان طويل لإنه بدنا نثبت ال
+
+58
+00:06:23,430 --> 00:06:28,310
+existence وبدنا نثبت من ال uniqueness ويا ما
+
+59
+00:06:28,310 --> 00:06:33,470
+اثبتنا هذا في جبر حديث واحد يبقى انسلط بعد مانعش
+
+60
+00:06:33,470 --> 00:06:38,030
+نضيع فيه وقت لكن كل اللي بدي أكي تعرفيه أن أي two
+
+61
+00:06:38,030 --> 00:06:42,250
+functions في نفس الفيلبقدر اكتب واحدة بدلالة
+
+62
+00:06:42,250 --> 00:06:46,710
+التانية على مين على الصيلة اللى قدامنا هذه يبقى
+
+63
+00:06:46,710 --> 00:06:52,030
+هذه الصيلة هتمر معانا كتير واحنا بنشتغل في ال
+
+64
+00:06:52,030 --> 00:07:00,850
+polynomial rings طيب لان نعطي مثال توضيحى كيف بدي
+
+65
+00:07:00,850 --> 00:07:06,420
+اجيب ال quotient وكيف بدي اجيب ال remainderقال
+
+66
+00:07:06,420 --> 00:07:12,420
+افترض F of X موجودة بالشكل هذا وهي موجودة في Z
+
+67
+00:07:12,420 --> 00:07:21,540
+خمسة of X تمام؟ and G of X موجودة كمان في Z خمسة
+
+68
+00:07:21,540 --> 00:07:25,560
+of X قال هاتلي ال quotient وهاتلي ال remain dark
+
+69
+00:07:25,560 --> 00:07:31,440
+لما نقسم ال F of X على مين؟ على ال G of X قبل
+
+70
+00:07:31,440 --> 00:07:38,850
+المبدأ بدي اسألي السؤال التاليبنفع ناخد polynomial
+
+71
+00:07:38,850 --> 00:07:46,530
+في Z6 و polynomial ثانية في Z6؟
+
+72
+00:07:46,530 --> 00:08:01,670
+بنفع بدون مشاكل؟ بنفع؟ طب أنا بدأ أسأل Z6 في Z6
+
+73
+00:08:01,670 --> 00:08:08,120
+في كيف؟فيها Zero وفيها Zero Divisor Z6 فيه؟ لأ
+
+74
+00:08:08,120 --> 00:08:12,820
+طبعا كيف؟ النظرية فيه من اللي اختلف بـ AFL يعني
+
+75
+00:08:12,820 --> 00:08:19,520
+مانفعش اخد في Z6 كلامنا غلط لإن Z6 is not AFL فيه
+
+76
+00:08:19,520 --> 00:08:24,160
+Non Zero Zero Divisor اتنين في تلاتة بستة يبقى
+
+77
+00:08:24,160 --> 00:08:27,800
+اتنين Zero Divisor والتلاتة Zero Divisor ولا واحد
+
+78
+00:08:27,800 --> 00:08:33,250
+فيهم اللي معكوس مصبوطيبقى Z6 is not a field وإحنا
+
+79
+00:08:33,250 --> 00:08:37,850
+نظريتنا محوطة على مين؟ على ال field يعني بلو
+
+80
+00:08:37,850 --> 00:08:44,790
+استبدل Z5 بZ6 بيكون كلامنا كله خطأ رأسا على عقب
+
+81
+00:08:44,790 --> 00:08:50,890
+ياري بالك، صح، عايز كويس Z5 ماشي الحال، Z7 ماشي
+
+82
+00:08:50,890 --> 00:08:56,910
+الحال، Z11 ماشي الحال، مدام هذا prime ماعناه مشكلة
+
+83
+00:08:56,910 --> 00:09:01,450
+قلص، بيكون هذا ياشفيرAny non-zero element has a
+
+84
+00:09:01,450 --> 00:09:05,450
+multiplicative inverse أي عنصر غير صفري له معكس
+
+85
+00:09:05,450 --> 00:09:10,470
+وبالتالي فهو field إذا إحنا شغولنا على مين؟ على ال
+
+86
+00:09:10,470 --> 00:09:16,890
+field اللي هو حالة خاصة من مين؟ من ال ring تمام؟
+
+87
+00:09:16,890 --> 00:09:23,690
+هي يبقى هي عندي دالة وهي دالة تانية وتنتين موجودة
+
+88
+00:09:23,690 --> 00:09:28,230
+في z خمسة طب ينفع أقول الأولى مثلا موجودة في z
+
+89
+00:09:28,230 --> 00:09:35,710
+خمسةوالتانية موجودة في زيت سبعة ونبدأ نجسب لأن انت
+
+90
+00:09:35,710 --> 00:09:40,590
+صرت بتشتغل في two fields مع بعض و هذا كلام قضى
+
+91
+00:09:40,590 --> 00:09:46,050
+احنا بنشغل دايما و انه أبدا داخل field واحد يبقى
+
+92
+00:09:46,050 --> 00:09:49,790
+كله بده يكون في نفس ال field و ليس في two
+
+93
+00:09:49,790 --> 00:09:56,020
+different fields طيب ماشيالان قليلة ال quotient و
+
+94
+00:09:56,020 --> 00:10:01,100
+هاتلة ال remainder يبقى بدنا نبدأ نقسم و نطلع خارج
+
+95
+00:10:01,100 --> 00:10:08,220
+القسمة و كذلك ال باقى قسمة مطولة زي ما كنا بنقسم
+
+96
+00:10:08,220 --> 00:10:14,180
+في الصف السابع و الصف التامن بس بالشرط شغلنا داخل
+
+97
+00:10:14,180 --> 00:10:18,680
+Z خامسة تمام؟ يبقى بقى اللي بقوله قد أجي ال
+
+98
+00:10:18,680 --> 00:10:24,830
+function اللي عندنا F of X اللي ثلاثة X و أربعزائد
+
+99
+00:10:24,830 --> 00:10:31,950
+اكس تكيب زائد اتنين اكس تربيع زائد واحد بدك زمها
+
+100
+00:10:31,950 --> 00:10:39,790
+عادي جدا على اكس تربيع زائد اربعة اكس زائد اتنين
+
+101
+00:10:39,790 --> 00:10:47,310
+بنبدأ بقسم الأكبر تيرم هي على أكبر تيرم والباقي
+
+102
+00:10:47,310 --> 00:10:53,770
+بالحجوهم طبيعيينيبقى تلاتة X أُس أربعة على X تربيع
+
+103
+00:10:53,770 --> 00:11:01,050
+بيطلع كدهش تلاتة X تربيع في X تربيع يبقى تلاتة X
+
+104
+00:11:01,050 --> 00:11:07,290
+أُس أربعة اللي بعديها تلاتة في أربعة باطماشر X
+
+105
+00:11:07,290 --> 00:11:13,070
+تكييب واحنا بنشغل في Z خمسة يبقى الأتناشر عبارة عن
+
+106
+00:11:13,070 --> 00:11:20,740
+اتنين شيلي خمسين يبقى زائدي اتنين X تكييباللي
+
+107
+00:11:20,740 --> 00:11:29,260
+بعدها زائد ثلاثة في اتنين في ستة X تربيع شيله خمسة
+
+108
+00:11:29,260 --> 00:11:37,340
+يبقى زائد X تربيع فقط هاي زائد بنغير الإشارات
+
+109
+00:11:37,340 --> 00:11:45,680
+وبنجمع يبقى هنا ناقص اتنين X تكيب وزايد X تكيببظل
+
+110
+00:11:45,680 --> 00:11:52,520
+سالب X تكييب واحدة يبقى سالب X تكييب واحدة عندك
+
+111
+00:11:52,520 --> 00:11:58,660
+هنا سالب X تربيع زي اتنين X تربيع بظل قداش زائد X
+
+112
+00:11:58,660 --> 00:12:04,400
+تربيع زائد واحد لكن ماعنديش سالب واحد في زيد خمسة
+
+113
+00:12:04,400 --> 00:12:11,760
+لكن سالب واحد بكافئة أربع يبقى هذه معناته هي أربع
+
+114
+00:12:11,760 --> 00:12:20,900
+X تكييبزائد X تربيع زائد واحد تمام؟ طيب صارت هذا
+
+115
+00:12:20,900 --> 00:12:25,480
+من الدرجة التالتة وهذا من الدرجة التانية بنواصل
+
+116
+00:12:25,480 --> 00:12:34,080
+عملية القسمة يبقى هنا زائد اربع X في X تربيع في
+
+117
+00:12:34,080 --> 00:12:43,130
+اربع X تكييف زائد اربع في اربع16 X تربيع يعني واحد
+
+118
+00:12:43,130 --> 00:12:51,650
+في X تربيع X تربيع واحدة هنا زائد تمانية X شيل من
+
+119
+00:12:51,650 --> 00:12:59,610
+الخمسة بظال ثلاثة X نيجي نغير الإشارات هذه زائد
+
+120
+00:12:59,610 --> 00:13:05,730
+بيصير ناقص ناقص ناقص مع السلامة وهذه غير ملسوف
+
+121
+00:13:05,730 --> 00:13:13,730
+عليهابيبقى ناقص ثلاثة X زائد واحد يبقى ناقص ثلاثة
+
+122
+00:13:13,730 --> 00:13:18,870
+X زائد واحد لكن ماعنديش ناقص ثلاثة في Z خمسة في
+
+123
+00:13:18,870 --> 00:13:25,310
+رقم يو كافر باضيفله قداشر خمسة لما اضفلها خمسة
+
+124
+00:13:25,310 --> 00:13:31,390
+بصير اتنين X زائد واحد هذا من الدرجة الأولى
+
+125
+00:13:31,390 --> 00:13:35,930
+والمقسوم عليهمن الدرجة التانية بقى بس الله يعطيك
+
+126
+00:13:35,930 --> 00:13:41,550
+العافية بيقدر تمشي ولا قطوع بعد ذلك إذا أصبحت ال
+
+127
+00:13:41,550 --> 00:13:47,070
+function اللي عندنا اللي هي ال F of X تساوي مين
+
+128
+00:13:47,070 --> 00:13:53,910
+تساوي تلاتة X أُص أربعة زائد X تخيب زائد اتنين X
+
+129
+00:13:53,910 --> 00:14:00,750
+تربيع زائد واحد تساوي اللي عندنا مين الدالة اللي
+
+130
+00:14:00,750 --> 00:14:07,090
+عندنا اللي هو X تربيعزائد أربع X زائد اتنين في
+
+131
+00:14:07,090 --> 00:14:15,290
+خارج القسمة خارج القسمة اللي هو تلاتة X تربيع زائد
+
+132
+00:14:15,290 --> 00:14:22,330
+أربع X لكن لسه ضايل عند مين يتنين X زائد واحد بده
+
+133
+00:14:22,330 --> 00:14:27,830
+ينقسم على هذا إذا قدرنا نحط ال function اللي عندنا
+
+134
+00:14:27,830 --> 00:14:33,090
+الأساسية على الشكل اللي عندنا هذايبقى هذه مين يا
+
+135
+00:14:33,090 --> 00:14:41,650
+ولد؟ هذه F of X وهذه مين؟ G of X وهذه مين؟ خارج
+
+136
+00:14:41,650 --> 00:14:49,390
+القسم اللي هو Q of X وهذه مين؟ ال remainder اللي
+
+137
+00:14:49,390 --> 00:14:55,050
+هو R of X السؤال كان ليهت الكوشن وهتلي ال
+
+138
+00:14:55,050 --> 00:14:59,870
+remainder لما تكسم اتنين على بعضفبروح بقوله the
+
+139
+00:14:59,870 --> 00:15:09,150
+quotient فارج القسمة is ثلاثة X ترابيع زائد اربعة
+
+140
+00:15:09,150 --> 00:15:15,690
+X and ال remainder الباقي
+
+141
+00:15:15,690 --> 00:15:24,330
+is اتنين X زائد واحد لذلك اشتغلنا شغل صحيحيبقى من
+
+142
+00:15:24,330 --> 00:15:28,650
+الألف أصعدا لما نقسم polynomial على polynomial
+
+143
+00:15:28,650 --> 00:15:34,850
+بطعة المقسوم عليه مضلوب في polynomial أخرى زائد ال
+
+144
+00:15:34,850 --> 00:15:40,190
+remainder درجة ال remainder أقل من درجة المقسوم
+
+145
+00:15:40,190 --> 00:15:46,410
+عليه أو ال remainder ب zero وبالتالي حطينا أي
+
+146
+00:15:46,410 --> 00:15:50,110
+function بدلالة ال function اللي بيعطاني في Q of X
+
+147
+00:15:50,110 --> 00:15:57,670
+زائد البافلة ومينROMPIX طيب فى عنا الآن بعض
+
+148
+00:15:57,670 --> 00:16:03,550
+التسميات هتمر علينا خلال شغلنا فى الpronomial ring
+
+149
+00:16:03,550 --> 00:16:10,070
+بدي اعرف مين هى هذه التسميات يبقى مرت علينا تسمية
+
+150
+00:16:10,070 --> 00:16:15,670
+ال quotient ومرت علينا تسمية ال remainder بدنا نحط
+
+151
+00:16:15,670 --> 00:16:20,650
+كمان تلات أشياء جديدة يبقى definition
+
+152
+00:16:38,240 --> 00:16:48,460
+الـ F of X والـ G of X موجودة في الـ Integral
+
+153
+00:16:48,460 --> 00:16:48,880
+Domain
+
+154
+00:16:53,220 --> 00:17:00,960
+we say that مروح
+
+155
+00:17:00,960 --> 00:17:11,420
+نقول ان ال G of X ال G of X divide ال F of X ان ال
+
+156
+00:17:11,420 --> 00:17:20,140
+G of X بتقسم ال F of X في ال D of X if they exist
+
+157
+00:17:22,860 --> 00:17:34,960
+there exists h of x and d of x such that
+
+158
+00:17:34,960 --> 00:17:45,060
+بحيث أن ال f of x بده يساوي ال g of x مضروبة في
+
+159
+00:17:45,060 --> 00:17:55,580
+من؟ مضروبة في ال h of xيبقى H of X مضروبة في الـ G
+
+160
+00:17:55,580 --> 00:18:06,120
+of X Also هو كذلك نقول نقول نقول نقول نقول نقول
+
+161
+00:18:06,120 --> 00:18:06,120
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+162
+00:18:06,120 --> 00:18:06,120
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+163
+00:18:06,120 --> 00:18:06,220
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+164
+00:18:06,220 --> 00:18:06,260
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+165
+00:18:06,260 --> 00:18:06,260
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+166
+00:18:06,260 --> 00:18:08,000
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+167
+00:18:08,000 --> 00:18:08,000
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+168
+00:18:08,000 --> 00:18:08,000
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+169
+00:18:08,000 --> 00:18:08,900
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+170
+00:18:08,900 --> 00:18:17,140
+نقول نقول نقول نقول
+
+171
+00:18:17,140 --> 00:18:17,600
+نقول
+
+172
+00:18:21,460 --> 00:18:27,960
+تعريف آخر Definition and
+
+173
+00:18:27,960 --> 00:18:40,760
+element a and element a is a zero is a zero أو
+
+174
+00:18:40,760 --> 00:18:53,220
+بنسمي root جذر يا إما zero يا إما root جذرof a
+
+175
+00:18:53,220 --> 00:19:07,080
+polynomial of a polynomial f of x البرنامج f ال f
+
+176
+00:19:07,080 --> 00:19:16,600
+of a تساوي 0 that is if
+
+177
+00:19:16,600 --> 00:19:25,280
+إذا كان ال a inالـ a to the power n a minus ال one
+
+178
+00:19:25,280 --> 00:19:32,920
+a to the power minus ال one زائد a one a زائد a
+
+179
+00:19:32,920 --> 00:19:41,100
+not تساوي زيه ال definition الأخيرة قلت ال FBA
+
+180
+00:19:41,100 --> 00:19:50,620
+field لك ال FBA field and let
+
+181
+00:19:56,940 --> 00:20:06,920
+فال F وال F of X موجود في كابتن F of X We say that
+
+182
+00:20:06,920 --> 00:20:13,580
+نقول
+
+183
+00:20:13,580 --> 00:20:16,640
+We
+
+184
+00:20:16,640 --> 00:20:33,540
+say that ان ال A is a zeroof multiplicity
+
+185
+00:20:33,540 --> 00:20:41,460
+K if
+
+186
+00:20:41,460 --> 00:20:51,040
+ال X ناقص ال A to the power K is a factor
+
+187
+00:20:58,050 --> 00:21:10,750
+is a factor of f of x and x نقص a to the power k
+
+188
+00:21:10,750 --> 00:21:21,390
+plus one is not a
+
+189
+00:21:21,390 --> 00:21:26,050
+factor of
+
+190
+00:21:26,050 --> 00:21:27,230
+f of x
+
+191
+00:21:31,810 --> 00:21:35,890
+R F O X
+
+192
+00:22:07,180 --> 00:22:17,080
+مثلًا احصل على طريق طريق
+
+193
+00:22:17,080 --> 00:22:28,460
+و مرتبطات و مرتبطات
+
+194
+00:22:28,460 --> 00:22:32,860
+كمان عندما نكتب
+
+195
+00:22:39,330 --> 00:22:45,950
+when we write the
+
+196
+00:22:45,950 --> 00:22:53,810
+polynomial when
+
+197
+00:22:53,810 --> 00:23:00,790
+we write the polynomial ال
+
+198
+00:23:00,790 --> 00:23:04,310
+F of X يساوي
+
+199
+00:23:28,660 --> 00:23:38,600
+في الشكل ال F of X يساوي X نقص ال A to the power K
+
+200
+00:23:38,600 --> 00:23:50,920
+LQO of X in the field Z5
+
+201
+00:24:04,400 --> 00:24:09,980
+نذهب الآن لكل تعريف من التعريف الثلاثة نشوف ما هو
+
+202
+00:24:09,980 --> 00:24:14,660
+المقصود بهذا التعريف فبقى بدنا نجي مع التعريف
+
+203
+00:24:14,660 --> 00:24:20,000
+الأول قال خدلي D integral domain خدلي two
+
+204
+00:24:20,000 --> 00:24:26,720
+polynomials موجودات في D of X we see that روح نقول
+
+205
+00:24:26,720 --> 00:24:33,860
+ان الـG of X ابتقسم ال F of X داخل ال domain هذا
+
+206
+00:24:34,250 --> 00:24:38,830
+إذا قدرت ألاقي دالة تانية داخل هذا الـ integral
+
+207
+00:24:38,830 --> 00:24:46,090
+اللي هو domain D هذه الدالة سميتها H of X بحيث أن
+
+208
+00:24:46,090 --> 00:24:52,750
+F of X يساوي G of X مضروبة 8 في الـ H of X يبقى
+
+209
+00:24:52,750 --> 00:24:57,330
+أنا عندي two polynomials واحدة F of X والثانية G
+
+210
+00:24:57,330 --> 00:25:02,730
+of X إذا قدرت ألاقي أن الـ F of Xيساوي ال
+
+211
+00:25:02,730 --> 00:25:07,510
+polynomial G of X مضروبة في polynomial تانية بقول
+
+212
+00:25:07,510 --> 00:25:12,570
+فعلا ال G of X بتقسم مين ال F of X القسمة بدون
+
+213
+00:25:12,570 --> 00:25:17,550
+باقي لاحظي ماقولتش زائد remainder ماعنديش
+
+214
+00:25:17,550 --> 00:25:22,530
+remainder يبقى إن حدث ذلك بقول يبقى ال polynomial
+
+215
+00:25:22,530 --> 00:25:29,630
+G of X بتقسم ال F of X وخارج القسمة هو مين ال H of
+
+216
+00:25:29,630 --> 00:25:29,710
+X
+
+217
+00:25:33,560 --> 00:25:38,100
+الـ R of X تساوي Zero ان شرطنا عند الـ R of X يا
+
+218
+00:25:38,100 --> 00:25:44,680
+Zero يا درجته أقل من درجة الـ G of X المرة هذه الـ
+
+219
+00:25:44,680 --> 00:25:51,000
+R of X بـ Zero إذا الـ G of X بتقسم الـ F of X
+
+220
+00:25:51,000 --> 00:25:58,360
+بدون باقى وكذلك بنقدر نقول ان الـ G of X هي أحد
+
+221
+00:25:58,360 --> 00:26:04,320
+عوامل من الـ F of X لأن لو ضربناالـ U of X في عامل
+
+222
+00:26:04,320 --> 00:26:09,560
+آخر طالع عند من F of X يبقى الـ U of X بسميها أحد
+
+223
+00:26:09,560 --> 00:26:14,020
+عوامل F of X هذا بالنسبة للتعريف الأول و زي ما
+
+224
+00:26:14,020 --> 00:26:19,880
+انتوا شايفين زي الأعداد تماما طيب التعريف التاني
+
+225
+00:26:19,880 --> 00:26:26,860
+ال element ايه بسميه Zero او بسميه ال gender تبعي
+
+226
+00:26:26,860 --> 00:26:31,120
+ال polynomial هو ال Zero تبعي ال polynomialيعني
+
+227
+00:26:31,120 --> 00:26:37,120
+الرقم اللي لو عوضته في ال X تبع ال polynomial بطلع
+
+228
+00:26:37,120 --> 00:26:44,240
+النتج يساوي Zero او بسميه جادر كثيرة الحدود F of X
+
+229
+00:26:44,240 --> 00:26:49,700
+إذا كان ال F of A بديه ساوي من؟ بديه ساوي الصفر
+
+230
+00:26:49,700 --> 00:26:56,120
+بمعنى جيت على كثيرة الحدود شيل كل X وعطيت مكانه
+
+231
+00:26:56,120 --> 00:27:03,590
+من؟و جمعت النتج جدّه Zero يبقى جيت مكان ال X حاطيت
+
+232
+00:27:03,590 --> 00:27:08,170
+A المعامل خلّيته زي ما هو بدل ال X to the power N
+
+233
+00:27:08,170 --> 00:27:12,230
+قلت A to the power N A to the power N minus one A
+
+234
+00:27:12,230 --> 00:27:17,110
+to the power one A naught وجمعت وجدت النتج يسوى
+
+235
+00:27:17,110 --> 00:27:22,910
+مين؟ يسوى Zero إن حدث ذلك يبقى ال A بسمي هو جذر ال
+
+236
+00:27:22,910 --> 00:27:29,290
+polynomial أوالرقم اللذي يجعل ال polynomial تساوي
+
+237
+00:27:29,290 --> 00:27:37,070
+صفرة تم تعريف التالب يقول خد ال F فيه وخد A، A
+
+238
+00:27:37,070 --> 00:27:42,890
+موجودة في ال F وال polynomial F of X موجودة في
+
+239
+00:27:42,890 --> 00:27:49,950
+capital F of X ال A هذا بسميه Zero of multiplicity
+
+240
+00:27:49,950 --> 00:27:56,080
+Kإذا كان ال X ناقص ال A to the power K هو أحد
+
+241
+00:27:56,080 --> 00:28:02,520
+عناصر main ال F of X يعني يا بنات ال F of X كتبتها
+
+242
+00:28:02,520 --> 00:28:08,580
+بدل ال G كتبت X ناقص ال A to the power K في main
+
+243
+00:28:08,580 --> 00:28:15,960
+في ال H of X تمام؟ يبقى ال G of X أصبحت هي X ناقص
+
+244
+00:28:15,960 --> 00:28:22,350
+ال A to the power Kيبقى ال X هو عامل من عوامل F of
+
+245
+00:28:22,350 --> 00:28:29,170
+X لكن لو بختل ال S واحد بصير ما هوش عامل من عوامل
+
+246
+00:28:29,170 --> 00:28:36,990
+مين الدالة F of X يعني وكان ال K أصغر رقم والله
+
+247
+00:28:36,990 --> 00:28:43,770
+أكبر رقم مش أصغر أكبر رقم بيخلي ال X نقص ال A هو
+
+248
+00:28:43,770 --> 00:28:49,470
+أحد عوامل مين ال F of Xهنوضح لكم المفاهيم هذه
+
+249
+00:28:49,470 --> 00:28:58,350
+بمثال عددي المثال بيقول ماذا؟ غليهد للجذر ال
+
+250
+00:28:58,350 --> 00:29:01,610
+multiplicity
+
+251
+00:29:01,610 --> 00:29:07,150
+k إذا جدرنا نكتب ال polynomial هذه على الشكل اللي
+
+252
+00:29:07,150 --> 00:29:12,550
+عندها هذا في ال fields الخامسة لازال شغلنا مع ال
+
+253
+00:29:12,550 --> 00:29:17,040
+field يعني المثال هذا على مين؟على الحالة اللي
+
+254
+00:29:17,040 --> 00:29:21,920
+عمناه الجئاني بتدور في Z خمسة أكام عنصر فيها Z
+
+255
+00:29:21,920 --> 00:29:28,260
+خمسة؟ خمسة عناصر من العنصر اللي من العناصر الخامسة
+
+256
+00:29:28,260 --> 00:29:33,100
+اللي بيخللي ال polynomial تساوي Zero بدي أبدأ
+
+257
+00:29:33,100 --> 00:29:41,060
+أحسبه بدي أقوله ال F of Zero اللي عوض بطلع جدير
+
+258
+00:29:41,710 --> 00:29:47,250
+أربعة يبقى زي مش جذر للchronome يعني لإنه مشان
+
+259
+00:29:47,250 --> 00:29:53,930
+تكون جذر بيطلع النتج يسوى الصفر فبتاجي لل F هو
+
+260
+00:29:53,930 --> 00:29:59,690
+واحد واحد وصف اربعة بواحد في اتنين باتنين وإن ضايل
+
+261
+00:29:59,690 --> 00:30:07,030
+واحد تلاتة و تلاتة ستة شيلي خمسة وضل واحد واحد و
+
+262
+00:30:07,030 --> 00:30:12,100
+اتنين تلاتة واربعةسبعة شيلي خمسة و بضلي اتنين
+
+263
+00:30:12,100 --> 00:30:17,860
+يتقال واحد ما هو مش جادر لل Polynomial تعالى نشوف
+
+264
+00:30:17,860 --> 00:30:26,600
+افقه باتنين نجا اتنين بص اربع ليه و بص اتناش شيلي
+
+265
+00:30:26,600 --> 00:30:32,260
+خمس تاش تانية و خمسة بضلي واحد في اتنين باتنين و
+
+266
+00:30:32,260 --> 00:30:39,780
+هنا تامانية واحد تسعةشيلي خمسة بيبقى القدر اربع
+
+267
+00:30:39,780 --> 00:30:46,660
+اربع وهذه اربع في تلاتة اتناش واربع ستاش شيلي
+
+268
+00:30:46,660 --> 00:30:52,620
+تلاتة خمسات بيبقى الواحد وهذا اتنين في اتنين باربع
+
+269
+00:30:52,620 --> 00:30:55,740
+اتنين
+
+270
+00:30:55,740 --> 00:31:01,080
+لأ لحظة شوية احنا غلطنا مرة تانية الحين هذه ستاش
+
+271
+00:31:01,080 --> 00:31:07,760
+مظبوط ستاش في اتنين في اتنين و تلاتينبيضل شيلي ست
+
+272
+00:31:07,760 --> 00:31:14,140
+خمسات بيضلي اتنين وهنا هنا تمانية تمانية و اتنين
+
+273
+00:31:14,140 --> 00:31:20,860
+عاشرة مع السلامة طيب نيجي هنا اربعة في تلاتة و
+
+274
+00:31:20,860 --> 00:31:27,380
+اتناش بيضلي اتنين اتنين في اتنين اربعة و اتنين
+
+275
+00:31:27,380 --> 00:31:34,380
+بيضلي اربعة و اتنين عاشرة يبقى Zero يبقى F of
+
+276
+00:31:34,380 --> 00:31:40,000
+اتنين يسوى Zeroيبقى الـ2 هو جدر لهذه البرنامج
+
+277
+00:31:40,000 --> 00:31:46,140
+السؤال هو فيها جذور أخرى ولا لأ بنا نكمل شغلنا في
+
+278
+00:31:46,140 --> 00:31:52,620
+زمن خمسة يبقى ضايل علينا ال F of تلاتة يبقى بنفس
+
+279
+00:31:52,620 --> 00:32:00,860
+الطريقة تلاتة في اتنين ستة واربعة صفر خمستين صفر
+
+280
+00:32:00,860 --> 00:32:06,420
+نجينا تلاتة في تلاتةتسعة في تلاتة، تسعة وعشرين،
+
+281
+00:32:06,420 --> 00:32:06,840
+تسعة وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة
+
+282
+00:32:06,840 --> 00:32:09,800
+وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة وعشرين،
+
+283
+00:32:09,800 --> 00:32:10,480
+تسعة وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة
+
+284
+00:32:10,480 --> 00:32:12,480
+وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة وعشرين،
+
+285
+00:32:12,480 --> 00:32:16,040
+تسعة وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة
+
+286
+00:32:16,040 --> 00:32:22,840
+وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة وعشرين،
+
+287
+00:32:22,840 --> 00:32:27,100
+تسعة وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة
+
+288
+00:32:27,100 --> 00:32:31,280
+وعشرين، تسعة
+
+289
+00:32:31,280 --> 00:32:40,260
+وعشريننجل ال F واربع اربع في اتنين تمانية شيلة
+
+290
+00:32:40,260 --> 00:32:44,960
+خمسة بيبقى تلاتة واربع سبعة شيلة خمسة بيبقى ليه
+
+291
+00:32:44,960 --> 00:32:51,340
+اتنين اتنين، هذه ستاش في تلاتة تمانية واربعين
+
+292
+00:32:51,340 --> 00:32:57,560
+واتنين خمسين راحوا هدول مع السلامة نجل هذه اربع
+
+293
+00:32:57,560 --> 00:33:03,030
+وستين اللي هي اربع تكعيبة في اربع وستينشيلي ستين
+
+294
+00:33:03,030 --> 00:33:10,750
+بيضل أربع نيجي هذه ستاشر بواحد وكمان ستاشر بواحد
+
+295
+00:33:10,750 --> 00:33:17,770
+في واحد بواحد في اتنين باتنين اتنين واربع ستة شيلي
+
+296
+00:33:17,770 --> 00:33:25,490
+خمسة يساوي واحد يبقى ماعنديش الا اتنين هو الجدد
+
+297
+00:33:25,490 --> 00:33:42,580
+يبقى هنا سا اتنين ازthe root of the polynomials f
+
+298
+00:33:42,580 --> 00:33:52,760
+of x because ال f of اتنين بده يساوي زيكي خلاصة
+
+299
+00:33:52,760 --> 00:33:59,140
+المطلوب الأول بدنا نيجي للمطلوب الثانيبنطلع الـ X
+
+300
+00:33:59,140 --> 00:34:05,220
+ناقص الـ A كم مرة مكررة يبقى بروح أقسم الفولونوميا
+
+301
+00:34:05,220 --> 00:34:10,780
+العالمية على X ناقص الـ A كدوش الـ A عندي طلعت؟
+
+302
+00:34:10,780 --> 00:34:17,860
+كدوش؟ بإتنين يبقى بدي أقسم الفولونوميا إتنين X و
+
+303
+00:34:17,860 --> 00:34:26,740
+أربع زائد X تكيب زائد تلاتة X ترابيعزائد اتنين X
+
+304
+00:34:26,740 --> 00:34:36,300
+زائد اربعة تقسيم ال X ناقص اتنين طيب نقسم اتنين X
+
+305
+00:34:36,300 --> 00:34:43,860
+قصة اربعة ال X باتنين X تكييف اتنين X تكييف باتنين
+
+306
+00:34:43,860 --> 00:34:52,400
+X قصة اربعة ناقص اربعة X تكييف ناقص اربعة X تكييف
+
+307
+00:34:52,400 --> 00:34:59,820
+تمام؟هذه ازاي؟ بنغير انتشارات وبنبدأ نجمعها اربع
+
+308
+00:34:59,820 --> 00:35:07,400
+واحد خمسة يبقى راحة بي Zero الله سهل عليها تمام؟
+
+309
+00:35:07,400 --> 00:35:12,560
+طيب مين ضلع ان لا يبقى دول خلصوا راح خارج الخصمة
+
+310
+00:35:12,560 --> 00:35:18,420
+تماما اتنين X تقييمة بدي اكسب ثلاثة X تربيع على X
+
+311
+00:35:18,420 --> 00:35:25,680
+يبقى فيها كده؟ ثلاثة Xتلاتة اكس في اكس في تلاتة
+
+312
+00:35:25,680 --> 00:35:34,320
+اكس تربيع تلاتة اكس في ناقص ستة اكس شيلي خمسة وضع
+
+313
+00:35:34,320 --> 00:35:43,300
+ناقص اكس هم بنغير الإشارات بالشكل اللي عندنا هنا
+
+314
+00:35:43,300 --> 00:35:50,640
+بقى القدر شبنة تلاتة اكس زائد الأربع الباقي من
+
+315
+00:35:50,640 --> 00:35:55,730
+الدرجة الأولىوالمقسوم عليه من الدرجة الأولى بنواصل
+
+316
+00:35:55,730 --> 00:36:03,570
+عملية انقسمها تلاتة X على X هي تلاتة تلاتة في X
+
+317
+00:36:03,570 --> 00:36:12,370
+بتلاتة X وتلاتة في ناقص اتنين ناقص ستة شيلي خمسة
+
+318
+00:36:12,370 --> 00:36:20,540
+وظل ناقص واحد نغير الإشارات ونبدأ نجمعواحد واربع
+
+319
+00:36:20,540 --> 00:36:27,160
+خمسة يبقى كل الناتج ب zero يبقى طالع خارج القسمة
+
+320
+00:36:27,160 --> 00:36:35,040
+بدون باقية يبقى صارت ال F of X الأصلية مكتوبة على
+
+321
+00:36:35,040 --> 00:36:42,460
+شكل X ناقص اتنين في مين في اتنين X تكعيد زائد
+
+322
+00:36:42,460 --> 00:36:51,100
+تلاتة X زائد تلاتةهل يا ترى لحد هنا و stop بيجسمش
+
+323
+00:36:51,100 --> 00:36:56,940
+والله بتجسم منقول تعالى نشوف بدي قسمة بدون باقي
+
+324
+00:36:56,940 --> 00:37:00,560
+عندما اوصل لباقي بقول stop الله عطاك الله عافية
+
+325
+00:37:00,560 --> 00:37:07,860
+طيب الان بدي اشوف هذه تجسم على X نقص اتنين ولا لأ
+
+326
+00:37:07,860 --> 00:37:13,020
+اذا عوضت فيها باتنين وطلع انها جساوي Zero يبقى
+
+327
+00:37:13,020 --> 00:37:17,530
+بتجسم وبعدين روحها تجسم الجوس التاني يعنيبتعوض
+
+328
+00:37:17,530 --> 00:37:25,830
+باتنين تمانية اتنين ثم واحد اتنين و تلاتة ستة ثم
+
+329
+00:37:25,830 --> 00:37:32,190
+واحد و واحد و تلاتة ستة تبتجسم و هي التانية بتجسم
+
+330
+00:37:32,190 --> 00:37:37,590
+كمان مرة اذا انا بدى اروح الهامس بنفس الطريقة بدي
+
+331
+00:37:37,590 --> 00:37:45,450
+اجسم اتنين X تكيين زي التلاتة X زي التلاتةعلى اكس
+
+332
+00:37:45,450 --> 00:37:53,970
+ناقص اتنين يبقى فيها اتنين اكس ترابيع باتنين اكس
+
+333
+00:37:53,970 --> 00:38:03,290
+تكيين ناقص اربع اكس ترابيع هذه زاد بصير ناقص وهذه
+
+334
+00:38:03,290 --> 00:38:10,150
+زاد الاربع اكس ترابيع مافيش غيرها وظل تلاتة اكس
+
+335
+00:38:10,150 --> 00:38:16,420
+زائد تلاتةمن الدرجة الثانية من الدرجة الأولى بواصل
+
+336
+00:38:16,420 --> 00:38:21,700
+عملية القسمة اربعة اكس تربيع على اكس بطلع عندك
+
+337
+00:38:21,700 --> 00:38:31,040
+داشر اربعة اكس في اكس اربعة اكس تربيع وهنا اربعة
+
+338
+00:38:31,040 --> 00:38:39,440
+سالب اتنين سالب تمانية اشيل خمسة بظل سالب تلاتة
+
+339
+00:38:39,440 --> 00:38:47,190
+اكسوعندك اه خلصنا يبقى هذه زاد تصير ناقص وهذه زاد
+
+340
+00:38:47,190 --> 00:38:55,690
+مع السلامة تلاتة X و تلاتة X بستة X ستة X شيلي
+
+341
+00:38:55,690 --> 00:39:03,790
+خمسة بيظل واحد مضروف X يبقى ب X زائد تلاتة ال X
+
+342
+00:39:03,790 --> 00:39:11,280
+على X فيها جدير واحد يبقى زائد واحدواحد في اكس
+
+343
+00:39:11,280 --> 00:39:18,040
+باكس وواحد في سالبي اتنين بسالبي اتنين هذه زائد
+
+344
+00:39:18,040 --> 00:39:24,260
+تصبح ناقص وهذه زائد مع السلامة اتنين و تلاتة و
+
+345
+00:39:24,260 --> 00:39:32,240
+خمسة يبقى zero يبقى صارت هذه تساوي ال X ناقص اتنين
+
+346
+00:39:32,240 --> 00:39:40,070
+اجا كمان X ناقص اتنين ضال عند اتنين X تربيعزائد
+
+347
+00:39:40,070 --> 00:39:47,770
+أربعة X زائد واحدة يعني صارت X نقص اتنين لكل
+
+348
+00:39:47,770 --> 00:39:56,730
+ترابيع نين X ترابيع زائد أربعة X زائد واحدة انشوف
+
+349
+00:39:56,730 --> 00:40:02,470
+فيه كمان تكرار و الله خلصنا بنفس المفهوم إذا جيت
+
+350
+00:40:02,470 --> 00:40:08,560
+عوّقت هنا ب X يساوي اتنينوطالع الناتج يساوي Zero
+
+351
+00:40:08,560 --> 00:40:15,980
+كده في عندي كمان X ناقص اتنين اعوض باتنين اربعة في
+
+352
+00:40:15,980 --> 00:40:23,440
+اتنين تمانية شيلة خمسة بظل تلاتة هنا اتنين في
+
+353
+00:40:23,440 --> 00:40:30,240
+اربعة تمانية شيلة خمسة بظل تلاتة و تلاتة ستة بظل
+
+354
+00:40:30,240 --> 00:40:38,000
+واحد واحدمش ممكن يبقى اكتر من هيك ماعنديش تمام
+
+355
+00:40:38,000 --> 00:40:45,540
+يبقى كده مقدار ال multiplicity اتنين تمام يبقى هنا
+
+356
+00:40:45,540 --> 00:40:51,080
+Multiplicity
+
+357
+00:40:51,080 --> 00:40:58,180
+Multiplicity
+
+358
+00:41:00,810 --> 00:41:11,930
+X ناقص اتنين is اتنين.يعني هذا الجسم كرر مرتين، لا
+
+359
+00:41:11,930 --> 00:41:18,390
+ثالثة لأمان. تمام؟ طيب الآن بدنا ندخل على بعض
+
+360
+00:41:18,390 --> 00:41:25,630
+النتائج على النظرية وعنا بدأ للنتيجة تلاتة للمرة
+
+361
+00:41:25,630 --> 00:41:28,230
+القادمة ان شاء الله تعالى.
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ad44861854b5771f2530c31989dd4feab1e6642c
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo.srt
@@ -0,0 +1,1211 @@
+1
+00:00:21,020 --> 00:00:26,040
+بسم الله الرحمن الرحيم. انتهينا من chapter 12 و
+
+2
+00:00:26,040 --> 00:00:31,720
+chapter 13، والآن بنجي لـ chapter 14 اللي العمود
+
+3
+00:00:31,720 --> 00:00:37,760
+الفقري فيه عبارة عن نقطتين: الـ ideals وهي حالة
+
+4
+00:00:37,760 --> 00:00:42,740
+خاصة من الـ subrings، والنقطة الثانية هي الـ
+
+5
+00:00:42,740 --> 00:00:47,660
+factorings، تماماً كما أخذنا factor group أو
+
+6
+00:00:47,660 --> 00:00:53,260
+quotient group قبل ذلك. اليوم هنبدأ فقط بالـ ideals
+
+7
+00:00:53,260 --> 00:00:58,320
+والـ factor rings بنخليه للمرة القادمة إن شاء الله.
+
+8
+00:00:58,320 --> 00:01:04,740
+يبقى بدنا نبدأ بتعريف الـ ideal، ثم ناخد بعض الأمثلة
+
+9
+00:01:04,740 --> 00:01:08,480
+عليه، وكيف نحكم على الـ subring اللي بناخدها من الـ
+
+10
+00:01:08,480 --> 00:01:14,400
+ring، هل هي ideal أم ليست ideal؟ طب أروح أقول
+
+11
+00:01:14,400 --> 00:01:23,880
+التعريف كالتالي: يبقى a subring A
+
+12
+00:01:23,880 --> 00:01:31,640
+of a ring R is called a two-sided ideal. كلمة two
+
+13
+00:01:31,640 --> 00:01:36,500
+-sided حطيناها لهدف، ممكن ما نقولش two-sided، نقول
+
+14
+00:01:36,500 --> 00:01:41,160
+ideal ونسكت. والآن هنقولك ليش سميناها two-sided
+
+15
+00:01:41,160 --> 00:01:46,760
+ideal. يبقى subring A of a ring R is called a two
+
+16
+00:01:46,760 --> 00:01:48,740
+-sided ideal of R.
+
+17
+00:02:00,700 --> 00:02:07,200
+السؤال هو: ما هو الفرق بين الـ ideal وبين الـ subring؟
+
+18
+00:02:07,200 --> 00:02:14,660
+طبعاً الفرق واضح من خلال الـ definition. اتنين من
+
+19
+00:02:14,660 --> 00:02:20,570
+هذا الكلام صحيح. النقطة الثانية: إنه لما ناخد
+
+20
+00:02:20,570 --> 00:02:27,210
+حاصل ضرب element من R  و element من A، و
+
+21
+00:02:27,210 --> 00:02:32,550
+element من A، بدي يكون الناتج في A. هذا في الـ ideal، لكن
+
+22
+00:02:32,550 --> 00:02:36,750
+لما كنا في الـ ring، بجينا نأخذ اتنين من نفس الـ set
+
+23
+00:02:36,750 --> 00:02:42,190
+يعني بأخذ عنصرين من نفس الـ A، بدي يكون حاصل ضربهما
+
+24
+00:02:42,190 --> 00:02:48,640
+موجود في A. هنا لأ، بأخذ أي عنصر من الـ subring A وأي
+
+25
+00:02:48,640 --> 00:02:53,760
+عنصر من الـ ring، نضربهما معاً، بدي يكون موجود داخل
+
+26
+00:02:53,760 --> 00:02:59,060
+الـ subring. إن حدث ذلك، يبقى بنسميه هذا ideal، سواء
+
+27
+00:02:59,060 --> 00:03:05,100
+كان الضرب من اليمين أو من الشمال. فلما كان الضرب من
+
+28
+00:03:05,100 --> 00:03:10,740
+الشمال وهنا من اليمين، سميناه ايه؟ two-sided ideal.
+
+29
+00:03:10,740 --> 00:03:17,420
+فإن قلنا two-sided ideal أو ideal وسكتنا، الإثنين
+
+30
+00:03:17,420 --> 00:03:22,420
+كله بنفس المعنى، تمام؟ يعني وأنت بتقول الكلمة two-sided ideal وما بتقول كلمة ideal، بدك
+
+31
+00:03:22,420 --> 00:03:26,500
+تفهمي أن هذه هي two-sided ideal. التعريف هذا، بدي
+
+32
+00:03:26,500 --> 00:03:31,660
+أعيد صياغته بطريقة أخرى، بقول: this definition can
+
+33
+00:03:31,660 --> 00:03:37,440
+be written as: هذا التعريف أتركه على الشكل التالي:
+
+34
+00:03:37,440 --> 00:03:41,920
+الـ subring A of a ring R is called ideal of R إذا
+
+35
+00:03:42,140 --> 00:03:48,220
+كان لو ضربت الـ R في عناصر الـ ideal، كله بيطلع عندي
+
+36
+00:03:48,220 --> 00:03:54,560
+set، وهذه الـ set subset من مين؟ من A الأصلية. بالمثل لو
+
+37
+00:03:54,560 --> 00:04:02,240
+ضربت في R من جهة اليمين جميع عناصر الـ A، بيطلع لي
+
+38
+00:04:02,240 --> 00:04:09,260
+set، subset من مين؟ من A. إن تحققت لأي R موجودة في R،
+
+39
+00:04:09,260 --> 00:04:15,380
+إن تحققت الـ two conditions لإثنين هدول، بقول إن الـ
+
+40
+00:04:15,380 --> 00:04:19,760
+A هو عبارة عن ideal أو two-sided ideal، هذه أو
+
+41
+00:04:19,760 --> 00:04:26,460
+كلمتَين إثنين are the same. بنجي الآن للتعريف الثاني،
+
+42
+00:04:26,460 --> 00:04:33,040
+A is called the proper ideal of A، proper ideal إذا
+
+43
+00:04:33,040 --> 00:04:39,110
+كان الـ A هو proper subset من الـ R. إيش يعني
+
+44
+00:04:39,110 --> 00:04:43,870
+معنى proper مثل ما درسناه في الـ group؟ إيش يعني
+
+45
+00:04:43,870 --> 00:04:47,670
+proper يا مناد؟ إنه subset من الـ group الأصلية
+
+46
+00:04:47,670 --> 00:04:53,370
+وكان لا يساوي هذه الـ group. وهنا نفس القصة، الـ ideal
+
+47
+00:04:53,370 --> 00:04:59,230
+هو proper subset، يعني لا يساوي الـ group، لا يساوي
+
+48
+00:04:59,230 --> 00:05:06,310
+الـ ring الأصلية. طب إيش معنى Improper؟ ممكن احتمال
+
+49
+00:05:06,310 --> 00:05:12,540
+يتساوي، ممكن احتمال يتساوي...
+
+50
+00:05:12,540 --> 00:05:18,340
+(repeated "ممكن احتمال يتساوي" several times)
+
+51
+00:05:18,340 --> 00:05:19,780
+(repeated "ممكن احتمال يتساوي" several times)
+
+52
+00:05:19,780 --> 00:05:21,300
+(repeated "ممكن احتمال يتساوي" several times)
+
+53
+00:05:21,300 --> 00:05:21,780
+(repeated "ممكن احتمال يتساوي" several times)
+
+54
+00:05:21,780 --> 00:05:25,260
+(repeated "ممكن احتمال يتساوي" several times)
+
+55
+00:05:25,260 --> 00:05:26,000
+(repeated "ممكن احتمال يتساوي" several times)
+
+56
+00:05:26,000 --> 00:05:30,040
+(repeated "ممكن احتمال يتساوي" several times)
+
+57
+00:05:30,040 --> 00:05:31,840
+(repeated "ممكن احتمال يتساوي" several times)
+
+58
+00:05:35,790 --> 00:05:40,270
+لكن من الآن فصاعداً، أقول لك proper، بدك تفهمي أن الـ ideal
+
+59
+00:05:40,270 --> 00:05:45,330
+عدد عناصره أقل من عدد عناصر الـ ring، دائماً هو لا
+
+60
+00:05:45,330 --> 00:05:52,530
+يمكن أن يتساوي. طيب الآن، كيف بدي أفحص أن الـ set اللي
+
+61
+00:05:52,530 --> 00:05:56,570
+أخذتها، أو الـ subset اللي أخذتها من الـ ring الأصلية
+
+62
+00:05:56,570 --> 00:06:03,190
+هي ideal؟ بثلاثة شروط. الشرط الأول: أن تبقى الـ subset
+
+63
+00:06:03,190 --> 00:06:10,160
+هذه non-empty. non-empty subset A of a ring R
+
+64
+00:06:10,160 --> 00:06:17,000
+بقول عنها ideal إذا كان أخذت عنصرين من الـ set اللي
+
+65
+00:06:17,000 --> 00:06:22,140
+طرحتهم من بعض، بدي يكون الناتج في A. يبقى A ناقص الـ
+
+66
+00:06:22,140 --> 00:06:27,540
+B موجود في A، whenever الـ A والـ B موجودين في A.
+
+67
+00:06:27,540 --> 00:06:33,160
+اللي بعده: الـ R في A موجود في A، والـ A في R موجود في
+
+68
+00:06:33,160 --> 00:06:40,670
+A، لكل الـ A الموجودة في A، والـ R الموجودة في R. إذا هذه
+
+69
+00:06:40,670 --> 00:06:45,250
+هي اللي بيقول لي: مشان تفحص هل اللي عندك هذا
+
+70
+00:06:45,250 --> 00:06:51,730
+ideal ولا لأ، بدنا نثبت ثلاث نقاط. النقطة الأولى: أن
+
+71
+00:06:51,730 --> 00:06:55,790
+الـ subset اللي أخذتها non-empty. النقطة الثانية: بدي
+
+72
+00:06:55,790 --> 00:07:00,390
+آخذ أي عنصرين من هذه الـ subset، بدي أثبت أن الفرق
+
+73
+00:07:00,390 --> 00:07:06,370
+بينهما موجود في نفس الـ subset. الأمر الثالث: بدي آخذ
+
+74
+00:07:06,370 --> 00:07:10,590
+أي عنصر من هذا الـ subset أو أي عنصر من الـ ring، بدي
+
+75
+00:07:10,590 --> 00:07:14,110
+أضربه فيه من اليمين ومن الشمال، بدي أطلع عنصر
+
+76
+00:07:14,110 --> 00:07:19,470
+موجود وين؟ موجود في نفس الـ set A. إن حدث ذلك، بقول
+
+77
+00:07:19,470 --> 00:07:25,410
+يبقى هذا ideal، ومن هنا صار هناك فرق ما بين الـ
+
+78
+00:07:25,410 --> 00:07:29,950
+ideal وما بين الـ subring، والفرق بسيط في الـ
+
+79
+00:07:29,950 --> 00:07:35,780
+condition الأخير، مثل ما كنا... اللي هو main، ها تمام؟ في
+
+80
+00:07:35,780 --> 00:07:40,160
+حالة الـ subring، قلنا بتأخذ عنصرين من نفس الـ set.
+
+81
+00:07:40,160 --> 00:07:44,500
+لأ، لأ، بدي آخذ عنصر من الـ set وعنصر من الـ ring
+
+82
+00:07:44,500 --> 00:07:48,620
+الأصلية، أضرب الاثنين في بعض من اليمين ومن الشمال،
+
+83
+00:07:48,620 --> 00:07:53,300
+بدي أطلع عنصر في الـ subset اللي أخذته. هذه تماماً. طب
+
+84
+00:07:53,300 --> 00:07:57,960
+بدنا نروح نثبت صحة هذا الكلام. يبقى a non-empty
+
+85
+00:07:57,960 --> 00:08:03,270
+subset A of a ring R is an ideal. يبقى أنا أخذت الـ
+
+86
+00:08:03,270 --> 00:08:07,410
+subset من الـ ring الأصلية، وكانت هذه الـ non-empty،
+
+87
+00:08:07,410 --> 00:08:12,350
+إذا أنت حققت الـ condition اللي مضال علينا، main الـ
+
+88
+00:08:12,350 --> 00:08:18,290
+two conditions الآخرين. السؤال هو: هذا مش هو الشرط
+
+89
+00:08:18,290 --> 00:08:25,230
+الأول من شروط الـ subring؟ صح. طيب هذا أليس هذا هو
+
+90
+00:08:25,230 --> 00:08:30,390
+الشرط الثاني من الـ subring، وزيادة شوية؟ كيف زيادة
+
+91
+00:08:30,390 --> 00:08:38,170
+شوية؟ لأن بجينا جوا عنصرين من الـ A، عنصرين هنا
+
+92
+00:08:38,170 --> 00:08:42,810
+بيقولوا: لأ، عنصر من A والآخر من R، والآخر اللي
+
+93
+00:08:42,810 --> 00:08:48,350
+بدي أضربه من R، قد يكون من A وقد لا يكون من A، فإن
+
+94
+00:08:48,350 --> 00:08:53,730
+كان من A هو تحصيل حاصل، وإن كان من R فهو زيادة عما
+
+95
+00:08:53,730 --> 00:08:59,240
+كان من في حالة الـ subrings. يبقى الآن بروح بقول له: the
+
+96
+00:08:59,240 --> 00:09:15,760
+conditions اللي هو I و II make the set is
+
+97
+00:09:15,760 --> 00:09:20,620
+subring. طبعاً؟
+
+98
+00:09:20,620 --> 00:09:26,440
+طب الـ condition الثالث لحاله، بيخلّيه إيش؟ بيخلّيه ideal.
+
+99
+00:09:26,440 --> 00:09:42,760
+but the second condition، الشرط الثاني، make الـ A is
+
+100
+00:09:42,760 --> 00:09:51,280
+an ideal. يبقى الشرط الثاني لحاله بيخلّي هذا ideal. إذا من
+
+101
+00:09:51,280 --> 00:09:56,150
+الآن فصاعداً، لما يعطيني الـ set ويقول لي: أثبت أن هذه
+
+102
+00:09:56,150 --> 00:10:00,990
+ideal من الـ ring الفلانية، بدي أثبت له ثلاثة شروط،
+
+103
+00:10:00,990 --> 00:10:04,830
+أن هذا الـ subset non-empty، اثنين: بدي آخذ عنصرين من
+
+104
+00:10:04,830 --> 00:10:08,470
+نفس الـ subset، الفرق بينهما بدي يكون في نفس الـ
+
+105
+00:10:08,470 --> 00:10:11,470
+subset اللي أخذناها، ثلاثة: بدي آخذ element من الـ
+
+106
+00:10:11,470 --> 00:10:14,900
+subset وelement من الـ ring الأصلية، أضربهما في بعض
+
+107
+00:10:14,900 --> 00:10:18,960
+من جهة اليمين أو جهة الشمال، بدي يطلع عنصر موجود في
+
+108
+00:10:18,960 --> 00:10:22,980
+الـ subset. لأن إن حدث ذلك، يبقى هذه الـ subset بقول
+
+109
+00:10:22,980 --> 00:10:30,900
+عليها ideal من الـ ring الأصلي. نعطي أمثلة. يبقى
+
+110
+00:10:30,900 --> 00:10:35,680
+examples، أول
+
+111
+00:10:35,680 --> 00:10:40,380
+مثال: دائماً وأبداً في حالة الـ subgroup،
+
+112
+00:10:43,270 --> 00:10:47,410
+اللي هو main، الـ identity element أو الـ group
+
+113
+00:10:47,410 --> 00:10:51,870
+الأصلي. هدول إثنين subset من الـ group الأصلي، صحيح
+
+114
+00:10:51,870 --> 00:10:55,790
+ولا لأ؟ طب وإحنا هنا نفس القصة في حالة الـ ring،
+
+115
+00:10:55,790 --> 00:11:04,970
+يبقى هنا بقول له: is zero as a set, and the are are
+
+116
+00:11:04,970 --> 00:11:24,400
+subrings of A and hence ideals in
+
+117
+00:11:24,400 --> 00:11:28,960
+A. الـ
+
+118
+00:11:28,960 --> 00:11:38,680
+zero. هذه الـ zero is called the trivial
+
+119
+00:11:38,680 --> 00:11:40,940
+ideal.
+
+120
+00:11:42,790 --> 00:11:49,490
+(repeated "او" several times)
+
+121
+00:11:49,490 --> 00:11:50,530
+(repeated "او" several times)
+
+122
+00:11:50,530 --> 00:12:00,750
+(repeated "او" several times)
+
+123
+00:12:00,750 --> 00:12:00,790
+(repeated "او" several times)
+
+124
+00:12:00,790 --> 00:12:00,850
+(repeated "او" several times)
+
+125
+00:12:00,850 --> 00:12:04,790
+(repeated "او" several times)
+
+126
+00:12:04,790 --> 00:12:04,810
+(repeated "او" several times)
+
+127
+00:12:12,760 --> 00:12:18,380
+بتأخذ الـ zero من هنا، وأي element R من R، نضرب R
+
+128
+00:12:18,380 --> 00:12:25,640
+في zero أو zero في R، بـ zero. موجود هنا، فلذلك يبقى
+
+129
+00:12:25,640 --> 00:12:31,340
+هيه صار ideal، والـ ring الأصلية هي نفسها، يبقى
+
+130
+00:12:31,340 --> 00:12:36,700
+صارت ideal من نفسها، الـ subring من نفسها، وينطبق
+
+131
+00:12:36,700 --> 00:12:39,500
+تأخذ منها element من الـ ring الأصلية، الـ ring
+
+132
+00:12:39,500 --> 00:12:45,470
+الأصلية نفسها. any two elements موجودة في نفس الـ
+
+133
+00:12:45,470 --> 00:12:47,910
+ring، because it is closed under multiplication.
+
+134
+00:12:47,910 --> 00:12:53,930
+وبالتالي هي subring، ووضع طبيعي، وهذه أبسط أنواع
+
+135
+00:12:53,930 --> 00:12:59,670
+الأمثلة على الـ subrings وعلى الـ ideals. طيب ننتقل
+
+136
+00:12:59,670 --> 00:13:09,770
+الكلام شوية. مثال اثنين. مثال اثنين بيقول: لدرست أن
+
+137
+00:13:11,320 --> 00:13:18,000
+اللي عناصرها هي zero، زائد ونقص n، زائد ونقص اثنين n،
+
+138
+00:13:18,000 --> 00:13:25,180
+زائد ونقص ثلاثة n، وهكذا إلى ما شاء الله، is an
+
+139
+00:13:25,180 --> 00:13:34,480
+ideal of Z، is an ideal of a set of integers Z
+
+140
+00:13:34,480 --> 00:13:44,660
+because: يعرف شو السبب؟ النقطة الأولى: MT على جالها
+
+141
+00:13:44,660 --> 00:13:49,180
+فيه قدامنا الـ zero، تمام؟ لأن الـ zero موجود في
+
+142
+00:13:49,180 --> 00:13:54,900
+Z، تضربه في أي عنصر من عناصر الـ Z، بيطلع الـ zero. يبقى
+
+143
+00:13:54,900 --> 00:14:05,420
+الـ nZ is non-empty since لأن الـ zero موجود في
+
+144
+00:14:05,420 --> 00:14:14,670
+الـ nZ. النقطة الثانية: بدي آخذ عنصرين x و y موجودين
+
+145
+00:14:14,670 --> 00:14:22,330
+في الـ nZ. then، إيش ممكن يكون شكل الـ x يا بنات؟ n
+
+146
+00:14:22,330 --> 00:14:33,390
+مضروب في عنصر من Z، يعني بقدر أقول n في z1، for some z1 and
+
+147
+00:14:33,390 --> 00:14:46,060
+الـ y، بدي أساويها n في z2، for some z1 و z2 اللي
+
+148
+00:14:46,060 --> 00:14:57,120
+موجودة في Z. بدي آخذ الـ x ناقص الـ y، يبقى n z1 ناقص
+
+149
+00:14:57,120 --> 00:15:02,680
+الـ n z2. بدي أستخدم الـ distributive law، قانون
+
+150
+00:15:02,680 --> 00:15:12,350
+التوزيع. يبقى هذا الكلام بيساوي n (z1 ناقص z2).
+
+151
+00:15:12,350 --> 00:15:22,670
+موجود في Z1؟ لأ، لأ، موجود في nZ. ليش؟ لأن z1 ناقص z2
+
+152
+00:15:22,670 --> 00:15:28,270
+موجودة في Z. the difference between any two integers is an
+
+153
+00:15:28,270 --> 00:15:38,650
+integer. يبقى هذا موجود هنا لأن الـ z1 ناقص z2 موجودة
+
+154
+00:15:38,650 --> 00:15:43,170
+في set of integers. يبقى مطابق الـ condition الثاني.
+
+155
+00:15:43,170 --> 00:15:48,390
+بدي أروح لمين؟ للـ condition الثالث. بدي آخذ عنصر في
+
+156
+00:15:48,390 --> 00:15:59,490
+Z وعنصر في nZ. يبقى هنا، let x اللي بتساوي n z1
+
+157
+00:15:59,490 --> 00:16:12,620
+موجودة في nZ، and m موجودة في Z. then بتأخذ
+
+158
+00:16:12,620 --> 00:16:21,500
+x m، بتشوف هل هو موجود في nZ ولا لأ؟ هذا الكلام
+
+159
+00:16:21,500 --> 00:16:32,340
+بيعطيني x m، بنجدها n z1 m. يبقى n z1 مضروبة في m.
+
+160
+00:16:33,020 --> 00:16:37,620
+هدول integers، كلهم. خاصية الـ associativity صحيحة
+
+161
+00:16:37,620 --> 00:16:46,080
+على الـ integers. يبقى هذا بدي يعطيني n z1 m. هذه
+
+162
+00:16:46,080 --> 00:16:54,520
+موجودة في nZ ولا لأ؟ موجودة في nZ. z1 m موجودة
+
+163
+00:16:54,520 --> 00:17:00,840
+في Z، وبالتالي صارت هذه كلها موجودة في nZ، وفي نفس
+
+164
+00:17:00,840 --> 00:17:11,960
+الوقت، لو أخذت m x، يبقى بده يساوي الـ m في n z1. طيب
+
+165
+00:17:11,960 --> 00:17:16,920
+الآن هدول الثلاث integers، خاصية الـ
+
+166
+00:17:16,920 --> 00:17:21,680
+associativity صحيحة على الـ integers، وزيادة على ذلك،
+
+167
+00:17:21,680 --> 00:17:26,780
+عملية الضرب commutative على Z ولا لأ؟ commutative.
+
+168
+00:17:26,780 --> 00:17:34,340
+يبقى بناء عليه هذا بده يساوي الـ n في الـ m z1، اللي
+
+169
+00:17:34,340 --> 00:17:40,320
+موجودة وين؟ في الـ nZ. يبقى مطابق الـ condition الثالث.
+
+170
+00:17:40,320 --> 00:17:52,980
+وبناء عليه، بناء عليه، غصب، الـ n في Z is an ideal of
+
+171
+00:17:52,980 --> 00:17:59,320
+the ring of integers، اللي هم
+
+223
+00:24:16,500 --> 00:24:24,200
+التالت بدي آخذ عنصر موجود هنا، وأي عنصر موجود في R
+
+224
+00:24:24,200 --> 00:24:32,540
+يبقى بدي أقول افترض أن R موجود في R، والـ X اللي
+
+225
+00:24:32,540 --> 00:24:40,960
+هو بده يساوي R1A، موجودة في مين؟ موجودة في الـ set
+
+226
+00:24:40,960 --> 00:24:46,440
+اللي عندها دي، then فده
+
+227
+00:24:46,440 --> 00:24:55,280
+ياخذ الـ RX بده يشوف عشان تساوي، يبقى الـ RX عبارة
+
+228
+00:24:55,280 --> 00:25:02,770
+عن R، والـ X R1A، خاصية الـ associativity الصحيحة على
+
+229
+00:25:02,770 --> 00:25:10,930
+الـ things، يبقى RR1A، يبقى هذا موجود في الـ set اللي
+
+230
+00:25:10,930 --> 00:25:17,210
+فوق ولا لا؟ يبقى هذا موجود في الـ set اللي عندنا
+
+231
+00:25:17,210 --> 00:25:27,790
+هذه ليش؟ because RR1 موجودة في R، لأنه R مغلقة تحت
+
+232
+00:25:27,790 --> 00:25:34,120
+عملية الضرب، طبعاً، طيب ضل اتجاه الثاني، هنا ضربنا الـ R
+
+233
+00:25:34,120 --> 00:25:39,860
+من جهتي الشمال، بدنا نروح نضرب أين؟ من جهتي اليمين
+
+234
+00:25:39,860 --> 00:25:48,040
+لكن الـ R commutative، يبقى هنا also وكذلك الـ XR
+
+235
+00:25:48,040 --> 00:25:58,440
+موجودة في ايه؟ because الـ R is commutative، يبقى لو
+
+236
+00:25:58,440 --> 00:26:03,340
+شيلنا شرط الـ commutative من هنا، من هنا بيطلع هذا
+
+237
+00:26:03,340 --> 00:26:07,640
+ring، من هنا بيطلع هذا ideal، الإجابة لأ، لأن ما
+
+238
+00:26:07,640 --> 00:26:14,360
+نقدرش نحط الجزء الثاني، إلا أن thus، وهكذا الـ
+
+239
+00:26:14,360 --> 00:26:23,660
+principle ideal generated by A is an ideal of A،
+
+240
+00:26:23,660 --> 00:26:26,560
+يبقى هذا ideal في ring A
+
+241
+00:26:31,480 --> 00:26:38,600
+طب هل كل ideal في الـ ring A يكون الـ principle؟
+
+242
+00:26:38,600 --> 00:26:45,880
+ليس بالضرورة، ليس بالضرورة كما سنراه من خلال
+
+243
+00:26:45,880 --> 00:26:53,380
+الأمثلة القادمة إن شاء الله. طيب هذا كان المثال رقم
+
+244
+00:26:53,380 --> 00:27:00,180
+3، بدنا نروح للمثال رقم 4، رقم 4
+
+245
+00:27:03,170 --> 00:27:19,690
+the ring Z is a subring of the Q هو مجموعة
+
+246
+00:27:19,690 --> 00:27:25,230
+الأعداد الصحيحة، subring من مجموعة الأعداد النسبية
+
+247
+00:27:25,230 --> 00:27:32,000
+السؤال هو هل Z هذه ideal؟ يعني مش كل subring هي الـ
+
+248
+00:27:32,000 --> 00:27:37,000
+ideal، بعضهم بِينفع تكون ideal وبعضهم ما بِينفعش تكون
+
+249
+00:27:37,000 --> 00:27:42,180
+ideal، طيب هذه ليش؟ يكفينا counterexample واحد
+
+250
+00:27:42,180 --> 00:27:54,320
+تمام؟ يبقى هذه Z subring من Q، ولكن Z is not an
+
+251
+00:27:54,320 --> 00:28:04,350
+ideal of Q، السبب because بدنا نأخذ element موجود في
+
+252
+00:28:04,350 --> 00:28:14,650
+Z، خمسة مثلاً، موجود في Z، عدد صحيح، وطبعاً موجود في الـ
+
+253
+00:28:14,650 --> 00:28:23,230
+Q، طيب لو كانت ideal، بدي يكون حاصل الضرب موجود في Z، طيب
+
+254
+00:28:23,230 --> 00:28:31,700
+خمسة مضروبة في ثلث، يساوي خمسة على ثلاثة، ليست عدداً
+
+255
+00:28:31,700 --> 00:28:38,440
+صحيحًا، إذاً الـ Z هي عبارة عن subring، لكنها في
+
+256
+00:28:38,440 --> 00:28:46,580
+الحقيقة ليست ideal في مجموعة الأعداد النسبية، نعطي
+
+257
+00:28:46,580 --> 00:28:56,740
+مثالاً آخر، الـ R الخامس بيقول لي الـ R of X
+
+258
+00:28:58,110 --> 00:29:02,950
+denote the
+
+259
+00:29:02,950 --> 00:29:13,270
+set of all polynomials، مجموعة
+
+260
+00:29:13,270 --> 00:29:23,630
+كثيرات الحدود، with real coefficients، المعاملات
+
+261
+00:29:23,630 --> 00:29:27,450
+كلها أعداد حقيقية
+
+262
+00:29:29,800 --> 00:29:41,240
+و there are coefficients، and let A be the set
+
+263
+00:29:41,240 --> 00:29:49,880
+of all polynomials، كل كثيرات الحدود، with constant
+
+264
+00:29:49,880 --> 00:29:56,700
+term zero، with constant term
+
+265
+00:29:56,700 --> 00:30:06,070
+zero، then A
+
+266
+00:30:06,070 --> 00:30:20,870
+is an ideal، is an ideal of R of X، زيادة على ذلك
+
+267
+00:30:20,870 --> 00:30:30,110
+نمر بـ، الـ A تساوي الـ group generated by
+
+268
+00:30:30,110 --> 00:30:35,850
+X، هو الـ principle generated by اللي هو
+
+269
+00:30:35,850 --> 00:30:36,950
+X
+
+270
+00:31:03,490 --> 00:31:08,350
+خلينا نفهم السؤال مرة ثانية قبل ما نبدأ نشتغل، قال
+
+271
+00:31:08,350 --> 00:31:14,970
+الـ R of X تمثل مجموعة كثيرات الحدود اللي معاملاتها
+
+272
+00:31:14,970 --> 00:31:21,390
+أعداد حقيقية، موجبة، سالبة، كسرية، صفر، المهم، مين
+
+273
+00:31:21,390 --> 00:31:27,490
+الـ A هي كل كثيرات الحدود with
+
+274
+00:31:27,490 --> 00:31:34,060
+constant term zero، يعني آخر حد فيها بيكون مين؟ الحد
+
+275
+00:31:34,060 --> 00:31:41,160
+اللي  جابله constant في X، بس الأولانية constant في
+
+276
+00:31:41,160 --> 00:31:46,280
+X زائد constant، زي ما هنشوفه، لأ، يبقى بدأنا نثبت أن
+
+277
+00:31:46,280 --> 00:31:54,320
+هذا عبارة عن ideal، يبقى عناصر الـ R of X من هنا هذه
+
+278
+00:31:54,320 --> 00:32:02,780
+هي كل العناصر F of X بحيث أن الـ F of X بده يساوي
+
+279
+00:32:02,780 --> 00:32:09,120
+an x to the power n، an-1 x to the power
+
+280
+00:32:09,120 --> 00:32:17,640
+one، ونضل ماشيين لغاية a1 x زائد a0، يبقى a
+
+281
+00:32:17,640 --> 00:32:24,600
+0 هو مقدار ثابت، الـ a0 بـ zero، مش
+
+282
+00:32:24,600 --> 00:32:31,530
+موجود، يبقى بدنا نجي للثانية، الـ set اللي أخذناها، كل الـ
+
+283
+00:32:31,530 --> 00:32:39,430
+polynomial G of X بحيث أن الـ G of X يساوي bn x to
+
+284
+00:32:39,430 --> 00:32:44,390
+the power n، bn-1 x to the power n
+
+285
+00:32:44,390 --> 00:32:52,330
+minus 1، زائد b1 x فقط، لغير المقدار الثابت
+
+286
+00:32:52,330 --> 00:32:57,570
+بصفر، يبقى طار، مش موجود، بنثبت له أن هذه عبارة عن
+
+287
+00:32:57,570 --> 00:33:05,530
+إيش؟ ideal، طيب النقطة الأولى، النقطة الأولى، هل هذه
+
+288
+00:33:05,530 --> 00:33:13,530
+non-empty، على الأقل فيها الـ F of 0، كلهم هذول
+
+289
+00:33:13,530 --> 00:33:19,250
+بيغيروا بـ 0، يبقى صار الـ constant term 0
+
+290
+00:33:19,250 --> 00:33:33,090
+صحيح ولا لا؟ يبقى هنا الـ F of 0 ممكن، because الـ G
+
+291
+00:33:33,090 --> 00:33:43,570
+of 0 بده يساوي 0، وهذا موجود في A، هذا النقطة
+
+292
+00:33:43,570 --> 00:33:51,830
+الثانية، بدنا نأخذ عنصرين موجودين في A، ونطرح اتنين
+
+293
+00:33:51,830 --> 00:34:01,190
+من بعض، يبقى لازم أقول له ليه، مثلاً الـ G1 والـ G2
+
+294
+00:34:01,190 --> 00:34:07,710
+موجودات في A، then بدي أعرف إيش الشكل كل واحد
+
+295
+00:34:07,710 --> 00:34:15,030
+فيهم، G1 of X بدي اسميه زي ما احنا مسمينه، هذه زي ما
+
+296
+00:34:15,030 --> 00:34:27,880
+هي الـ bn X to the power n، bn-1 x n-1 زائد زائد b1 x
+
+297
+00:34:27,880 --> 00:34:41,100
+والـ G2، والـ G2 of X، بدل الـ b ممكن اسميه cn x n
+
+298
+00:34:41,100 --> 00:34:48,680
+cn-1 x n-1 زائد c1 x
+
+299
+00:34:51,110 --> 00:35:00,530
+يبقى بدي آخذ g1 ناقص g2، تأثيره على x، هذا الكلام
+
+300
+00:35:00,530 --> 00:35:09,090
+بدّه يساوي g1 of x ناقص g2 of x، بدي أشوف هل هذا
+
+301
+00:35:09,090 --> 00:35:15,730
+موجود في A ولا لأ، بمعنى آخر، هل آخر term يساوي
+
+302
+00:35:15,730 --> 00:35:21,950
+zero ولا لأ، إذا بدنا نطرح كل عنصر من نظيره، يبقى هذا
+
+303
+00:35:21,950 --> 00:35:32,070
+بيصير bn ناقص cn في X to the power n، ثانياً bn-1
+
+304
+00:35:32,070 --> 00:35:43,790
+ناقص cn-1، cn-1 كله في X n-1
+
+305
+00:35:43,790 --> 00:35:49,650
+plus n-1، زائد لغاية ما نوصل لآخر حد اللي
+
+306
+00:35:49,650 --> 00:35:56,400
+هو b1 ناقص c1 كله في x، يبقى الـ constant term  كده إيش
+
+307
+00:35:56,400 --> 00:36:02,560
+طالع عندنا بـ 0، إذا هذه موجودة في A ولا لأ، إذا
+
+308
+00:36:02,560 --> 00:36:07,040
+هذه موجودة في A، بدنا نروح الآن للـ condition
+
+309
+00:36:07,040 --> 00:36:12,140
+الثالثة، بدنا نضرب اثنين في بعض، يبقى بدءاً للـ
+
+310
+00:36:12,140 --> 00:36:20,080
+condition الثالثة، بدي آخذ عنصر من الـ ring R، وبدي
+
+311
+00:36:20,080 --> 00:36:30,560
+آخذ عنصر من A، يبقى هنا F، الـ F موجودة في الـ R of X
+
+312
+00:36:30,560 --> 00:36:41,720
+and اللي هو الـ G موجودة في A، then بدي
+
+313
+00:36:41,720 --> 00:36:50,680
+آخذ F G of X، يبقى هذه بدها تساوي الـ F of X في الـ G
+
+314
+00:36:50,680 --> 00:36:57,500
+of X، يساوي، يبقى بدنا نجي نضرب، ضرب وين الـ F هاي
+
+315
+00:36:57,500 --> 00:37:05,900
+يبقى هذه الـ F اللي أخذناها تمام؟ بدها تضرب في عنصر
+
+316
+00:37:05,900 --> 00:37:12,160
+من هنا اللي هو G، term اللي عندنا، يبقى لو ضربتها بصير
+
+317
+00:37:12,160 --> 00:37:26,440
+an bn x أوسي 2n، يبقى بصير an bn x أوسي 2n، زي
+
+318
+00:37:26,440 --> 00:37:33,440
+...لما أضرب اللي بعد هذه، an-1 في الـ bn
+
+319
+00:37:33,440 --> 00:37:43,790
+يبقى an
+
+320
+00:37:43,790 --> 00:37:51,010
+واحد، ونفضل ماشيين لغاية ما نوصل لمين؟ لغاية ما نوصل
+
+321
+00:37:51,010 --> 00:37:58,670
+لهذه، بدها تصير مين؟ آخر حاجة في القوس، هذه آخر حاجة
+
+322
+00:37:58,670 --> 00:38:11,580
+عند مين؟ a0، يبقى زائد اللي هو a0 bn أو
+
+323
+00:38:11,580 --> 00:38:18,480
+هنا x to the power n، بعد هيك نضل ماشيين لسه
+
+324
+00:38:18,480 --> 00:38:24,880
+ما خلصناش لغاية ما نوصل لحاصل ضرب آخر term من هنا في
+
+325
+00:38:24,880 --> 00:38:30,360
+آخر term، يبقى من اللي يكون عندنا a0 b1 x
+
+326
+00:38:30,360 --> 00:38:41,500
+يبقى زائد a0 b1 x، في عندي ثابت؟ لأ، يبقى هذه
+
+327
+00:38:41,500 --> 00:38:48,220
+بصير كلها موجودة وين؟ موجودة في الـ A، يبقى تحققت
+
+328
+00:38:48,220 --> 00:38:54,660
+الشروط الثلاثة، إذًا A is an ideal، صارت A
+
+329
+00:38:54,660 --> 00:39:02,890
+هذا لما ضربنا، ضربنا من وين؟ ضربنا لسه الـ
+
+330
+00:39:02,890 --> 00:39:12,590
+F في G، Similarly، يبقى Similarly بنفس الطريقة الـ G
+
+331
+00:39:12,590 --> 00:39:20,150
+في الـ F as a function of X يساوي الـ G of X في الـ F
+
+332
+00:39:20,150 --> 00:39:26,950
+of X، هذه كمان موجودة في الـ A، يبقى بناء عليه إذًا
+
+333
+00:39:26,950 --> 00:39:39,760
+وهكذا الـ A is an ideal of R of X، نجي لنمر B
+
+334
+00:39:39,760 --> 00:39:47,420
+بيقول لي إيش في B؟ بيقول لي الـ ideal اللي عندك هذا
+
+335
+00:39:47,420 --> 00:39:57,850
+يمكن أن يولد بعنصر واحد، هالنقطة B هي  I(b)، هو
+
+336
+00:39:57,850 --> 00:40:04,010
+العنصر الذي يولد به هذا العنصر، طيب الآن لما نجي يا
+
+337
+00:40:04,010 --> 00:40:13,890
+بنات نقول بدي آجي آخذ الـ Z F من وين؟ من R، و آجي
+
+338
+00:40:13,890 --> 00:40:24,910
+آخذ F of X في G of X، بحيث الـ F موجودة في R of
+
+339
+00:40:24,910 --> 00:40:33,130
+X، and الـ G موجودة في إيش؟
+
+340
+00:40:33,130 --> 00:40:39,630
+هذا الكلام بالشكل اللي عندنا هذا مش هو الخاصية
+
+341
+00:40:39,630 --> 00:40:46,030
+اللي فوق هذه؟ وين طلعت؟ موجودة في إيش؟ طيب حسب
+
+342
+00:40:46,030 --> 00:40:51,550
+تعريف الـ principle ideal generated by X، مش هي
+
+343
+00:40:51,550 --> 00:40:58,400
+هذه؟ صح ولا لأ؟ يبقى هذه هنا اللي هي الـ principle
+
+344
+00:40:58,400 --> 00:41:06,940
+ideal generated by X، هذا الكلام جبناه من وين؟ from
+
+345
+00:41:06,940 --> 00:41:17,480
+part اللي هو  III of A
+
+346
+00:41:17,480 --> 00:41:23,860
+يبقى هذا من المطلوب الأول، النقطة الثالثة فيه، يبقى
+
+347
+00:41:23,860 --> 00:41:30,880
+صار هذا هو الذي يولد به هذا العنصر، يبقى صارت الـ G of
+
+348
+00:41:30,880 --> 00:41:36,300
+X هذه هو الـ principle ideal generated by A، يبقى كل
+
+349
+00:41:36,300 --> 00:41:42,460
+الـ polynomials اللي أواخرها فيها مقدار ثابت
+
+350
+00:41:42,460 --> 00:41:48,260
+بكونوا صفر، وبالتالي ideal، بسميه الـ principle
+
+351
+00:41:48,260 --> 00:41:54,820
+ideal generated by واحدة منهم، اللي هي مثلاً الـ G of
+
+352
+00:41:54,820 --> 00:42:00,380
+X، اللي الحد الثابت فيها يساوي مين؟ يساوي K،  هنا،
+
+353
+00:42:00,380 --> 00:42:09,080
+تمام؟ طيب، إلى هنا يكفينا اليوم، ولسة لا يزال
+
+354
+00:42:09,080 --> 00:42:14,680
+قدامنا مزيد من الأمثلة للمرة القادمة
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..bcac0594d40901a02bd968101e0fd431629ad0f6
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 5036, "start": 21.02, "end": 50.36, "text": "بسم الله الرحمن الرحيم انتهينا من chapter 12 و chapter 13 و الآن بنجي ل chapter 14 اللي العمود الفقري فيه عبارة عن نقطتين ال ideals و هي حالة خاصة من ال subrings و النقطة الثانية هي ال factorings تماما كما أخذنا factor group أو quotient group قبل ذلك", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16472, 47395, 1829, 8315, 9154, 7187, 2272, 4032, 7187, 3705, 4032, 6024, 48506, 44945, 7435, 1829, 5296, 7187, 3499, 13672, 1829, 18863, 2304, 23328, 27188, 4587, 16572, 8978, 3224, 6225, 3555, 9640, 3660, 18871, 8717, 47432, 2655, 9957, 2423, 30956, 4032, 39896, 11331, 6027, 3660, 16490, 33546, 3660, 9154, 2423, 1422, 25782, 4032, 28239, 47432, 3660, 6024, 104, 7649, 10632, 39896, 2423, 5952, 1109, 46811, 10943, 995, 9122, 15042, 5551, 9778, 8848, 8315, 5952, 1594, 34051, 9641, 1196, 1594, 12174, 36150, 29910, 23275], "avg_logprob": -0.17489918778019567, "compression_ratio": 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{"start": 96.5, "end": 97.18, "word": " ideal", "probability": 0.58203125}, {"start": 97.18, "end": 97.38, "word": " و", "probability": 0.99267578125}, {"start": 97.38, "end": 97.86, "word": " نسكت", "probability": 0.85595703125}, {"start": 97.86, "end": 98.04, "word": " و", "probability": 0.63916015625}, {"start": 98.04, "end": 98.4, "word": " الآن", "probability": 0.6494140625}, {"start": 98.4, "end": 99.08, "word": " هنقولك", "probability": 0.8717041015625}, {"start": 99.08, "end": 99.36, "word": " ليش", "probability": 0.896484375}, {"start": 99.36, "end": 100.14, "word": " سميناها", "probability": 0.764599609375}, {"start": 100.14, "end": 100.7, "word": " two", "probability": 0.94384765625}, {"start": 100.7, "end": 101.16, "word": "-sided", "probability": 0.953857421875}, {"start": 101.16, "end": 101.8, "word": " ideal", "probability": 0.93994140625}, {"start": 101.8, "end": 102.74, "word": " يبقى", "probability": 0.96484375}, {"start": 102.74, "end": 103.1, "word": " sub", 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"temperature": 1.0}, {"id": 5, "seek": 16773, "start": 139.25, "end": 167.73, "text": "إنه لما ناخد حاصل ضرب element من أين و اين راح element من a و element من a بدي يكون الناتج في a هذا في ال ID لكن لما كنا في ال ring بجينا أخدي اتنين من نفس ال six يعني باخد عنصرين من نفس ال a بدي يكون حاصل ضربهم موجود في a هنا لأ خدي أي عنصر من ال sub ring a", "tokens": [28814, 1863, 3224, 5296, 15042, 8717, 47283, 3215, 11331, 33546, 1211, 48812, 25513, 4478, 9154, 5551, 9957, 4032, 1975, 9957, 12602, 39319, 4478, 9154, 257, 4032, 4478, 9154, 257, 4724, 16254, 7251, 30544, 28239, 9307, 7435, 8978, 257, 23758, 8978, 2423, 7348, 44381, 5296, 15042, 9122, 8315, 8978, 2423, 4875, 4724, 7435, 1829, 8315, 5551, 9778, 16254, 1975, 2655, 1863, 9957, 9154, 8717, 36178, 2423, 2309, 37495, 22653, 4724, 47283, 3215, 18871, 9381, 2288, 9957, 9154, 8717, 36178, 2423, 257, 4724, 16254, 7251, 30544, 11331, 33546, 1211, 48812, 25513, 16095, 3714, 29245, 23328, 8978, 257, 34105, 5296, 10721, 16490, 16254, 36632, 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بدي", "probability": 0.8583984375}, {"start": 160.87, "end": 161.11, "word": " يكون", "probability": 0.922119140625}, {"start": 161.11, "end": 161.57, "word": " حاصل", "probability": 0.9825846354166666}, {"start": 161.57, "end": 162.19, "word": " ضربهم", "probability": 0.9700520833333334}, {"start": 162.19, "end": 162.97, "word": " موجود", "probability": 0.978515625}, {"start": 162.97, "end": 163.23, "word": " في", "probability": 0.93798828125}, {"start": 163.23, "end": 163.33, "word": " a", "probability": 0.515625}, {"start": 163.33, "end": 163.61, "word": " هنا", "probability": 0.8427734375}, {"start": 163.61, "end": 164.07, "word": " لأ", "probability": 0.798828125}, {"start": 164.07, "end": 164.87, "word": " خدي", "probability": 0.62939453125}, {"start": 164.87, "end": 165.19, "word": " أي", "probability": 0.63671875}, {"start": 165.19, "end": 166.03, "word": " عنصر", "probability": 0.98828125}, {"start": 166.03, "end": 166.47, "word": " من", "probability": 0.9951171875}, {"start": 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ال", "probability": 0.912109375}, {"start": 362.87, "end": 363.19, "word": " subset", "probability": 0.9482421875}, {"start": 363.19, "end": 363.57, "word": " هذه", "probability": 0.5087890625}, {"start": 363.57, "end": 364.13, "word": " مالها", "probability": 0.9376627604166666}], "temperature": 1.0}, {"id": 13, "seek": 39350, "start": 364.48, "end": 393.5, "text": "non-empty non-empty subset A of A ring R بقول عنها ideal إذا كان أخدت عمصرين من الستة اللي طرحتهم من بعض بدي يكون الناتج في A يبقى A minus ال B موجود في A whenever ال A و ال B موجودين في A اللي بعده ال R في A موجود في A وال A في R موجود في A", "tokens": [30092, 12, 4543, 88, 2107, 12, 4543, 88, 25993, 316, 295, 316, 4875, 497, 4724, 39648, 18871, 11296, 7157, 11933, 15730, 25961, 5551, 9778, 3215, 2655, 6225, 2304, 9381, 2288, 9957, 9154, 21136, 2655, 3660, 13672, 1829, 23032, 2288, 33753, 16095, 9154, 45030, 11242, 4724, 16254, 7251, 30544, 28239, 9307, 7435, 8978, 316, 7251, 3555, 4587, 7578, 316, 3175, 2423, 363, 3714, 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" اللي", "probability": 0.851806640625}, {"start": 388.4, "end": 388.86, "word": " بعده", "probability": 0.828125}, {"start": 388.86, "end": 389.02, "word": " ال", "probability": 0.84130859375}, {"start": 389.02, "end": 389.34, "word": " R", "probability": 0.80126953125}, {"start": 389.34, "end": 389.64, "word": " في", "probability": 0.95947265625}, {"start": 389.64, "end": 390.06, "word": " A", "probability": 0.9921875}, {"start": 390.06, "end": 390.76, "word": " موجود", "probability": 0.9889322916666666}, {"start": 390.76, "end": 391.0, "word": " في", "probability": 0.98291015625}, {"start": 391.0, "end": 391.26, "word": " A", "probability": 0.9931640625}, {"start": 391.26, "end": 391.54, "word": " وال", "probability": 0.64794921875}, {"start": 391.54, "end": 391.86, "word": " A", "probability": 0.64794921875}, {"start": 391.86, "end": 392.02, "word": " في", "probability": 0.94287109375}, {"start": 392.02, "end": 392.3, "word": " R", "probability": 0.98583984375}, {"start": 392.3, 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بدنا نروح نضرب اين؟ من جهتي اليمين لكن الار commutative يبقى هنا also وكذلك ال XR موجودة في ايه؟ because الار is commutative", "tokens": [9566, 3555, 3615, 995, 23032, 1829, 3555, 48812, 1211, 1975, 2655, 7435, 40294, 6024, 104, 7649, 1829, 34105, 48812, 25513, 8315, 2423, 9640, 9154, 10874, 3224, 31371, 25124, 2304, 6027, 47525, 8315, 8717, 32887, 5016, 8717, 11242, 25513, 1975, 9957, 22807, 9154, 10874, 3224, 31371, 2423, 32640, 9957, 44381, 2423, 9640, 800, 325, 1166, 7251, 3555, 4587, 7578, 34105, 611, 4032, 4117, 8848, 23275, 2423, 1783, 49, 3714, 29245, 23328, 3660, 8978, 1975, 1829, 3224, 22807, 570, 2423, 9640, 307, 800, 325, 1166], "avg_logprob": -0.19996279442594164, "compression_ratio": 1.6089385474860336, "no_speech_prob": 0.0, "words": [{"start": 1529.92, "end": 1530.54, "word": "طبعا", "probability": 0.75732421875}, {"start": 1530.54, "end": 1531.5, "word": " طيب", "probability": 0.82275390625}, {"start": 1531.5, "end": 1531.84, "word": " ضل", "probability": 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"probability": 0.712890625}, {"start": 1548.04, "end": 1549.5, "word": " موجودة", "probability": 0.9833984375}, {"start": 1549.5, "end": 1549.8, "word": " في", "probability": 0.92236328125}, {"start": 1549.8, "end": 1550.74, "word": " ايه؟", "probability": 0.790771484375}, {"start": 1550.74, "end": 1552.38, "word": " because", "probability": 0.6015625}, {"start": 1552.38, "end": 1554.3, "word": " الار", "probability": 0.9267578125}, {"start": 1554.3, "end": 1555.48, "word": " is", "probability": 0.93212890625}, {"start": 1555.48, "end": 1556.8, "word": " commutative", "probability": 0.9783528645833334}], "temperature": 1.0}, {"id": 54, "seek": 158656, "start": 1557.76, "end": 1586.56, "text": "يبقى لو شيلنا شرط ال commutative من هنا، من هنا بطلع هذا ring، من هنا بطلع هذا ideal، الإجابة لأ لإن ما نقدرش نحط الجزء الثاني إلا أن thus و هكذا ال principle ideal generated by A is an ideal of A، يبقى هذا ideal في ring A", "tokens": [1829, 3555, 4587, 7578, 45164, 13412, 26895, 8315, 13412, 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2455.07, "end": 2455.65, "word": " هذه", "probability": 0.79638671875}, {"start": 2455.65, "end": 2456.03, "word": " هنا", "probability": 0.81591796875}], "temperature": 1.0}, {"id": 85, "seek": 248484, "start": 2456.56, "end": 2484.84, "text": "اللي هي ال principle id generated by gx هذا الكلام جيبناه من وين from part اللي هو triple I of A يبقى هذا من المطلوب الأول النقطة التالتة فيه يبقى صار هذا", "tokens": [6027, 20292, 39896, 2423, 8665, 4496, 10833, 538, 290, 87, 23758, 2423, 28820, 10943, 10874, 1829, 3555, 8315, 3224, 9154, 4032, 9957, 490, 644, 13672, 1829, 31439, 15508, 286, 295, 316, 7251, 3555, 4587, 7578, 23758, 9154, 9673, 9566, 1211, 37746, 16247, 12610, 28239, 47432, 3660, 16712, 6027, 2655, 3660, 8978, 3224, 7251, 3555, 4587, 7578, 20328, 9640, 23758], "avg_logprob": -0.2236979216337204, "compression_ratio": 1.4506172839506173, "no_speech_prob": 0.0, "words": [{"start": 2456.56, "end": 2457.06, "word": "اللي", "probability": 0.80517578125}, {"start": 2457.06, "end": 2457.48, "word": " هي", "probability": 0.759765625}, {"start": 2457.48, "end": 2457.74, "word": " ال", "probability": 0.60107421875}, {"start": 2457.74, "end": 2458.4, "word": " principle", "probability": 0.54736328125}, {"start": 2458.4, "end": 2459.36, "word": " id", "probability": 0.250244140625}, {"start": 2459.36, "end": 2460.92, "word": " generated", "probability": 0.658203125}, {"start": 2460.92, "end": 2462.0, "word": " by", "probability": 0.9599609375}, {"start": 2462.0, "end": 2462.88, "word": " gx", "probability": 0.65771484375}, {"start": 2462.88, "end": 2463.7, "word": " هذا", "probability": 0.890625}, {"start": 2463.7, "end": 2464.42, "word": " الكلام", "probability": 0.9163411458333334}, {"start": 2464.42, "end": 2465.06, "word": " جيبناه", "probability": 0.846484375}, {"start": 2465.06, "end": 2465.28, "word": " من", "probability": 0.990234375}, {"start": 2465.28, "end": 2465.92, "word": " وين", "probability": 0.91650390625}, {"start": 2465.92, "end": 2466.94, "word": " from", "probability": 0.380859375}, {"start": 2466.94, "end": 2469.28, "word": " part", "probability": 0.916015625}, {"start": 2469.28, "end": 2470.58, "word": " اللي", "probability": 0.6114501953125}, {"start": 2470.58, "end": 2470.92, "word": " هو", "probability": 0.9794921875}, {"start": 2470.92, "end": 2471.5, "word": " triple", "probability": 0.227294921875}, {"start": 2471.5, "end": 2472.48, "word": " I", "probability": 0.75048828125}, {"start": 2472.48, "end": 2473.96, "word": " of", "probability": 0.951171875}, {"start": 2473.96, "end": 2477.48, "word": " A", "probability": 0.6796875}, {"start": 2477.48, "end": 2478.94, "word": " يبقى", "probability": 0.949951171875}, {"start": 2478.94, "end": 2479.2, "word": " هذا", "probability": 0.83544921875}, {"start": 2479.2, "end": 2479.46, "word": " من", "probability": 0.9501953125}, {"start": 2479.46, "end": 2480.2, "word": " المطلوب", "probability": 0.81219482421875}, {"start": 2480.2, "end": 2480.68, "word": " الأول", "probability": 0.93359375}, {"start": 2480.68, "end": 2481.56, "word": " النقطة", "probability": 0.9446614583333334}, {"start": 2481.56, "end": 2482.5, "word": " التالتة", "probability": 0.9013671875}, {"start": 2482.5, "end": 2483.06, "word": " فيه", "probability": 0.975830078125}, {"start": 2483.06, "end": 2483.86, "word": " يبقى", "probability": 0.96533203125}, {"start": 2483.86, "end": 2484.34, "word": " صار", "probability": 0.972412109375}, {"start": 2484.34, "end": 2484.84, "word": " هذا", "probability": 0.962890625}], "temperature": 1.0}, {"id": 86, "seek": 251250, "start": 2485.16, "end": 2512.5, "text": "هو الذي يولد بهذا العمصر يبقى صارة الـG of X هذه هو ال principle ideal generated by A يبقى كل ال polynomials اللي آخرتين فيهم مقدارا ثابتا بكونون صبرا وبالتالي ideal بسميه ال principle ideal generated by واحدة منهم", "tokens": [3224, 2407, 43527, 7251, 12610, 3215, 39627, 15730, 18863, 2304, 9381, 2288, 7251, 3555, 4587, 7578, 20328, 9640, 3660, 2423, 39184, 38, 295, 1783, 29538, 31439, 2423, 8665, 7157, 10833, 538, 316, 7251, 3555, 4587, 7578, 28242, 2423, 22560, 12356, 13672, 1829, 19753, 34740, 2655, 9957, 8978, 16095, 3714, 28543, 9640, 995, 38637, 16758, 2655, 995, 4724, 30544, 11536, 20328, 3555, 23557, 46599, 6027, 2655, 6027, 1829, 7157, 4724, 38251, 1829, 3224, 2423, 8665, 7157, 10833, 538, 36764, 24401, 3660, 9154, 16095], "avg_logprob": -0.18928841079574033, "compression_ratio": 1.5714285714285714, "no_speech_prob": 0.0, "words": [{"start": 2485.16, "end": 2485.52, "word": "هو", "probability": 0.86376953125}, {"start": 2485.52, "end": 2485.92, "word": " الذي", "probability": 0.67529296875}, {"start": 2485.92, "end": 2486.78, "word": " يولد", "probability": 0.9899088541666666}, {"start": 2486.78, "end": 2487.64, "word": " بهذا", "probability": 0.956787109375}, {"start": 2487.64, "end": 2488.54, "word": " العمصر", "probability": 0.8929443359375}, {"start": 2488.54, "end": 2489.42, "word": " يبقى", "probability": 0.9161376953125}, {"start": 2489.42, "end": 2490.0, "word": " صارة", "probability": 0.7779947916666666}, {"start": 2490.0, "end": 2490.5, "word": " الـG", "probability": 0.6456705729166666}, {"start": 2490.5, "end": 2490.88, "word": " of", "probability": 0.44775390625}, {"start": 2490.88, "end": 2491.28, "word": " X", "probability": 0.970703125}, {"start": 2491.28, "end": 2491.7, "word": " هذه", "probability": 0.65087890625}, {"start": 2491.7, "end": 2492.26, "word": " هو", "probability": 0.80859375}, {"start": 2492.26, "end": 2492.46, "word": " ال", "probability": 0.93994140625}, {"start": 2492.46, "end": 2492.92, "word": " principle", "probability": 0.460205078125}, {"start": 2492.92, "end": 2493.5, "word": " ideal", "probability": 0.671875}, {"start": 2493.5, "end": 2494.1, "word": " generated", "probability": 0.8271484375}, {"start": 2494.1, "end": 2494.56, "word": " by", "probability": 0.95068359375}, {"start": 2494.56, "end": 2494.88, "word": " A", "probability": 0.759765625}, {"start": 2494.88, "end": 2495.72, "word": " يبقى", "probability": 0.9720458984375}, {"start": 2495.72, "end": 2496.3, "word": " كل", "probability": 0.9833984375}, {"start": 2496.3, "end": 2496.6, "word": " ال", "probability": 0.953125}, {"start": 2496.6, "end": 2498.08, "word": " polynomials", "probability": 0.6376953125}, {"start": 2498.08, "end": 2499.08, "word": " اللي", "probability": 0.937255859375}, {"start": 2499.08, "end": 2499.98, "word": " آخرتين", "probability": 0.8724365234375}, {"start": 2499.98, "end": 2500.52, "word": " فيهم", "probability": 0.918701171875}, {"start": 2500.52, "end": 2501.48, "word": " مقدارا", "probability": 0.876708984375}, {"start": 2501.48, "end": 2502.46, "word": " ثابتا", "probability": 0.9835205078125}, {"start": 2502.46, "end": 2503.88, "word": " بكونون", "probability": 0.8102213541666666}, {"start": 2503.88, "end": 2504.88, "word": " صبرا", "probability": 0.412353515625}, {"start": 2504.88, "end": 2506.12, "word": " وبالتالي", "probability": 0.9107421875}, {"start": 2506.12, "end": 2506.8, "word": " ideal", "probability": 0.437255859375}, {"start": 2506.8, "end": 2507.7, "word": " بسميه", "probability": 0.9466552734375}, {"start": 2507.7, "end": 2507.8, "word": " ال", "probability": 0.57275390625}, {"start": 2507.8, "end": 2508.26, "word": " principle", "probability": 0.86279296875}, {"start": 2508.26, "end": 2508.92, "word": " ideal", "probability": 0.8623046875}, {"start": 2508.92, "end": 2509.6, "word": " generated", "probability": 0.84716796875}, {"start": 2509.6, "end": 2510.52, "word": " by", "probability": 0.97265625}, {"start": 2510.52, "end": 2511.78, "word": " واحدة", "probability": 0.9344075520833334}, {"start": 2511.78, "end": 2512.5, "word": " منهم", "probability": 0.98974609375}], "temperature": 1.0}, {"id": 87, "seek": 253467, "start": 2512.7, "end": 2534.68, "text": "اللي هي مثلا الـ G of X اللي الحد فيها يساوي مين؟ يساوي K نص طن هنا، تمام؟ طيب، إلى هنا يكفينا اليوم و لسه لا يزال قدامنا مزيد من الأمثلة للمرة الحاضرة", "tokens": [6027, 20292, 39896, 50113, 15040, 2423, 39184, 460, 295, 1783, 13672, 1829, 21542, 3215, 8978, 11296, 7251, 3794, 995, 45865, 3714, 9957, 22807, 7251, 3794, 995, 45865, 591, 8717, 9381, 23032, 1863, 34105, 12399, 46811, 10943, 22807, 23032, 1829, 3555, 12399, 30731, 34105, 7251, 4117, 41185, 8315, 45595, 20498, 4032, 5296, 3794, 3224, 20193, 7251, 11622, 6027, 12174, 3215, 10943, 8315, 3714, 11622, 25708, 9154, 16247, 2304, 12984, 37977, 5296, 19528, 25720, 21542, 46958, 25720], "avg_logprob": -0.2619243275962378, "compression_ratio": 1.5963855421686748, "no_speech_prob": 0.0, "words": [{"start": 2512.7, "end": 2513.06, "word": "اللي", "probability": 0.934814453125}, {"start": 2513.06, "end": 2513.24, "word": " هي", "probability": 0.529296875}, {"start": 2513.24, "end": 2513.76, "word": " مثلا", "probability": 0.9609375}, {"start": 2513.76, "end": 2514.36, "word": " الـ", "probability": 0.622314453125}, {"start": 2514.36, "end": 2514.46, "word": " G", "probability": 0.2802734375}, {"start": 2514.46, "end": 2514.82, "word": " of", "probability": 0.5625}, {"start": 2514.82, "end": 2515.18, "word": " X", "probability": 0.87451171875}, {"start": 2515.18, "end": 2515.72, "word": " اللي", "probability": 0.6085205078125}, {"start": 2515.72, "end": 2516.12, "word": " الحد", "probability": 0.93798828125}, {"start": 2516.12, "end": 2516.46, "word": " فيها", "probability": 0.986328125}, {"start": 2516.46, "end": 2516.94, "word": " يساوي", "probability": 0.94384765625}, {"start": 2516.94, "end": 2517.66, "word": " مين؟", "probability": 0.8356119791666666}, {"start": 2517.66, "end": 2518.36, "word": " يساوي", "probability": 0.9666748046875}, {"start": 2518.36, "end": 2518.64, "word": " K", "probability": 0.1702880859375}, {"start": 2518.64, "end": 2519.02, "word": " نص", "probability": 0.880126953125}, {"start": 2519.02, "end": 2519.46, "word": " طن", "probability": 0.54345703125}, {"start": 2519.46, "end": 2520.38, "word": " هنا،", "probability": 0.229888916015625}, {"start": 2520.38, "end": 2522.56, "word": " تمام؟", "probability": 0.9187825520833334}, {"start": 2522.56, "end": 2523.36, "word": " طيب،", "probability": 0.855224609375}, {"start": 2523.36, "end": 2525.22, "word": " إلى", "probability": 0.7333984375}, {"start": 2525.22, "end": 2525.68, "word": " هنا", "probability": 0.9873046875}, {"start": 2525.68, "end": 2526.4, "word": " يكفينا", "probability": 0.9542236328125}, {"start": 2526.4, "end": 2526.94, "word": " اليوم", "probability": 0.959228515625}, {"start": 2526.94, "end": 2527.94, "word": " و", "probability": 0.35888671875}, {"start": 2527.94, "end": 2528.42, "word": " لسه", "probability": 0.8079427083333334}, {"start": 2528.42, "end": 2528.58, "word": " لا", "probability": 0.83984375}, {"start": 2528.58, "end": 2529.08, "word": " يزال", "probability": 0.9695638020833334}, {"start": 2529.08, "end": 2529.74, "word": " قدامنا", "probability": 0.9873046875}, {"start": 2529.74, "end": 2530.72, "word": " مزيد", "probability": 0.7472330729166666}, {"start": 2530.72, "end": 2531.34, "word": " من", "probability": 0.98828125}, {"start": 2531.34, "end": 2532.74, "word": " الأمثلة", "probability": 0.8616943359375}, {"start": 2532.74, "end": 2533.94, "word": " للمرة", "probability": 0.8035481770833334}, {"start": 2533.94, "end": 2534.68, "word": " الحاضرة", "probability": 0.731201171875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2535.0153125, "duration_after_vad": 2423.711249999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..605dcec89c26c5ba343387d00ab96089a2261043
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_raw.srt
@@ -0,0 +1,1420 @@
+1
+00:00:21,020 --> 00:00:26,040
+بسم الله الرحمن الرحيم انتهينا من chapter 12 و
+
+2
+00:00:26,040 --> 00:00:31,720
+chapter 13 و الآن بنجي ل chapter 14 اللي العمود
+
+3
+00:00:31,720 --> 00:00:37,760
+الفقري فيه عبارة عن نقطتين ال ideals و هي حالة
+
+4
+00:00:37,760 --> 00:00:42,740
+خاصة من ال subrings و النقطة الثانية هي ال
+
+5
+00:00:42,740 --> 00:00:47,660
+factorings تماما كما أخذنا factor group أو
+
+6
+00:00:47,660 --> 00:00:53,260
+quotient group قبل ذلكاليوم هنبدأ فقط بال ideals
+
+7
+00:00:53,260 --> 00:00:58,320
+وال factor rings بنخليه للمرة القادمة ان شاء الله
+
+8
+00:00:58,320 --> 00:01:04,740
+يبقى بدنا نبدأ بتعريف ال ideal ثم ناخد بعض الأمثلة
+
+9
+00:01:04,740 --> 00:01:08,480
+عليه وكيف نحكم على ال subsidy اللي بناخدها من ال
+
+10
+00:01:08,480 --> 00:01:14,400
+ring هل هي ideal او ليست ideal طب اروح نقول
+
+11
+00:01:14,400 --> 00:01:23,880
+التعريف كتالي يبقى a sub ringA sub ring A
+
+12
+00:01:23,880 --> 00:01:31,640
+of A ring R is called a two-sided ideal كلمة two
+
+13
+00:01:31,640 --> 00:01:36,500
+-sided حطيناها لهدف ممكن ما نقولش two-sided نقول
+
+14
+00:01:36,500 --> 00:01:41,160
+ideal و نسكت و الآن هنقولك ليش سميناها two-sided
+
+15
+00:01:41,160 --> 00:01:46,760
+ideal يبقى sub ring A of A ring R is called a two
+
+16
+00:01:46,760 --> 00:01:48,740
+-sided ideal of R
+
+17
+00:02:00,700 --> 00:02:07,200
+السؤال هو ما هو الفرق بين ال ID و بين ال subring
+
+18
+00:02:07,200 --> 00:02:14,660
+طبعا الفرق واضح من خلال ال definition اتنين من
+
+19
+00:02:14,660 --> 00:02:20,570
+empty هذا كلام صحيح النقطة الثانيةإنه لما ناخد
+
+20
+00:02:20,570 --> 00:02:27,210
+حاصل ضرب element من أين و اين راح element من a و
+
+21
+00:02:27,210 --> 00:02:32,550
+element من a بدي يكون الناتج في a هذا في ال ID لكن
+
+22
+00:02:32,550 --> 00:02:36,750
+لما كنا في ال ring بجينا أخدي اتنين من نفس ال six
+
+23
+00:02:36,750 --> 00:02:42,190
+يعني باخد عنصرين من نفس ال a بدي يكون حاصل ضربهم
+
+24
+00:02:42,190 --> 00:02:48,640
+موجود في a هنا لأ خدي أي عنصر من ال sub ring aو أي
+
+25
+00:02:48,640 --> 00:02:53,760
+عنصر من ال ring نضربهم معاهم بدي يكون موجود داخل
+
+26
+00:02:53,760 --> 00:02:59,060
+ال sub ring ان حدث ذلك يبقى بنسمي هذا ideal سواء
+
+27
+00:02:59,060 --> 00:03:05,100
+كان الضرب من اليمين او من الشمال فلما كان الضرب من
+
+28
+00:03:05,100 --> 00:03:10,740
+الشمال و هنا من اليمين سمنا ايه؟ two sided ideal
+
+29
+00:03:10,740 --> 00:03:17,420
+فإن قلنا two sided ideal او ideal و سكتناالاتنين
+
+30
+00:03:17,420 --> 00:03:22,420
+كله بنفس المعنى، تمام؟ يعني وانت بتقول اللي جيتي
+
+31
+00:03:22,420 --> 00:03:26,500
+كلمة two-sided ideal وما لجيتي كلمة ideal، بدك
+
+32
+00:03:26,500 --> 00:03:31,660
+تفهمي هذه انها two-sided ideal التعريف هذا، بدي
+
+33
+00:03:31,660 --> 00:03:37,440
+أعيد صياغته بطريقة أخرى، بقول this definition can
+
+34
+00:03:37,440 --> 00:03:41,920
+be written as هذا التعريف اتركته على الشكل التالف
+
+35
+00:03:42,140 --> 00:03:48,220
+ال sub ring A of A ring R is called ideal of R إذا
+
+36
+00:03:48,220 --> 00:03:54,560
+كان لو ضربت ال R في عناصر ال ideal كله بتطلع عندي
+
+37
+00:03:54,560 --> 00:04:02,240
+set وهذه set subset من مين؟ من A الأصلية بالمثل لو
+
+38
+00:04:02,240 --> 00:04:09,260
+ضربت في R من جهة اليمين جميع عناصر ال A بيطلع ل
+
+39
+00:04:09,260 --> 00:04:15,380
+set subset من مين؟ من Aإن تحققت لأي R موجودة في R،
+
+40
+00:04:15,380 --> 00:04:19,760
+إن تحققت ال two conditions لإتنين هدول، بقول إن ال
+
+41
+00:04:19,760 --> 00:04:26,460
+A هو عبارة عن ideal أو two-sided ideal، هذه أو
+
+42
+00:04:26,460 --> 00:04:33,040
+كلتل إتنين are the same.بنجر الآن للتعريف الثاني،
+
+43
+00:04:33,040 --> 00:04:39,110
+A is called the proper ideal of Aproper ideal إذا
+
+44
+00:04:39,110 --> 00:04:43,870
+كان الـA هو proper subset من من من الـA إيش يعني
+
+45
+00:04:43,870 --> 00:04:47,670
+معنى proper مثل ما درسناه في ال group؟ إيش يعني
+
+46
+00:04:47,670 --> 00:04:53,370
+proper يا مناد؟ انه subset من ال group الأصلية
+
+47
+00:04:53,370 --> 00:04:59,230
+وكان لا يساوي هذه ال group وهنا نفس القصة ال ideal
+
+48
+00:04:59,230 --> 00:05:06,310
+هو proper subset يعني لا يساوي ال group لا يساوي
+
+49
+00:05:06,310 --> 00:05:12,540
+ال ring الأصليةطب ايش معنى Improper؟ ممكن احتمال
+
+50
+00:05:12,540 --> 00:05:18,340
+يتساوي ممكن احتمال يتساوي ممكن احتمال يتساوي ممكن
+
+51
+00:05:18,340 --> 00:05:19,780
+احتمال يتساوي ممكن احتمال يتساوي ممكن احتمال
+
+52
+00:05:19,780 --> 00:05:21,300
+يتساوي ممكن احتمال يتساوي ممكن احتمال يتساوي ممكن
+
+53
+00:05:21,300 --> 00:05:21,780
+احتمال يتساوي ممكن احتمال يتساوي ممكن احتمال
+
+54
+00:05:21,780 --> 00:05:25,260
+يتساوي ممكن احتمال يتساوي ممكن احتمال يتساوي ممكن
+
+55
+00:05:25,260 --> 00:05:26,000
+احتمال يتساوي ممكن احتمال يتساوي ممكن احتمال
+
+56
+00:05:26,000 --> 00:05:30,040
+يتساوي ممكن احتمال يتساوي ممكن احتمال يتساوي ممكن
+
+57
+00:05:30,040 --> 00:05:31,840
+احتمال يتساوي ممكن ا
+
+58
+00:05:35,790 --> 00:05:40,270
+لكن من حد ما اقولك proper بدك تفهمي ان ال ideal
+
+59
+00:05:40,270 --> 00:05:45,330
+عدد عناصره اقل من عدد عناصر ال ring دائما هو لا
+
+60
+00:05:45,330 --> 00:05:52,530
+يمكن ان يتساوية طيب الآن كيف بدي افحص ان ال 6 اللي
+
+61
+00:05:52,530 --> 00:05:56,570
+خدتها او ال subset اللي خدتها من ال ring الأصلية
+
+62
+00:05:56,570 --> 00:06:03,190
+هي ideal بثلاثة شروط الشرط الأول ان تبقى ال subset
+
+63
+00:06:03,190 --> 00:06:10,160
+هذه مالهاnon-empty non-empty subset A of A ring R
+
+64
+00:06:10,160 --> 00:06:17,000
+بقول عنها ideal إذا كان أخدت عمصرين من الستة اللي
+
+65
+00:06:17,000 --> 00:06:22,140
+طرحتهم من بعض بدي يكون الناتج في A يبقى A minus ال
+
+66
+00:06:22,140 --> 00:06:27,540
+B موجود في A whenever ال A و ال B موجودين في A
+
+67
+00:06:27,540 --> 00:06:33,160
+اللي بعده ال R في A موجود في A وال A في R موجود في
+
+68
+00:06:33,160 --> 00:06:40,670
+Aلكل الـA الموجودة في A والـR الموجودة في R إذا ها
+
+69
+00:06:40,670 --> 00:06:45,250
+ها هذي اللي بيقوللي مشان تفحص هل اللي عندك هذا
+
+70
+00:06:45,250 --> 00:06:51,730
+ideal ولا لأ بدنا نثبت ثلاث نقاط النقطة الأولى أن
+
+71
+00:06:51,730 --> 00:06:55,790
+ال subset اللي أخدتها non-empty النقطة الثانية بدي
+
+72
+00:06:55,790 --> 00:07:00,390
+أخد أي عنصرين من هذه ال subset بدني أثبت أن الفرق
+
+73
+00:07:00,390 --> 00:07:06,370
+بينهما موجودفي نفس ال subset الأمر التالت بدي أخد
+
+74
+00:07:06,370 --> 00:07:10,590
+أي عنصر من هذا ال subset أو أي عنصر من ال ring بدي
+
+75
+00:07:10,590 --> 00:07:14,110
+أضربه فيه من اليمين و الله من الشمال بدي أطلع عنصر
+
+76
+00:07:14,110 --> 00:07:19,470
+موجود وين موجود في نفس ال set A إن حدث ذلك بقول
+
+77
+00:07:19,470 --> 00:07:25,410
+يبقى هذا ideal و من هنا صار هناك فرق ما بين ال
+
+78
+00:07:25,410 --> 00:07:29,950
+ideal و ما بين ال sub ring والفرق بسيط في ال
+
+79
+00:07:29,950 --> 00:07:35,780
+condition الأخر مثل ما كنااللي هو main ها تمام في
+
+80
+00:07:35,780 --> 00:07:40,160
+حالة ال sub ring قولنا بتاخد عنصرين من نفس الستين
+
+81
+00:07:40,160 --> 00:07:44,500
+لأ لأ بدي أخد عنصر من الست و عنصر من ال ring
+
+82
+00:07:44,500 --> 00:07:48,620
+الأصلية أضرب اتنين في بعض من الأمين و من الشمال
+
+83
+00:07:48,620 --> 00:07:53,300
+بدي أطلع عنصر في ال subset اللي أخدت هذه تماما طب
+
+84
+00:07:53,300 --> 00:07:57,960
+بدنا نروح نثبت صحة هذا الكلام يبقى a non empty
+
+85
+00:07:57,960 --> 00:08:03,270
+subset A of A ring R is an idealيبقى أنا خدت ال
+
+86
+00:08:03,270 --> 00:08:07,410
+subset من ال ring الأصلية وكانت هذه ال non-empty
+
+87
+00:08:07,410 --> 00:08:12,350
+إذا انت حقق ال condition اللي مضال علينا main ال
+
+88
+00:08:12,350 --> 00:08:18,290
+two conditions الأخرين السؤال هو هذا مش هو الشرط
+
+89
+00:08:18,290 --> 00:08:25,230
+الأول من شروط ال sub ring صح طيب هذا أليس هذا هو
+
+90
+00:08:25,230 --> 00:08:30,390
+الشرط التاني من ال sub ring وزيادة شويةكيف زيادة
+
+91
+00:08:30,390 --> 00:08:38,170
+شوية؟ لان بجينا جوا عنصرين من ال A عنصرين هنا
+
+92
+00:08:38,170 --> 00:08:42,810
+بيقولوا لأ عنصر من A والتاني من R، والتاني اللي
+
+93
+00:08:42,810 --> 00:08:48,350
+بدي أخطره من R قد يكون من A وقد لا يكون من A، فإن
+
+94
+00:08:48,350 --> 00:08:53,730
+كان من A هو تحصيل حاصل، وإن كان من R فهو زيادة عما
+
+95
+00:08:53,730 --> 00:08:59,240
+كان منين في حالة الصبرينيبقى الأن بروح بقوله the
+
+96
+00:08:59,240 --> 00:09:15,760
+conditions اللي هو I and II make the set is
+
+97
+00:09:15,760 --> 00:09:20,620
+suffering طبعا؟
+
+98
+00:09:20,620 --> 00:09:26,440
+طب ال condition اتالت لحالهبيخلّيه ايش بيخلّيه ID
+
+99
+00:09:26,440 --> 00:09:42,760
+but the second condition الشرط التاني make ال A is
+
+100
+00:09:42,760 --> 00:09:51,280
+an ID يبقى الشرط الثاني لحاله بيخلّي هذا ID إذا من
+
+101
+00:09:51,280 --> 00:09:56,150
+الألف صاعدالما يعطيني الست ويقولي اثبت انها هذه
+
+102
+00:09:56,150 --> 00:10:00,990
+ideal من ال ring الفلانية، بدي اثبتله ثلاثة شروط،
+
+103
+00:10:00,990 --> 00:10:04,830
+ان هذا subset non-empty، اتنين بدي اخد عنصري من
+
+104
+00:10:04,830 --> 00:10:08,470
+نفس ال subset، الفرق بينهما بدي يكون في نفس ال
+
+105
+00:10:08,470 --> 00:10:11,470
+subset اللي أخدناها، تلاتة بدي اخد element من ال
+
+106
+00:10:11,470 --> 00:10:14,900
+subset و element من ال ring الأصلية،أضربه في بعض
+
+107
+00:10:14,900 --> 00:10:18,960
+من جهة اليمين أو جهة الشمال بدي يطلع عنصر موجود في
+
+108
+00:10:18,960 --> 00:10:22,980
+ال subset لأن إن حدث ذلك يبقى هذه ال subset بقول
+
+109
+00:10:22,980 --> 00:10:30,900
+عليها Ideal من ال ring الأصلي نعطي أمثلة يبقى
+
+110
+00:10:30,900 --> 00:10:35,680
+examples أول
+
+111
+00:10:35,680 --> 00:10:40,380
+مثل دائما وابدا في حالة ال subgroup
+
+112
+00:10:43,270 --> 00:10:47,410
+اللي هو main ال identity element او ال group
+
+113
+00:10:47,410 --> 00:10:51,870
+الأصلي هدول اتنين subset من ال group الأصلي صحيح
+
+114
+00:10:51,870 --> 00:10:55,790
+ولا لأ طب و احنا هنا نفس القصة في حالة ال ring
+
+115
+00:10:55,790 --> 00:11:04,970
+يبقى هنا بقوله is zero as a pair and ال are are
+
+116
+00:11:04,970 --> 00:11:24,400
+sub are sub ringsof a and hence a ومن ثم ideals in
+
+117
+00:11:24,400 --> 00:11:28,960
+a ال
+
+118
+00:11:28,960 --> 00:11:38,680
+zero هده الو اشد ال zero is called the atrivial
+
+119
+00:11:38,680 --> 00:11:40,940
+ideal
+
+120
+00:11:42,790 --> 00:11:49,490
+او او او او او او او او او او او او او او او او او
+
+121
+00:11:49,490 --> 00:11:50,530
+او او او او او او او او او او او او او او او او او
+
+122
+00:11:50,530 --> 00:12:00,750
+او او او او او او او او او او او او او او او
+
+123
+00:12:00,750 --> 00:12:00,790
+او او او او او او او او او او او او او او او او او
+
+124
+00:12:00,790 --> 00:12:00,790
+او او او او او او او او او او او او او او او او او
+
+125
+00:12:00,790 --> 00:12:00,850
+او او او او او او او او او او او او او او او او او
+
+126
+00:12:00,850 --> 00:12:04,790
+او او او او او او او او او او او
+
+127
+00:12:04,790 --> 00:12:04,810
+او
+
+128
+00:12:12,760 --> 00:12:18,380
+بتاخد الـ zero من هنا و أي element R من R نضرب R
+
+129
+00:12:18,380 --> 00:12:25,640
+في Zero او Zero في R ب Zero موجود هنا فلسنا يبقى
+
+130
+00:12:25,640 --> 00:12:31,340
+هيه صار ايديل و ال ring الأصلية مهي نفسها يبقى
+
+131
+00:12:31,340 --> 00:12:36,700
+صارت ايديل من نفسها ال sub ring من نفسها و ينطق
+
+132
+00:12:36,700 --> 00:12:39,500
+تاخد منها element من ال ring الأصلية ال ring
+
+133
+00:12:39,500 --> 00:12:45,470
+الأصلية نفسهاany two elements موجودات في نفس ال
+
+134
+00:12:45,470 --> 00:12:47,910
+ring because it is a clause under multiplication
+
+135
+00:12:47,910 --> 00:12:53,930
+وبالتالي هي sub ring ووضع طبيعي وهذه أبسط أنواع
+
+136
+00:12:53,930 --> 00:12:59,670
+الأمثلة على ال sub rings وعلى ال ideals طيب نتجل
+
+137
+00:12:59,670 --> 00:13:09,770
+الكلام شوية مثال اثنين مثال اثنين بيقول لدرست ان
+
+138
+00:13:11,320 --> 00:13:18,000
+اللي عناصرها هي Zero زيدة ونقص N زيدة ونقص اتنين N
+
+139
+00:13:18,000 --> 00:13:25,180
+زيدة ونقص تلاتة N و هلوم مجرم لما شاء الله is an
+
+140
+00:13:25,180 --> 00:13:34,480
+ideal of Z is an ideal of a set of integers Z
+
+141
+00:13:34,480 --> 00:13:44,660
+because يعرف شو السبب النقطة الأولىMT على جالها
+
+142
+00:13:44,660 --> 00:13:49,180
+يفيها قدامنا الـ Zero تمام؟ لأن الـ Zero موجود في
+
+143
+00:13:49,180 --> 00:13:54,900
+Z تضربيه في أي عنصر من عناصر الـ Z بطلع الـ Z يبقى
+
+144
+00:13:54,900 --> 00:14:05,420
+الـ NZ as non-empty since لإن الـ Zero موجود في
+
+145
+00:14:05,420 --> 00:14:14,670
+الـ NZ النقطة الثانيةبدي اخد عنصرين x و y موجودات
+
+146
+00:14:14,670 --> 00:14:22,330
+في ال n z then ايش ممكن يكون شكل ال x يا بنات n
+
+147
+00:14:22,330 --> 00:14:33,390
+مضروب في عنصر من z يعني بقدر اقول n في z to n and
+
+148
+00:14:33,390 --> 00:14:46,060
+ال y بدي ساوي ال n في z tofor some z1 و z2 اللى
+
+149
+00:14:46,060 --> 00:14:57,120
+موجودة فيه z بدي اخد ال x ناقص ال y يبقى n z1 ناقص
+
+150
+00:14:57,120 --> 00:15:02,680
+ال n z2 بدي استخدم ال distributive law قانون
+
+151
+00:15:02,680 --> 00:15:12,350
+التوزيع يبقى هذا الكلام بيساويموجود في Z1 ناقص Z2
+
+152
+00:15:12,350 --> 00:15:22,670
+موجود في Z1 لا لا موجود في Z1 ليش لإن Z1 ناقص Z2
+
+153
+00:15:22,670 --> 00:15:28,270
+موجودة في Z الفرق بين any two integers is any
+
+154
+00:15:28,270 --> 00:15:38,650
+integer يبقى هذا موجود هنا لإن ال Z1 ناقص Z2موجودة
+
+155
+00:15:38,650 --> 00:15:43,170
+في set of integers يبقى مطابق ال condition التاني
+
+156
+00:15:43,170 --> 00:15:48,390
+بدي أروح لمين لل condition التالت بدي أخد عنصر في
+
+157
+00:15:48,390 --> 00:15:59,490
+z و عنصر في nz يبقى هنا f ال x اللي بتساوي nz1
+
+158
+00:15:59,490 --> 00:16:12,620
+موجودة في nz and ال mموجودة في Z then بتاخد
+
+159
+00:16:12,620 --> 00:16:21,500
+X M بتشوف هل هو موجود في N Z ولا لأ هذا الكلام
+
+160
+00:16:21,500 --> 00:16:32,340
+يثير ال X عندى مجددش N Z 1 يبقى N Z 1 مضروبة في M
+
+161
+00:16:33,020 --> 00:16:37,620
+هدول integers كلهم خاصية ال associativity صحيحة
+
+162
+00:16:37,620 --> 00:16:46,080
+على ال integers يبقى هذا بدي يعطيني N Z 1 M هذه
+
+163
+00:16:46,080 --> 00:16:54,520
+موجودة في N Z ولا لا؟ موجودة في N Z Z 1 M موجودة
+
+164
+00:16:54,520 --> 00:17:00,840
+في Z وبالتالي صارت هذه كلها موجودة في N Z وفي نفس
+
+165
+00:17:00,840 --> 00:17:11,960
+الوقتلو أخدت MX يبقى بده يساوي ال M في NZ1 طيب
+
+166
+00:17:11,960 --> 00:17:16,920
+الآن هذول التلات هار integers خاصية ال
+
+167
+00:17:16,920 --> 00:17:21,680
+associativity صحيحة على ال integers وزيادة على ذلك
+
+168
+00:17:21,680 --> 00:17:26,780
+عملية ضرب commutative على Z ولا لا؟ commutative
+
+169
+00:17:26,780 --> 00:17:34,340
+يبقى بناء عليه هذا بده يساوي ال Nفي ال MZ1 اللى
+
+170
+00:17:34,340 --> 00:17:40,320
+موجودة وين في ال MZ1 يبقى مطابق ال condition اتالت
+
+171
+00:17:40,320 --> 00:17:52,980
+وبناء عليه بناء عليه غصب ال N في Z is an ideal of
+
+172
+00:17:52,980 --> 00:17:59,320
+the ring of integers اللى همين اللى هى ال Z itself
+
+173
+00:18:19,740 --> 00:18:31,360
+ننتقل الى مثال ثالث مثال ثلاثه يقول
+
+174
+00:18:31,360 --> 00:18:43,460
+لات افترض ان الار بيه كميوتاتيف ring with unity
+
+175
+00:18:43,460 --> 00:18:48,960
+ring with unity
+
+176
+00:18:53,120 --> 00:18:59,520
+يتلقى belonging to R افترض ان في عنصر A موجود في
+
+177
+00:18:59,520 --> 00:19:09,800
+set A then the set يبقى set اللي بدأ اكتبها على
+
+178
+00:19:09,800 --> 00:19:15,840
+الشكل اللي عندنا هذا اللي هي تساوي كل ال R في A
+
+179
+00:19:15,840 --> 00:19:27,180
+بحيث ال R موجودة في R is an ideal of Aan ideal of
+
+180
+00:19:27,180 --> 00:19:35,320
+a called .. إيش كنتوا بتسموها في حالة إجروبة هنا؟
+
+181
+00:19:35,320 --> 00:19:42,460
+إيش كنتوا بتسموها؟ Cyclic group؟ ولا كنتوا بتسموها
+
+182
+00:19:42,460 --> 00:19:45,860
+the principle ideal .. the principle ما بعرفيه
+
+183
+00:19:45,860 --> 00:19:50,000
+generated by ايه؟ ال principle صح بيقولوا طيب على
+
+184
+00:19:50,000 --> 00:19:59,600
+أي حالبنسميه the principle ideal
+
+185
+00:19:59,600 --> 00:20:03,900
+generated
+
+186
+00:20:03,900 --> 00:20:07,320
+by
+
+187
+00:20:07,320 --> 00:20:15,400
+A نبقى هذا هو ال principle ideal generated by A
+
+188
+00:20:15,400 --> 00:20:19,340
+ليش هذا كان ideal؟
+
+189
+00:20:25,140 --> 00:20:32,460
+يبقى براحة بقوله Firstly هذا
+
+190
+00:20:32,460 --> 00:20:39,880
+is an ideal بعد
+
+191
+00:20:39,880 --> 00:20:47,480
+ما نثبت انه ideal خيص بدنا نطلق عليه تسمية ال
+
+192
+00:20:47,480 --> 00:20:51,600
+principle ideal generated by A يبقى هو ال ideal
+
+193
+00:20:51,600 --> 00:20:56,750
+المتولد بالأمصر AR commutative ring with unity
+
+194
+00:20:56,750 --> 00:21:01,050
+كميوتاتيف ضرورية زي ما هنشوفه الآن و احنا بنشترك
+
+195
+00:21:01,050 --> 00:21:08,550
+خدي عنصر A موجود في R يبقى ال 6 هذه اللي بنعرفها
+
+196
+00:21:08,550 --> 00:21:16,130
+على انها حاصل ضرب جميع أناصر R كبتة في A بده يطلع
+
+197
+00:21:16,130 --> 00:21:21,550
+عنصر موجود في A موجود في A اللي هو الشكل ان هذا is
+
+198
+00:21:21,550 --> 00:21:26,240
+an ideal of Rالـ ideal هذا هو اللي بيسميه ال
+
+199
+00:21:26,240 --> 00:21:31,240
+principle ideal generated by النقطة الأولى ال
+
+200
+00:21:31,240 --> 00:21:37,380
+principle ideal is non-empty
+
+201
+00:21:37,380 --> 00:21:44,420
+أكيد؟ نقدر نجيب؟ في نفسه بدل ال answer اتنين بس
+
+202
+00:21:44,420 --> 00:21:50,040
+بتاعي مش Zero في R يبقى Zero في A اللي هو بده
+
+203
+00:21:50,040 --> 00:21:55,120
+يساوي Zero موجود في Aصح وها تاني قلت لأ ممكن
+
+204
+00:21:55,120 --> 00:21:59,020
+بيكميوتة ت bring with unity بدل ازي هو دافن الواحد
+
+205
+00:21:59,020 --> 00:22:09,540
+يفجأ is non-empty because ال a بقدر اقول عليها
+
+206
+00:22:09,540 --> 00:22:16,720
+واحد في ايه؟ والواحد موجود في اين؟ موجود في R يعني
+
+207
+00:22:16,720 --> 00:22:24,930
+ال unityيبقى هذا واحد اللي هو موجود في A since
+
+208
+00:22:24,930 --> 00:22:31,290
+الواحد موجود او unity موجود في R يبقى على الأقل
+
+209
+00:22:31,290 --> 00:22:37,730
+إذا من الآن فصاعدا ال element A موجود في ال
+
+210
+00:22:37,730 --> 00:22:43,430
+principle ideal generated by A ال A itself بتكون
+
+211
+00:22:43,430 --> 00:22:48,890
+أحد عناصره تماميبقى هذا حطيه في دماغك مهم جدا، هي
+
+212
+00:22:48,890 --> 00:22:54,370
+النقطة الأولى، النقطة الثانية، بدي أخد عنصريا
+
+213
+00:22:54,370 --> 00:22:59,690
+موجودة في الست اللي عندنا، يبقى لو قل little x و
+
+214
+00:22:59,690 --> 00:23:05,670
+ال y موجودة في الست اللي عندنا، يبقى بدي أعرف قداش
+
+215
+00:23:05,670 --> 00:23:08,450
+أو ما هو شكل ال X
+
+216
+00:23:11,410 --> 00:23:20,370
+يبقى عنصر من R مضروب في A يبقى بقدر اقول R1A وال Y
+
+217
+00:23:20,370 --> 00:23:30,490
+بده ساوي R2A والR1 والR2 عناصر موجودة في ال ring R
+
+218
+00:23:30,490 --> 00:23:42,050
+بدي اخد ال X ناطس ال Yيبقى ال X R1A ناقص R2A طبق
+
+219
+00:23:42,050 --> 00:23:49,370
+ال distributive law بدي أعطيني R1 ناقص R2 في سواد
+
+220
+00:23:49,370 --> 00:23:56,550
+هل هذا موجود في الست اللي عندنا؟ لإن ال R1 موجودة
+
+221
+00:23:56,550 --> 00:24:03,330
+وين؟ في ال R itself يبقى هذا موجود في A because
+
+222
+00:24:05,020 --> 00:24:12,640
+السبب R1 ناقص R2 موجودة في ال ring R يبقى تحقق ال
+
+223
+00:24:12,640 --> 00:24:16,500
+conditioning الثاني بدي أروح لل conditioning
+
+224
+00:24:16,500 --> 00:24:24,200
+التالت بدي أخد عنصر موجود هنا و أي عنصر موجود في R
+
+225
+00:24:24,200 --> 00:24:32,540
+يبقى بدي أقول افترض ان R موجود في R and ال Xاللي
+
+226
+00:24:32,540 --> 00:24:40,960
+هو بده يساوي R 1A موجودة في مين؟ موجودة في الست
+
+227
+00:24:40,960 --> 00:24:46,440
+اللي عندها دي then فده
+
+228
+00:24:46,440 --> 00:24:55,280
+ياخد ال R X بده يشوف عشان تساوي يبقى ال R X عبارة
+
+229
+00:24:55,280 --> 00:25:02,770
+عن R وال X R 1Aخاصية ال associativity الصحيحة على
+
+230
+00:25:02,770 --> 00:25:10,930
+ال things يبقى RR1A يبقى هذا موجود في ال set اللي
+
+231
+00:25:10,930 --> 00:25:17,210
+فوق ولا لا؟ يبقى هذا موجود في ال set اللي عندنا
+
+232
+00:25:17,210 --> 00:25:27,790
+هذه ليش؟ because RR1 موجودة في R لأنه R مغلقة تحت
+
+233
+00:25:27,790 --> 00:25:34,120
+عملية الظبططبعا طيب ضل اتجاه الثاني هنا ضربنا الار
+
+234
+00:25:34,120 --> 00:25:39,860
+من جهتي الشمال بدنا نروح نضرب اين؟ من جهتي اليمين
+
+235
+00:25:39,860 --> 00:25:48,040
+لكن الار commutative يبقى هنا also وكذلك ال XR
+
+236
+00:25:48,040 --> 00:25:58,440
+موجودة في ايه؟ because الار is commutativeيبقى لو
+
+237
+00:25:58,440 --> 00:26:03,340
+شيلنا شرط ال commutative من هنا، من هنا بطلع هذا
+
+238
+00:26:03,340 --> 00:26:07,640
+ring، من هنا بطلع هذا ideal، الإجابة لأ لإن ما
+
+239
+00:26:07,640 --> 00:26:14,360
+نقدرش نحط الجزء الثاني إلا أن thus و هكذا ال
+
+240
+00:26:14,360 --> 00:26:23,660
+principle ideal generated by A is an ideal of A،
+
+241
+00:26:23,660 --> 00:26:26,560
+يبقى هذا ideal في ring A
+
+242
+00:26:31,480 --> 00:26:38,600
+طب هل كل ideal في ال ring اه يكون ال principle؟
+
+243
+00:26:38,600 --> 00:26:45,880
+ليس بالضرورة، ليس بالضرورة كما سنراه من خلال
+
+244
+00:26:45,880 --> 00:26:53,380
+الأمثلة القائمة إن شاء الله.طيب هذا كان المثال رقم
+
+245
+00:26:53,380 --> 00:27:00,180
+3، بدنا نروح للمثال رقم 4، رقم 4
+
+246
+00:27:03,170 --> 00:27:19,690
+the ring z is a sub ring of the cube هو مجموعة
+
+247
+00:27:19,690 --> 00:27:25,230
+الأعداد الصحيحة sub ring من مجموعة الأعداد النسبية
+
+248
+00:27:25,230 --> 00:27:32,000
+السؤال هو هل z هذه idيعني مش كل subring بس هي ال
+
+249
+00:27:32,000 --> 00:27:37,000
+ideal بعضهم بنفع تكون ideal وبعضهم بنفعش تكون
+
+250
+00:27:37,000 --> 00:27:42,180
+ideal طيب هذه ليش؟ يكفينا counterexample واحد
+
+251
+00:27:42,180 --> 00:27:54,320
+تمام؟ يبقى هذه Z subring من Q بقى ولكن Z is not an
+
+252
+00:27:54,320 --> 00:28:04,350
+ideal of Qالسبب because بدنا ناخد element موجود في
+
+253
+00:28:04,350 --> 00:28:14,650
+z خمسة مثلا موجود في z عدد صحيح و طول موجود في ال
+
+254
+00:28:14,650 --> 00:28:23,230
+IQ بط لو كانت ID بدي يكون حاصل ضرب و موجود في z بط
+
+255
+00:28:23,230 --> 00:28:31,700
+خمسة مضروبة في طوليساوي خمسة ع تلاتة ليست عددا
+
+256
+00:28:31,700 --> 00:28:38,440
+صحيحة إذا الـ Z هي عبارة عن sub ring لكنها في
+
+257
+00:28:38,440 --> 00:28:46,580
+الحقيقة ليست ideal في مجموعة الأعداد النسبية نعطي
+
+258
+00:28:46,580 --> 00:28:56,740
+مثال من مواقع آخر الـ R الخامسة بيقول للـ R of X
+
+259
+00:28:58,110 --> 00:29:02,950
+denote the
+
+260
+00:29:02,950 --> 00:29:13,270
+set of all polynomials مجموعة
+
+261
+00:29:13,270 --> 00:29:23,630
+كثيرات الحدود with real coefficients المعاملات
+
+262
+00:29:23,630 --> 00:29:27,450
+كلها أعداد حقيقية
+
+263
+00:29:29,800 --> 00:29:41,240
+و there are coefficients and let ال a be the set
+
+264
+00:29:41,240 --> 00:29:49,880
+of all polynomials كل كثيرات الحدود with constant
+
+265
+00:29:49,880 --> 00:29:56,700
+term zero with constant term
+
+266
+00:29:56,700 --> 00:30:06,070
+zerothen a
+
+267
+00:30:06,070 --> 00:30:20,870
+is an ideal is an ideal of r of x زيادة على ذلك
+
+268
+00:30:20,870 --> 00:30:30,110
+نمر بيه ال a تساويالـ group generated by
+
+269
+00:30:30,110 --> 00:30:35,850
+Geographics هو الـ principle generated by اللي هو
+
+270
+00:30:35,850 --> 00:30:36,950
+Geographics
+
+271
+00:31:03,490 --> 00:31:08,350
+خلّينا نفهم السؤال مرة ثانية قبل ما نبدأ نشتغل قال
+
+272
+00:31:08,350 --> 00:31:14,970
+الاروافكس تمثل مجموعة كثيرات الحدود اللي معاملاتها
+
+273
+00:31:14,970 --> 00:31:21,390
+أعداد حقيقية موجبة، سالبة، كسرية، صفر، بهمنيش، مين
+
+274
+00:31:21,390 --> 00:31:27,490
+المكان يكون خد السد ايه هي كل كثيرات الحدود with
+
+275
+00:31:27,490 --> 00:31:34,060
+constant term zero يعني آخر حد فيها بديكون مينالحد
+
+276
+00:31:34,060 --> 00:31:41,160
+اللي جابله constant في X بس الأولانية constant في
+
+277
+00:31:41,160 --> 00:31:46,280
+X زائد constant زي ما هنشوفه لأ يبقى بدأ نثبت أن
+
+278
+00:31:46,280 --> 00:31:54,320
+هذا عبارة عن ideal يبقى بنات ال R of X من هنا هذه
+
+279
+00:31:54,320 --> 00:32:02,780
+هي كل العناصر F of X بحيث أناالـ f of x بده يساوي
+
+280
+00:32:02,780 --> 00:32:09,120
+a n x to the power n a n minus one x to the power
+
+281
+00:32:09,120 --> 00:32:17,640
+one وضل ماشيين لغاية a one x زائد a naught يبقى a
+
+282
+00:32:17,640 --> 00:32:24,600
+naught هو مقدار ثابت ال a فيها a naught ب zero مش
+
+283
+00:32:24,600 --> 00:32:31,530
+موجوديبقى بدنا نجي لتانية الست اللي أخدناها كل ال
+
+284
+00:32:31,530 --> 00:32:39,430
+polynomial g of x بحيث ان ال g of x يسوى b in x to
+
+285
+00:32:39,430 --> 00:32:44,390
+the power n b in minus ال one x to the power n
+
+286
+00:32:44,390 --> 00:32:52,330
+minus ال one زائد b one x فقط لغير المقدار الثابت
+
+287
+00:32:52,330 --> 00:32:57,570
+بصفر يبقى طار مش موجودبنثبت له ان هذه عبارة عن
+
+288
+00:32:57,570 --> 00:33:05,530
+ايش؟ ideal طيب النقطة الأولى النقطة الأولى هل هذه
+
+289
+00:33:05,530 --> 00:33:13,530
+non-empty على الأقل فيها ال F of Zero كلهم هذول
+
+290
+00:33:13,530 --> 00:33:19,250
+بيقيروا ب Zero يبقى صار ال constant terminal Zero
+
+291
+00:33:19,250 --> 00:33:33,090
+صحيح ولا لا؟ يبقى هنا ال F asممكن because الـG
+
+292
+00:33:33,090 --> 00:33:43,570
+of Zero بدر ساوي Zero وهذا موجود في A هذا النقطة
+
+293
+00:33:43,570 --> 00:33:51,830
+الثانية بدنا ناخد عنصرين موجودين في A ونطرح اتنين
+
+294
+00:33:51,830 --> 00:34:01,190
+من بعضيبقى فاجب اقوله ليه مثلا ال G1 و ال G2
+
+295
+00:34:01,190 --> 00:34:07,710
+موجودات في ايه؟ then بدي اعرف ايه الشكل كل واحد
+
+296
+00:34:07,710 --> 00:34:15,030
+فيهم G1 of X بدي اسميه زي ما احنا مسميه هذه زي ما
+
+297
+00:34:15,030 --> 00:34:27,880
+هي ال B X to the power NBn-1x⁻¹n-1 زائد زائد B1x
+
+298
+00:34:27,880 --> 00:34:41,100
+والـ G2 والـ G2 of X بدل الـ B ممكن أسميه Cnx⁻¹n
+
+299
+00:34:41,100 --> 00:34:48,680
+Cn-1x⁻¹n-1 زائد C1x
+
+300
+00:34:51,110 --> 00:35:00,530
+يبقى بدي أخد g1 ناقص g2 كتأثيره على x هذا الكلام
+
+301
+00:35:00,530 --> 00:35:09,090
+بدي يساوي g1 of x ناقص g2 of x بدي أشوف هل هذا
+
+302
+00:35:09,090 --> 00:35:15,730
+موجود في ايه ولا لأ بمعنى آخر هل آخر term يساوي
+
+303
+00:35:15,730 --> 00:35:21,950
+zero ولا لأ إذا بدنا نطرح كل عنصر من نظيرهيبقى هذا
+
+304
+00:35:21,950 --> 00:35:32,070
+بيصير BN ناقص CN في X to the power N ثالث BN minus
+
+305
+00:35:32,070 --> 00:35:43,790
+ال 1 ناقص CN minus ال 1 CN minus ال 1 كله في X
+
+306
+00:35:43,790 --> 00:35:49,650
+plus N minus ال 1 زايد لغاية ما نوصل لآخر K اللي
+
+307
+00:35:49,650 --> 00:35:56,400
+هو B1نقص c1 كله في x يبقى ال constant term كده اش
+
+308
+00:35:56,400 --> 00:36:02,560
+طالع عندنا ب zero إذا هذه موجودة في ايه ولا لأ إذا
+
+309
+00:36:02,560 --> 00:36:07,040
+هذه موجودة في ايه بدنا نروح الأن لل condition
+
+310
+00:36:07,040 --> 00:36:12,140
+التالت بدنا نضرب اتنين في بعض يبقى بدأي لل
+
+311
+00:36:12,140 --> 00:36:20,080
+condition التالت بدأي أخد عنصر من من ال ring Rوبدي
+
+312
+00:36:20,080 --> 00:36:30,560
+اخد عنصر من A يبقى هنا F ال F موجودة في ال R of X
+
+313
+00:36:30,560 --> 00:36:41,720
+and اللي هو ال G موجودة في A then بدي
+
+314
+00:36:41,720 --> 00:36:50,680
+اخد F G of Xيبقى هذه بدها تساوي ال F of X في ال G
+
+315
+00:36:50,680 --> 00:36:57,500
+of X يساوي يبقى بدنا نيجي نضرب ضرب وين ال F هاي
+
+316
+00:36:57,500 --> 00:37:05,900
+يبقى هذه ال F اللي ناخدتها تمام؟ بدها ضبها في عنصر
+
+317
+00:37:05,900 --> 00:37:12,160
+من هنا اللي هو G term اللي عندنايبقى لو ضربتش بصير
+
+318
+00:37:12,160 --> 00:37:26,440
+a n b n x أوسي 2n يبقى بصير a n b n x أوسي 2n زي
+
+319
+00:37:26,440 --> 00:37:33,440
+.. لما أدرب اللي بعد هذه a n minus ال one في ال b
+
+320
+00:37:33,440 --> 00:37:43,790
+n يبقى aن نقص
+
+321
+00:37:43,790 --> 00:37:51,010
+واحد ونفضل ماشيين لغاية ما نوصل لمين لغاية ما نوصل
+
+322
+00:37:51,010 --> 00:37:58,670
+هذهها بدها تصير مين اخر حاجة في القهر هذه اخر حاجة
+
+323
+00:37:58,670 --> 00:38:11,580
+عند مين a naught يبقى زائداللي هو a نود b in او
+
+324
+00:38:11,580 --> 00:38:18,480
+هنا x to the power n بعد هيك نبقى الماشي لسه
+
+325
+00:38:18,480 --> 00:38:24,880
+مخلصناش لغاية ما نوصل لحاصل ضرب اخر term من هنا في
+
+326
+00:38:24,880 --> 00:38:30,360
+اخر term يبقى من اللي يكون عندنا a نود b one x
+
+327
+00:38:30,360 --> 00:38:41,500
+يبقى زائدA نار B one X في عندي ثابت؟ لأ يبقى هذه
+
+328
+00:38:41,500 --> 00:38:48,220
+بصير كلها موجودة وين؟ موجودة في ال A يبقى تحققت
+
+329
+00:38:48,220 --> 00:38:54,660
+الشروط التلاتة بلا ان علي أصبحت ال A is A صارت A
+
+330
+00:38:54,660 --> 00:39:02,890
+هذا لما ضربنا ضربنا من وين؟ ضربنا لسهاللي هو من ال
+
+331
+00:39:02,890 --> 00:39:12,590
+F في G Similarly يبقى Similarly بنفس الطريقة ال G
+
+332
+00:39:12,590 --> 00:39:20,150
+في ال F as a function of X يساوي ال G of X في ال F
+
+333
+00:39:20,150 --> 00:39:26,950
+of X هذه كمان موجودة في ال A يبقى بناء عليه ضاص
+
+334
+00:39:26,950 --> 00:39:39,760
+وهكذا ال P is anideal of R of X نجي لنمرى B
+
+335
+00:39:39,760 --> 00:39:47,420
+بيقوللي ايش في B؟ بيقوللي ال ideal اللي عندك هذا
+
+336
+00:39:47,420 --> 00:39:57,850
+يمكن ان يولد بعنصر واحد هالي ونمرى B هي IBهو
+
+337
+00:39:57,850 --> 00:40:04,010
+العنصر الذي يولد بهذا العنصر طيب الآن لما نجي يا
+
+338
+00:40:04,010 --> 00:40:13,890
+بنات نقول بدي أجي أاخد ال Z F من وين من R و أجي
+
+339
+00:40:13,890 --> 00:40:24,910
+أاخد F of X في ال G of X بحيث ال F موجودة في R of
+
+340
+00:40:24,910 --> 00:40:33,130
+X andالـ G موجودة في إيه؟
+
+341
+00:40:33,130 --> 00:40:39,630
+هذا الكلام بالشكل اللي عندنا هذا مش هو الخاصية
+
+342
+00:40:39,630 --> 00:40:46,030
+اللي فوق هذه؟ وين طلعت؟ موجودة في إيه؟ طيب حسب
+
+343
+00:40:46,030 --> 00:40:51,550
+تعريف ال principle ideal generated by GeoVix مش هي
+
+344
+00:40:51,550 --> 00:40:58,400
+هذه؟ صح ولا لأ؟ يبقى هذه هنااللي هي ال principle
+
+345
+00:40:58,400 --> 00:41:06,940
+id generated by gx هذا الكلام جيبناه من وين from
+
+346
+00:41:06,940 --> 00:41:17,480
+part اللي هو triple I of A
+
+347
+00:41:17,480 --> 00:41:23,860
+يبقى هذا من المطلوب الأول النقطة التالتة فيه يبقى
+
+348
+00:41:23,860 --> 00:41:30,880
+صار هذاهو الذي يولد بهذا العمصر يبقى صارة الـG of
+
+349
+00:41:30,880 --> 00:41:36,300
+X هذه هو ال principle ideal generated by A يبقى كل
+
+350
+00:41:36,300 --> 00:41:42,460
+ال polynomials اللي آخرتين فيهم مقدارا ثابتا
+
+351
+00:41:42,460 --> 00:41:48,260
+بكونون صبرا وبالتالي ideal بسميه ال principle
+
+352
+00:41:48,260 --> 00:41:54,820
+ideal generated by واحدة منهماللي هي مثلا الـ G of
+
+353
+00:41:54,820 --> 00:42:00,380
+X اللي الحد فيها يساوي مين؟ يساوي K نص طن هنا،
+
+354
+00:42:00,380 --> 00:42:09,080
+تمام؟ طيب، إلى هنا يكفينا اليوم و لسه لا يزال
+
+355
+00:42:09,080 --> 00:42:14,680
+قدامنا مزيد من الأمثلة للمرة الحاضرة
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..63b6702133e6f88d12bdd4fbc18684d18c2267bc
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ.srt
@@ -0,0 +1,1304 @@
+1
+00:00:20,990 --> 00:00:25,430
+بسم الله الرحمن الرحيم نكمل اليوم ما ابتدأناه في
+
+2
+00:00:25,430 --> 00:00:29,970
+المرة الماضية وهو موضوع الـ ring homomorphism اللي
+
+3
+00:00:29,970 --> 00:00:36,790
+هو chapter 15 من الكتاب. فينا نظرية اليوم، النظرية
+
+4
+00:00:36,790 --> 00:00:41,070
+بتقول: افترض أن Φ من R إلى S عبارة عن ring
+
+5
+00:00:41,070 --> 00:00:47,010
+homomorphism. نحاول نثبت أن الـ kernel لهذا الـ
+
+6
+00:00:47,010 --> 00:00:50,430
+homomorphism هو عبارة عن ideal.
+
+7
+00:00:53,080 --> 00:00:58,600
+البرهان كالتالي: بأن نروح نثبت الـ three conditions
+
+8
+00:00:58,600 --> 00:01:06,020
+تبعات الـ I. دي، فبالتالي الـ condition الأول وهو أن
+
+9
+00:01:06,020 --> 00:01:14,220
+الـ kernel للـ Φ is non-empty. ما هو السبب لذلك؟
+
+10
+00:01:14,220 --> 00:01:24,440
+because Φ(0) = 0. هذا يعني أن الـ
+
+11
+00:01:24,440 --> 00:01:32,520
+zero موجود في kernel الـ Φ، ولذلك kernel الـ
+
+12
+00:01:32,520 --> 00:01:38,940
+هذا is non-empty. النقطة الثانية: بدي آخذ عنصرين
+
+13
+00:01:38,940 --> 00:01:43,960
+موجودين في الـ kernel. يبقى بدي أقول له: افترض أن r<sub>1</sub>
+
+14
+00:01:43,960 --> 00:01:51,030
+و r<sub>2</sub> موجودين في kernel للـ Φ. إذًا، أيش
+
+15
+00:01:51,030 --> 00:01:57,510
+بدنا نثبت؟ بدنا نثبت أن الفرق بينهما موجود في
+
+16
+00:01:57,510 --> 00:02:05,290
+الـ kernel. طيب، r<sub>1</sub> موجود في الـ kernel. ماذا يعني هذا؟ هذا
+
+17
+00:02:05,290 --> 00:02:12,410
+يعني أن Φ(r<sub>1</sub>) = 0، اللي هو
+
+18
+00:02:12,410 --> 00:02:23,010
+تبع من؟ تبع الـ S، و Φ(r<sub>2</sub>) = 0 كذلك
+
+19
+00:02:23,010 --> 00:02:30,770
+تبع الـ S. طيب، الآن لو روحنا وطرحناهم من بعض، طرحنا
+
+20
+00:02:30,770 --> 00:02:37,770
+الاثنين من بعض. في أي واحد؟ فبدي أقول له: Φ(r<sub>1</sub>)
+
+21
+00:02:37,770 --> 00:02:44,080
+− Φ(r<sub>2</sub>) = 0 − 0 =
+
+22
+00:02:44,080 --> 00:02:50,040
+كم؟ 0. هذا بدي يوقفني، قال لي في رأسي المسألة
+
+23
+00:02:50,040 --> 00:02:55,280
+Φ عبارة عن homomorphism. قال: خاصية الأولى من خواص
+
+24
+00:02:55,280 --> 00:03:02,940
+الـ homomorphism أن Φ(r<sub>1</sub> − r<sub>2</sub>) =
+
+25
+00:03:02,940 --> 00:03:07,740
+يساوي مين؟ يساوي 0. هذا معناه إيه؟ أن
+
+26
+00:03:07,740 --> 00:03:15,170
+r<sub>1</sub> − r<sub>2</sub> موجود في kernel اللي،  أعني أن صورته تساوي الـ
+
+27
+00:03:15,170 --> 00:03:23,170
+zero element تبع الـ S. يبقى هذا معناه أن r<sub>1</sub> − r<sub>2</sub> كله
+
+28
+00:03:23,170 --> 00:03:29,590
+موجود في kernel الـ Φ. إذًا أثبتنا النقطة
+
+29
+00:03:29,590 --> 00:03:30,370
+الثانية.
+
+30
+00:03:33,700 --> 00:03:40,320
+النقطة الثالثة والأخيرة اللي بدنا نثبت فيها أن
+
+31
+00:03:40,320 --> 00:03:46,940
+الـ kernel هو عبارة عن ideal. يبقى بدنا نأخذ element من
+
+32
+00:03:46,940 --> 00:03:52,180
+الـ set اللي عندنا، و element من الـ ring الأصلية ونثبت
+
+33
+00:03:52,180 --> 00:03:57,850
+أن حاصل ضربهما موجود في الـ kernel.  أو إذا حاصل
+
+34
+00:03:57,850 --> 00:04:03,410
+ضربِهما يساوي 0. إن حدث ذلك يبقى بقول له في
+
+35
+00:04:03,410 --> 00:04:08,670
+هذه الحالة أن الـ set اللي عندنا، أو الـ kernel
+
+36
+00:04:08,670 --> 00:04:17,830
+صار عبارة عن ideal. يبقى بجي بقول له: if r موجودة في R
+
+37
+00:04:17,830 --> 00:04:29,110
+and نأخذ element في الـ kernel، و مثلاً الـ x موجود
+
+38
+00:04:29,110 --> 00:04:40,050
+في kernel الـ Φ. Φ(r) وين بدها تكون موجودة؟
+
+39
+00:04:40,050 --> 00:04:51,050
+في S. يبقى then Φ(r) موجودة في S، و Φ
+
+40
+00:04:51,050 --> 00:05:00,010
+(x) = 0. بنروح نأخذ Φ(rx).
+
+41
+00:05:00,010 --> 00:05:06,090
+نظراً لأن Φ عبارة عن homomorphism، إذًا الهدف
+
+42
+00:05:06,090 --> 00:05:12,670
+بده يساوي Φ(r)Φ(x). Φ(x) عندي
+
+43
+00:05:12,670 --> 00:05:19,010
+بكم؟ هشيلها وأحط مكانها 0. يبقى بده يساوي Φ
+
+44
+00:05:19,010 --> 00:05:25,240
+(r)(0) = كم؟ 0. إذًا، صار
+
+45
+00:05:25,240 --> 00:05:30,380
+تأثير Φ على الـ element rx بده يساوي 0. معناه
+
+46
+00:05:30,380 --> 00:05:36,900
+هذا الكلام أن rx موجودة وين؟ في الـ kernel اللي
+
+47
+00:05:36,900 --> 00:05:44,520
+فيه. بنفس الطريقة، Similarly، بنفس الطريقة اللي هو الـ
+
+48
+00:05:44,520 --> 00:05:50,000
+xr موجودة في الـ kernel لمين؟  في الـ Φ. يبقى
+
+49
+00:05:50,000 --> 00:05:56,570
+أثبتنا شروط الـ ideal وخلصنا. يبقى بقول: الله أكبر! صحيح
+
+50
+00:05:56,570 --> 00:06:08,570
+وهكذا، kernel للـ Φ is an ideal of R وهو
+
+51
+00:06:08,570 --> 00:06:16,430
+المفروض نجي الآن للنظرية التي تليها، وهذه نظرية
+
+52
+00:06:16,430 --> 00:06:21,330
+مهمة ومشهورة في كل كتب الجبر، اللي بيسموها الـ first
+
+53
+00:06:21,330 --> 00:06:26,490
+isomorphism، أو الـ Fundamental Theorem of Ring
+
+54
+00:06:26,490 --> 00:06:34,070
+Homomorphism. يبقى الـ Theorem بنسميها
+
+55
+00:06:34,070 --> 00:06:40,150
+الـ First Isomorphism
+
+56
+00:06:40,150 --> 00:06:49,750
+Theorem، أو بنسميها الـ Fundamental Theorem
+
+57
+00:06:49,750 --> 00:06:51,910
+of
+
+58
+00:06:52,880 --> 00:06:57,040
+Ring Homomorphism.
+
+59
+00:06:57,040 --> 00:07:00,640
+الآن
+
+60
+00:07:00,640 --> 00:07:07,760
+بدنا نجلع نص النظرية، ومن ثم نقوم ببرهانها. نص
+
+61
+00:07:07,760 --> 00:07:17,100
+النظرية بيقول: If Φ من R إلى S ring
+
+62
+00:07:17,100 --> 00:07:18,640
+homomorphism،
+
+63
+00:07:23,120 --> 00:07:31,820
+then the mapping، then the mapping
+
+64
+00:07:31,820 --> 00:07:41,400
+الدالة أو الـ function،  Ψ من R modulo kernel
+
+65
+00:07:41,400 --> 00:07:55,350
+الـ Φ إلى Φ(R) defined by defined by
+
+66
+00:07:55,350 --> 00:08:05,790
+والمعرفة بالشكل التالي: Ψ(r + ker Φ)
+
+67
+00:08:05,790 --> 00:08:14,150
+= Φ(r)، لكل الـ r اللي موجودة في R،
+
+68
+00:08:14,150 --> 00:08:20,650
+is an isomorphism. is an isomorphism.
+
+69
+00:08:21,410 --> 00:08:31,230
+that is، بطريقة مختصرة، that is، اللي هو R modulo
+
+70
+00:08:31,230 --> 00:08:48,710
+kernel للـ Φ isomorphic لمين؟ للـ Φ(R). نرجع
+
+71
+00:08:48,710 --> 00:08:54,670
+لنص النظرية مرة ثانية. نحاول نفهم شو الشغل اللي بدنا
+
+72
+00:08:54,670 --> 00:09:00,890
+نشتغله حتى نشتغل شغل صحيح. قال لي: Φ من R إلى S
+
+73
+00:09:00,890 --> 00:09:07,390
+homomorphism، ماشي. بعدين قال لي: عرف دالة Ψ من
+
+74
+00:09:07,390 --> 00:09:13,470
+الـ factor ring، R modulo kernel الـ Φ، إلى Φ(R)،
+
+75
+00:09:13,470 --> 00:09:21,310
+يعني لمين؟ للـ range تبع من؟ تبع الـ Φ.
+
+76
+00:09:21,620 --> 00:09:26,480
+الـ ring تبع الـ Φ هذا موجود وين؟ في S. تمام، يعني
+
+77
+00:09:26,480 --> 00:09:32,300
+مش الـ S كله، وإنما لمين؟ للـ ring تبع الـ Φ. Φ
+
+78
+00:09:32,300 --> 00:09:39,900
+(R).  المعرفة كالتالي: Ψ(r + ker Φ) =
+
+79
+00:09:39,900 --> 00:09:46,620
+Φ(r)، اللي موجودة في Φ(R).  يبقى r +
+
+80
+00:09:46,620 --> 00:09:51,940
+ker Φ  Element موجود في الـ factor ring R
+
+81
+00:09:51,940 --> 00:09:58,020
+modulo ker Φ.  و Φ(r) هو Element موجود في Φ
+
+82
+00:09:58,020 --> 00:10:03,400
+(R). لكل الـ r اللي موجودة فيها. مش بدنا نثبت، بدنا
+
+83
+00:10:03,400 --> 00:10:09,740
+نثبت أن Ψ عبارة عن isomorphism. يبقى بدنا نثبت
+
+84
+00:10:09,740 --> 00:10:17,960
+homomorphism، one to one، و onto. خلاص؟ لأ، ما خلصش.
+
+85
+00:10:18,260 --> 00:10:23,240
+هذه الـ left cosets. يجب أن تثبت أيضاً أن هذه الـ
+
+86
+00:10:23,240 --> 00:10:28,740
+function is well-defined،  معرفة تعريفاً صحيحاً. يبقى
+
+87
+00:10:28,740 --> 00:10:32,780
+هذه الخطوة الأولى اللي بنبدأ فيها، وبعدين بنروح
+
+88
+00:10:32,780 --> 00:10:37,920
+لمين؟ لـ isomorphism. يبقى الخطوة الأولى اللي بدي
+
+89
+00:10:37,920 --> 00:10:42,840
+أثبت له أن Ψ is well-defined.
+
+90
+00:10:45,910 --> 00:10:51,590
+كيف عرفنا، كيف علمنا نثبت هذا well-defined؟ بنقول
+
+91
+00:10:51,590 --> 00:10:57,090
+عكس إثبات أنه Ψ one to one. يعني أنا بأخذ
+
+92
+00:10:57,090 --> 00:11:05,230
+عنصرين متساويين، وأثبت أن صورتهما متساويتان،
+
+93
+00:11:05,230 --> 00:11:11,410
+مظبوط هيك؟ يبقى بالطريقة دي أقول له: let، افترض أن
+
+94
+00:11:11,410 --> 00:11:24,780
+r<sub>1</sub> + ker Φ = r<sub>2</sub> + ker Φ. بدي أثبت
+
+95
+00:11:24,780 --> 00:11:29,960
+أن صورة العنصر الأول هي نفس صورة العنصر الثاني.
+
+96
+00:11:29,960 --> 00:11:38,260
+يبقى then، هذه بدي أحاول أكتبها بطريقة أخرى. لو جينا
+
+97
+00:11:38,260 --> 00:11:44,120
+قلنا: r<sub>1</sub> − r<sub>2</sub> + ker Φ =
+
+98
+00:11:44,360 --> 00:11:50,000
+ker Φ.  على الجهة اليمين اللي هو مع ker Φ.
+
+99
+00:11:50,000 --> 00:11:57,420
+ما تفسيرك لهذه الجملة؟ r<sub>1</sub> − r<sub>2</sub> موجودة في
+
+100
+00:11:57,420 --> 00:12:04,160
+الـ kernel. يبقى هذا بده يعطينا أن r<sub>1</sub> − r<sub>2</sub>
+
+101
+00:12:04,160 --> 00:12:12,180
+موجودة في الـ kernel. موجودة في الـ kernel.
+
+102
+00:12:13,150 --> 00:12:18,970
+مدام موجودة في الـ kernel يبقى صورتها 0. يبقى هذا
+
+103
+00:12:18,970 --> 00:12:27,230
+معناه أن Φ(r<sub>1</sub> − r<sub>2</sub>) = مين؟ الـ 0
+
+104
+00:12:27,230 --> 00:12:33,310
+تبع Φ(R). تمام؟ طيب كويس. أيش قال في رأسي
+
+105
+00:12:33,310 --> 00:12:38,770
+المسألة؟ Φ معنو؟ مدام Φ homomorphism، إذًا بقدر
+
+106
+00:12:38,770 --> 00:12:45,450
+أفك هذه، أو أجزل هذه. يبقى هذا معناه أن Φ(r<sub>1</sub>)
+
+107
+00:12:45,450 --> 00:12:53,090
+− Φ(r<sub>2</sub>) = 0. أو هذا معناه أن Φ
+
+108
+00:12:53,090 --> 00:13:02,430
+(r<sub>1</sub>) = Φ(r<sub>2</sub>). لكن لو رجعنا للتعريف، Φ
+
+109
+00:13:02,430 --> 00:13:11,150
+(r<sub>1</sub>) هو Ψ(r<sub>1</sub> + ker Φ). صح؟ من التعريف. يبقى
+
+110
+00:13:11,150 --> 00:13:17,810
+هذا بده يعطينا مين؟ أن Ψ(r<sub>1</sub> + ker
+
+111
+00:13:17,810 --> 00:13:25,990
+Φ) = Ψ(r<sub>2</sub> + ker Φ).
+
+112
+00:13:25,990 --> 00:13:32,170
+هذا ما جبناهوش عشوائياً، ولكن from the definition،
+
+113
+00:13:32,170 --> 00:13:38,340
+من التعريف جبناه. أيوة. يبقى شو اللي حصل؟ أخدت
+
+114
+00:13:38,340 --> 00:13:46,000
+عنصرين متساويين، أثبت أن صورتهما متساويتان، زي ما
+
+115
+00:13:46,000 --> 00:13:51,620
+أنتم شايفين. طيب. يبقى أثبتنا الـ well-defined. بدنا
+
+116
+00:13:51,620 --> 00:13:58,040
+نجي: الـ Ψ is a homomorphism. يبقى الـ Ψ is a
+
+117
+00:13:58,040 --> 00:14:04,620
+homomorphism.  white. يبقى بدنا نأخذ تأثير Ψ على
+
+118
+00:14:04,620 --> 00:14:12,550
+مجموع عنصرين، وعلى حاصل ضربهما. يبقى بتأخذ Ψ
+
+119
+00:14:12,550 --> 00:14:20,510
+العنصر الأول من الـ factor ring، هو r<sub>1</sub> + ker
+
+120
+00:14:20,510 --> 00:14:29,610
+Φ + العنصر الثاني، اللي هو r<sub>2</sub> + ker
+
+121
+00:14:29,610 --> 00:14:38,220
+Φ. بتأخذ تأثير الـ Ψ عليهما. هيك بقدرش أخلي اللي
+
+122
+00:14:38,220 --> 00:14:47,240
+بقى يتأثر عليهما إلا بعد أن أجعلهم عنصراً واحداً. يبقى
+
+123
+00:14:47,240 --> 00:14:56,140
+هذا وهذا معناته r<sub>1</sub> + r<sub>2</sub> + ker Φ.
+
+124
+00:14:56,140 --> 00:14:59,500
+تمام؟
+
+125
+00:14:59,500 --> 00:15:04,200
+يبقى صار هذا اللي كان مجموع عنصرين، صار عنصراً واحداً.
+
+126
+00:15:05,120 --> 00:15:10,060
+التعريف بيقول: إذا Ψ(r + ker Φ) = Ψ
+
+127
+00:15:10,060 --> 00:15:12,580
+(r + ker Φ) Ψ(r + ker Φ) Ψ(r + ker Φ)
+
+128
+00:15:12,580 --> 00:15:15,180
+Ψ(r + ker Φ) Ψ(r + ker Φ) Ψ(r + ker Φ)
+
+129
+00:15:15,180 --> 00:15:19,520
+Ψ(r + ker Φ) Ψ(r + ker Φ) Ψ(r + ker Φ)
+
+130
+00:15:19,520 --> 00:15:19,900
+Ψ(r + ker Φ) Ψ(r + ker Φ) Ψ(r + ker Φ)
+
+131
+00:15:19,900 --> 00:15:24,600
+Ψ(r + ker Φ) Ψ(r + ker Φ) P
+
+132
+00:15:33,570 --> 00:15:43,070
+بده يساوي: اللي هو Φ(r<sub>1</sub>) + Φ(r<sub>2</sub>). ليش
+
+133
+00:15:43,070 --> 00:15:48,990
+كتبت الخطوة هذه؟ لأن Φ عبارة عن homomorphism. بدي
+
+134
+00:15:48,990 --> 00:15:56,090
+أرجع للتعريف ثانيةً. Φ(r<sub>1</sub>) هي Ψ(Φ(r<sub>1</sub>) + ker
+
+135
+00:15:56,090 --> 00:16:04,230
+Φ). يبقى هذه تساوي Φ(r<sub>1</sub>) +
+
+136
+00:16:04,230 --> 00:16:13,090
+ker Φ + Ψ(r<sub>2</sub>) + ker
+
+137
+00:16:13,090 --> 00:16:18,250
+Φ. يبقى تحققت الخطوة الأولى من الخطوات
+
+138
+00:16:18,250 --> 00:16:25,370
+الـ homomorphism. بدنا نروح للخطوة الثانية.  and Φ بدل
+
+139
+00:16:25,370 --> 00:16:32,750
+المجموع بدي آخذ حاصل الضرب. يبقى r<sub>1</sub> + ker
+
+140
+00:16:32,750 --> 00:16:43,210
+Φ بدي أضربه في r<sub>2</sub> + ker Φ. هذا طبعاً
+
+141
+00:16:43,210 --> 00:16:52,770
+Ψ، Ψ، ونجد Ψ، أو تمام. يبقى هذا الكلام
+
+142
+00:16:52,770 --> 00:17:02,870
+بده يساوي Ψ. نضرب هذول، يبقى r<sub>1</sub>r<sub>2</sub> + ker
+
+143
+00:17:02,870 --> 00:17:10,270
+Φ. الآن، r<sub>1</sub>r<sub>2</sub> عنصر موجود وين؟ في R. يبقى على
+
+144
+00:17:10,270 --> 00:17:18,210
+طول الخط هذا بقدر أقول هو مين؟ Φ(r<sub>1</sub>r<sub>2</sub>). يبقى
+
+145
+00:17:18,210 --> 00:17:26,890
+هذا بده يساوي Φ(r<sub>1</sub>r<sub>2</sub>). فهي تمام. Φ قال لي في
+
+146
+00:17:26,890 --> 00:17:32,490
+رأسي المسألة homomorphism. إذًا، هذا بده يساوي Φ
+
+147
+00:17:32,490 --> 00:17:41,890
+(r<sub>1</sub>)Φ(r<sub>2</sub>). هذا بده يساوي مين؟ بده يساوي Ψ
+
+148
+00:17:41,890 --> 00:17:51,430
+(r<sub>1</sub> + ker Φ) مضروباً في Ψ(r<sub>2</sub>
+
+149
+00:17:51,430 --> 00:17:59,270
++ ker Φ). يبقى تحقق الشرطان الخاصان بالـ
+
+150
+00:17:59,270 --> 00:18:05,470
+homomorphism. إذًا، أصبح Ψ is a homomorphism. باين
+
+151
+00:18:05,470 --> 00:18:12,470
+علينا إيش؟ شغلتين: نثبت أن الـ Ψ هذه is one to
+
+152
+00:18:12,470 --> 00:18:19,310
+one، و onto.  إن تحقق ذلك بقول: يبقى هذه عبارة عن
+
+153
+00:18:19,310 --> 00:18:26,030
+إيش؟ عبارة عن إيش؟ isomorphism. تمام. إذًا بدنا نجي
+
+154
+00:18:26,030 --> 00:18:34,490
+نثبت أن Ψ is one to one. يبقى بدنا نأخذ صورتين
+
+155
+00:18:34,490 --> 00:18:42,430
+متساويتين، ونثبت أن أصلهما متساويان.  بعدين بقول:
+
+156
+00:18:42,430 --> 00:18:50,170
+assume، افترض أن في عندنا صورتين متساويتين، يعني Ψ
+
+157
+00:18:50,170 --> 00:18:58,980
+(r<sub>1</sub> + ker Φ) = Ψ(r<sub>2</sub> + ker
+
+158
+00:18:58,980 --> 00:19:07,480
+Φ). ثم هذه
+
+159
+00:19:07,480 --> 00:19:15,800
+مين صورتها؟ Φ(r<sub>1</sub>). والثانية صورتها مين؟ Φ
+
+160
+00:19:15,800 --> 00:19:28,710
+(r<sub>1</sub>) = Φ(r<sub>2</sub>). هذا معناه أن Φ(r<sub>1</sub>)
+
+161
+00:19:28,710 --> 00:19:35,590
+− Φ(r<sub>2</sub>) = 0. نرجع، في رأسي
+
+162
+00:19:35,590 --> 00:19:41,410
+المسألة Φ homomorphism، إذًا هذا بده يعطينا مين؟ أن
+
+163
+00:19:41,410 --> 00:19:46,550
+Φ(r<sub>1</sub> − r<sub>2</sub>) = 0.
+
+164
+00:19:50,830 --> 00:19:57,950
+موجودة في الـ kernel. يبقى هذا معناه أن r<sub>1</sub> −
+
+165
+00:19:57,950 --> 00:20:07,010
+r<sub>2</sub> موجودة في الـ kernel للـ Φ. أو معناه أن r<sub>1</sub>
+
+166
+00:20:07,010 --> 00:20:11,770
+− r<sub>2</sub> + ker Φ
+
+167
+00:20:18,030 --> 00:20:27,510
+أو بمعنى آخر، r<sub>1</sub> + ker Φ =
+
+168
+00:20:27,510 --> 00:20:37,650
+r<sub>2</sub> + ker Φ. مظبوط؟ هم؟ 7.1؟ خلاص؟
+
+169
+00:20:37,650 --> 00:20:45,320
+يبقى أنا أخذت صورتين متساويتين، أثبت أن أصليهما
+
+223
+00:28:04,960 --> 00:28:11,040
+هذا الكلام يسوي حسب الـ definition اللي عندك
+
+224
+00:28:11,040 --> 00:28:20,780
+يسوي R1 زائد R2 زائد الـ ideal A يبقى R1 زائد R2
+
+225
+00:28:20,780 --> 00:28:26,540
+زائد الـ ideal A اللي بقدر اكتبه على الشكل التالي
+
+226
+00:28:26,540 --> 00:28:36,270
+R1 زائد الـ ideal A زائد الـ R2 زائد الـ ideal A هذه
+
+227
+00:28:36,270 --> 00:28:44,410
+من أيه يا عزيزي؟ FI of R1 يبقى هذه FI of R1 plus
+
+228
+00:28:44,410 --> 00:28:59,050
+FI of R2 and تاخد FI of R1 مضروبة في R2 يبقى R1 R2
+
+229
+00:28:59,050 --> 00:29:06,560
+زائد الـ A اللي بقدر اكتبه على صيغة حاصل ضرب الـ two
+
+230
+00:29:06,560 --> 00:29:14,520
+elements R1 plus A في R2 plus A يعني اللي هو mean
+
+231
+00:29:14,520 --> 00:29:28,640
+Phi of R1 في Phi of R2 so Phi is a homomorphism
+
+232
+00:29:28,640 --> 00:29:34,630
+الجدال اللي أعطاه هالي هذا الـ mapping أثبت له إنه
+
+233
+00:29:34,630 --> 00:29:40,670
+هي homomorphism وهي المعرفة بهذا الشكل. بدي أثبت إن
+
+234
+00:29:40,670 --> 00:29:49,930
+كيرن لـ Phi هو مين؟ هو الـ ideal A؟ يبقى باجي
+
+235
+00:29:49,930 --> 00:29:55,870
+بقوله finally I want to prove that
+
+236
+00:30:00,540 --> 00:30:07,800
+إن الكيرن للـ Phi هو الـ ID لـ A طبعا اتعلمنا في
+
+237
+00:30:07,800 --> 00:30:12,800
+الـ principle of mathematics two sets are equal إذا
+
+238
+00:30:12,800 --> 00:30:16,800
+كانت الأولى subset من الثانية والثانية subset من
+
+239
+00:30:16,800 --> 00:30:23,040
+الأولى لذلك بدأ نستخدم نفس الفكرة هذه إذا لو جيت
+
+240
+00:30:23,040 --> 00:30:30,550
+قلت لك خدي لي X موجود في كيرن للـ Phi إذا قدرت أثبت
+
+241
+00:30:30,550 --> 00:30:35,850
+إن الـ X موجودة في الـ A بيكون تم المطلوب يبقى
+
+242
+00:30:35,850 --> 00:30:43,750
+then كداش الـ 5 of X و أنا؟ صفر يساوي كداش؟ يساوي
+
+243
+00:30:43,750 --> 00:30:50,850
+Zero طيب، احنا عندنا الـ function من وين؟ من هذه ل
+
+244
+00:30:50,850 --> 00:30:58,960
+.. من R إلى R modulo A، من الـ Zero هنا؟ الـ L Zero
+
+245
+00:30:58,960 --> 00:31:06,160
+زائد الـ L والـ A الصلفة يبقى هذا Zero زائد الـ L
+
+246
+00:31:06,160 --> 00:31:15,320
+والـ A الصلفة لكن حسب التعريف but from the
+
+247
+00:31:15,320 --> 00:31:26,300
+definition of Phi we have أن Phi of Xبدو يساوي ال
+
+248
+00:31:26,300 --> 00:31:33,460
+X زائد الـ A تعريف مظبوط؟ طيب من الاتنين هدول مع
+
+249
+00:31:33,460 --> 00:31:40,160
+بعض فـ I of X يساوي A؟ فـ I of X يساوي X زائد الـ A
+
+250
+00:31:40,160 --> 00:31:47,600
+يبقى بصير عندنا الـ X زائد الـ A يساوي كداش؟ الـ A إيش
+
+251
+00:31:47,600 --> 00:31:54,030
+معنى هذا الكلام؟ الـ X وين موجودة؟ الـ A طيب أخد X
+
+252
+00:31:54,030 --> 00:32:00,830
+موجودة في الكيرن اللي جيه تمين يبقى
+
+253
+00:32:00,830 --> 00:32:07,410
+ساق الكيرن اللي الـ five subset من الـ A ويعتبر هذه
+
+254
+00:32:07,410 --> 00:32:12,670
+العلاقة رقم واحد بدي أمشي الاتجاه الثاني يبقى on
+
+255
+00:32:12,670 --> 00:32:20,910
+the other hand بدي أخد X موجودة في الـ ID الـ A
+
+256
+00:32:24,000 --> 00:32:30,660
+الـ X موجودة في الـ ID الـ A بدي أثبت إنها موجودة في
+
+257
+00:32:30,660 --> 00:32:36,920
+الـ kernel يبقى ذلك مدام الـ X موجودة في الـ A يبقى
+
+258
+00:32:36,920 --> 00:32:45,960
+الـ X زائد الـ A بيساوي مين؟ بيساوي الـ A، أه؟ طيب الـ
+
+259
+00:32:45,960 --> 00:32:53,000
+X زائد الـ A من هنا حسب التعريف الـ X زائد الـ A هي
+
+260
+00:32:53,000 --> 00:33:01,100
+مين؟ الـ Phi of X يبقى هذا بده يعطينا أن هذه Phi
+
+261
+00:33:01,100 --> 00:33:10,520
+of X بده يساوي الـ A مين هو الـ A؟ Zero element في
+
+262
+00:33:10,520 --> 00:33:16,500
+الـ factoring يبقى معنى الـ X وين موجودة هذه؟ وين؟
+
+263
+00:33:16,500 --> 00:33:24,020
+في الـ kernel تبع الـ Phi صح؟ يبقى هذا معناه أن الـ X
+
+264
+00:33:24,020 --> 00:33:30,060
+موجودة في الـ kernel للفاي يبقى أخدت الـ X موجودة في
+
+265
+00:33:30,060 --> 00:33:35,260
+الـ ID الـ A طلعت الـ X موجودة وين؟ في الـ kernel
+
+266
+00:33:35,260 --> 00:33:42,000
+فبروح بقول له Sir الـ ID الـ A subset من الـ kernel
+
+267
+00:33:42,000 --> 00:33:48,120
+للفاي وهذه العلاقة رقم اتنين طلعولي من واحد واتنين
+
+268
+00:33:48,420 --> 00:33:57,240
+طب اروح و اقول from واحد and اتنين we have أن
+
+269
+00:33:57,240 --> 00:34:04,940
+الكيرنل للـ Phi بده يساوي الـ ideal A كما هو مطلوب
+
+270
+00:34:04,940 --> 00:34:13,160
+في النظرية يبقى الـ ideal A هو الكيرنل لمين؟ لهذا الـ
+
+271
+00:34:13,160 --> 00:34:16,540
+homomorphism نعطي مثال
+
+272
+00:34:19,810 --> 00:34:30,430
+نربط هذا المثال بالـ chapter الماضي الـ example
+
+273
+00:34:30,430 --> 00:34:38,410
+بيقول ما يعني show that five
+
+274
+00:34:38,410 --> 00:34:45,330
+المعرفة من Z of x onto
+
+275
+00:34:47,770 --> 00:34:55,610
+on to Z given by والمعطى
+
+276
+00:34:55,610 --> 00:35:09,010
+بي five للـ F of X بده يساوي الـ F of zero is a ring
+
+277
+00:35:09,010 --> 00:35:12,190
+homomorphism
+
+278
+00:35:12,190 --> 00:35:14,710
+with
+
+279
+00:35:17,120 --> 00:35:21,900
+الكرنة للـ 5 بدو يساوي لـ principle ideal
+
+280
+00:35:21,900 --> 00:35:23,780
+generated by X
+
+281
+00:35:50,400 --> 00:35:54,840
+خلّيني أعطيكم دالة
+
+282
+00:35:54,840 --> 00:36:01,060
+في من مجموعة الـ functions اللي العرامل تبعتهم
+
+283
+00:36:01,060 --> 00:36:09,260
+أعداد صحيحة on to Z يعني بغطي الـ Z كلها given by
+
+284
+00:36:09,260 --> 00:36:14,340
+في of f of x بده يساوي f of zero قال لي بدك تثبت أن
+
+285
+00:36:14,340 --> 00:36:18,900
+هذا ring homomorphism الخطوة الأولى الخطوة الثانية
+
+286
+00:36:19,190 --> 00:36:23,150
+تثبت أن الـ Kernel هو الـ principal ideal
+
+287
+00:36:23,150 --> 00:36:28,650
+generated by X طبعا لأول واحدة بنقول إيش جاب لجاب
+
+288
+00:36:28,650 --> 00:36:32,730
+هذا في شُجة وأنا إيش جابهم لبعض لكن بنقوله بسيطة
+
+289
+00:36:32,730 --> 00:36:36,750
+تعالى يشوفها الحين خلينا في الأول نثبت بس حكاية الـ
+
+290
+00:36:36,750 --> 00:36:40,690
+ring homomorphic الـ Phi homomorphism يبقى بداجي
+
+291
+00:36:40,690 --> 00:36:48,370
+أقولهم Phi is a homomorphism أيه اللي بنكتبه إذا
+
+292
+00:36:48,370 --> 00:36:55,750
+بتاخد two elements  بتقوله let الـ F of X
+
+293
+00:36:55,750 --> 00:37:06,550
+والـ G of X موجودة في الـ ring اللي عندها then بتاخد
+
+294
+00:37:06,550 --> 00:37:15,030
+تأثير الـ Phi على مين؟ على الـ F of X زائد الـ G of X
+
+295
+00:37:15,850 --> 00:37:21,930
+هدول مجموع دالتين مجموعهم من الـ calculus بكتبوا F
+
+296
+00:37:21,930 --> 00:37:29,830
+زائد G كله as a one function of X بيطبق اللي
+
+297
+00:37:29,830 --> 00:37:36,570
+التعريف اللي احنا حطنا هذا بده يساوي تأثير هذه الـ
+
+298
+00:37:36,570 --> 00:37:43,410
+function على الـ zero يبقى هذا بده يساوي الـ F زائد G
+
+299
+00:37:43,410 --> 00:37:50,630
+تأثيره على الـ zero أو إن شئتم فقولوا الـ F of Zero
+
+300
+00:37:50,630 --> 00:37:57,850
+زائد الـ G of Zero لو رجعت للتعريف Of الـ F of Zero
+
+301
+00:37:57,850 --> 00:38:06,710
+هو Phi للـ F of X يبقى هذا يساوي Phi للـ F of X زائد
+
+302
+00:38:06,710 --> 00:38:14,810
+Phi لمين؟ للـ G of X إذا أثبتنا الشرط الأول من شروط
+
+303
+00:38:14,810 --> 00:38:20,630
+الـ homomorphism بروح بقوله الآن بجيب الشرط الثاني
+
+304
+00:38:20,630 --> 00:38:28,650
+five للـ F of X مضروبة في G of X لو رجعنا إلى الـ
+
+305
+00:38:28,650 --> 00:38:35,970
+calculus نقول هذه كل F مضروبة في G as a function
+
+306
+00:38:35,970 --> 00:38:43,370
+of X يبقى صارت function واحدة نتيجة من حاصل الضرب للـ
+
+307
+00:38:43,370 --> 00:38:49,110
+FG حسب الـ definition اللي احنا حاطينه هذا الكلام
+
+308
+00:38:49,110 --> 00:38:57,250
+بدو يساوي FG as a function of zero طيب هذا من الـ
+
+309
+00:38:57,250 --> 00:39:04,630
+calculus بقوله F of zero الـ G of zero F of zero
+
+310
+00:39:04,630 --> 00:39:13,970
+فاي للـ F of X يبقى هذا فاي للـ F of X مضروبة في Phi
+
+311
+00:39:13,970 --> 00:39:22,090
+للـ G of X يبقى  صارت الـ
+
+312
+00:39:22,090 --> 00:39:28,810
+Phi is a homomorphism انتهينا من المقبض الأول
+
+313
+00:39:28,810 --> 00:39:34,710
+المقبض الثاني قال لي with كيرن اللي الـ Phi بتساوي لـ
+
+314
+00:39:34,710 --> 00:39:39,650
+principle ideal generated by x لو رجعنا إلى المثال
+
+315
+00:39:39,650 --> 00:39:47,010
+الأخر من شابتر 14 السابق تمام؟ المثال الأخير عرفني
+
+316
+00:39:47,010 --> 00:39:55,170
+الـ principle ideal generated by X وقول لها أن الـ
+
+317
+00:39:55,170 --> 00:40:01,090
+principle ideal generated by X كل الـ X مضروبة في G
+
+318
+00:40:01,090 --> 00:40:10,890
+of X بحيث أن الـ G of X موجودة في Z of X مفروض يا
+
+319
+00:40:10,890 --> 00:40:19,810
+بنات؟ صح؟ و أثبتنا أن هذا الكلام بالضبط هو كل الـ F
+
+320
+00:40:19,810 --> 00:40:29,750
+of X اللي موجودة في Z of X such that الـ F of Zero
+
+321
+00:40:29,750 --> 00:40:34,620
+بده يساوي Zero أثبتنا أن اتنين هذول نفس الشيء لأن
+
+322
+00:40:34,620 --> 00:40:40,400
+أراء كبيرة هذا كلام في آخر مثال في chapter 14
+
+323
+00:40:40,400 --> 00:40:46,500
+مظبوط هيك؟ بناء على هذه المعلومات بدنا نروح
+
+324
+00:40:46,500 --> 00:40:54,740
+نستخدمها نستخدمها في إثبات أن الكيرنل الها ده كله
+
+325
+00:40:54,740 --> 00:40:58,780
+يساوي مين؟ الـ principle ideal generated by it إذا
+
+326
+00:40:58,780 --> 00:41:07,900
+برووح كله افترض أن الـ F of X موجودة في كيرنل الفا
+
+327
+00:41:07,900 --> 00:41:13,640
+تجي واحد يقول طب احنا بناخد دايما X موجودة في
+
+328
+00:41:13,640 --> 00:41:19,080
+الكيرنل لأ الـ ring اللي عندنا Z of X كل اللي فيها
+
+329
+00:41:19,080 --> 00:41:26,440
+functions إذا بروح باخد function يبقى then مادام
+
+330
+00:41:26,440 --> 00:41:32,030
+هذه موجودة في الكيرنل يبقى تأثير الفاي على الـ F of X
+
+331
+00:41:32,030 --> 00:41:40,930
+كداش؟ Zero يبقى هذا الكلام متساوي Zero طيب الفاي لـ
+
+332
+00:41:40,930 --> 00:41:49,110
+الـ F of X حسب التعريف اللي عندنا كداش؟ Zero يبقى
+
+333
+00:41:49,110 --> 00:41:54,350
+هذا بده يعطينا هذه هشيل او اكتب دالة F of Zero
+
+334
+00:41:54,350 --> 00:42:00,350
+متساوي مين؟ Zero اللي هو مين؟ اللي عندنا هذا يبقى
+
+335
+00:42:00,350 --> 00:42:05,270
+الـ F of X موجودة في الـ principle ideal generated
+
+336
+00:42:05,270 --> 00:42:11,610
+by X من التعريف اللي عندنا يبقى هذا بده يعطينا أن
+
+337
+00:42:11,610 --> 00:42:16,870
+الـ F of X موجودة في الـ principle ideal generated
+
+338
+00:42:16,870 --> 00:42:24,550
+by X يبقى الـ kernel اللي الـ Phi هو subset من الـ
+
+339
+00:42:24,550 --> 00:42:30,330
+principle ideal generated by X يمشي لاتجاه الثاني
+
+340
+00:42:30,330 --> 00:42:41,770
+يبقى on the other hand بدي اخذ الـ F of X موجودة في
+
+341
+00:42:41,770 --> 00:42:48,890
+الـ principle ideal generated by X then إيه شكل الـ
+
+342
+00:42:48,890 --> 00:42:55,650
+F of X يا بناه حسب التعريف هو X في الـ G of X
+
+343
+00:42:56,270 --> 00:43:03,670
+يبقى هذا الكلام بده يساوي X في G of X طب لو حبيت
+
+344
+00:43:03,670 --> 00:43:12,850
+أحسب الـ F of Zero يبقى بدها تساوي Zero في G of
+
+345
+00:43:12,850 --> 00:43:19,370
+Zero يبقى طالع عند الـ F of Zero كداش؟ بده يساوي Zero
+
+346
+00:43:19,370 --> 00:43:25,560
+يبقى طالع عندنا الـ F of Zero بده يساوي Zero معناته
+
+347
+00:43:25,560 --> 00:43:31,580
+.. معناته إيش؟ مين هي الـ F of Zero حسب الـ
+
+348
+00:43:31,580 --> 00:43:37,940
+definition؟ هي الـ Phi للـ F of X يبقى هذا معناته إن
+
+349
+00:43:37,940 --> 00:43:45,220
+الـ Phi للـ F of X بده يساوي Zero هذه إيش معناها؟ الـ
+
+350
+00:43:45,220 --> 00:43:51,270
+F of X موجودة في الـ kernel يبقى هذا معناه أن F of X
+
+351
+00:43:51,270 --> 00:43:59,150
+موجودة في الكيرنل للـ فاي تمام؟ يبقى أخد F of X
+
+352
+00:43:59,150 --> 00:44:03,610
+موجودة في الـ principle ID الـ generated by X وجدتها
+
+353
+00:44:03,610 --> 00:44:08,070
+موجودة في الكيرنل يبقى فاجي بقول للثالث الـ
+
+354
+00:44:08,070 --> 00:44:13,070
+principle ID الـ generated by X subset من الكيرنل
+
+355
+00:44:13,070 --> 00:44:19,570
+للفاي الأولى هذه العلاقة رقم واحدة هذه العلاقة رقم
+
+356
+00:44:19,570 --> 00:44:27,910
+اتنين بقول له from واحد and اتنين we have أن الـ
+
+357
+00:44:27,910 --> 00:44:32,810
+principle او الـ kernel للفاي هو الـ principle
+
+358
+00:44:32,810 --> 00:44:40,730
+ideal generated by X طبعا شو نشتغل فيه من نفاية و
+
+359
+00:44:40,730 --> 00:44:47,960
+الله كله كلام طب احنا إيش أثبتنا في آخر مثال في
+
+360
+00:44:47,960 --> 00:44:52,520
+chapter 14 أيوة أيوة أيوة أيوة أيوة أيوة أيوة أيوة
+
+361
+00:44:52,520 --> 00:44:55,000
+أيوة أيوة أيوة أيوة أيوة أيوة أيوة أيوة أيوة أيوة
+
+362
+00:44:55,000 --> 00:44:55,740
+أيوة
+
+363
+00:45:16,000 --> 00:45:21,920
+يبقى ضيّاع لطريقة أسهل للحل من الطريقة اللي حلناها
+
+364
+00:45:21,920 --> 00:45:28,800
+في شابتر أربعة عشر آخر مثال كيف الآن لحد هنا انتهى
+
+365
+00:45:28,800 --> 00:45:34,880
+شغلنا فنتبهنا النظرية لكن بدنا نستفيد من هذه
+
+366
+00:45:34,880 --> 00:45:41,940
+النظرية فباجي نقول هنا from from
+
+367
+00:45:41,940 --> 00:45:50,560
+first isomorphism theorem we
+
+368
+00:45:50,560 --> 00:46:01,880
+have أن الـ Z of X اللي هي الـ ring modulo كيرن
+
+369
+00:46:01,880 --> 00:46:15,020
+للفاي هذه isomorphic لمن؟ للفاي of R للفاي of Z of
+
+370
+00:46:15,020 --> 00:46:18,880
+x مظبوط
+
+371
+00:46:18,880 --> 00:46:26,980
+؟ طيب هنا أثبتنا هذه بالشكل اللي عندنا هذه إشارة
+
+372
+00:46:26,980 --> 00:46:32,680
+عن اللي هو هذه الصورة اللي عندنا لما كانت أنتو
+
+373
+00:46:32,680 --> 00:46:39,400
+غطتها كلها يعني هذه بقول عليها مين؟ بقول عليها Z
+
+374
+00:46:39,400 --> 00:46:46,850
+itself تمام؟ يبقى من الـ first isomorphism theorem
+
+375
+00:46:46,850 --> 00:46:53,510
+الـ Z of X modulo kernel isomorphic لمين؟ للـ Phi of
+
+376
+00:46:53,510 --> 00:46:59,950
+R؟ مين R هون؟ Z of X Z of X اللي هي مين هنا؟ Z
+
+377
+00:46:59,950 --> 00:47:07,110
+تمام يعني Z أجت مكان Phi of R بالطبع تمام طيب الـ
+
+378
+00:47:07,110 --> 00:47:13,210
+kernel هذا أثبتنا و أنا مين؟ بتشيله وحط دالة الـ
+
+379
+00:47:13,210 --> 00:47:18,250
+principal ideal generated by X يبقى هذا بده يعطينا
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5f5e3fe748b7d9373bab1a74c39f7a8da25e6932
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_postprocess.srt
@@ -0,0 +1,1516 @@
+1
+00:00:20,990 --> 00:00:25,430
+بسم الله الرحمن الرحيم نكمل اليوم ما ابتدأناه في
+
+2
+00:00:25,430 --> 00:00:29,970
+المرة الماضية وهو موضوع ال ring homomorphism اللي
+
+3
+00:00:29,970 --> 00:00:36,790
+هو chapter 15 من الكتاب فينا نظرية اليوم، النظرية
+
+4
+00:00:36,790 --> 00:00:41,070
+بتقول افترض ان Phi من R الى S عبارة عن ring
+
+5
+00:00:41,070 --> 00:00:47,010
+homomorphism نحاول نثبت ان ال kernel لهذا ال
+
+6
+00:00:47,010 --> 00:00:50,430
+homomorphism هو عبارة عن ideal
+
+7
+00:00:53,080 --> 00:00:58,600
+البرهان كالتالي بان نروح نثبت ال three conditions
+
+8
+00:00:58,600 --> 00:01:06,020
+تبعات ال I دى فبدالي ال condition الأول وهو ان
+
+9
+00:01:06,020 --> 00:01:14,220
+الكرن اللى الفاى is non-empty ما هو السبب لذلك
+
+10
+00:01:14,220 --> 00:01:24,440
+because الفاىof zero بده يساوي zero هذا يعني ان ال
+
+11
+00:01:24,440 --> 00:01:32,520
+zero موجود في كيرنل الفارق و لذلك الكيرنل
+
+12
+00:01:32,520 --> 00:01:38,940
+هذا is non-empty النقطة الثانية بدي اخد عنصرين
+
+13
+00:01:38,940 --> 00:01:43,960
+موجودات في الكيرنل يبقى بدي اقول له افترض ان اقار
+
+14
+00:01:43,960 --> 00:01:51,030
+واحد و اقار اتنينموجودات الكيرنل للـ Phi اذا ايش
+
+15
+00:01:51,030 --> 00:01:57,510
+بدنا نثبت؟ بدنا نثبت ان الفرق بينهما موجود في
+
+16
+00:01:57,510 --> 00:02:05,290
+الكيرنل طيب R1 موجود في الكيرنل ماذا يعني هذا؟ هذا
+
+17
+00:02:05,290 --> 00:02:12,410
+يعني ان Phi of R1 بدي سوى ال zero element اللي هو
+
+18
+00:02:12,410 --> 00:02:23,010
+تبع من؟ تبع ال Sو and ال 5 of R2 بدي سوى 0 كذلك
+
+19
+00:02:23,010 --> 00:02:30,770
+تبع ال S طيب الان لو روحنا و طرحناهم من بعض طرحنا
+
+20
+00:02:30,770 --> 00:02:37,770
+ال اتنين من بعض في اي واحد فبدي بقوله ال 5 of R1
+
+21
+00:02:37,770 --> 00:02:44,080
+ناقص 5 of R2بديوا يساوي Zero ناقص Zero بديوا يساوي
+
+22
+00:02:44,080 --> 00:02:50,040
+كده؟ Zero هذا بديوا يعطينا قاللي في راسي المسألة
+
+23
+00:02:50,040 --> 00:02:55,280
+Phi عبارة عن homomorphism قال خاصية الأولى من خواص
+
+24
+00:02:55,280 --> 00:03:02,940
+ال homomorphism ان Phi of R1 ناقص R2 كله بديوا
+
+25
+00:03:02,940 --> 00:03:07,740
+يساوي مين؟ بديوا يساوي Zero هذا معناه ايه؟ ان ال
+
+26
+00:03:07,740 --> 00:03:15,170
+R1-R2 موجود في الكيرن اللى فاعد ان صورته تسوى الـ
+
+27
+00:03:15,170 --> 00:03:23,170
+zero element تبع الاسم يبقى هذا معناه ان R1-R2 كله
+
+28
+00:03:23,170 --> 00:03:29,590
+موجود في الكيرن اللى الفاعد إذا أثبتنا النقطة
+
+29
+00:03:29,590 --> 00:03:30,370
+الثانية
+
+30
+00:03:33,700 --> 00:03:40,320
+النقطة الثالثة والاخيرة اللى بدنا نثبت فيها ان ال
+
+31
+00:03:40,320 --> 00:03:46,940
+kernel هو عبارة عن ID يبقى بدنا ناخد element من ال
+
+32
+00:03:46,940 --> 00:03:52,180
+set اللى عندنا و element من ال ring الأصلية ونثبت
+
+33
+00:03:52,180 --> 00:03:57,850
+ان حاصر ضربه ما موجود في ال kernel اوفاي لحاصل
+
+34
+00:03:57,850 --> 00:04:03,410
+ضرفيها مابتساوة كده Zero ان حدث ذلك يبقى بقوله في
+
+35
+00:04:03,410 --> 00:04:08,670
+هذه الحالة ان ال set اللي عندها هذه او ال kernel
+
+36
+00:04:08,670 --> 00:04:17,830
+صار عبارة عن id يبقى بجي بقوله if ال R موجودة في R
+
+37
+00:04:17,830 --> 00:04:29,110
+and ناخد element في ال kernel and مثلاالـ X موجود
+
+38
+00:04:29,110 --> 00:04:40,050
+في كيرن الـ Phi الـ Phi of R وين بدها تكون موجودة؟
+
+39
+00:04:40,050 --> 00:04:51,050
+في S يبقى then ال Phi of R موجودة في S and ال Phi
+
+40
+00:04:51,050 --> 00:05:00,010
+of X بدها تسوي قداش Zeroبنروح أخد Phi of R في X
+
+41
+00:05:00,010 --> 00:05:06,090
+نظرا لإن ال Phi عبارة عن homomorphism إذا الهدف
+
+42
+00:05:06,090 --> 00:05:12,670
+بده يساوي Phi of R في Phi of X Phi of X عندي
+
+43
+00:05:12,670 --> 00:05:19,010
+بقداشر هشيلها و أحط مكانها Zero يبقى بده يساوي Phi
+
+44
+00:05:19,010 --> 00:05:25,240
+of R is Zero اللي هو بده يساوي قداشر؟ Zeroإذا صار
+
+45
+00:05:25,240 --> 00:05:30,380
+تأثير Phi على ال element Rx بده يساوي Zero معناه
+
+46
+00:05:30,380 --> 00:05:36,900
+هذا الكلام ان ال Rx موجودة وين؟ في ال Kern اللي
+
+47
+00:05:36,900 --> 00:05:44,520
+فيه بنفس الطريقة Similarly بنفس الطريقة اللي هو ال
+
+48
+00:05:44,520 --> 00:05:50,000
+XR موجودة في ال Kern اللي مين؟ في ال Phi يبقى
+
+49
+00:05:50,000 --> 00:05:56,570
+أثبتنا شروط ال Ideal وخلصنايبقى بقول الله صحيح
+
+50
+00:05:56,570 --> 00:06:08,570
+وهكذا الـ Kernel للـ Phi is an ideal of R وهو
+
+51
+00:06:08,570 --> 00:06:16,430
+المفروض بنجي الآن للنظرية التي تليها وهذه نظرية
+
+52
+00:06:16,430 --> 00:06:21,330
+مهمة ومشهورة في كل كتب الجبر اللي بيسموها ال first
+
+53
+00:06:21,330 --> 00:06:26,490
+isomorphismأو الـ Fundamental Theorem of Ring
+
+54
+00:06:26,490 --> 00:06:34,070
+Homomorphism يبقى الـ Theorem بنسميها
+
+55
+00:06:34,070 --> 00:06:40,150
+الـ First Isomorphism
+
+56
+00:06:40,150 --> 00:06:49,750
+Theorem أو بنسميها الـ Fundamental Theorem
+
+57
+00:06:49,750 --> 00:06:51,910
+of
+
+58
+00:06:52,880 --> 00:06:57,040
+bearing homomorphism
+
+59
+00:06:57,040 --> 00:07:00,640
+الان
+
+60
+00:07:00,640 --> 00:07:07,760
+بدنا نجلع نص النظرية ومن ثم نقوم ببرهانها نص
+
+61
+00:07:07,760 --> 00:07:17,100
+النظرية بيقول my little five من a الى s bearing
+
+62
+00:07:17,100 --> 00:07:18,640
+homomorphism
+
+63
+00:07:23,120 --> 00:07:31,820
+Homomorphism then the mapping then the mapping
+
+64
+00:07:31,820 --> 00:07:41,400
+الدلة او ال function F psi من ال R موديول الكيرن
+
+65
+00:07:41,400 --> 00:07:55,350
+للفاي إلى فاي of capital R defined bydefined by
+
+66
+00:07:55,350 --> 00:08:05,790
+والمعرفة بيه شكل التالي Psi of R زي الكون للـ Phi
+
+67
+00:08:05,790 --> 00:08:14,150
+بتساوي Phi of R لكل الـ R اللي موجودة في capital R
+
+68
+00:08:14,150 --> 00:08:20,650
+is an isomorphism is an isomorphism
+
+69
+00:08:21,410 --> 00:08:31,230
+that is بطريقة مختصرة that is اللي هو ال R modulo
+
+70
+00:08:31,230 --> 00:08:48,710
+الكيرني لل FI isomorphic لمين لل FI of R نرجع
+
+71
+00:08:48,710 --> 00:08:54,670
+لنص النظرية مرة ثانيةحاول نفهم شو الشغل اللى بدنا
+
+72
+00:08:54,670 --> 00:09:00,890
+نشتغله حتى نشتغل شغل صحيح قال لي فاي من R إلى S
+
+73
+00:09:00,890 --> 00:09:07,390
+همومورفيزيوم ماشي بعدين قال لي أعرف دالة إبساعد من
+
+74
+00:09:07,390 --> 00:09:13,470
+ال factor ring ال R modular kernel لفاي لفاي of R
+
+75
+00:09:13,470 --> 00:09:21,310
+يعني لمين اللي بناد؟ لل range تبع من؟ تبع الفاي
+
+76
+00:09:21,620 --> 00:09:26,480
+الرينج تبع الفاي هذا موجود وين؟ في ارس تمام يعني
+
+77
+00:09:26,480 --> 00:09:32,300
+مش الارس كله وإنما لمن؟ للرينج تبع الفاي الفاي of
+
+78
+00:09:32,300 --> 00:09:39,900
+R العرفه كالتاني ابصيه R زائد الكيرن للفاي بده سوى
+
+79
+00:09:39,900 --> 00:09:46,620
+فاي of R اللي موجودة في فاي of R كبتة يبقى R زائد
+
+80
+00:09:46,620 --> 00:09:51,940
+الكيرن لفوهاElement موجود في ال factor ring R
+
+81
+00:09:51,940 --> 00:09:58,020
+modulo curly فما Phi of R هو Element موجود في Phi
+
+82
+00:09:58,020 --> 00:10:03,400
+of R لكل الـR اللي موجودة فيها مش بدنا نثبت بدنا
+
+83
+00:10:03,400 --> 00:10:09,740
+نثبت ان Phi عبارة عن isomorphism يبقى بدنا نثبت
+
+84
+00:10:09,740 --> 00:10:17,960
+homomorphism one to one و one to و خلاص لأ ما خلصش
+
+85
+00:10:18,260 --> 00:10:23,240
+هذه الـ left cosets يجب أن تثبت أيضًا إن هذه الـ
+
+86
+00:10:23,240 --> 00:10:28,740
+function is well-defined معظفة تعريفًا صحيحة يبقى
+
+87
+00:10:28,740 --> 00:10:32,780
+هذه الخطوة الأولى اللى بنبدأ فيها وبعدين بنروح
+
+88
+00:10:32,780 --> 00:10:37,920
+لمين؟ لـ isomorphism يبقى الخطوة الأولى اللى بدى
+
+89
+00:10:37,920 --> 00:10:42,840
+أثبتله إن Psi is well-defined
+
+90
+00:10:45,910 --> 00:10:51,590
+كيف عرفنا كيف علمنا كتثبت هذا well defined؟ بنقول
+
+91
+00:10:51,590 --> 00:10:57,090
+عكس اثبات انه لبساي one to one يعني انا باخد
+
+92
+00:10:57,090 --> 00:11:05,230
+عنصرين متساويين و باثبت ان صورتيهما متساويتان،
+
+93
+00:11:05,230 --> 00:11:11,410
+مظبوط هيك؟ يبقى بلاء العلم دي اقوله let افترض ان
+
+94
+00:11:11,410 --> 00:11:24,780
+اه الواحد زي ال kernel للفعلبدي أثبت
+
+95
+00:11:24,780 --> 00:11:29,960
+أن صورة العنصر الأول هي نفس صورة العنصر الثاني
+
+96
+00:11:29,960 --> 00:11:38,260
+يبقى then هذه بدي أحاول أكتبها بطريقة أخرى لو جينا
+
+97
+00:11:38,260 --> 00:11:44,120
+قلنا R واحد ناقص R اتنين زائد ال kernel للـ Phi
+
+98
+00:11:44,360 --> 00:11:50,000
+يبقى على الشجة اليمين اللي هو main الكيرنل الفائض
+
+99
+00:11:50,000 --> 00:11:57,420
+ما تفسيرك لهذه الجملة أرواح ناقص R2 موجودة في
+
+100
+00:11:57,420 --> 00:12:04,160
+الكيرنل يبقى هذا بده يعطينا أن أرواح ناقص R2
+
+101
+00:12:04,160 --> 00:12:12,180
+موجودة في الكيرنل الفائض موجودة في الكيرنل الفائض
+
+102
+00:12:13,150 --> 00:12:18,970
+مدام موجودة في الكيرنال يبقى صورتها Zero يبقى هذا
+
+103
+00:12:18,970 --> 00:12:27,230
+معناه ان Phi of R1 minus R2 بيساوي مين؟ ال Zero
+
+104
+00:12:27,230 --> 00:12:33,310
+تبع Phi of R تمام؟ طيب كويس، ايش قال في رأس
+
+105
+00:12:33,310 --> 00:12:38,770
+المسألة؟ Phi معنو؟ مدام Phi هومومورفزين، اذا بقدر
+
+106
+00:12:38,770 --> 00:12:45,450
+اجلز اهدي او افكهايبقى هذا معناه ان فاي of R1
+
+107
+00:12:45,450 --> 00:12:53,090
+minus فاي of R2 بده يسوي Zero او هذا معناه ان فاي
+
+108
+00:12:53,090 --> 00:13:02,430
+of R1 بده يسوي فاي of R2 لكن لو رجعنا للتعريف فاي
+
+109
+00:13:02,430 --> 00:13:11,150
+of R1 هو XI لل R1 زي الكيرنيت صح؟ من التعريفيبقى
+
+110
+00:13:11,150 --> 00:13:17,810
+هذا بده يعطينا مين؟ ان إبسايد of R1 زائد الكرن
+
+111
+00:13:17,810 --> 00:13:25,990
+للفاية بده يساوي L إبسايد of R2 زائد الكرن للفاية
+
+112
+00:13:25,990 --> 00:13:32,170
+هذا ما جيبناهوش عشوائيا ولكن from the definition
+
+113
+00:13:32,170 --> 00:13:38,340
+من التعريف جيبناه أيوة يبقى شو اللي حصل؟أخدت
+
+114
+00:13:38,340 --> 00:13:46,000
+عنصرين متساويين أثبت أن صورتيهم متساويتان زي ما
+
+115
+00:13:46,000 --> 00:13:51,620
+انتوا شايفين طيب يبقى أثبتنا ال will define بدنا
+
+116
+00:13:51,620 --> 00:13:58,040
+نيجي الإبصاي is homomorphism يبقى الإبصاي is a
+
+117
+00:13:58,040 --> 00:14:04,620
+homomorphism white يبقى بدأ أخد تأثير إبصاي على
+
+118
+00:14:04,620 --> 00:14:12,550
+مجموع عنصرين ثمعلى حصل ضربهما يبقى بتاخد إبساي of
+
+119
+00:14:12,550 --> 00:14:20,510
+العنصر الأول من ال factoring هو R1 زائد الكيرنل
+
+120
+00:14:20,510 --> 00:14:29,610
+للفاي زائد العنصر الثاني اللي هو R2 زائد الكيرنل
+
+121
+00:14:29,610 --> 00:14:38,220
+للفاي بتاخد تأثير الإبساي عليهمهك بقدرش اخل اللي
+
+122
+00:14:38,220 --> 00:14:47,240
+بقى يتأثر عليهم إلا بعد أن أجعلهم عنصرا واحدا يبقى
+
+123
+00:14:47,240 --> 00:14:56,140
+هذا و هذا معناته R1 زائد R2 زائد الكيرن للفار
+
+124
+00:14:56,140 --> 00:14:59,500
+تمام؟
+
+125
+00:14:59,500 --> 00:15:04,200
+يبقى صار هذا اللي كان مجموع عنصرين صار عنصرا واحدة
+
+126
+00:15:05,120 --> 00:15:10,060
+التعريف بيقول إذا Psi of R زي الكرنل بيكون Psi of
+
+127
+00:15:10,060 --> 00:15:12,580
+R زي الكرنل Psi of R زي الكرنل Psi of R زي الكرنل
+
+128
+00:15:12,580 --> 00:15:15,180
+Psi of R زي الكرنل Psi of R زي الكرنل Psi of R زي
+
+129
+00:15:15,180 --> 00:15:19,520
+الكرنل Psi of R زي الكرنل Psi of R زي الكرنل Psi
+
+130
+00:15:19,520 --> 00:15:19,900
+of R زي الكرنل Psi of R زي الكرنل Psi of R زي
+
+131
+00:15:19,900 --> 00:15:24,600
+of R زي الكرنل Psi of R زي الكرنل P
+
+132
+00:15:33,570 --> 00:15:43,070
+بدي اساوي منه اللي هو Phi of R1 زائد Phi of R2 ليش
+
+133
+00:15:43,070 --> 00:15:48,990
+كتبت الخطوة هذه لأن Phi عبارة عن homomorphism بدي
+
+134
+00:15:48,990 --> 00:15:56,090
+أرجع للتعريف ثماني Phi of R1 هي Minimum of Phi of
+
+135
+00:15:56,090 --> 00:16:04,230
+R1 زائد الكيرنات يبقى هذه تساوي Phi of R1زائد
+
+136
+00:16:04,230 --> 00:16:13,090
+الكيرن للـ Phi زائد إبسايد of R2 زائد الكيرن للـ
+
+137
+00:16:13,090 --> 00:16:18,250
+Phi يبقى تحققت الخطوة الأولى من الخطوات
+
+138
+00:16:18,250 --> 00:16:25,370
+الهمومورفزية بدأ أروح للخطوة الثانية and Phi بدل
+
+139
+00:16:25,370 --> 00:16:32,750
+المجموع بدي أخد حاصل الضرب يبقى R1زايد الكيرنل
+
+140
+00:16:32,750 --> 00:16:43,210
+للفاي بدي اضربه في R2 زايد الكيرنل للفاي هذا طبعا
+
+141
+00:16:43,210 --> 00:16:52,770
+إبساي إبساي ونجد فاي إبساي او تمام يبقى هذا الكلام
+
+142
+00:16:52,770 --> 00:17:02,870
+بدي يسوي إبساي او نضرب هدول يبقى R1 R2زائد الكيرن
+
+143
+00:17:02,870 --> 00:17:10,270
+للـ Phi الان R1 R2 عنصر موجود وين؟ في R يبقى على
+
+144
+00:17:10,270 --> 00:17:18,210
+طول الخاط هذا بقدر أقول هو مين Phi of R1 R2 يبقى
+
+145
+00:17:18,210 --> 00:17:26,890
+هذا بده يسوي Phi of R1 R2 فهي تمام Phi قاللي في
+
+146
+00:17:26,890 --> 00:17:32,490
+راسي المسألة homomorphismإذا هذا بده يساوي Phi of
+
+147
+00:17:32,490 --> 00:17:41,890
+R1 في Phi of R2 هذا بده يساوي مين؟ بده يساوي Epsi
+
+148
+00:17:41,890 --> 00:17:51,430
+of R1 زائد الكيرنل للـ Phi مضغوبا في Epsi of R2
+
+149
+00:17:51,430 --> 00:17:59,270
+زائد الكيرنل للـ Phi يبقى تحقق الشرطانالخاصان بالـ
+
+150
+00:17:59,270 --> 00:18:05,470
+Homomorphism إذا أصبح إبساي is a homomorphism باين
+
+151
+00:18:05,470 --> 00:18:12,470
+علينا إيش؟ شغلتين نثبت إن الإبساي هذه is one to
+
+152
+00:18:12,470 --> 00:18:19,310
+one and undo إن تملنا ذلك بقول يبقى هذه عبارة عن
+
+153
+00:18:19,310 --> 00:18:26,030
+إيش؟ عبارة عن إيش؟ Isomorphism تمامإذا بدنا نيجي
+
+154
+00:18:26,030 --> 00:18:34,490
+نثبت ان Psi is one to one يبقى بداخل صورتين
+
+155
+00:18:34,490 --> 00:18:42,430
+متساويتين و أثبت أن أصلهما متساوين فبعدين بقول ا
+
+156
+00:18:42,430 --> 00:18:50,170
+assume افترض ان في عندنا صورتين متساويتين يعني Psi
+
+157
+00:18:50,170 --> 00:18:58,980
+of R1 زائد الكيرنل للـPhiبتساوي F Psi of R2 زائد
+
+158
+00:18:58,980 --> 00:19:07,480
+الكيرن للـ Phi ثم هذه
+
+159
+00:19:07,480 --> 00:19:15,800
+مين صورتها؟ Phi of R1 والتانية صورتها مين؟ Phi of
+
+160
+00:19:15,800 --> 00:19:28,710
+R1 بتساوي Phi of R2هذا معناه إن الـ Phi of R1
+
+161
+00:19:28,710 --> 00:19:35,590
+minus الـ Phi of R2 بديوا يسووا Zero. نرجع، في رأس
+
+162
+00:19:35,590 --> 00:19:41,410
+المسألة Phi هم مورفزيه، إذا هذا بده يعطينا ميم، إن
+
+163
+00:19:41,410 --> 00:19:46,550
+الـ Phi of R1 ناقص R2 بديوا يسووا 200.
+
+164
+00:19:50,830 --> 00:19:57,950
+موجودة في ال kernel يبقى هذا معناه ان ال R1 minus
+
+165
+00:19:57,950 --> 00:20:07,010
+R2 موجودة في ال kernel الفاية او معناه ان ال R1
+
+166
+00:20:07,010 --> 00:20:11,770
+ناقص R2 زائد ال kernel
+
+167
+00:20:18,030 --> 00:20:27,510
+أو بمعنى أخر ار واحد زائد الكيرنل للفاي بده يساوي
+
+168
+00:20:27,510 --> 00:20:37,650
+R اتنين زائد الكيرنل للفاي، مصبوط هم؟ 7.1؟ خلاص؟
+
+169
+00:20:37,650 --> 00:20:45,320
+يبقى أنا أخد صورتين متساويتينأثبت أن أصليهما
+
+170
+00:20:45,320 --> 00:20:52,640
+متساوين R1 زايد كيرنل للـ Phi يساوي R2 زايد كيرنل
+
+171
+00:20:52,640 --> 00:21:03,020
+للـ Phi بقيت النقطة الأخيرة if Psi is onto R تبقى
+
+172
+00:21:03,020 --> 00:21:09,180
+بدى أروح أخد element في الـ Phi of Rإذا قدرت أن
+
+173
+00:21:09,180 --> 00:21:15,020
+أجيله أصل في ال factor A، يكون خلاصنا، يبقى بناءً
+
+174
+00:21:15,020 --> 00:21:22,640
+عليه. بدأ اقول له افترض ان ال X موجودة في ال Phi
+
+175
+00:21:22,640 --> 00:21:32,360
+of R. يبقى موجودة في ال Phi of R. لأن بدي أعرف أيش
+
+176
+00:21:32,360 --> 00:21:40,190
+شكلها ال X هذه.يبقى ال X بدأ يساوي في of R one
+
+177
+00:21:40,190 --> 00:21:48,070
+مثلا تمام four والله خليا في of R دوري في of R
+
+178
+00:21:48,070 --> 00:21:57,190
+four some R اللي موجودة في R يبقى عنصر شكله بدأ
+
+179
+00:21:57,190 --> 00:22:04,520
+يكون على شكل في of Rيبقى الـ X سواء فيه of R بتدري
+
+180
+00:22:04,520 --> 00:22:10,540
+على التعريف مين هي الـ Fi of R؟ إب ساي of R زي ال
+
+181
+00:22:10,540 --> 00:22:17,840
+kernel يبقى هذه بدها تساوي إب ساي لل R زي ال
+
+182
+00:22:17,840 --> 00:22:26,000
+kernel لل Fi يبقى أي element في ال Fi of R لاجتله
+
+183
+00:22:26,000 --> 00:22:32,620
+أصل في ال R موديل الكرنلمظبوط ولا لا يبقى Phi is
+
+184
+00:22:32,620 --> 00:22:39,760
+unto خلص كل ما يلزم يبقى Phi إبساى إيش صارت؟ أزو
+
+185
+00:22:39,760 --> 00:22:49,140
+مورفزي يبقى بص وهكذا الإبساى من ال ring اللي عندنا
+
+186
+00:22:49,140 --> 00:22:56,970
+هذه اللي قلناها ال R موديول الكيرن لل Phi إلىاللي
+
+187
+00:22:56,970 --> 00:23:08,150
+هو five of arcs and isomorphism وهو المفلوض هذه
+
+188
+00:23:08,150 --> 00:23:13,490
+النظرية بتلعب دور كبير في شغلنا في الجبر خلال
+
+189
+00:23:13,490 --> 00:23:21,550
+تدريسنا لمادة الجبر الحديد وهذه لا يكاد يحلو منها
+
+190
+00:23:21,550 --> 00:23:29,820
+أي كتاب جبر بتحدث عناللي هو ال rings نجي للنظرية
+
+191
+00:23:29,820 --> 00:23:43,120
+اللتي تاليها بتقول ما يأتي every ideals
+
+192
+00:23:43,120 --> 00:23:54,860
+of the ring are is the kernel is the kernel
+
+193
+00:23:56,750 --> 00:24:01,450
+of a ring
+
+194
+00:24:01,450 --> 00:24:06,550
+homomorphism
+
+195
+00:24:06,550 --> 00:24:20,410
+of a ring are itself in particular an ideal
+
+196
+00:24:20,410 --> 00:24:21,130
+I
+
+197
+00:24:28,070 --> 00:24:33,790
+الآن قاعدين A
+
+198
+00:24:33,790 --> 00:24:45,430
+is the kernel of the
+
+199
+00:24:45,430 --> 00:24:46,210
+mapping.
+
+200
+00:24:49,990 --> 00:25:02,110
+the mapping Phi من R إلى Rmodulo a given by given
+
+201
+00:25:02,110 --> 00:25:15,990
+by phi of r تساوي ال R زائد ال a اللحية
+
+202
+00:25:15,990 --> 00:25:17,650
+هذه حد بده منها شيء
+
+203
+00:25:49,460 --> 00:25:55,180
+نرجع لنص النظرية مرة ثانية يقول أي ايديل في ال
+
+204
+00:25:55,180 --> 00:26:03,020
+ring R هو يمثل كيرنل ل ring homomorphism على R مين
+
+205
+00:26:03,020 --> 00:26:08,620
+ما يكون هذا ال homomorphism له كيرنل الكيرنل هو
+
+206
+00:26:08,620 --> 00:26:13,900
+احد ال ideals اللي موجودة في ال ring R بدي اوضح
+
+207
+00:26:13,900 --> 00:26:19,700
+هذا الكلام فرح اقولك ال ideal ايههو الـ Kernel
+
+208
+00:26:19,700 --> 00:26:25,800
+لمن؟ لل homomorphism هذا تمام؟ لل homomorphism هذا
+
+209
+00:26:25,800 --> 00:26:31,480
+او للدالة هذه given by five of R يساوي R زي ليه؟
+
+210
+00:26:31,480 --> 00:26:38,320
+ماجليش homomorphism قللي مافيه ماعليش مقلوبة او
+
+211
+00:26:38,320 --> 00:26:42,660
+الخطوة الأولى بتثبتى انه homomorphism من البداية
+
+212
+00:26:42,660 --> 00:26:53,060
+ثم بعد ذلك نثبتان الكيرنل هذا هو ايش المعرف بهذه
+
+213
+00:26:53,060 --> 00:26:59,880
+الطريقة هو عبارة عن الكيرنل تبع هذه الـ Phi مرة
+
+214
+00:26:59,880 --> 00:27:07,360
+تانية ال ideal A اللي أخده من ال ring R هو يمثل
+
+215
+00:27:07,360 --> 00:27:12,520
+الكيرنل لهذه ال function يبقى أنا بدي أعمل قطوة
+
+216
+00:27:12,520 --> 00:27:16,470
+تانيةالخطوة الأولى بدي أثبت انه Phi homomorphism
+
+217
+00:27:16,470 --> 00:27:22,630
+المعطى اثنين بدي أثبت ان الكيرن لهذه ال Phi هو ال
+
+218
+00:27:22,630 --> 00:27:28,890
+ideal A إذا تم ذلك من خلاص برهنة نظرية والحمد لله
+
+219
+00:27:28,890 --> 00:27:33,150
+يبقى هنا ال proof بدي أمشي بالشكل التام
+
+220
+00:27:38,100 --> 00:27:47,300
+بنثبت إن الـ Phi is a homomorphic لذلك بنروح ناخد
+
+221
+00:27:47,300 --> 00:27:55,200
+عنصرين في R فبده أجي أقول له افترض عندي R واحد وR
+
+222
+00:27:55,200 --> 00:28:04,960
+اتنين موجودة في أرضان بدي أخد Phi of R واحد زائد R
+
+223
+00:28:04,960 --> 00:28:11,040
+اتنينهذا الكلام يسوي حسب ال definition اللي عندك
+
+224
+00:28:11,040 --> 00:28:20,780
+يسوي R1 زائد R2 زائد ال ideal A يبقى R1 زائد R2
+
+225
+00:28:20,780 --> 00:28:26,540
+زائد ال ideal A اللي بقدر اكتبه على الشكل التالي
+
+226
+00:28:26,540 --> 00:28:36,270
+R1 زائد ال ideal A زائد ال R2 زائد ال ideal Aهذه
+
+227
+00:28:36,270 --> 00:28:44,410
+من ايه يا عزيزي؟ FI of R1 يبقى هذه FI of R1 plus
+
+228
+00:28:44,410 --> 00:28:59,050
+FI of R2 and تاخد FI of R1 مضروبة في R2 يبقى R1 R2
+
+229
+00:28:59,050 --> 00:29:06,560
+زائد ال A اللي بقدر اكتبه على صيغة حاصل ضربالـ two
+
+230
+00:29:06,560 --> 00:29:14,520
+elements R1 plus A في R2 plus A يعني اللي هو mean
+
+231
+00:29:14,520 --> 00:29:28,640
+Phi of R1 في Phi of R2 so Phi is a homomorphism
+
+232
+00:29:28,640 --> 00:29:34,630
+الجدال اللي أعطاه هالي هذا ال mapping أثبت لهإنه
+
+233
+00:29:34,630 --> 00:29:40,670
+هي homomorphism وهي المعرفة بهذا الشكل.بدي أثبت إن
+
+234
+00:29:40,670 --> 00:29:49,930
+كيرن لـ Phi هو مين هو الـ ideal إيه؟ يبقى باجي
+
+235
+00:29:49,930 --> 00:29:55,870
+بقوله finally I want to prove that
+
+236
+00:30:00,540 --> 00:30:07,800
+إن الكيرن للـ Phi هو الـ ID لإيه طبعا اتعلمنا في
+
+237
+00:30:07,800 --> 00:30:12,800
+ال principle of mathematics two sets are equal إذا
+
+238
+00:30:12,800 --> 00:30:16,800
+كانت الأولى subset من الثانية والثانية subset من
+
+239
+00:30:16,800 --> 00:30:23,040
+الأولى لذلك بدأ نستخدم نفس الفكرة هذه إذا لو جيت
+
+240
+00:30:23,040 --> 00:30:30,550
+قلت لك خدي لي X موجود في كيرن للـ Phiإذا قدرت أثبت
+
+241
+00:30:30,550 --> 00:30:35,850
+إن الـ X موجودة في الـ A بيكون تم المطلوب يبقى
+
+242
+00:30:35,850 --> 00:30:43,750
+then كداش ال 5 of X و أنا؟ سفر يسوى كداش؟ يسوى
+
+243
+00:30:43,750 --> 00:30:50,850
+Zero طيب، احنا عندنا ال function من وين؟ من هذه ل
+
+244
+00:30:50,850 --> 00:30:58,960
+.. من R إلى R modulo A، من ال Zero هنا؟الـ L Zero
+
+245
+00:30:58,960 --> 00:31:06,160
+زائد الـ L والـ A الصلفة يبقى هذا Zero زائد الـ L
+
+246
+00:31:06,160 --> 00:31:15,320
+والـ A الصلفة لكن حسب التعريف but from the
+
+247
+00:31:15,320 --> 00:31:26,300
+definition of Phi we have ان Phi of Xبدو يساوي ال
+
+248
+00:31:26,300 --> 00:31:33,460
+X زائد ال A تعريف مظبوط؟ طيب من الاتنين هدول مع
+
+249
+00:31:33,460 --> 00:31:40,160
+بعض ف I of X يساوي ايه؟ ف I of X يساوي X زائد ال A
+
+250
+00:31:40,160 --> 00:31:47,600
+يبقى بصير عندنا ال X زائد ال A يساوي كده؟ ال A ايش
+
+251
+00:31:47,600 --> 00:31:54,030
+معنى هذا الكلام؟ ال X وين موجودة؟ ال Aطيب أخد X
+
+252
+00:31:54,030 --> 00:32:00,830
+موجودة في الكيرن اللي جيه تمين يبقى
+
+253
+00:32:00,830 --> 00:32:07,410
+ساق الكيرن اللي ال five subset من ال A ويعتبر هذه
+
+254
+00:32:07,410 --> 00:32:12,670
+العلاقة رقم واحد بدي أمشي الاتجاه الثاني يبقى on
+
+255
+00:32:12,670 --> 00:32:20,910
+the other hand بدي أخد X موجودة في ال ID ال A
+
+256
+00:32:24,000 --> 00:32:30,660
+ال X موجودة في ال ID ال A مدي أثبت إنها موجودة في
+
+257
+00:32:30,660 --> 00:32:36,920
+ال kernel يبقى ذلك مدام ال X موجودة في ال A يبقى
+
+258
+00:32:36,920 --> 00:32:45,960
+ال X زائد ال A بيساوي مين؟ بيساوي ال A، أه؟ طيب ال
+
+259
+00:32:45,960 --> 00:32:53,000
+X زائد ال A من هنا حسب التعريفالـ X زائد الـ A هي
+
+260
+00:32:53,000 --> 00:33:01,100
+مين؟ الـ Phi of X يبقى هذا بده يعطينا ان هذه Phi
+
+261
+00:33:01,100 --> 00:33:10,520
+of X بده ساوي الـ A مين هو الـ A؟ Zero element في
+
+262
+00:33:10,520 --> 00:33:16,500
+ال factoring يبقى معنى الـ X وين موجودة هذه؟ وين؟
+
+263
+00:33:16,500 --> 00:33:24,020
+في ال kernel تبع الـ Phi صح؟يبقى هذا معناه ان ال X
+
+264
+00:33:24,020 --> 00:33:30,060
+موجودة في ال kernel للفاي يبقى أخدت ال X موجودة في
+
+265
+00:33:30,060 --> 00:33:35,260
+ال ID ال A طلعت ال X موجودة وين؟ في ال kernel
+
+266
+00:33:35,260 --> 00:33:42,000
+فبروح بقول له Sir ال ID ال A صابست من ال kernel
+
+267
+00:33:42,000 --> 00:33:48,120
+للفاي وهذه العلاقة رقم اتنين طلعولي من واحد واتنين
+
+268
+00:33:48,420 --> 00:33:57,240
+طب اروح و اقول from واحد and اتنين we have ان
+
+269
+00:33:57,240 --> 00:34:04,940
+الكيرنل للـ Phi بده يساوي ال ideal A كما هو مطلوب
+
+270
+00:34:04,940 --> 00:34:13,160
+في النظرية يبقى ال ideal A هو الكيرنل لمين لهذا ال
+
+271
+00:34:13,160 --> 00:34:16,540
+homomorphism نعطي مثال
+
+272
+00:34:19,810 --> 00:34:30,430
+نربط هذا المثال بال chapter الماضي ال example
+
+273
+00:34:30,430 --> 00:34:38,410
+بيقول ما يعني show that five
+
+274
+00:34:38,410 --> 00:34:45,330
+المعرفة من z of x onto
+
+275
+00:34:47,770 --> 00:34:55,610
+on to z given by والمعطى
+
+276
+00:34:55,610 --> 00:35:09,010
+بي five لل F of X بده يساوي ال F of zero is a ring
+
+277
+00:35:09,010 --> 00:35:12,190
+homomorphism
+
+278
+00:35:12,190 --> 00:35:14,710
+with
+
+279
+00:35:17,120 --> 00:35:21,900
+الكرنة للـ 5 بدى يساوي لـ principle ideal
+
+280
+00:35:21,900 --> 00:35:23,780
+generated by X
+
+281
+00:35:50,400 --> 00:35:54,840
+خلّيني أعطيكم دلّة
+
+282
+00:35:54,840 --> 00:36:01,060
+في من مجموعة الـ functions اللي العرامل تبعتهم
+
+283
+00:36:01,060 --> 00:36:09,260
+أعداد صحيحة on to z يعني بغطي الـ z كلها given by
+
+284
+00:36:09,260 --> 00:36:14,340
+في of f of x بده ساوي f of zero قال لي بدك تثبت أن
+
+285
+00:36:14,340 --> 00:36:18,900
+هذا ring همو مرتزم الخطوة الأولى الخطوة الثانية
+
+286
+00:36:19,190 --> 00:36:23,150
+تثبت أن الـ Kernel هو الـ principal ideal
+
+287
+00:36:23,150 --> 00:36:28,650
+generated by X طبعا لأول واحدة بنقول إيش جاب لجاب
+
+288
+00:36:28,650 --> 00:36:32,730
+هذا في شجة وانا إيش جابهم لبعض لكن بنقوله بسيطة
+
+289
+00:36:32,730 --> 00:36:36,750
+تعالى يشوفها الحين خلينا في الأول نثبت بس حكاية ال
+
+290
+00:36:36,750 --> 00:36:40,690
+ring homomorphic الـ Phi homomorphism يبقى بداجي
+
+291
+00:36:40,690 --> 00:36:48,370
+أقولهم Phi is a homomorphism أيه اللي بنكتبهإذا
+
+292
+00:36:48,370 --> 00:36:55,750
+بتاخد two element sales يرجى بتقوله let ال F of X
+
+293
+00:36:55,750 --> 00:37:06,550
+وال G of X موجودة في ال ring اللي عندها then بتاخد
+
+294
+00:37:06,550 --> 00:37:15,030
+تأثير ال Phi على مين على ال F of X زائد ال G of X
+
+295
+00:37:15,850 --> 00:37:21,930
+هدول مجموع دلتين مجموعهم من ال calculus بكتبوا F
+
+296
+00:37:21,930 --> 00:37:29,830
+زائد G كله as a one function of X بيطبق اللي
+
+297
+00:37:29,830 --> 00:37:36,570
+التعريف اللي احنا حطنا هذا بدر ساوي تأثير هذه ال
+
+298
+00:37:36,570 --> 00:37:43,410
+function على ال zero يبقى هذا بدر ساوي ال F زائد G
+
+299
+00:37:43,410 --> 00:37:50,630
+تأثيره على ال zeroأو ان شئتم فقولوا ال F of Zero
+
+300
+00:37:50,630 --> 00:37:57,850
+زائد ال G of Zero لو رجعت للتعريف Of ال F of Zero
+
+301
+00:37:57,850 --> 00:38:06,710
+هو Phi لل F of X يبقى هذا يساوي Phi لل F of X زائد
+
+302
+00:38:06,710 --> 00:38:14,810
+Phi لمين لل G of Xإذا أثبتنا الشرط الأول من شروط
+
+303
+00:38:14,810 --> 00:38:20,630
+ال homomorphism بروح بقوله الآن بجيب الشرط الثاني
+
+304
+00:38:20,630 --> 00:38:28,650
+five لل F of X مضروبة في G of X لو رجعنا إلى ال
+
+305
+00:38:28,650 --> 00:38:35,970
+calculus نقول هذه كل F مضروبة في G as a function
+
+306
+00:38:35,970 --> 00:38:43,370
+of X يبقى صارت function واحدةنتجة من حاصل الضرب لل
+
+307
+00:38:43,370 --> 00:38:49,110
+FG حسب ال definition اللي احنا حاطينه هذا الكلام
+
+308
+00:38:49,110 --> 00:38:57,250
+بدي يسوى FG as a function of zero طيب هذا من ال
+
+309
+00:38:57,250 --> 00:39:04,630
+calculus بقوله F of zero ال G of zero F of zero
+
+310
+00:39:04,630 --> 00:39:13,970
+فاي لل F of X يبقى هذا فايلل F of X مضروبة في Phi
+
+311
+00:39:13,970 --> 00:39:22,090
+لل G of X يبقى ندالك صارت ال
+
+312
+00:39:22,090 --> 00:39:28,810
+Phi is a homomorphism انتهينا من المقبض الأول
+
+313
+00:39:28,810 --> 00:39:34,710
+المقبض الثاني قال لي with كيرن اللي ال Phi بتسوي ل
+
+314
+00:39:34,710 --> 00:39:39,650
+principle ideal generated biasلو رجعنا الى المثال
+
+315
+00:39:39,650 --> 00:39:47,010
+الأخر من شفتر 14 السابق تمام؟ المثال الأخير عرفني
+
+316
+00:39:47,010 --> 00:39:55,170
+ال principle ideal generated by X وقول لها ان ال
+
+317
+00:39:55,170 --> 00:40:01,090
+principle ideal generated by X كل ال X مضوبة في G
+
+318
+00:40:01,090 --> 00:40:10,890
+of X بحيث ان ال G of Xموجودة في Z of X مفروض يا
+
+319
+00:40:10,890 --> 00:40:19,810
+بنات؟ صح؟ و أثبتنا ان هذا الكلام بالضبط هو كل ال F
+
+320
+00:40:19,810 --> 00:40:29,750
+of X اللي موجودة في Z of X such that ال F of Zero
+
+321
+00:40:29,750 --> 00:40:34,620
+بده يساوي Zero أثبتنا ان اتنين هذول نفس الشيءلأن
+
+322
+00:40:34,620 --> 00:40:40,400
+آراء كبيرة هذا كلام في آخر مثال في chapter 14
+
+323
+00:40:40,400 --> 00:40:46,500
+مظبوط هيك؟ بناء على هذه المعلومات بدنا نروح
+
+324
+00:40:46,500 --> 00:40:54,740
+نستخدمها نستخدمها في اثبات ان الكيرن الها ده كله
+
+325
+00:40:54,740 --> 00:40:58,780
+سوى مين؟ ال principle idea generated by it اذا
+
+326
+00:40:58,780 --> 00:41:07,900
+بزوحها كله افترضإن ال F of X موجودة في كيرنل الفا
+
+327
+00:41:07,900 --> 00:41:13,640
+تجي واحد يقول طب احنا بناخد دايما X موجودة في
+
+328
+00:41:13,640 --> 00:41:19,080
+الكيرنل لأ ال ring اللي عندنا Z of X كل اللي فيها
+
+329
+00:41:19,080 --> 00:41:26,440
+functions إذا بروح باخد function يبقى then مادام
+
+330
+00:41:26,440 --> 00:41:32,030
+هذه موجودة في الكيرنل يبقى تأثير الفاعلى ال F of X
+
+331
+00:41:32,030 --> 00:41:40,930
+كده؟ Zero يبقى هذا الكلام متساوي Zero طيب الفايلة
+
+332
+00:41:40,930 --> 00:41:49,110
+ال F of X حسب التعريف اللي عندنا كده؟ Zero يبقى
+
+333
+00:41:49,110 --> 00:41:54,350
+هذا بدي يعطينا هذه هشيل او اكتب فدالة F of Zero
+
+334
+00:41:54,350 --> 00:42:00,350
+متساوي مين؟ Zero اللي هو مين؟اللي عندنا هذا يبقى
+
+335
+00:42:00,350 --> 00:42:05,270
+ال F of X موجودة في ال principle ideal generated
+
+336
+00:42:05,270 --> 00:42:11,610
+by X من التعريف اللي عندنا يبقى هذا بده يعطينا ان
+
+337
+00:42:11,610 --> 00:42:16,870
+ال F of X موجودة في ال principle ideal generated
+
+338
+00:42:16,870 --> 00:42:24,550
+by X يبقى ال kern اللي ال Phi هو صادر من ال
+
+339
+00:42:24,550 --> 00:42:30,330
+principle ideal generated by Xيمشي لاتجاه الثاني
+
+340
+00:42:30,330 --> 00:42:41,770
+يبقى on the other hand بدي اخد ال F of X موجودة في
+
+341
+00:42:41,770 --> 00:42:48,890
+ال principle ideal generated by X then ايه شكل ال
+
+342
+00:42:48,890 --> 00:42:55,650
+F of X يا بناه حسب التعريف هو من X في ال G of X
+
+343
+00:42:56,270 --> 00:43:03,670
+يبقى هذا الكلام بده يساوي X في G of X طب لو حبيت
+
+344
+00:43:03,670 --> 00:43:12,850
+أحسب ال F of Zero يبقى بدها تساوي Zero في G of
+
+345
+00:43:12,850 --> 00:43:19,370
+Zero يبقى طالع عند ال F of Zero كده بده يساوي Zero
+
+346
+00:43:19,370 --> 00:43:25,560
+يبقى طالع عندنا ال F of Zero بده يساوي Zeroمعناته
+
+347
+00:43:25,560 --> 00:43:31,580
+.. معناته إيش؟ مين هي ال F of Zero حسب ال
+
+348
+00:43:31,580 --> 00:43:37,940
+definition؟ هي ال Phi لل F of X يبجى هذا معناته إن
+
+349
+00:43:37,940 --> 00:43:45,220
+ال Phi لل F of X بدي يسوي Zero. هذه إيش معناها؟ ال
+
+350
+00:43:45,220 --> 00:43:51,270
+F of X موجودة في ال kernelيبقى هذا معناه ان F of X
+
+351
+00:43:51,270 --> 00:43:59,150
+موجودة في الكيرني للفارق تمام؟ يبقى أخد F of X
+
+352
+00:43:59,150 --> 00:44:03,610
+موجودة في ال principle ID ال generated by X وجدتها
+
+353
+00:44:03,610 --> 00:44:08,070
+موجودة في الكيرني يبقى فاجي بقول للثالث ال
+
+354
+00:44:08,070 --> 00:44:13,070
+principle ID ال generated by X صابست من الكيرني
+
+355
+00:44:13,070 --> 00:44:19,570
+للفارق الأولى هذه العلاقة رقم واحدةهذه العلاقة رقم
+
+356
+00:44:19,570 --> 00:44:27,910
+اتنين بقول له from واحد and اتنين we have ان ال
+
+357
+00:44:27,910 --> 00:44:32,810
+principle او ال kernel الفاية هو ال principle
+
+358
+00:44:32,810 --> 00:44:40,730
+ideal generated by X طبعا شو نشتغل فيه من نفاية و
+
+359
+00:44:40,730 --> 00:44:47,960
+الله كله كلام طب احنا ايش أثبتنافي آخر مثال في
+
+360
+00:44:47,960 --> 00:44:52,520
+chapter 14 ايوة ايوة ايوة ايوة ايوة ايوة ايوة ايوة
+
+361
+00:44:52,520 --> 00:44:55,000
+ايوة ايوة ايوة ايوة ايوة ايوة ايوة ايوة ايوة ايوة
+
+362
+00:44:55,000 --> 00:44:55,740
+ايوة
+
+363
+00:45:16,000 --> 00:45:21,920
+يبقى ضياب لطريقة أسهل للحل من الطريقة اللي حلناها
+
+364
+00:45:21,920 --> 00:45:28,800
+في شفتر أربع عشر آخر مثل كيف الآن لحد هنا انتهى
+
+365
+00:45:28,800 --> 00:45:34,880
+شغلنا فانتبهنا النظرية لكن بدنا نستفيد من هذه
+
+366
+00:45:34,880 --> 00:45:41,940
+النظرية فبجب نقول هنا from from
+
+367
+00:45:41,940 --> 00:45:50,560
+ايزو مارفزن فيرنfrom first isomorphism theorem we
+
+368
+00:45:50,560 --> 00:46:01,880
+have ان ال Z of X اللي هي ال ring modular كيرن
+
+369
+00:46:01,880 --> 00:46:15,020
+للفاي هذه isomorphic لمن؟ للفاي of R للفاي ofz of
+
+370
+00:46:15,020 --> 00:46:18,880
+x مظبوط
+
+371
+00:46:18,880 --> 00:46:26,980
+؟ طيب هنا أثبتنا هذي بالشكل اللي عندنا هذي إبارة
+
+372
+00:46:26,980 --> 00:46:32,680
+عن اللي هو هذي الصورة اللي عندنا لما كانت أنتوا
+
+373
+00:46:32,680 --> 00:46:39,400
+غطتها كلها يعني هذي بقول عليها مين بقول عليها z
+
+374
+00:46:39,400 --> 00:46:46,850
+itself تمام ؟يبقى من ال first isomorphism theorem
+
+375
+00:46:46,850 --> 00:46:53,510
+ال Z of X modular kernel isomorphic لمين لل Phi of
+
+376
+00:46:53,510 --> 00:46:59,950
+R؟ مين R ان دي؟ Z of X Z of X اللي هى مين هنا؟ Z
+
+377
+00:46:59,950 --> 00:47:07,110
+تمام يعني Z أجت مكان Phi of R بالطبع تمام طيب ال
+
+378
+00:47:07,110 --> 00:47:13,210
+kernel هذا أثبت و أنا مين؟بتشيله وحط مدالة الـ
+
+379
+00:47:13,210 --> 00:47:18,250
+principal ideal generated by X يبقى هذا بده يعطينا
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..4fccdebd35f20dcba6639c834479a23782f3d064
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 5043, "start": 20.99, "end": 50.43, "text": "بسم الله الرحمن الرحيم نكمل اليوم ما ابتدأناه في المرة الماضية وهو موضوع ال ring homomorphism اللي هو chapter 15 من الكتاب فينا نظرية اليوم، النظرية بتقول افترض ان Phi من R الى S عبارة عن ring homomorphism نحاول نثبت ان ال kernel لهذا ال homomorphism هو عبارة عن ideal", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 24793, 1211, 45595, 20498, 19446, 48127, 2655, 3215, 10721, 8315, 3224, 8978, 9673, 25720, 9673, 46958, 10632, 37037, 2407, 3714, 2407, 11242, 45367, 2423, 4875, 3655, 32702, 1434, 13672, 1829, 31439, 7187, 2119, 9154, 33251, 2655, 16758, 8978, 8315, 8717, 19913, 2288, 10632, 45595, 20498, 12399, 28239, 19913, 2288, 10632, 39894, 39648, 1975, 5172, 2655, 43042, 16472, 41435, 9154, 497, 2423, 7578, 318, 6225, 3555, 9640, 3660, 18871, 4875, 3655, 32702, 1434, 8717, 5016, 995, 12610, 8717, 12984, 3555, 2655, 16472, 2423, 28256, 46740, 15730, 2423, 3655, 32702, 1434, 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0.89013671875}, {"start": 248.07, "end": 248.23, "word": " ال", "probability": 0.849609375}, {"start": 248.23, "end": 248.67, "word": " kernel", "probability": 0.7314453125}, {"start": 248.67, "end": 249.67, "word": " صار", "probability": 0.9697265625}, {"start": 249.67, "end": 250.35, "word": " عبارة", "probability": 0.9930419921875}, {"start": 250.35, "end": 250.81, "word": " عن", "probability": 0.990234375}, {"start": 250.81, "end": 251.49, "word": " id", "probability": 0.1876220703125}, {"start": 251.49, "end": 252.49, "word": " يبقى", "probability": 0.9666748046875}, {"start": 252.49, "end": 252.89, "word": " بجي", "probability": 0.7449544270833334}, {"start": 252.89, "end": 253.85, "word": " بقوله", "probability": 0.7950846354166666}, {"start": 253.85, "end": 254.47, "word": " if", "probability": 0.55712890625}, {"start": 254.47, "end": 255.57, "word": " ال", "probability": 0.92724609375}, {"start": 255.57, "end": 256.23, "word": " R", "probability": 0.63623046875}, {"start": 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وين بدها تكون موجودة؟ في S يبقى then ال Phi of R موجودة في S and ال Phi of X بدها تسوي قداش Zero", "tokens": [6027, 39184, 1783, 3714, 29245, 23328, 8978, 9122, 13546, 1863, 2423, 39184, 41435, 2423, 39184, 41435, 295, 497, 4032, 9957, 47525, 11296, 6055, 30544, 3714, 29245, 23328, 3660, 22807, 8978, 318, 7251, 3555, 4587, 7578, 550, 2423, 41435, 295, 497, 3714, 29245, 23328, 3660, 8978, 318, 293, 2423, 41435, 295, 1783, 47525, 11296, 6055, 3794, 45865, 12174, 3215, 33599, 17182], "avg_logprob": -0.39779712919329036, "compression_ratio": 1.5648854961832062, "no_speech_prob": 0.0, "words": [{"start": 265.37, "end": 267.21, "word": "الـ", "probability": 0.3485107421875}, {"start": 267.21, "end": 267.57, "word": " X", "probability": 0.30126953125}, {"start": 267.57, "end": 269.11, "word": " موجود", "probability": 0.9765625}, {"start": 269.11, "end": 269.43, "word": " في", "probability": 0.85888671875}, {"start": 269.43, "end": 270.69, "word": " كيرن", "probability": 0.6537272135416666}, 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"word": " يبقى", "probability": 0.7293701171875}, {"start": 282.63, "end": 283.41, "word": " then", "probability": 0.128173828125}, {"start": 283.41, "end": 284.21, "word": " ال", "probability": 0.72802734375}, {"start": 284.21, "end": 284.67, "word": " Phi", "probability": 0.78857421875}, {"start": 284.67, "end": 285.29, "word": " of", "probability": 0.9658203125}, {"start": 285.29, "end": 285.89, "word": " R", "probability": 0.951171875}, {"start": 285.89, "end": 287.31, "word": " موجودة", "probability": 0.986083984375}, {"start": 287.31, "end": 287.67, "word": " في", "probability": 0.9814453125}, {"start": 287.67, "end": 288.25, "word": " S", "probability": 0.98486328125}, {"start": 288.25, "end": 289.47, "word": " and", "probability": 0.70654296875}, {"start": 289.47, "end": 290.57, "word": " ال", "probability": 0.77001953125}, {"start": 290.57, "end": 291.05, "word": " Phi", "probability": 0.96337890625}, {"start": 291.05, "end": 291.73, "word": " of", "probability": 0.96484375}, {"start": 291.73, "end": 292.31, "word": " X", "probability": 0.99560546875}, {"start": 292.31, "end": 292.89, "word": " بدها", "probability": 0.986083984375}, {"start": 292.89, "end": 293.29, "word": " تسوي", "probability": 0.7271321614583334}, {"start": 293.29, "end": 294.01, "word": " قداش", "probability": 0.6029459635416666}, {"start": 294.01, "end": 294.05, "word": " Zero", "probability": 0.67822265625}], "temperature": 1.0}, {"id": 11, "seek": 32395, "start": 295.51, "end": 323.95, "text": "بنروح أخد Phi of R في X نظرا لإن ال Phi عبارة عن homomorphism إذا الهدف بده يساوي Phi of R في Phi of X Phi of X عندي بقداشر هشيلها و أحط مكانها Zero يبقى بده يساوي Phi of R is Zero اللي هو بده يساوي قداشر؟ Zero", "tokens": [3555, 1863, 32887, 5016, 5551, 9778, 3215, 41435, 295, 497, 8978, 1783, 8717, 19913, 23557, 5296, 28814, 1863, 2423, 41435, 6225, 3555, 9640, 3660, 18871, 3655, 32702, 1434, 11933, 15730, 2423, 3224, 3215, 5172, 47525, 3224, 7251, 3794, 995, 45865, 41435, 295, 497, 8978, 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{"start": 300.01, "end": 301.45, "word": " نظرا", "probability": 0.9088541666666666}, {"start": 301.45, "end": 302.01, "word": " لإن", "probability": 0.70263671875}, {"start": 302.01, "end": 302.25, "word": " ال", "probability": 0.4765625}, {"start": 302.25, "end": 302.55, "word": " Phi", "probability": 0.68701171875}, {"start": 302.55, "end": 303.11, "word": " عبارة", "probability": 0.9222412109375}, {"start": 303.11, "end": 303.35, "word": " عن", "probability": 0.99560546875}, {"start": 303.35, "end": 304.73, "word": " homomorphism", "probability": 0.7845052083333334}, {"start": 304.73, "end": 305.51, "word": " إذا", "probability": 0.9462890625}, {"start": 305.51, "end": 306.09, "word": " الهدف", "probability": 0.9481201171875}, {"start": 306.09, "end": 306.55, "word": " بده", "probability": 0.469970703125}, {"start": 306.55, "end": 307.17, "word": " يساوي", "probability": 0.9273681640625}, {"start": 307.17, "end": 307.61, "word": " Phi", "probability": 0.92578125}, {"start": 307.61, "end": 308.33, "word": " of", "probability": 0.97314453125}, {"start": 308.33, "end": 308.95, "word": " R", "probability": 0.966796875}, {"start": 308.95, "end": 309.55, "word": " في", "probability": 0.88671875}, {"start": 309.55, "end": 310.29, "word": " Phi", "probability": 0.9169921875}, {"start": 310.29, "end": 310.69, "word": " of", "probability": 0.9765625}, {"start": 310.69, "end": 311.05, "word": " X", "probability": 0.99609375}, {"start": 311.05, "end": 311.85, "word": " Phi", "probability": 0.9228515625}, {"start": 311.85, "end": 312.09, "word": " of", "probability": 0.98193359375}, {"start": 312.09, "end": 312.37, "word": " X", "probability": 0.98486328125}, {"start": 312.37, "end": 312.67, "word": " عندي", "probability": 0.80615234375}, {"start": 312.67, "end": 313.51, "word": " بقداشر", "probability": 0.63720703125}, {"start": 313.51, "end": 314.67, "word": " هشيلها", "probability": 0.80560302734375}, {"start": 314.67, "end": 314.83, "word": " و", "probability": 0.9306640625}, {"start": 314.83, "end": 315.11, "word": " أحط", "probability": 0.87890625}, {"start": 315.11, "end": 315.77, "word": " مكانها", "probability": 0.9915364583333334}, {"start": 315.77, "end": 316.27, "word": " Zero", "probability": 0.55615234375}, {"start": 316.27, "end": 317.09, "word": " يبقى", "probability": 0.9420166015625}, {"start": 317.09, "end": 317.55, "word": " بده", "probability": 0.9267578125}, {"start": 317.55, "end": 318.21, "word": " يساوي", "probability": 0.98779296875}, {"start": 318.21, "end": 319.01, "word": " Phi", "probability": 0.931640625}, {"start": 319.01, "end": 319.69, "word": " of", "probability": 0.97802734375}, {"start": 319.69, "end": 320.37, "word": " R", "probability": 0.99560546875}, {"start": 320.37, "end": 320.87, "word": " is", "probability": 0.416748046875}, {"start": 320.87, "end": 321.31, "word": " Zero", "probability": 0.83642578125}, {"start": 321.31, "end": 321.79, "word": " اللي", "probability": 0.6893310546875}, {"start": 321.79, "end": 321.91, "word": " هو", "probability": 0.97900390625}, {"start": 321.91, "end": 322.17, "word": " بده", "probability": 0.900390625}, {"start": 322.17, "end": 322.43, "word": " يساوي", "probability": 0.98876953125}, {"start": 322.43, "end": 323.25, "word": " قداشر؟", "probability": 0.850146484375}, {"start": 323.25, "end": 323.95, "word": " Zero", "probability": 0.95751953125}], "temperature": 1.0}, {"id": 12, "seek": 35388, "start": 324.3, "end": 353.88, "text": "إذا صار تأثير Phi على ال element Rx بده يساوي Zero معناه هذا الكلام ان ال Rx موجودة وين؟ في ال Kern اللي فيه بنفس الطريقة Similarly بنفس الطريقة اللي هو ال XR موجودة في ال Kern اللي مين؟ في ال Phi يبقى أثبتنا شروط ال Ideal وخلصنا", "tokens": [28814, 15730, 20328, 9640, 6055, 10721, 12984, 13546, 41435, 15844, 2423, 4478, 497, 87, 47525, 3224, 7251, 3794, 995, 45865, 17182, 20449, 8315, 3224, 23758, 2423, 28820, 10943, 16472, 2423, 497, 87, 3714, 29245, 23328, 3660, 4032, 9957, 22807, 8978, 2423, 40224, 13672, 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0.7001139322916666}, {"start": 335.32, "end": 336.02, "word": " في", "probability": 0.56884765625}, {"start": 336.02, "end": 336.02, "word": " ال", "probability": 0.86474609375}, {"start": 336.02, "end": 336.6, "word": " Kern", "probability": 0.568359375}, {"start": 336.6, "end": 336.9, "word": " اللي", "probability": 0.8671875}, {"start": 336.9, "end": 337.44, "word": " فيه", "probability": 0.7139892578125}, {"start": 337.44, "end": 338.1, "word": " بنفس", "probability": 0.82080078125}, {"start": 338.1, "end": 338.98, "word": " الطريقة", "probability": 0.9931640625}, {"start": 338.98, "end": 340.06, "word": " Similarly", "probability": 0.42578125}, {"start": 340.06, "end": 342.42, "word": " بنفس", "probability": 0.851318359375}, {"start": 342.42, "end": 343.26, "word": " الطريقة", "probability": 0.99462890625}, {"start": 343.26, "end": 343.98, "word": " اللي", "probability": 0.952880859375}, {"start": 343.98, "end": 344.24, "word": " هو", "probability": 0.74462890625}, {"start": 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أثبتنا", "probability": 0.98095703125}, {"start": 350.72, "end": 351.24, "word": " شروط", "probability": 0.9347330729166666}, {"start": 351.24, "end": 351.44, "word": " ال", "probability": 0.955078125}, {"start": 351.44, "end": 352.62, "word": " Ideal", "probability": 0.79443359375}, {"start": 352.62, "end": 353.88, "word": " وخلصنا", "probability": 0.85205078125}], "temperature": 1.0}, {"id": 13, "seek": 38261, "start": 354.15, "end": 382.61, "text": "يبقى بقول الله صحيح وهكذا الـ Kernel للـ Phi is an ideal of R وهو المفروض بنجي الآن للنظرية التي تليها وهذه نظرية مهمة ومشهورة في كل كتب الجبر اللي بيسموها ال first isomorphism", "tokens": [1829, 3555, 4587, 7578, 4724, 39648, 21984, 20328, 5016, 1829, 5016, 37037, 4117, 15730, 2423, 39184, 40224, 338, 24976, 39184, 41435, 307, 364, 7157, 295, 497, 37037, 2407, 9673, 5172, 32887, 11242, 44945, 7435, 1829, 6024, 48506, 24976, 1863, 19913, 2288, 10632, 38392, 6055, 20292, 11296, 37037, 24192, 8717, 19913, 2288, 10632, 3714, 16095, 3660, 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0.841064453125}], "temperature": 1.0}, {"id": 23, "seek": 67513, "start": 645.91, "end": 675.13, "text": "كيف عرفنا كيف علمنا كتثبت هذا well defined؟ بنقول عكس اثبات انه لبساي one to one يعني انا باخد عنصرين متساويين و باثبت ان صورتيهما متساويتان، مظبوط هيك؟ يبقى بلاء العلم دي اقوله let افترض ان اه الواحد زي ال kernel للفعل", "tokens": [4117, 33911, 6225, 28480, 8315, 9122, 33911, 11203, 2304, 8315, 9122, 2655, 12984, 3555, 2655, 23758, 731, 7642, 22807, 44945, 39648, 6225, 4117, 3794, 1975, 12984, 3555, 9307, 16472, 3224, 5296, 3555, 3794, 47302, 472, 281, 472, 37495, 22653, 1975, 8315, 4724, 47283, 3215, 18871, 9381, 2288, 9957, 44650, 3794, 995, 45865, 9957, 4032, 4724, 995, 12984, 3555, 2655, 16472, 20328, 13063, 31371, 3224, 15042, 44650, 3794, 995, 45865, 2655, 7649, 12399, 3714, 19913, 3555, 2407, 9566, 39896, 4117, 22807, 7251, 3555, 4587, 7578, 4724, 1211, 16606, 18863, 19528, 11778, 1829, 1975, 39648, 3224, 718, 1975, 5172, 2655, 43042, 16472, 1975, 3224, 2423, 14407, 24401, 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"word": " للـPhi", "probability": 0.49847412109375}], "temperature": 1.0}, {"id": 40, "seek": 116266, "start": 1134.64, "end": 1162.66, "text": "بتساوي F Psi of R2 زائد الكيرن للـ Phi ثم هذه مين صورتها؟ Phi of R1 والتانية صورتها مين؟ Phi of R1 بتساوي Phi of R2", "tokens": [3555, 2655, 3794, 995, 45865, 479, 430, 7691, 295, 497, 17, 30767, 16373, 3215, 33251, 13546, 1863, 24976, 39184, 41435, 38637, 2304, 29538, 3714, 9957, 20328, 13063, 2655, 11296, 22807, 41435, 295, 497, 16, 16070, 2655, 7649, 10632, 20328, 13063, 2655, 11296, 3714, 9957, 22807, 41435, 295, 497, 16, 39894, 3794, 995, 45865, 41435, 295, 497, 17], "avg_logprob": -0.28529094365136376, "compression_ratio": 1.3951612903225807, "no_speech_prob": 0.0, "words": [{"start": 1134.64, "end": 1135.72, "word": "بتساوي", "probability": 0.84208984375}, {"start": 1135.72, "end": 1136.14, "word": " F", "probability": 0.255859375}, {"start": 1136.14, "end": 1136.74, "word": " Psi", "probability": 0.54412841796875}, {"start": 1136.74, 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1150.8, "word": " R1", "probability": 0.9931640625}, {"start": 1150.8, "end": 1152.34, "word": " والتانية", "probability": 0.8094482421875}, {"start": 1152.34, "end": 1153.08, "word": " صورتها", "probability": 0.9918212890625}, {"start": 1153.08, "end": 1153.76, "word": " مين؟", "probability": 0.9524739583333334}, {"start": 1153.76, "end": 1155.36, "word": " Phi", "probability": 0.890625}, {"start": 1155.36, "end": 1155.8, "word": " of", "probability": 0.97607421875}, {"start": 1155.8, "end": 1157.38, "word": " R1", "probability": 0.99169921875}, {"start": 1157.38, "end": 1159.44, "word": " بتساوي", "probability": 0.70916748046875}, {"start": 1159.44, "end": 1160.44, "word": " Phi", "probability": 0.92626953125}, {"start": 1160.44, "end": 1161.36, "word": " of", "probability": 0.9775390625}, {"start": 1161.36, "end": 1162.66, "word": " R2", "probability": 0.996826171875}], "temperature": 1.0}, {"id": 41, "seek": 118655, "start": 1163.31, "end": 1186.55, "text": "هذا معناه إن الـ Phi of R1 minus الـ Phi of R2 بديوا يسووا Zero. نرجع، في رأس المسألة Phi هم مورفزيه، إذا هذا بده يعطينا ميم، إن الـ Phi of R1 ناقص R2 بديوا يسووا 200.", "tokens": [3224, 15730, 20449, 8315, 3224, 36145, 2423, 39184, 41435, 295, 497, 16, 3175, 2423, 39184, 41435, 295, 497, 17, 4724, 16254, 14407, 7251, 3794, 2407, 14407, 17182, 13, 8717, 47341, 3615, 12399, 8978, 12602, 10721, 3794, 9673, 3794, 10721, 37977, 41435, 8032, 2304, 3714, 13063, 5172, 11622, 1829, 3224, 12399, 11933, 15730, 23758, 47525, 3224, 7251, 3615, 9566, 1829, 8315, 3714, 32640, 12399, 36145, 2423, 39184, 41435, 295, 497, 16, 8717, 995, 4587, 9381, 497, 17, 4724, 16254, 14407, 7251, 3794, 2407, 14407, 2331, 13], "avg_logprob": -0.2785247009853984, "compression_ratio": 1.5925925925925926, "no_speech_prob": 0.0, "words": [{"start": 1163.31, "end": 1163.89, "word": "هذا", "probability": 0.892578125}, {"start": 1163.89, "end": 1164.75, "word": " معناه", "probability": 0.9676106770833334}, {"start": 1164.75, "end": 1166.13, "word": " إن", "probability": 0.299560546875}, {"start": 1166.13, "end": 1166.57, "word": " الـ", "probability": 0.857421875}, {"start": 1166.57, "end": 1167.09, "word": " Phi", "probability": 0.4091796875}, {"start": 1167.09, "end": 1167.77, "word": " of", "probability": 0.859375}, {"start": 1167.77, "end": 1168.71, "word": " R1", "probability": 0.9482421875}, {"start": 1168.71, "end": 1169.63, "word": " minus", "probability": 0.57568359375}, {"start": 1169.63, "end": 1170.21, "word": " الـ", "probability": 0.8701171875}, {"start": 1170.21, "end": 1170.59, "word": " Phi", "probability": 0.85400390625}, {"start": 1170.59, "end": 1171.15, "word": " of", "probability": 0.97509765625}, {"start": 1171.15, "end": 1172.23, "word": " R2", "probability": 0.998779296875}, {"start": 1172.23, "end": 1172.93, "word": " بديوا", "probability": 0.4383138020833333}, {"start": 1172.93, "end": 1173.31, "word": " يسووا", "probability": 0.824951171875}, {"start": 1173.31, "end": 1173.67, "word": " Zero.", "probability": 0.56201171875}, {"start": 1174.27, "end": 1175.15, "word": " نرجع،", "probability": 0.7611083984375}, {"start": 1175.15, "end": 1175.33, "word": " في", "probability": 0.77685546875}, {"start": 1175.33, "end": 1175.59, "word": " رأس", "probability": 0.9752604166666666}, {"start": 1175.59, "end": 1176.19, "word": " المسألة", "probability": 0.876220703125}, {"start": 1176.19, "end": 1176.53, "word": " Phi", "probability": 0.7685546875}, {"start": 1176.53, "end": 1176.85, "word": " هم", "probability": 0.69580078125}, {"start": 1176.85, "end": 1178.17, "word": " مورفزيه،", "probability": 0.5838099888392857}, {"start": 1178.17, "end": 1178.45, "word": " إذا", "probability": 0.820556640625}, {"start": 1178.45, "end": 1179.03, "word": " هذا", "probability": 0.70458984375}, {"start": 1179.03, "end": 1179.49, "word": " بده", "probability": 0.3841552734375}, {"start": 1179.49, "end": 1180.13, "word": " يعطينا", "probability": 0.8916015625}, {"start": 1180.13, "end": 1181.03, "word": " ميم،", "probability": 0.6123046875}, {"start": 1181.03, "end": 1181.41, "word": " إن", "probability": 0.841796875}, {"start": 1181.41, "end": 1181.81, "word": " الـ", "probability": 0.89892578125}, {"start": 1181.81, "end": 1182.19, "word": " Phi", "probability": 0.82275390625}, {"start": 1182.19, "end": 1182.71, "word": " of", "probability": 0.95556640625}, {"start": 1182.71, "end": 1183.59, "word": " R1", "probability": 0.996826171875}, {"start": 1183.59, "end": 1184.79, "word": " ناقص", "probability": 0.81927490234375}, {"start": 1184.79, "end": 1185.53, "word": " R2", "probability": 0.990478515625}, {"start": 1185.53, "end": 1185.87, "word": " بديوا", "probability": 0.87353515625}, {"start": 1185.87, "end": 1186.17, "word": " يسووا", "probability": 0.9564208984375}, {"start": 1186.17, "end": 1186.55, "word": " 200.", "probability": 0.74267578125}], "temperature": 1.0}, {"id": 42, "seek": 121177, "start": 1190.83, "end": 1211.77, "text": "موجودة في ال kernel يبقى هذا معناه ان ال R1 minus R2 موجودة في ال kernel الفاية او معناه ان ال R1 ناقص R2 زائد ال kernel", "tokens": [2304, 29245, 23328, 3660, 8978, 2423, 28256, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 16472, 2423, 497, 16, 3175, 497, 17, 3714, 29245, 23328, 3660, 8978, 2423, 28256, 27188, 995, 10632, 1975, 2407, 20449, 8315, 3224, 16472, 2423, 497, 16, 8717, 995, 4587, 9381, 497, 17, 30767, 16373, 3215, 2423, 28256], "avg_logprob": -0.26518277852040417, "compression_ratio": 1.564102564102564, "no_speech_prob": 0.0, "words": [{"start": 1190.83, "end": 1192.23, "word": "موجودة", "probability": 0.566650390625}, {"start": 1192.23, "end": 1192.39, "word": " في", "probability": 0.93017578125}, {"start": 1192.39, "end": 1192.53, "word": " ال", "probability": 0.71435546875}, {"start": 1192.53, "end": 1193.13, "word": " kernel", "probability": 0.2392578125}, {"start": 1193.13, "end": 1194.29, "word": " يبقى", "probability": 0.875732421875}, {"start": 1194.29, "end": 1194.71, "word": " هذا", "probability": 0.91162109375}, {"start": 1194.71, "end": 1195.59, "word": " معناه", "probability": 0.9583333333333334}, {"start": 1195.59, "end": 1196.11, "word": " ان", "probability": 0.78466796875}, {"start": 1196.11, "end": 1196.39, "word": " ال", "probability": 0.91943359375}, {"start": 1196.39, "end": 1197.01, "word": " R1", "probability": 0.720947265625}, {"start": 1197.01, "end": 1197.95, "word": " minus", "probability": 0.572265625}, {"start": 1197.95, "end": 1198.99, "word": " R2", "probability": 0.988525390625}, {"start": 1198.99, "end": 1200.53, "word": " موجودة", "probability": 0.9588623046875}, {"start": 1200.53, "end": 1200.75, "word": " في", "probability": 0.94970703125}, {"start": 1200.75, "end": 1201.03, "word": " ال", "probability": 0.74072265625}, {"start": 1201.03, "end": 1201.75, "word": " kernel", "probability": 0.7841796875}, {"start": 1201.75, "end": 1202.89, "word": " الفاية", "probability": 0.4256998697916667}, {"start": 1202.89, "end": 1203.57, "word": " او", "probability": 0.882568359375}, {"start": 1203.57, "end": 1205.03, "word": " معناه", "probability": 0.9724934895833334}, {"start": 1205.03, "end": 1205.83, "word": " ان", "probability": 0.94921875}, {"start": 1205.83, "end": 1206.17, "word": " ال", "probability": 0.83154296875}, {"start": 1206.17, "end": 1207.01, "word": " R1", "probability": 0.96337890625}, {"start": 1207.01, "end": 1208.19, "word": " ناقص", "probability": 0.80224609375}, {"start": 1208.19, "end": 1209.07, "word": " R2", "probability": 0.98388671875}, {"start": 1209.07, "end": 1210.33, "word": " زائد", "probability": 0.94091796875}, {"start": 1210.33, "end": 1210.83, "word": " ال", "probability": 0.79443359375}, {"start": 1210.83, "end": 1211.77, "word": " kernel", "probability": 0.8017578125}], "temperature": 1.0}, {"id": 43, "seek": 124117, "start": 1218.03, "end": 1241.17, "text": "أو بمعنى أخر ار واحد زائد الكيرنل للفاي بده يساوي R اتنين زائد الكيرنل للفاي، مصبوط هم؟ 7.1؟ خلاص؟ يبقى أنا أخد صورتين متساويتين", "tokens": [10721, 2407, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 1975, 2288, 36764, 24401, 30767, 16373, 3215, 33251, 13546, 1863, 1211, 24976, 5172, 47302, 47525, 3224, 7251, 3794, 995, 45865, 497, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 33251, 13546, 1863, 1211, 24976, 5172, 47302, 12399, 3714, 9381, 3555, 2407, 9566, 8032, 2304, 22807, 1614, 13, 16, 22807, 16490, 1211, 33546, 22807, 7251, 3555, 4587, 7578, 41850, 5551, 9778, 3215, 20328, 13063, 2655, 9957, 44650, 3794, 995, 2407, 36081, 9957], "avg_logprob": -0.403125012665987, "compression_ratio": 1.5902777777777777, "no_speech_prob": 0.0, "words": [{"start": 1218.03, "end": 1219.43, "word": "أو", "probability": 0.481292724609375}, {"start": 1219.43, "end": 1220.09, "word": " بمعنى", "probability": 0.86650390625}, {"start": 1220.09, "end": 1220.73, "word": " أخر", "probability": 0.729248046875}, {"start": 1220.73, "end": 1221.69, "word": " ار", "probability": 0.2628173828125}, {"start": 1221.69, "end": 1222.73, "word": " واحد", "probability": 0.884765625}, {"start": 1222.73, "end": 1224.17, "word": " زائد", "probability": 0.830078125}, {"start": 1224.17, "end": 1225.37, "word": " الكيرنل", "probability": 0.751220703125}, {"start": 1225.37, "end": 1226.27, "word": " للفاي", "probability": 0.6205240885416666}, {"start": 1226.27, "end": 1227.09, "word": " بده", "probability": 0.312347412109375}, {"start": 1227.09, "end": 1227.51, "word": " يساوي", "probability": 0.65301513671875}, {"start": 1227.51, "end": 1227.97, "word": " R", "probability": 0.4248046875}, {"start": 1227.97, "end": 1228.73, "word": " اتنين", "probability": 0.8497314453125}, {"start": 1228.73, "end": 1229.97, "word": " زائد", "probability": 0.9189453125}, {"start": 1229.97, "end": 1231.33, "word": " الكيرنل", "probability": 0.9544677734375}, {"start": 1231.33, "end": 1232.17, "word": " للفاي،", "probability": 0.705963134765625}, {"start": 1232.17, "end": 1232.95, "word": " مصبوط", "probability": 0.783251953125}, {"start": 1232.95, "end": 1234.51, "word": " هم؟", "probability": 0.4033610026041667}, {"start": 1234.51, "end": 1234.75, "word": " 7", "probability": 0.189453125}, {"start": 1234.75, "end": 1235.85, "word": ".1؟", "probability": 0.6209309895833334}, {"start": 1235.85, "end": 1237.65, "word": " خلاص؟", "probability": 0.885986328125}, {"start": 1237.65, "end": 1237.99, "word": " يبقى", "probability": 0.9066162109375}, {"start": 1237.99, "end": 1238.27, "word": " أنا", "probability": 0.5546875}, {"start": 1238.27, "end": 1238.83, "word": " أخد", "probability": 0.9025065104166666}, {"start": 1238.83, "end": 1239.75, "word": " صورتين", "probability": 0.8812255859375}, {"start": 1239.75, "end": 1241.17, "word": " متساويتين", "probability": 0.87548828125}], "temperature": 1.0}, {"id": 44, "seek": 126718, "start": 1241.48, "end": 1267.18, "text": "أثبت أن أصليهما متساوين R1 زايد كيرنل للـ Phi يساوي R2 زايد كيرنل للـ Phi بقيت النقطة الأخيرة if Psi is onto R تبقى بدى أروح أخد element في الـ Phi of R", "tokens": [10721, 12984, 3555, 2655, 14739, 5551, 9381, 20292, 3224, 15042, 44650, 3794, 995, 2407, 9957, 497, 16, 30767, 995, 25708, 9122, 13546, 1863, 1211, 24976, 39184, 41435, 7251, 3794, 995, 45865, 497, 17, 30767, 995, 25708, 9122, 13546, 1863, 1211, 24976, 39184, 41435, 4724, 4587, 36081, 28239, 47432, 3660, 16247, 9778, 48923, 498, 430, 7691, 307, 3911, 497, 6055, 3555, 4587, 7578, 47525, 7578, 5551, 32887, 5016, 5551, 9778, 3215, 4478, 8978, 2423, 39184, 41435, 295, 497], "avg_logprob": -0.26221955128205127, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 1241.48, "end": 1242.34, "word": "أثبت", "probability": 0.94677734375}, {"start": 1242.34, "end": 1242.92, "word": " أن", "probability": 0.69970703125}, {"start": 1242.92, "end": 1245.32, "word": " أصليهما", "probability": 0.83916015625}, {"start": 1245.32, "end": 1247.2, "word": " متساوين", "probability": 0.901953125}, {"start": 1247.2, "end": 1248.18, "word": " R1", "probability": 0.658447265625}, {"start": 1248.18, "end": 1248.68, "word": " زايد", "probability": 0.5459798177083334}, {"start": 1248.68, "end": 1249.26, "word": " كيرنل", "probability": 0.8082275390625}, {"start": 1249.26, "end": 1249.64, "word": " للـ", "probability": 0.57861328125}, {"start": 1249.64, "end": 1249.86, "word": " Phi", "probability": 0.20947265625}, {"start": 1249.86, "end": 1250.7, "word": " يساوي", "probability": 0.90234375}, {"start": 1250.7, "end": 1251.38, "word": " R2", "probability": 0.9677734375}, {"start": 1251.38, "end": 1251.92, "word": " زايد", "probability": 0.9879557291666666}, {"start": 1251.92, "end": 1252.64, "word": " كيرنل", "probability": 0.990966796875}, {"start": 1252.64, "end": 1252.94, "word": " للـ", "probability": 0.93603515625}, {"start": 1252.94, "end": 1253.24, "word": " Phi", "probability": 0.81689453125}, {"start": 1253.24, "end": 1254.16, "word": " بقيت", "probability": 0.7771809895833334}, {"start": 1254.16, "end": 1255.16, "word": " النقطة", "probability": 0.982421875}, {"start": 1255.16, "end": 1256.14, "word": " الأخيرة", "probability": 0.9752604166666666}, {"start": 1256.14, "end": 1256.94, "word": " if", "probability": 0.258544921875}, {"start": 1256.94, "end": 1257.58, "word": " Psi", "probability": 0.7037353515625}, {"start": 1257.58, "end": 1258.34, "word": " is", "probability": 0.955078125}, {"start": 1258.34, "end": 1259.22, "word": " onto", "probability": 0.2264404296875}, {"start": 1259.22, "end": 1259.64, "word": " R", "probability": 0.318359375}, {"start": 1259.64, "end": 1263.02, "word": " تبقى", "probability": 0.806396484375}, {"start": 1263.02, "end": 1263.26, "word": " بدى", "probability": 0.3553466796875}, {"start": 1263.26, "end": 1263.52, "word": " أروح", "probability": 0.8904622395833334}, {"start": 1263.52, "end": 1264.18, "word": " أخد", "probability": 0.8380533854166666}, {"start": 1264.18, "end": 1265.12, "word": " element", "probability": 0.71435546875}, {"start": 1265.12, "end": 1265.58, "word": " في", "probability": 0.9228515625}, 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{"id": 56, "seek": 163284, "start": 1605.62, "end": 1632.84, "text": "ان الكيرنل هذا هو ايش المعرف بهذه الطريقة هو عبارة عن الكيرنل تبع هذه الـ Phi مرة تانية ال ideal A اللي أخده من ال ring R هو يمثل الكيرنل لهذه ال function يبقى أنا بدي أعمل قطوة تانية", "tokens": [7649, 33251, 13546, 1863, 1211, 23758, 31439, 1975, 1829, 8592, 9673, 3615, 28480, 39627, 24192, 41950, 16572, 28671, 31439, 6225, 3555, 9640, 3660, 18871, 33251, 13546, 1863, 1211, 6055, 3555, 3615, 29538, 2423, 39184, 41435, 3714, 25720, 6055, 7649, 10632, 2423, 7157, 316, 13672, 1829, 5551, 9778, 3215, 3224, 9154, 2423, 4875, 497, 31439, 7251, 2304, 12984, 1211, 33251, 13546, 1863, 1211, 46740, 24192, 2423, 2445, 7251, 3555, 4587, 7578, 41850, 4724, 16254, 5551, 25957, 1211, 12174, 9566, 2407, 3660, 6055, 7649, 10632], "avg_logprob": -0.22488839356672197, "compression_ratio": 1.6813186813186813, "no_speech_prob": 0.0, "words": [{"start": 1605.62, "end": 1606.1, "word": "ان", "probability": 0.1888427734375}, {"start": 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"word": " قطوة", "probability": 0.875}, {"start": 1632.52, "end": 1632.84, "word": " تانية", "probability": 0.787109375}], "temperature": 1.0}, {"id": 57, "seek": 165315, "start": 1632.99, "end": 1653.15, "text": "الخطوة الأولى بدي أثبت انه Phi homomorphism المعطى اثنين بدي أثبت ان الكيرن لهذه ال Phi هو ال ideal A إذا تم ذلك من خلاص برهنة نظرية والحمد لله يبقى هنا ال proof بدي أمشي بالشكل التام", "tokens": [6027, 9778, 9566, 2407, 3660, 16247, 12610, 7578, 4724, 16254, 5551, 12984, 3555, 2655, 16472, 3224, 41435, 3655, 32702, 1434, 9673, 3615, 9566, 7578, 1975, 12984, 1863, 9957, 4724, 16254, 5551, 12984, 3555, 2655, 16472, 33251, 13546, 1863, 46740, 24192, 2423, 41435, 31439, 2423, 7157, 316, 11933, 15730, 46811, 29910, 23275, 9154, 16490, 1211, 33546, 4724, 2288, 3224, 1863, 3660, 8717, 19913, 2288, 10632, 16070, 35571, 3215, 24976, 3224, 7251, 3555, 4587, 7578, 34105, 2423, 8177, 4724, 16254, 5551, 2304, 8592, 1829, 20666, 8592, 28820, 16712, 10943], "avg_logprob": 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{"id": 59, "seek": 171520, "start": 1686.54, "end": 1715.2, "text": "هذا الكلام يسوي حسب ال definition اللي عندك يسوي R1 زائد R2 زائد ال ideal A يبقى R1 زائد R2 زائد ال ideal A اللي بقدر اكتبه على الشكل التالي R1 زائد ال ideal A زائد ال R2 زائد ال ideal A", "tokens": [3224, 15730, 2423, 28820, 10943, 7251, 3794, 45865, 11331, 35457, 2423, 7123, 13672, 1829, 43242, 4117, 7251, 3794, 45865, 497, 16, 30767, 16373, 3215, 497, 17, 30767, 16373, 3215, 2423, 7157, 316, 7251, 3555, 4587, 7578, 497, 16, 30767, 16373, 3215, 497, 17, 30767, 16373, 3215, 2423, 7157, 316, 13672, 1829, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 3224, 15844, 25124, 28820, 16712, 6027, 1829, 497, 16, 30767, 16373, 3215, 2423, 7157, 316, 30767, 16373, 3215, 2423, 497, 17, 30767, 16373, 3215, 2423, 7157, 316], "avg_logprob": -0.12300145444135334, "compression_ratio": 1.952054794520548, "no_speech_prob": 0.0, "words": [{"start": 1686.54, "end": 1686.98, "word": "هذا", "probability": 0.954345703125}, {"start": 1686.98, 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"end": 1704.66, "word": " بقدر", "probability": 0.84814453125}, {"start": 1704.66, "end": 1705.22, "word": " اكتبه", "probability": 0.85888671875}, {"start": 1705.22, "end": 1705.38, "word": " على", "probability": 0.82080078125}, {"start": 1705.38, "end": 1705.94, "word": " الشكل", "probability": 0.98046875}, {"start": 1705.94, "end": 1706.54, "word": " التالي", "probability": 0.9581705729166666}, {"start": 1706.54, "end": 1707.92, "word": " R1", "probability": 0.9375}, {"start": 1707.92, "end": 1708.88, "word": " زائد", "probability": 0.9737955729166666}, {"start": 1708.88, "end": 1709.12, "word": " ال", "probability": 0.95458984375}, {"start": 1709.12, "end": 1709.8, "word": " ideal", "probability": 0.94384765625}, {"start": 1709.8, "end": 1710.42, "word": " A", "probability": 0.99169921875}, {"start": 1710.42, "end": 1711.46, "word": " زائد", "probability": 0.990234375}, {"start": 1711.46, "end": 1711.72, "word": " ال", "probability": 0.91845703125}, {"start": 1711.72, "end": 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"end": 1720.97, "word": " هذه", "probability": 0.6328125}, {"start": 1720.97, "end": 1722.09, "word": " FI", "probability": 0.864013671875}, {"start": 1722.09, "end": 1722.53, "word": " of", "probability": 0.9248046875}, {"start": 1722.53, "end": 1723.51, "word": " R1", "probability": 0.987060546875}, {"start": 1723.51, "end": 1724.41, "word": " plus", "probability": 0.470703125}, {"start": 1724.41, "end": 1725.67, "word": " FI", "probability": 0.9462890625}, {"start": 1725.67, "end": 1726.31, "word": " of", "probability": 0.96240234375}, {"start": 1726.31, "end": 1727.19, "word": " R2", "probability": 0.98974609375}, {"start": 1727.19, "end": 1728.99, "word": " and", "probability": 0.52001953125}, {"start": 1728.99, "end": 1731.47, "word": " تاخد", "probability": 0.66949462890625}, {"start": 1731.47, "end": 1732.21, "word": " FI", "probability": 0.918701171875}, {"start": 1732.21, "end": 1732.53, "word": " of", "probability": 0.96875}, {"start": 1732.53, "end": 1733.77, "word": " R1", "probability": 0.994384765625}, {"start": 1733.77, "end": 1734.55, "word": " مضروبة", "probability": 0.884033203125}, {"start": 1734.55, "end": 1734.83, "word": " في", "probability": 0.939453125}, {"start": 1734.83, "end": 1735.57, "word": " R2", "probability": 0.987548828125}, {"start": 1735.57, "end": 1736.65, "word": " يبقى", "probability": 0.9813232421875}, {"start": 1736.65, "end": 1737.55, "word": " R1", "probability": 0.9716796875}, {"start": 1737.55, "end": 1739.05, "word": " R2", "probability": 0.821044921875}, {"start": 1739.05, "end": 1740.31, "word": " زائد", "probability": 0.8777669270833334}, {"start": 1740.31, "end": 1740.69, "word": " ال", "probability": 0.7666015625}, {"start": 1740.69, "end": 1741.03, "word": " A", "probability": 0.2042236328125}, {"start": 1741.03, "end": 1742.09, "word": " اللي", "probability": 0.860595703125}, {"start": 1742.09, "end": 1742.53, "word": " بقدر", "probability": 0.9664713541666666}, {"start": 1742.53, "end": 1743.11, "word": " اكتبه", "probability": 0.82890625}, {"start": 1743.11, "end": 1743.33, "word": " على", "probability": 0.818359375}, {"start": 1743.33, "end": 1743.87, "word": " صيغة", "probability": 0.641143798828125}, {"start": 1743.87, "end": 1745.03, "word": " حاصل", "probability": 0.7939453125}, {"start": 1745.03, "end": 1745.51, "word": " ضرب", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 61, "seek": 177390, "start": 1745.84, "end": 1773.9, "text": "الـ two elements R1 plus A في R2 plus A يعني اللي هو mean Phi of R1 في Phi of R2 so Phi is a homomorphism الجدال اللي أعطاه هالي هذا ال mapping أثبت له", "tokens": [6027, 39184, 732, 4959, 497, 16, 1804, 316, 8978, 497, 17, 1804, 316, 37495, 22653, 13672, 1829, 31439, 914, 41435, 295, 497, 16, 8978, 41435, 295, 497, 17, 370, 41435, 307, 257, 3655, 32702, 1434, 25724, 3215, 6027, 13672, 1829, 5551, 3615, 9566, 40294, 8032, 6027, 1829, 23758, 2423, 18350, 5551, 12984, 3555, 2655, 46740], "avg_logprob": -0.3571428677865437, "compression_ratio": 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اللي", "probability": 0.6778564453125}, {"start": 1753.92, "end": 1754.16, "word": " هو", "probability": 0.978515625}, {"start": 1754.16, "end": 1754.52, "word": " mean", "probability": 0.11724853515625}, {"start": 1754.52, "end": 1755.32, "word": " Phi", "probability": 0.2685546875}, {"start": 1755.32, "end": 1755.78, "word": " of", "probability": 0.88232421875}, {"start": 1755.78, "end": 1756.7, "word": " R1", "probability": 0.988525390625}, {"start": 1756.7, "end": 1757.36, "word": " في", "probability": 0.85107421875}, {"start": 1757.36, "end": 1758.12, "word": " Phi", "probability": 0.8857421875}, {"start": 1758.12, "end": 1759.02, "word": " of", "probability": 0.96875}, {"start": 1759.02, "end": 1760.6, "word": " R2", "probability": 0.997314453125}, {"start": 1760.6, "end": 1761.76, "word": " so", "probability": 0.10601806640625}, {"start": 1761.76, "end": 1764.18, "word": " Phi", "probability": 0.73193359375}, {"start": 1764.18, "end": 1765.42, "word": " is", "probability": 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1795.87, "text": "إنه هي homomorphism وهي المعرفة بهذا الشكل.بدي أثبت إن كيرن لـ Phi هو مين هو الـ ideal إيه؟ يبقى باجي بقوله finally I want to prove that", "tokens": [28814, 1863, 3224, 39896, 3655, 32702, 1434, 37037, 1829, 9673, 3615, 28480, 3660, 39627, 15730, 25124, 28820, 13, 3555, 16254, 5551, 12984, 3555, 2655, 36145, 9122, 13546, 1863, 5296, 39184, 41435, 31439, 3714, 9957, 31439, 2423, 39184, 7157, 11933, 1829, 3224, 22807, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 2721, 286, 528, 281, 7081, 300], "avg_logprob": -0.3281249878770214, "compression_ratio": 1.2242424242424241, "no_speech_prob": 0.0, "words": [{"start": 1774.13, "end": 1774.63, "word": "إنه", "probability": 0.6724446614583334}, {"start": 1774.63, "end": 1774.95, "word": " هي", "probability": 0.73486328125}, {"start": 1774.95, "end": 1776.27, "word": " homomorphism", "probability": 0.8307291666666666}, {"start": 1776.27, "end": 1776.67, "word": " وهي", "probability": 0.64453125}, {"start": 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{"start": 2008.26, "end": 2008.9, "word": " أخدت", "probability": 0.887451171875}, {"start": 2008.9, "end": 2009.06, "word": " ال", "probability": 0.95703125}, {"start": 2009.06, "end": 2009.3, "word": " X", "probability": 0.978515625}, {"start": 2009.3, "end": 2009.92, "word": " موجودة", "probability": 0.9814453125}, {"start": 2009.92, "end": 2010.06, "word": " في", "probability": 0.94921875}, {"start": 2010.06, "end": 2010.26, "word": " ال", "probability": 0.8603515625}, {"start": 2010.26, "end": 2010.72, "word": " ID", "probability": 0.72314453125}, {"start": 2010.72, "end": 2011.08, "word": " ال", "probability": 0.3955078125}, {"start": 2011.08, "end": 2011.4, "word": " A", "probability": 0.583984375}, {"start": 2011.4, "end": 2012.24, "word": " طلعت", "probability": 0.9345703125}, {"start": 2012.24, "end": 2012.44, "word": " ال", "probability": 0.97412109375}, {"start": 2012.44, "end": 2012.68, "word": " X", "probability": 0.99462890625}, {"start": 2012.68, "end": 2013.28, "word": " موجودة", "probability": 0.99072265625}, {"start": 2013.28, "end": 2013.98, "word": " وين؟", "probability": 0.6221516927083334}, {"start": 2013.98, "end": 2014.28, "word": " في", "probability": 0.69384765625}, {"start": 2014.28, "end": 2014.72, "word": " ال", "probability": 0.95068359375}, {"start": 2014.72, "end": 2015.26, "word": " kernel", "probability": 0.841796875}, {"start": 2015.26, "end": 2016.38, "word": " فبروح", "probability": 0.90234375}, {"start": 2016.38, "end": 2016.88, "word": " بقول", "probability": 0.934326171875}, {"start": 2016.88, "end": 2017.2, "word": " له", "probability": 0.2734375}, {"start": 2017.2, "end": 2017.6, "word": " Sir", "probability": 0.365478515625}, {"start": 2017.6, "end": 2018.28, "word": " ال", "probability": 0.92041015625}, {"start": 2018.28, "end": 2018.78, "word": " ID", "probability": 0.97412109375}, {"start": 2018.78, "end": 2019.06, "word": " ال", "probability": 0.8837890625}, {"start": 2019.06, "end": 2019.48, "word": " A", "probability": 0.97802734375}, {"start": 2019.48, "end": 2020.9, "word": " صابست", "probability": 0.7127278645833334}, {"start": 2020.9, "end": 2021.26, "word": " من", "probability": 0.9931640625}, {"start": 2021.26, "end": 2021.58, "word": " ال", "probability": 0.91162109375}, {"start": 2021.58, "end": 2022.0, "word": " kernel", "probability": 0.86572265625}, {"start": 2022.0, "end": 2022.92, "word": " للفاي", "probability": 0.8720703125}, {"start": 2022.92, "end": 2023.88, "word": " وهذه", "probability": 0.643798828125}, {"start": 2023.88, "end": 2024.52, "word": " العلاقة", "probability": 0.9264322916666666}, {"start": 2024.52, "end": 2025.18, "word": " رقم", "probability": 0.9915364583333334}, {"start": 2025.18, "end": 2025.74, "word": " اتنين", "probability": 0.7896728515625}, {"start": 2025.74, "end": 2026.74, "word": " طلعولي", "probability": 0.834521484375}, {"start": 2026.74, "end": 2026.94, "word": " من", "probability": 0.99072265625}, {"start": 2026.94, "end": 2027.32, "word": " واحد", "probability": 0.975830078125}, {"start": 2027.32, "end": 2028.12, "word": " واتنين", "probability": 0.84393310546875}], "temperature": 1.0}, {"id": 71, "seek": 205654, "start": 2028.42, "end": 2056.54, "text": "طب اروح و اقول from واحد and اتنين we have ان الكيرنل للـ Phi بده يساوي ال ideal A كما هو مطلوب في النظرية يبقى ال ideal A هو الكيرنل لمين لهذا ال homomorphism نعطي مثال", "tokens": [9566, 3555, 1975, 32887, 5016, 4032, 1975, 39648, 490, 36764, 24401, 293, 1975, 2655, 1863, 9957, 321, 362, 16472, 33251, 13546, 1863, 1211, 24976, 39184, 41435, 47525, 3224, 7251, 3794, 995, 45865, 2423, 7157, 316, 9122, 15042, 31439, 3714, 9566, 1211, 37746, 8978, 28239, 19913, 2288, 10632, 7251, 3555, 4587, 7578, 2423, 7157, 316, 31439, 33251, 13546, 1863, 1211, 32767, 9957, 46740, 15730, 2423, 3655, 32702, 1434, 8717, 3615, 9566, 1829, 50113, 6027], "avg_logprob": -0.29645268900974375, "compression_ratio": 1.4775280898876404, "no_speech_prob": 0.0, "words": [{"start": 2028.42, 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2039.9, "word": " للـ", "probability": 0.40484619140625}, {"start": 2039.9, "end": 2040.16, "word": " Phi", "probability": 0.1707763671875}, {"start": 2040.16, "end": 2040.96, "word": " بده", "probability": 0.44818115234375}, {"start": 2040.96, "end": 2041.42, "word": " يساوي", "probability": 0.9254150390625}, {"start": 2041.42, "end": 2041.64, "word": " ال", "probability": 0.92578125}, {"start": 2041.64, "end": 2042.3, "word": " ideal", "probability": 0.54345703125}, {"start": 2042.3, "end": 2042.82, "word": " A", "probability": 0.6484375}, {"start": 2042.82, "end": 2043.66, "word": " كما", "probability": 0.964599609375}, {"start": 2043.66, "end": 2043.96, "word": " هو", "probability": 0.9931640625}, {"start": 2043.96, "end": 2044.94, "word": " مطلوب", "probability": 0.89892578125}, {"start": 2044.94, "end": 2045.32, "word": " في", "probability": 0.85009765625}, {"start": 2045.32, "end": 2046.52, "word": " النظرية", "probability": 0.9063720703125}, {"start": 2046.52, "end": 2048.52, 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72, "seek": 208533, "start": 2059.81, "end": 2085.33, "text": "نربط هذا المثال بال chapter الماضي ال example بيقول ما يعني show that five المعرفة من z of x onto", "tokens": [1863, 25513, 9566, 23758, 9673, 12984, 6027, 20666, 7187, 9673, 46958, 1829, 2423, 1365, 4724, 1829, 39648, 19446, 37495, 22653, 855, 300, 1732, 9673, 3615, 28480, 3660, 9154, 710, 295, 2031, 3911], "avg_logprob": -0.37263257575757575, "compression_ratio": 1.205128205128205, "no_speech_prob": 0.0, "words": [{"start": 2059.81, "end": 2060.85, "word": "نربط", "probability": 0.7635091145833334}, {"start": 2060.85, "end": 2061.23, "word": " هذا", "probability": 0.71923828125}, {"start": 2061.23, "end": 2062.19, "word": " المثال", "probability": 0.955078125}, {"start": 2062.19, "end": 2062.93, "word": " بال", "probability": 0.3955078125}, {"start": 2062.93, "end": 2063.37, "word": " chapter", "probability": 0.389892578125}, {"start": 2063.37, "end": 2064.45, "word": " الماضي", "probability": 0.86181640625}, {"start": 2064.45, "end": 2065.85, "word": " ال", "probability": 0.307861328125}, {"start": 2065.85, "end": 2070.43, "word": " example", "probability": 0.85595703125}, {"start": 2070.43, "end": 2071.03, "word": " بيقول", "probability": 0.9246419270833334}, {"start": 2071.03, "end": 2071.33, "word": " ما", "probability": 0.495849609375}, {"start": 2071.33, "end": 2071.81, "word": " يعني", "probability": 0.56756591796875}, {"start": 2071.81, "end": 2072.21, "word": " show", "probability": 0.5146484375}, {"start": 2072.21, "end": 2072.83, "word": " that", "probability": 0.89599609375}, {"start": 2072.83, "end": 2078.41, "word": " five", "probability": 0.216796875}, {"start": 2078.41, "end": 2080.87, "word": " المعرفة", "probability": 0.9625244140625}, {"start": 2080.87, "end": 2081.77, "word": " من", "probability": 0.96435546875}, {"start": 2081.77, "end": 2082.69, "word": " z", "probability": 0.46240234375}, {"start": 2082.69, "end": 2083.33, "word": " of", "probability": 0.84765625}, {"start": 2083.33, "end": 2084.01, "word": " x", "probability": 0.970703125}, {"start": 2084.01, "end": 2085.33, "word": " onto", "probability": 0.489990234375}], "temperature": 1.0}, {"id": 73, "seek": 211471, "start": 2087.77, "end": 2114.71, "text": "on to z given by والمعطى بي five لل F of X بده يساوي ال F of zero is a ring homomorphism with", "tokens": [266, 281, 710, 2212, 538, 4032, 45340, 3615, 9566, 7578, 4724, 1829, 1732, 24976, 479, 295, 1783, 47525, 3224, 7251, 3794, 995, 45865, 2423, 479, 295, 4018, 307, 257, 4875, 3655, 32702, 1434, 365], "avg_logprob": -0.36763393538338796, "compression_ratio": 1.0555555555555556, "no_speech_prob": 0.0, "words": [{"start": 2087.77, "end": 2088.23, "word": "on", "probability": 0.1182861328125}, {"start": 2088.23, "end": 2088.65, "word": " to", "probability": 0.82666015625}, {"start": 2088.65, "end": 2089.51, "word": " z", "probability": 0.79052734375}, {"start": 2089.51, "end": 2091.55, "word": " given", "probability": 0.73828125}, {"start": 2091.55, "end": 2092.33, "word": " by", "probability": 0.9892578125}, {"start": 2092.33, "end": 2095.61, "word": " والمعطى", "probability": 0.74873046875}, {"start": 2095.61, "end": 2096.27, "word": " بي", "probability": 0.735595703125}, {"start": 2096.27, "end": 2098.65, "word": " five", "probability": 0.169189453125}, {"start": 2098.65, "end": 2099.95, "word": " لل", "probability": 0.7255859375}, {"start": 2099.95, "end": 2100.49, "word": " F", "probability": 0.50390625}, {"start": 2100.49, "end": 2100.99, "word": " of", "probability": 0.87109375}, {"start": 2100.99, "end": 2101.61, "word": " X", "probability": 0.7998046875}, {"start": 2101.61, "end": 2102.53, "word": " بده", "probability": 0.3538818359375}, {"start": 2102.53, "end": 2103.15, "word": " يساوي", "probability": 0.8912353515625}, {"start": 2103.15, "end": 2103.59, "word": " ال", "probability": 0.65234375}, {"start": 2103.59, "end": 2103.99, "word": " F", "probability": 0.935546875}, {"start": 2103.99, "end": 2104.61, "word": " of", "probability": 0.93505859375}, {"start": 2104.61, "end": 2105.23, "word": " zero", "probability": 0.391357421875}, {"start": 2105.23, "end": 2106.59, "word": " is", "probability": 0.89013671875}, {"start": 2106.59, "end": 2108.07, "word": " a", "probability": 0.9013671875}, {"start": 2108.07, "end": 2109.01, "word": " ring", "probability": 0.966796875}, {"start": 2109.01, "end": 2112.19, "word": " homomorphism", "probability": 0.8899739583333334}, {"start": 2112.19, "end": 2114.71, "word": " with", "probability": 0.90087890625}], "temperature": 1.0}, {"id": 74, "seek": 212378, "start": 2117.12, "end": 2123.78, "text": "الكرنة للـ 5 بدى يساوي لـ principle ideal generated by X", "tokens": [6027, 37983, 1863, 3660, 24976, 39184, 1025, 47525, 7578, 7251, 3794, 995, 45865, 5296, 39184, 8665, 7157, 10833, 538, 1783], "avg_logprob": -0.5621279988970075, "compression_ratio": 0.9259259259259259, "no_speech_prob": 0.0, "words": [{"start": 2117.1200000000003, "end": 2118.28, "word": "الكرنة", "probability": 0.65155029296875}, {"start": 2118.28, "end": 2119.1, "word": " للـ", "probability": 0.5426025390625}, {"start": 2119.1, "end": 2119.54, "word": " 5", "probability": 0.25830078125}, {"start": 2119.54, "end": 2120.18, "word": " بدى", "probability": 0.20098876953125}, {"start": 2120.18, "end": 2120.6, "word": " يساوي", "probability": 0.8365478515625}, {"start": 2120.6, "end": 2120.86, "word": " لـ", "probability": 0.5325927734375}, {"start": 2120.86, "end": 2121.32, "word": " principle", "probability": 0.31884765625}, {"start": 2121.32, "end": 2121.9, "word": " ideal", "probability": 0.6435546875}, {"start": 2121.9, "end": 2122.62, "word": " generated", "probability": 0.9072265625}, {"start": 2122.62, "end": 2123.16, "word": " by", "probability": 0.970703125}, {"start": 2123.16, "end": 2123.78, "word": " X", "probability": 0.7578125}], "temperature": 1.0}, {"id": 75, "seek": 217890, "start": 2150.4, "end": 2178.9, "text": "خلّيني أعطيكم دلّة في من مجموعة الـ functions اللي العرامل تبعتهم أعداد صحيحة on to z يعني بغطي الـ z كلها given by في of f of x بده ساوي f of zero قال لي بدك تثبت أن هذا ring همو مرتزم الخطوة الأولى الخطوة الثانية", "tokens": [9778, 1211, 11703, 9957, 1829, 5551, 3615, 9566, 1829, 24793, 11778, 1211, 11703, 3660, 8978, 9154, 3714, 7435, 2304, 2407, 27884, 2423, 39184, 6828, 13672, 1829, 18863, 2288, 10943, 1211, 6055, 3555, 34268, 16095, 5551, 22488, 18513, 20328, 5016, 1829, 5016, 3660, 322, 281, 710, 37495, 22653, 4724, 17082, 9566, 1829, 2423, 39184, 710, 28242, 11296, 2212, 538, 8978, 295, 283, 295, 2031, 47525, 3224, 8608, 995, 45865, 283, 295, 4018, 50239, 32239, 47525, 4117, 6055, 12984, 3555, 2655, 14739, 23758, 4875, 8032, 2304, 2407, 3714, 43500, 11622, 2304, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 33962, 9566, 2407, 3660, 6024, 104, 7649, 10632], "avg_logprob": -0.3973214240301223, "compression_ratio": 1.5495495495495495, "no_speech_prob": 0.0, "words": [{"start": 2150.4, "end": 2150.74, "word": 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12984, 3555, 2655, 8315, 8032, 8848, 1829, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 8032, 8848, 1829, 11933, 3555, 9640, 3660, 18871, 13672, 1829, 31439, 8032, 8848, 1829, 31767, 13063, 3660, 13672, 1829, 43242, 8315, 5296, 15042, 25961, 2655, 14739, 2655, 14407, 32771, 9566, 2655, 11296, 28242, 11296, 37495, 22653, 8032, 8848, 1829, 4724, 39648, 25894, 11296, 3714, 9957, 4724, 39648, 25894, 11296, 710, 2564, 46811, 10943, 45520], "avg_logprob": -0.20538403901709132, "compression_ratio": 1.7455621301775148, "no_speech_prob": 0.0, "words": [{"start": 2773.12, "end": 2773.9, "word": "z", "probability": 0.44140625}, {"start": 2773.9, "end": 2775.02, "word": " of", "probability": 0.93408203125}, {"start": 2775.02, "end": 2775.8, "word": " x", "probability": 0.94873046875}, {"start": 2775.8, "end": 2778.88, "word": " مظبوط", "probability": 0.89306640625}, {"start": 2778.88, "end": 2780.24, "word": " ؟", "probability": 0.436767578125}, {"start": 2780.24, "end": 2780.54, "word": " طيب", "probability": 0.8201497395833334}, {"start": 2780.54, "end": 2781.24, "word": " هنا", "probability": 0.943359375}, {"start": 2781.24, "end": 2783.26, "word": " أثبتنا", "probability": 0.919140625}, {"start": 2783.26, "end": 2784.5, "word": " هذي", "probability": 0.4564615885416667}, {"start": 2784.5, "end": 2785.14, "word": " بالشكل", "probability": 0.8929036458333334}, {"start": 2785.14, "end": 2785.38, "word": " اللي", "probability": 0.932861328125}, {"start": 2785.38, "end": 2785.8, "word": " عندنا", "probability": 0.76904296875}, {"start": 2785.8, "end": 2786.14, "word": " هذي", "probability": 0.5595703125}, {"start": 2786.14, "end": 2786.98, "word": " إبارة", "probability": 0.59478759765625}, {"start": 2786.98, "end": 2787.78, "word": " عن", "probability": 0.984375}, {"start": 2787.78, "end": 2788.42, "word": " اللي", "probability": 0.864013671875}, {"start": 2788.42, "end": 2788.74, "word": " هو", "probability": 0.97607421875}, {"start": 2788.74, "end": 2790.02, "word": " هذي", "probability": 0.82470703125}, {"start": 2790.02, "end": 2790.78, "word": " الصورة", "probability": 0.9886067708333334}, {"start": 2790.78, "end": 2790.92, "word": " اللي", "probability": 0.970458984375}, {"start": 2790.92, "end": 2791.28, "word": " عندنا", "probability": 0.986572265625}, {"start": 2791.28, "end": 2791.46, "word": " لما", "probability": 0.86328125}, {"start": 2791.46, "end": 2792.16, "word": " كانت", "probability": 0.911376953125}, {"start": 2792.16, "end": 2792.68, "word": " أنتوا", "probability": 0.7098795572916666}, {"start": 2792.68, "end": 2793.68, "word": " غطتها", "probability": 0.9527587890625}, {"start": 2793.68, "end": 2794.58, "word": " كلها", "probability": 0.993896484375}, {"start": 2794.58, "end": 2795.34, "word": " يعني", "probability": 0.925048828125}, {"start": 2795.34, "end": 2795.9, "word": " هذي", "probability": 0.8600260416666666}, {"start": 2795.9, "end": 2796.36, "word": " بقول", "probability": 0.96875}, {"start": 2796.36, "end": 2796.84, "word": " عليها", "probability": 0.98388671875}, {"start": 2796.84, "end": 2797.36, "word": " مين", "probability": 0.958984375}, {"start": 2797.36, "end": 2798.28, "word": " بقول", "probability": 0.938232421875}, {"start": 2798.28, "end": 2798.84, "word": " عليها", "probability": 0.988037109375}, {"start": 2798.84, "end": 2799.4, "word": " z", "probability": 0.84423828125}, {"start": 2799.4, "end": 2800.44, "word": " itself", "probability": 0.83251953125}, {"start": 2800.44, "end": 2802.16, "word": " تمام", "probability": 0.94677734375}, {"start": 2802.16, "end": 2802.36, "word": " ؟", "probability": 0.74462890625}], "temperature": 1.0}, {"id": 98, "seek": 282913, "start": 2802.83, "end": 2829.13, "text": "يبقى من ال first isomorphism theorem ال Z of X modular kernel isomorphic لمين لل Phi of R؟ مين R ان دي؟ Z of X Z of X اللي هى مين هنا؟ Z تمام يعني Z أجت مكان Phi of R بالطبع تمام طيب ال kernel هذا أثبت و أنا مين؟", "tokens": [1829, 3555, 4587, 7578, 9154, 2423, 700, 307, 32702, 1434, 20904, 2423, 1176, 295, 1783, 31111, 28256, 307, 32702, 299, 32767, 9957, 24976, 41435, 295, 497, 22807, 3714, 9957, 497, 16472, 11778, 1829, 22807, 1176, 295, 1783, 1176, 295, 1783, 13672, 1829, 8032, 7578, 3714, 9957, 34105, 22807, 1176, 46811, 10943, 37495, 22653, 1176, 5551, 7435, 2655, 3714, 41361, 41435, 295, 497, 20666, 9566, 3555, 3615, 46811, 10943, 23032, 1829, 3555, 2423, 28256, 23758, 5551, 12984, 3555, 2655, 4032, 41850, 3714, 9957, 22807], "avg_logprob": -0.27808780577920733, "compression_ratio": 1.5364583333333333, "no_speech_prob": 0.0, "words": [{"start": 2802.83, "end": 2803.67, "word": "يبقى", "probability": 0.9163818359375}, {"start": 2803.67, "end": 2803.93, "word": " من", "probability": 0.9794921875}, {"start": 2803.93, "end": 2804.15, "word": " ال", "probability": 0.923828125}, {"start": 2804.15, "end": 2804.69, "word": " first", "probability": 0.59326171875}, {"start": 2804.69, "end": 2806.09, "word": " isomorphism", "probability": 0.9353841145833334}, {"start": 2806.09, "end": 2806.85, "word": " theorem", "probability": 0.88623046875}, {"start": 2806.85, "end": 2807.55, "word": " ال", "probability": 0.50439453125}, {"start": 2807.55, "end": 2807.79, "word": " Z", "probability": 0.50341796875}, {"start": 2807.79, "end": 2808.15, "word": " of", "probability": 0.69482421875}, {"start": 2808.15, "end": 2808.45, "word": " X", "probability": 0.974609375}, {"start": 2808.45, "end": 2809.03, "word": " modular", "probability": 0.328369140625}, {"start": 2809.03, "end": 2809.75, "word": " kernel", "probability": 0.69140625}, {"start": 2809.75, "end": 2811.51, "word": " isomorphic", "probability": 0.7669270833333334}, {"start": 2811.51, "end": 2812.35, "word": " لمين", "probability": 0.6998291015625}, {"start": 2812.35, "end": 2812.61, "word": " لل", "probability": 0.80712890625}, {"start": 2812.61, "end": 2813.07, "word": " Phi", "probability": 0.3759765625}, {"start": 2813.07, "end": 2813.51, "word": " of", "probability": 0.91357421875}, {"start": 2813.51, "end": 2814.01, "word": " R؟", "probability": 0.6695556640625}, {"start": 2814.01, "end": 2814.25, "word": " مين", "probability": 0.90869140625}, {"start": 2814.25, "end": 2814.59, "word": " R", "probability": 0.84521484375}, {"start": 2814.59, "end": 2814.99, "word": " ان", "probability": 0.1522216796875}, {"start": 2814.99, "end": 2815.49, "word": " دي؟", "probability": 0.740478515625}, {"start": 2815.49, "end": 2815.95, "word": " Z", "probability": 0.84326171875}, {"start": 2815.95, "end": 2816.33, "word": " of", "probability": 0.95751953125}, {"start": 2816.33, "end": 2816.71, "word": " X", "probability": 0.99658203125}, {"start": 2816.71, "end": 2817.31, "word": " Z", "probability": 0.192626953125}, {"start": 2817.31, "end": 2817.73, "word": " of", "probability": 0.9384765625}, {"start": 2817.73, "end": 2818.01, "word": " X", "probability": 0.99609375}, {"start": 2818.01, "end": 2818.21, "word": " اللي", "probability": 0.872314453125}, {"start": 2818.21, "end": 2818.37, "word": " هى", "probability": 0.656982421875}, {"start": 2818.37, "end": 2818.65, "word": " مين", "probability": 0.94873046875}, {"start": 2818.65, "end": 2819.51, "word": " هنا؟", "probability": 0.9248046875}, {"start": 2819.51, "end": 2819.95, "word": " Z", "probability": 0.919921875}, {"start": 2819.95, "end": 2820.79, "word": " تمام", "probability": 0.66650390625}, {"start": 2820.79, "end": 2821.53, "word": " يعني", "probability": 0.770263671875}, {"start": 2821.53, "end": 2822.13, "word": " Z", "probability": 0.79345703125}, {"start": 2822.13, "end": 2822.73, "word": " أجت", "probability": 0.78564453125}, {"start": 2822.73, "end": 2823.29, "word": " مكان", "probability": 0.984619140625}, {"start": 2823.29, "end": 2823.99, "word": " Phi", "probability": 0.9365234375}, {"start": 2823.99, "end": 2824.43, "word": " of", "probability": 0.9580078125}, {"start": 2824.43, "end": 2824.77, "word": " R", "probability": 0.9931640625}, {"start": 2824.77, "end": 2825.35, "word": " بالطبع", "probability": 0.8673095703125}, {"start": 2825.35, "end": 2825.97, "word": " تمام", "probability": 0.895751953125}, {"start": 2825.97, "end": 2826.89, "word": " طيب", "probability": 0.9612630208333334}, {"start": 2826.89, "end": 2827.11, "word": " ال", "probability": 0.798828125}, {"start": 2827.11, "end": 2827.47, "word": " kernel", "probability": 0.822265625}, {"start": 2827.47, "end": 2827.85, "word": " هذا", "probability": 0.71435546875}, {"start": 2827.85, "end": 2828.35, "word": " أثبت", "probability": 0.9293212890625}, {"start": 2828.35, "end": 2828.53, "word": " و", "probability": 0.35595703125}, {"start": 2828.53, "end": 2828.69, "word": " أنا", "probability": 0.52392578125}, {"start": 2828.69, "end": 2829.13, "word": " مين؟", "probability": 0.6285807291666666}], "temperature": 1.0}, {"id": 99, "seek": 283825, "start": 2831.15, "end": 2838.25, "text": "بتشيله وحط مدالة الـ principal ideal generated by X يبقى هذا بده يعطينا", "tokens": [3555, 2655, 8592, 26895, 3224, 4032, 5016, 9566, 3714, 3215, 6027, 3660, 2423, 39184, 9716, 7157, 10833, 538, 1783, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 37495, 9566, 1829, 8315], "avg_logprob": -0.5625000115363828, "compression_ratio": 1.0, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 2831.15, "end": 2832.11, "word": "بتشيله", "probability": 0.48524169921875}, {"start": 2832.11, "end": 2832.51, "word": " وحط", "probability": 0.7285970052083334}, {"start": 2832.51, "end": 2832.99, "word": " مدالة", "probability": 0.736083984375}, {"start": 2832.99, "end": 2833.21, "word": " الـ", "probability": 0.322509765625}, {"start": 2833.21, "end": 2833.57, "word": " principal", "probability": 0.1875}, {"start": 2833.57, "end": 2834.07, "word": " ideal", "probability": 0.358154296875}, {"start": 2834.07, "end": 2834.75, "word": " generated", "probability": 0.84912109375}, {"start": 2834.75, "end": 2835.23, "word": " by", "probability": 0.9375}, {"start": 2835.23, "end": 2835.65, "word": " X", "probability": 0.736328125}, {"start": 2835.65, "end": 2836.63, "word": " يبقى", "probability": 0.884765625}, {"start": 2836.63, "end": 2836.99, "word": " هذا", "probability": 0.8916015625}, {"start": 2836.99, "end": 2837.49, "word": " بده", "probability": 0.42449951171875}, {"start": 2837.49, "end": 2838.25, "word": " يعطينا", "probability": 0.96728515625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2839.6146875, "duration_after_vad": 2723.0112499999937}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eeed8dbdff20e0f099b69ee6fc7744b8b84beb63
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_postprocess.srt
@@ -0,0 +1,1992 @@
+1
+00:00:20,910 --> 00:00:25,930
+بسم الله الرحمن الرحيم نكمل ما كنا نعمل بيه المرة
+
+2
+00:00:25,930 --> 00:00:29,950
+الماضية في نفس الشفقة. ولمرة اللي فاتت في نهاية
+
+3
+00:00:29,950 --> 00:00:34,630
+المحاضرة أعطيناكوا مثال ولمّا ننتهي منه. يبقى بدنا
+
+4
+00:00:34,630 --> 00:00:39,390
+نعمل عليه مرة سريعة ثم ننهي هذا المثال ثم ننتقل
+
+5
+00:00:39,390 --> 00:00:44,510
+إلى المثال اللي يليه. We will construct a field of
+
+6
+00:00:44,510 --> 00:00:51,810
+order تمام.باقي 8 ايش ممكن احطها عدد مرفوع ل أس
+
+7
+00:00:51,810 --> 00:00:57,790
+عدد او ال prime مرفوع ل أس يبقى 8 لي عبارة عن مين؟
+
+8
+00:00:57,790 --> 00:01:06,890
+2 أس 3 ممتاز جدا يبقى هذه 2 أس 3 ل 2 هو ال prime و
+
+9
+00:01:06,890 --> 00:01:14,240
+3 هو الأس 7 وكأنه بيقول لي هذه polynomialمن الدرجة
+
+10
+00:01:14,240 --> 00:01:20,640
+التالتة و تكون irreducible على زكوك واضح؟ كأنه
+
+11
+00:01:20,640 --> 00:01:25,240
+بيقوللي ها هذه وسيلة الرقم اللي عندي أحطه prime
+
+12
+00:01:25,240 --> 00:01:30,880
+مرفوع لأسفل ال prime بيكون هو مين؟ هو ال field زد
+
+13
+00:01:30,880 --> 00:01:36,320
+لهذا الرقم بيكون هو ال fieldوالقصد اللى فوق بيكون
+
+14
+00:01:36,320 --> 00:01:40,320
+هو درجتي ال follow on هو نفسه كأنه مغششني بيقول
+
+15
+00:01:40,320 --> 00:01:46,380
+اتفضل خد اللى هو السؤال هذا اقوله تفضل طيب يبقى
+
+16
+00:01:46,380 --> 00:01:53,780
+احنا جينا للحل المرة اللى فاتت وقلنا let ال F of X
+
+17
+00:01:53,780 --> 00:02:02,100
+تساوي قداشر X تكيب زيديش أخدنا X زي واحد زي X زي
+
+18
+00:02:02,100 --> 00:02:10,220
+واحد مش هيكطيب تلقاه بدي اجي على ZP قولنا on ZP
+
+19
+00:02:10,220 --> 00:02:15,940
+مين P عندنا قولنا هنا بقراه اتنين على Z اتنين we
+
+20
+00:02:15,940 --> 00:02:21,760
+have بدنا نحسب قيمة الدالة عند Zero العنصر الأول
+
+21
+00:02:21,760 --> 00:02:28,060
+من Z2 يبقى بيعطيني جداش واحد بدنا نحسب قيمة الدالة
+
+22
+00:02:28,060 --> 00:02:34,290
+عند F of واحدواحد زي واحد زي واحد تلاتة في زيته
+
+23
+00:02:34,290 --> 00:02:40,150
+جديد معناته ان الدل هذه مالهاش zeros على زيت دي
+
+24
+00:02:40,150 --> 00:02:49,990
+اتنين يبقى هنا Sir ال F of X has no zeros on زيت
+
+25
+00:02:49,990 --> 00:02:55,190
+دي اتنين فهيبقى معاه no zeros على زيت دي اتنين
+
+26
+00:02:55,190 --> 00:02:59,550
+اتفجر مافيش ولا حاجة ولا واحدايه بيساويها؟ طيب ال
+
+27
+00:02:59,550 --> 00:03:09,010
+degree تبعت ال F جدت؟ تلاتة و ال degree على ال F
+
+28
+00:03:09,010 --> 00:03:13,790
+بده يساوي تلاتة طبعا أخدنا ال degree على ال F
+
+29
+00:03:13,790 --> 00:03:17,990
+اتنين او تلاتة او النظرية معانا مشكلة صحيح ولا لا؟
+
+30
+00:03:18,060 --> 00:03:23,560
+ما دام الانواج دول يبجي الدالة irreducible على Z2
+
+31
+00:03:23,560 --> 00:03:27,300
+وبالتالي irreducible على ال EQ مش هيك اخد نص
+
+32
+00:03:27,300 --> 00:03:36,680
+النظرية يبجي هنا بروح بقولهم فال F of X بده تساوي
+
+33
+00:03:36,680 --> 00:03:45,940
+X تكيب زائد X زائد 1 is irreducible over
+
+34
+00:03:46,830 --> 00:03:56,530
+اللي هو Z2 هذا بدي يعطينا by a previous theorem
+
+35
+00:03:56,530 --> 00:04:06,070
+بدي يكون ال F of X اللي هو X تكييف زي X زي واحد is
+
+36
+00:04:06,070 --> 00:04:12,990
+irreducible over ال Q
+
+37
+00:04:21,430 --> 00:04:27,470
+Irreducible على ال EQ عالي كويس لما ده ال F of X
+
+38
+00:04:27,470 --> 00:04:33,850
+صارت Irreducible على ال EQ هذا بيولدلي Ideal و
+
+39
+00:04:33,850 --> 00:04:39,890
+Ideal Value maximum نتيجة رقم واحد أخدناها على
+
+40
+00:04:39,890 --> 00:04:47,250
+اللي هو النظرية الأخيرة المرضى الماضييبقى هنا سا
+
+41
+00:04:47,250 --> 00:04:53,970
+اللي هو ال X تكييب زي X زي واحد هذا ال ideal is
+
+42
+00:04:53,970 --> 00:05:02,750
+maximal مدام maximal هذا بده يعطينا ان Z2 of X اه
+
+43
+00:05:02,750 --> 00:05:08,710
+موديون ال principle ideal generated by X تكييب زي
+
+44
+00:05:08,710 --> 00:05:17,380
+X زي واحد is A في الدقهذا ال field زعمنا انه يحتوي
+
+45
+00:05:17,380 --> 00:05:25,180
+على ثمانية عناصر وقلنا شكله على الشكل التالي Z2 of
+
+46
+00:05:25,180 --> 00:05:31,960
+X modulo principle ideal generated by X تكييف زائد
+
+47
+00:05:31,960 --> 00:05:38,180
+واحد بالدوي ساعة ها ال ideal من الدرجة التالتة
+
+48
+00:05:38,180 --> 00:05:43,100
+يبقى اللي قبله من الدرجة التالتةالثانية او الاولى
+
+49
+00:05:43,100 --> 00:05:48,060
+او الصفرية يعني اقل من الدرجة الثالثة يبقى هذا
+
+50
+00:05:48,060 --> 00:05:54,600
+بيكون على الشكل ax زائد bx زائد c زائد ال
+
+51
+00:05:54,600 --> 00:06:00,240
+principle ideal generated by x تكييب زائد واحد
+
+52
+00:06:00,240 --> 00:06:06,890
+وبحيث ان ال a و ال b و ال c كلها موجودة وينموجودة
+
+53
+00:06:06,890 --> 00:06:14,030
+في Z2 يعني يا إما صفر يا إما .. يا إما واحد. إحنا
+
+54
+00:06:14,030 --> 00:06:20,350
+زعمنا إنه هدف يتمانية عناصر. بدنا نعرف ما هي هذه
+
+55
+00:06:20,350 --> 00:06:25,530
+تمانية عناصر وقلنا لكوا يلا حضروها للمرة القادمة
+
+56
+00:06:25,530 --> 00:06:32,460
+وها قد حضرت المرة القادمة وصارت المرة الحالية.يبقى
+
+57
+00:06:32,460 --> 00:06:39,000
+هذه العناصر عبارة عن مين انا انا انا انا انا انا
+
+58
+00:06:39,000 --> 00:06:39,640
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+59
+00:06:39,640 --> 00:06:39,900
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+60
+00:06:39,900 --> 00:06:40,300
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+61
+00:06:40,300 --> 00:06:40,820
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+62
+00:06:40,820 --> 00:06:41,580
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+63
+00:06:41,580 --> 00:06:45,700
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+64
+00:06:45,700 --> 00:06:49,460
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+65
+00:06:49,460 --> 00:06:51,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+66
+00:06:51,260 --> 00:06:59,520
+انا
+
+67
+00:06:59,520 --> 00:07:05,610
+اناطيب ماذا؟ و X تربيه زائد واحد و X تربيه زائد X
+
+68
+00:07:05,610 --> 00:07:11,050
+و X تربيها زائد X زائد واحد واحد اتنين، تلاتة،
+
+69
+00:07:11,050 --> 00:07:16,010
+اربعة، خمسة، ستة، سبعة، تمانية هدول على كل واحد
+
+70
+00:07:16,010 --> 00:07:20,750
+فيهم بدي اضيف ال principle ideal generated by X
+
+71
+00:07:20,750 --> 00:07:27,590
+تكييف زائد X زائد واحد هاي جميع العناصر هدول كلهم
+
+72
+00:07:27,590 --> 00:07:32,500
+تمانية عناصريعني يا بنات عندنا zero زي ده ده left
+
+73
+00:07:32,500 --> 00:07:37,860
+coset عندنا الواحد زي ال principle ID left coset
+
+74
+00:07:37,860 --> 00:07:42,260
+تانية X زي ال principle left coset تالتة وهكذا
+
+75
+00:07:42,260 --> 00:07:48,780
+بالنسبة لمن للباقي هاي العناصر يبقى هدول ثمانية
+
+76
+00:07:48,780 --> 00:07:57,420
+عناصر يبقى لما أكتب هيك كأنه أنا بغششك جداشاللي هو
+
+77
+00:07:57,420 --> 00:08:01,880
+ال ZP بدي يكون مين هو ال prime اللي بدك تاخديه
+
+78
+00:08:01,880 --> 00:08:06,700
+وقدش درجة ال polynomial اللي لازم تاخديها مشان
+
+79
+00:08:06,700 --> 00:08:13,380
+يطلع كلامك صحيح وسنثبت أيه لك كذا كمان بمثال بعده
+
+80
+00:08:13,380 --> 00:08:17,280
+المثال اللي بعده .. اه قبل المثال اللي بعده لو
+
+81
+00:08:17,280 --> 00:08:24,370
+بدنا نضرب عنصرين في بعض من هذا ال fieldالنسج بدي
+
+82
+00:08:24,370 --> 00:08:29,430
+يطلع داخل ولا برا؟ طب تعالى نضرب ونشوف يطلع داخل
+
+83
+00:08:29,430 --> 00:08:34,670
+ولا برا؟ مش احنا بنزعو انه في ال و close under
+
+84
+00:08:34,670 --> 00:08:37,550
+multiplication و close under الجامعة وغيرها
+
+85
+00:08:37,550 --> 00:08:41,630
+الجامعة مش هيرايا للدرجة، يبقى مافيش فيه مشكلة،
+
+86
+00:08:41,630 --> 00:08:47,070
+المشكلة في الضرب، يبقى لو جينا نضرب على ضرب داخل
+
+87
+00:08:47,070 --> 00:08:52,410
+هدفي، مثلا لو رحت أخدعلى سبيل المثال X تربيه زايد
+
+88
+00:08:52,410 --> 00:08:58,090
+واحد مع هذا مع الاول principle ideal يبقى لو بدى
+
+89
+00:08:58,090 --> 00:09:02,830
+اضرب على ضرب العناصر داخل هذا الفيلم بدى اخد X
+
+90
+00:09:02,830 --> 00:09:09,970
+تربيه زايد واحد زايد principle ideal بدى اضربه في
+
+91
+00:09:09,970 --> 00:09:15,870
+من؟ في العنصر التاني X تربيه زايد X زايد واحد زايد
+
+92
+00:09:15,870 --> 00:09:24,010
+principle idealx تكيب زائد x زائد واحد اشوف النتج
+
+93
+00:09:24,010 --> 00:09:29,410
+جديش بده يساوي يبقى x تربيه في x تربيه في جديه اش؟
+
+94
+00:09:29,410 --> 00:09:37,110
+x أقصر اربعة وهنا زائد x تكيب وهنا زائد x تربيه
+
+95
+00:09:37,110 --> 00:09:46,390
+وزائد كمان x تربيه وزائد x زائد واحد زائد ل
+
+96
+00:09:46,390 --> 00:09:53,350
+principle idealgenerated by ال X تكييف زايد X زايد
+
+97
+00:09:53,350 --> 00:09:59,550
+واحد طلعوني هدول مع بعض كده ش بيعطونيه نين X ترويه
+
+98
+00:09:59,550 --> 00:10:04,630
+داخل زيدي اتنين مع السلامة الله سهل عليهم و غير
+
+99
+00:10:04,630 --> 00:10:09,950
+مقصوف عليهم يبقى بقى لعندي بنات ميم بقى لعندي X وص
+
+100
+00:10:09,950 --> 00:10:17,780
+أربع واطلع X تكييف زايد X زايد واحد موجود هنايبقى
+
+101
+00:10:17,780 --> 00:10:24,640
+بدي يطلع نفس الهمصر هذا يبقى x أُص أربع زائد ال x
+
+102
+00:10:24,640 --> 00:10:30,960
+تكيب زائد ال x زائد واحد يبقى طلعت polynomial من
+
+103
+00:10:30,960 --> 00:10:37,160
+الدرجة الرابعة ك left coset مع ال x تكيب زائد x
+
+104
+00:10:37,160 --> 00:10:42,000
+زائد واحد واحنا بنزعم هنا ان هذا بدي يكون من
+
+105
+00:10:42,000 --> 00:10:48,290
+الدرجة مية متربنشوف هل هذا الكلام صحيح، والله مش
+
+106
+00:10:48,290 --> 00:10:52,890
+صحيح، يعني بنخفض الدرجة، بحيث تصير منها الدرجة
+
+107
+00:10:52,890 --> 00:10:58,410
+الثانية، يعني انا لو روحته وخليته تصير شغلة نقص
+
+108
+00:10:58,410 --> 00:11:03,350
+شوية، بننقص درجات، بتكملي بحيث فعلا يكون على
+
+109
+00:11:03,350 --> 00:11:07,930
+الصيغة اللي عندنا هذه، طب كيف بتخفضه؟ هناك
+
+110
+00:11:07,930 --> 00:11:14,490
+طريقتان، الطريقة الأولى long division، إيش يعني؟
+
+111
+00:11:14,850 --> 00:11:20,010
+قسم المطول نقسم قسم المطول عادي ونشوف وين ماتوصل
+
+112
+00:11:20,010 --> 00:11:25,870
+معانا الدنيا إذا لو جيت في الهامش بدي أقسم X أُس
+
+113
+00:11:25,870 --> 00:11:33,470
+أربعة تأسيب ال X تكيب زائد X زائد واحد X أُس أربعة
+
+114
+00:11:33,470 --> 00:11:39,930
+على X تكيب هي أجدد ال X والباقي ملحقة فيها يبقى
+
+115
+00:11:39,930 --> 00:11:48,390
+هاي X أُس أربعة زائد X تربيعزائد X بنغير الإشارات
+
+116
+00:11:48,390 --> 00:11:55,310
+وبنجمع مع السلامة بظل عندي ناقص X تربيع ناقص X لكن
+
+117
+00:11:55,310 --> 00:12:00,230
+احنا بنشتغل وين؟ في Z دي اتنين في Z دي اتنين بدي
+
+118
+00:12:00,230 --> 00:12:08,210
+اضيف هنا اتنين بظل X تربيع وهذه زيها X يبقى صارت
+
+119
+00:12:08,210 --> 00:12:15,500
+ال X أُس أربعة زائد ال principle IDgenerated by
+
+120
+00:12:15,500 --> 00:12:21,560
+هذا ال element بتساوي خارج القسمة اللي هو mean X
+
+121
+00:12:21,560 --> 00:12:28,560
+في X تكييب زائد X زائد واحد زائد خارج القسمة اللي
+
+122
+00:12:28,560 --> 00:12:33,220
+هو X تربيها زائد X زائد ال principle ideal
+
+123
+00:12:33,220 --> 00:12:39,860
+generated by X تكييب زائد X زائد واحد تمام
+
+124
+00:12:42,380 --> 00:12:47,260
+طيب كويس هذا ال element موجود في ال principle ولا
+
+125
+00:12:47,260 --> 00:12:54,660
+لا يبقى على طول الخط هذا بتساوي ال X تربيع زائد X
+
+126
+00:12:54,660 --> 00:13:01,200
+زائد ال principle ideal generated by X تكييب زائد
+
+127
+00:13:01,200 --> 00:13:07,760
+X زائد 1 صرت من أي درجات؟ داليا بهذا يتفق مع
+
+128
+00:13:07,760 --> 00:13:13,670
+الكلام اللي احنا زعمناه قبل قليل تمام؟طبعا زعمناه
+
+129
+00:13:13,670 --> 00:13:19,950
+مش شكاك، زعمناه يعني من ضمانة، ضامنين مية لمية إن
+
+130
+00:13:19,950 --> 00:13:24,370
+هذا الكلام طبعا هذا كلام اللي أنا بقوله مش من
+
+131
+00:13:24,370 --> 00:13:31,090
+عندي، من القرآن الكريم و لما في قصة سيدنا يوسف لما
+
+132
+00:13:31,090 --> 00:13:36,890
+المكيال اللي جال، اللي بيجيب المكيال هذا، إله حمله
+
+133
+00:13:36,890 --> 00:13:41,610
+بعير و أنا به زعيميعني اللي يجيب هو أنا بعطيه حمل
+
+134
+00:13:41,610 --> 00:13:47,390
+بقير زيادة يبقى نضاما من الضمانة وليس للشك يبقى
+
+135
+00:13:47,390 --> 00:13:53,070
+احنا هنا اللي زعمناه قبل قليل هيأكدنا بمين عمليا
+
+136
+00:13:53,070 --> 00:13:58,550
+بهذا الكلام هذه هي الطريقة من الأولى وكأن X أُص
+
+137
+00:13:58,550 --> 00:14:05,430
+أربعة في هذا ال field تكافئ X تربية زائد X لأنه
+
+138
+00:14:05,430 --> 00:14:10,820
+شيلناها وحطينا بدلها X تربيةزايد X ونستطيع أن نؤكد
+
+139
+00:14:10,820 --> 00:14:17,180
+هذا الكلام بطريقة أخرى ما هي الطريقة الأخرى هنشوف
+
+140
+00:14:17,180 --> 00:14:22,100
+احنا عندنا X تكييف زايد X زايد 1 زايد ال principle
+
+141
+00:14:22,100 --> 00:14:27,480
+ideal generated by X تكييف زايد X زايد 1 هو ال
+
+142
+00:14:27,480 --> 00:14:33,120
+principle ideal generated by X تكييف زايد 1 صح
+
+143
+00:14:33,120 --> 00:14:40,760
+يعني هذا بزياد تماميعني هذا بيصير x تكييب زاد ال x
+
+144
+00:14:40,760 --> 00:14:46,720
+زاد واحد بيصير zero يعني ال x تكييب تساوي ناقص x
+
+145
+00:14:46,720 --> 00:14:54,420
+ناقص واحد احنا بيشتغلوا اين؟ في z two في z two هذا
+
+146
+00:14:54,420 --> 00:15:00,880
+معناه ان x زاد واحد in z twoبتنضروا بال X يبقى يصر
+
+147
+00:15:00,880 --> 00:15:06,100
+ان كمان ال X تكيب في الشغل اللي بنشتغله هذا ممكن
+
+148
+00:15:06,100 --> 00:15:11,120
+ابدلها مين؟ X زائد واحد يعني لو مرت في السؤال كان
+
+149
+00:15:11,120 --> 00:15:15,360
+في عندي X تكيب يمكن استبداله ب X زائد واحد يبقى
+
+150
+00:15:15,360 --> 00:15:19,920
+نزلنا الدرجة التالتة إلى الدرجة الأولى زي ما نزلنا
+
+151
+00:15:19,920 --> 00:15:24,890
+الدرجة الرابعة إلى الدرجة الثانيةطب هذه المعادلة
+
+152
+00:15:24,890 --> 00:15:31,470
+لو ضربت الطرفين في X بصير X قص 4 يساوي X في X زائد
+
+153
+00:15:31,470 --> 00:15:38,630
+1 يعني X تربيها زائد X هي اللي فور مظبوط؟ يبقى
+
+154
+00:15:38,630 --> 00:15:44,490
+صارت هي عندك مدى الطريقة طريقتين مشان ننزل الدرجة
+
+155
+00:15:44,490 --> 00:15:48,290
+من الدرجة الرابعة إلى الدرجة الثانية أو الأولى أو
+
+156
+00:15:48,290 --> 00:15:52,540
+الصفرية حسب طبيعة ميم المثلفلو جنا سؤال في
+
+157
+00:15:52,540 --> 00:15:57,060
+الامتحان او قلنا لك اتي لل multiplicative تبع ال
+
+158
+00:15:57,060 --> 00:16:03,360
+two elements ووصلتي الى شغل زى هذا وقول والله حلت
+
+159
+00:16:03,360 --> 00:16:08,380
+صح وجماشى لأ انت حلته نص الحل ضايل عليك النص
+
+160
+00:16:08,380 --> 00:16:13,560
+التانى انه اتنزلت درجة الى درجة مين ا الثانية و
+
+161
+00:16:13,560 --> 00:16:21,000
+هكذا طيب الان فينا كمان مثال اخربس بتغير عدد
+
+162
+00:16:21,000 --> 00:16:27,340
+العناصر كده عدد العناصر هنا تمانية بدي أغير هذه
+
+163
+00:16:27,340 --> 00:16:34,200
+الطريقة المثال اللي بعده هو بيقول
+
+164
+00:16:34,200 --> 00:16:40,120
+بنفس الطريقة example construct
+
+165
+00:16:40,120 --> 00:16:43,260
+a
+
+166
+00:16:43,260 --> 00:16:47,160
+field construct
+
+167
+00:16:47,160 --> 00:17:00,510
+a fieldof order of order تسعة مش تمانع تسعة تانية
+
+168
+00:17:00,510 --> 00:17:04,750
+تلاتة تربية يعني
+
+169
+00:17:04,750 --> 00:17:09,130
+أنا بدي أشغل لبدل ما كنت أشتغل في Z دي اتنين بدي
+
+170
+00:17:09,130 --> 00:17:15,910
+أشتغل في Z ثلاثة ونقل نمية من الدرجة الثانية تمام
+
+171
+00:17:16,310 --> 00:17:21,410
+يبقى اخدي اي polynomial من الدرجة الثانية تناسب
+
+172
+00:17:21,410 --> 00:17:26,450
+اللي هو Z3 انا ممكن اخد polynomial انت تاخد اخر
+
+173
+00:17:26,450 --> 00:17:31,410
+واحدة تاخد التالتة وكله صح ان حقق المطلوب تبع
+
+174
+00:17:31,410 --> 00:17:37,710
+السؤال الجبال يبقى قوله solution بدى
+
+175
+00:17:37,710 --> 00:17:46,070
+افترض ان ال F of X بدها تسوي مثلا X ترابيع زائدة
+
+176
+00:17:48,150 --> 00:17:55,210
+الان ال P بتلاتة يبقى بدي أشتغل في Z D3 فاجي بقوله
+
+177
+00:17:55,210 --> 00:18:06,150
+N Z D3 We have .. بدي أخد F of Zero F of Zero
+
+178
+00:18:06,150 --> 00:18:14,610
+بواحد بدي أخد F of واحد باتنين بدي أخد F of اتنين
+
+179
+00:18:14,610 --> 00:18:20,880
+بواحد بخمسة خمسة اتنينF of اتنين اربعة واحد خمسة
+
+180
+00:18:20,880 --> 00:18:26,260
+فيه زي دي ثلاث اتنين يبقى معناته ايش هذه ال
+
+181
+00:18:26,260 --> 00:18:32,320
+function مالهاش زي رزة وال degree تبعها جد ايش
+
+182
+00:18:32,320 --> 00:18:36,900
+اتنين يبقى طبقة النظرية اللي اشتغلنا عليها في
+
+183
+00:18:36,900 --> 00:18:52,870
+المثال الأول يبقى سواء ال F أتنين زي رزةزي T3 and
+
+184
+00:18:52,870 --> 00:19:03,210
+ال degree لل F بده يساوي كده؟ بده يساوي اتنى معنى
+
+185
+00:19:03,210 --> 00:19:09,630
+هذا الكلام ان ال F of X is ال reduce وعلى Z تلت
+
+186
+00:19:09,630 --> 00:19:20,430
+يبقى صح ال F of X تساوي ال X ترابيعترابية زائد
+
+187
+00:19:20,430 --> 00:19:28,930
+واحد is irreducible irreducible
+
+188
+00:19:28,930 --> 00:19:32,930
+over
+
+189
+00:19:32,930 --> 00:19:42,930
+Z3 هذا بده يعطينا ان ال F of X ال F X ترابية زائد
+
+190
+00:19:42,930 --> 00:19:47,010
+واحد is irreducible
+
+191
+00:19:48,100 --> 00:20:00,280
+of the cube نفس التكتيك اللي مشيناه Z D3 of X
+
+192
+00:20:00,280 --> 00:20:05,440
+Module ال principle ideals generated by X ترابية
+
+193
+00:20:05,440 --> 00:20:11,760
+زي واحد is a في طبعا استخدمنا ال crawlery واحد
+
+194
+00:20:11,760 --> 00:20:15,040
+اللي عالميا على النظرية المرة اللي فاتة أخدنا two
+
+195
+00:20:15,040 --> 00:20:19,460
+crawleries هذه هي ال crawleryالأول دكتور احنا
+
+196
+00:20:19,460 --> 00:20:24,020
+فرضنا FFX من هنا اه من اللي بتاعك من اللي بتاعك
+
+197
+00:20:24,020 --> 00:20:32,160
+كده اه ايه يعني اي FFX بشرف ترجع إلى تلاتة نزيتش
+
+198
+00:20:32,160 --> 00:20:39,420
+ايه نعم طيب يبقى صار Z تلاتة و FX مضى من X أربع هي
+
+199
+00:20:39,420 --> 00:20:44,960
+عبارة عن field ما هو ما هي شكل العناصر في هذا ال
+
+200
+00:20:44,960 --> 00:20:51,950
+fieldيبقى z تلاتة of x modulo x ترمية زائد واحد
+
+201
+00:20:51,950 --> 00:20:59,070
+شكلها على الشكل التالي هاي ال x ترمية زائد واحد
+
+202
+00:20:59,070 --> 00:21:07,450
+كما يبقى زائد اقل منه في الدرجة بمقدار واحد يومين
+
+203
+00:21:07,450 --> 00:21:15,580
+a x زائد ال bو بحيث ال A و ال B موجودة في Z دي
+
+204
+00:21:15,580 --> 00:21:23,080
+ثلاثة تفضل هاي الشكل جتاش؟ ستة انا بدي اعطيكي
+
+205
+00:21:23,080 --> 00:21:30,540
+التلاتة Zero واحد و اتنين و X و X زيدي واحد و X
+
+206
+00:21:30,540 --> 00:21:35,580
+زيدي اتنين هاي ستة خلطنا؟ طب و اتنين X و اتنين X
+
+207
+00:21:35,580 --> 00:21:39,480
+زيدي واحد و اتنين X زيدي اتنين في غيرهم؟ جتاسعة
+
+208
+00:21:39,480 --> 00:21:43,550
+طالع مظمومتبقى راجع معلوماتك وإلا أخدتي ستة من
+
+209
+00:21:43,550 --> 00:21:51,350
+تسعة. يبقى هذا بتفهمه ولا خلاص؟ بتفهمه؟ خلاص
+
+210
+00:21:51,350 --> 00:22:00,370
+بتفهمه دايما تفهمه. يبقى هذا has nine talents. بعد
+
+211
+00:22:00,370 --> 00:22:04,430
+شوية هكبرتكوا الرقم هذا. بدون تمانية وتسعة بدي
+
+212
+00:22:04,430 --> 00:22:10,890
+أكبره. وشوهش بتسووا فيه؟ اسم الحلال الأسل.طيب،
+
+213
+00:22:10,890 --> 00:22:19,970
+اننا ندل ال exercises على chapter سبعة و عشر Yoga
+
+214
+00:22:19,970 --> 00:22:30,310
+exercises on chapter سبعة و عشر نروح
+
+215
+00:22:30,310 --> 00:22:36,870
+ناخد السؤال الخامس نظرا لإهميته السؤال الخامس
+
+216
+00:22:36,870 --> 00:22:42,160
+عبارة عن أربعة مسائلبتسيبك المطلب الأول والثاني
+
+217
+00:22:42,160 --> 00:22:47,560
+واحد لك التالت والرابع الأول والثاني زي التالت
+
+218
+00:22:47,560 --> 00:22:53,720
+بنفس الطريقة حرفية تمام؟ إذا بدي أروح لنمريا C
+
+219
+00:22:53,720 --> 00:22:59,960
+ونمرادى فبدي أخد نمريا C قبل نمريا C بنحط
+
+220
+00:22:59,960 --> 00:23:07,180
+المعلومات يبقى بقول ال F is a field ال F is a
+
+221
+00:23:07,180 --> 00:23:07,900
+field
+
+222
+00:23:10,410 --> 00:23:18,510
+و ال a non zero element f و ال a لا يساوي zero in
+
+223
+00:23:18,510 --> 00:23:24,790
+f يبقى ال a عنصر غير صفري و موجود في ال f المطموض
+
+224
+00:23:24,790 --> 00:23:33,450
+نمرى c بيقول إذا كان ال f of x زائد a is
+
+225
+00:23:33,450 --> 00:23:35,950
+irreducible
+
+226
+00:23:39,340 --> 00:23:52,140
+الـ Q ثم ال F is او ال F of X is irreducible
+
+227
+00:23:52,140 --> 00:24:00,400
+over الـ Q itself
+
+228
+00:24:00,400 --> 00:24:07,620
+المعلومة
+
+229
+00:24:07,620 --> 00:24:13,120
+اللي عندناإن ال F of X زائد A و ال A موجود في F
+
+230
+00:24:13,120 --> 00:24:18,080
+مين ماكان يكون بشرط ألا يكون العنصر الصفري لو كان
+
+231
+00:24:18,080 --> 00:24:23,140
+unity و الله unit كل ماعناه مش مشكلة يبقى هنا
+
+232
+00:24:23,140 --> 00:24:32,880
+بداجة أقول that ال F of X زائد A be irreducible
+
+233
+00:24:32,880 --> 00:24:42,900
+over liquidإيش بدون أثمة يا بنات؟ إن ال F of X
+
+234
+00:24:42,900 --> 00:24:49,380
+بدون A الرديوسة والعلامين على ال EQ طبعا هذا ال
+
+235
+00:24:49,380 --> 00:24:54,420
+chapter غلبه بالتناقض يبقى حدش يحسن من حد حنبرهن
+
+236
+00:24:54,420 --> 00:25:03,700
+بالتناقض كذلك يبقى باجي بيقول أسيون افترضوا that
+
+237
+00:25:03,700 --> 00:25:17,910
+إن ال F of X isreducible over ال Q فال
+
+238
+00:25:17,910 --> 00:25:26,690
+F of X بقدر اكتبها كحاصل ضارب two polynomials اللي
+
+239
+00:25:26,690 --> 00:25:36,530
+هما مين ال G of X في ال H of X بحيث ال G of Xو ال
+
+240
+00:25:36,530 --> 00:25:44,250
+H of X موجودة وين؟ فال Q of X و التنتين are of
+
+241
+00:25:44,250 --> 00:25:54,970
+lower degree موجودة and of lower degree يعني درجة
+
+242
+00:25:54,970 --> 00:26:02,470
+ال G و درجة ال H أقل من درجة من أقل من درجة اللي
+
+243
+00:26:02,470 --> 00:26:12,000
+هو L طيبالان بدنا نشيل كل X و الحكمة كان X زائد A
+
+244
+00:26:12,000 --> 00:26:19,500
+ونشوف ايش اللي بدي يحصل بلوحة F of X زائد A هتساوي
+
+245
+00:26:19,500 --> 00:26:30,180
+D of X زائد A في H of X زائد A طب استننا شوية خلي
+
+246
+00:26:30,180 --> 00:26:37,040
+المعلومة هنا بدنا نشوف هل هذا معناهإن ال F of X
+
+247
+00:26:37,040 --> 00:26:41,700
+زائد ال A is reduced to a point تعالى نشوف إذا
+
+248
+00:26:41,700 --> 00:26:46,400
+الدرجات جد بعض أه والله بصير مش جد بعض يبقى ليس
+
+249
+00:26:46,400 --> 00:26:51,360
+صحيحة خليني أسألكوا السؤال التالت لو قلتك أنا عندي
+
+250
+00:26:51,360 --> 00:26:58,560
+X تربية وعندي X زائد واحد لكل تربية قداش درجة
+
+251
+00:26:58,560 --> 00:27:05,470
+الأولى والتانية زي بعض لو قلتك عندي الأولى Xتربية
+
+252
+00:27:05,470 --> 00:27:15,290
+زائد واحد وعندي X زائد خمستاشر لكل تربية نفس الشيء
+
+253
+00:27:15,290 --> 00:27:20,430
+يبقى إضافة ال constant لا يغير من درجة ال
+
+254
+00:27:20,430 --> 00:27:25,410
+polynomial بغير من شكلها صحيح لكن لا يغير من درجة
+
+255
+00:27:25,410 --> 00:27:32,350
+ال polynomial يبقى بناء عليه لو بد ال degree لمين؟
+
+256
+00:27:33,280 --> 00:27:43,000
+للـ G of X زائد ال E هل هي ال degree لل G of X؟
+
+257
+00:27:43,000 --> 00:27:48,320
+مطبق تماما، لا بغيرهاش، طب وال degree لل G of X
+
+258
+00:27:48,320 --> 00:27:56,330
+أقل من ال degree لل F of X صحيح ولا لا؟و ال degree
+
+259
+00:27:56,330 --> 00:28:01,270
+لل f of x مش هي نفس ال degree تبع ال f of x زائد
+
+260
+00:28:01,270 --> 00:28:09,010
+ال a يبقى هو هي نفس ال degree تبع ال f of x زائد
+
+261
+00:28:09,010 --> 00:28:17,830
+ال a قريت اعجبتكم بس ان ال degree لل h of x زائد
+
+262
+00:28:17,830 --> 00:28:26,430
+ال a مش هي عبارة عن ال degree لل h of xصح؟ وال
+
+263
+00:28:26,430 --> 00:28:33,210
+degree لل H of X أقل من ال degree لل F of X اللي
+
+264
+00:28:33,210 --> 00:28:41,650
+هي بدها تساوي ال degree لل F of X زائد ال A إذا
+
+265
+00:28:41,650 --> 00:28:48,850
+صارت درجة F of X زائد ال A بده يقابلها درجة G
+
+266
+00:28:48,850 --> 00:28:56,230
+ودرجة ال H اللي هما أقلدرجة g of x زائد a اللي هم
+
+267
+00:28:56,230 --> 00:29:02,950
+اقل من درجة f of x زائد a يبقى صاروا اتنين هذول of
+
+268
+00:29:02,950 --> 00:29:09,630
+lower degree صحيح ولا لأ؟ يبقى صار هذه بتوصف بشكل
+
+269
+00:29:09,630 --> 00:29:18,090
+هذا ال f of x زائد a بتساوي ال g of x زائد a في ال
+
+270
+00:29:18,090 --> 00:29:21,130
+h of x زائد a
+
+271
+00:29:25,380 --> 00:29:35,720
+زائد ال a وال h of x زائد ال a are of lower degree
+
+272
+00:29:35,720 --> 00:29:42,500
+مدام lower degree يبقى هذا principle ولا لا just
+
+273
+00:29:42,500 --> 00:29:52,080
+irreducible ولا لا صحيح يبقى this means that هذا
+
+274
+00:29:52,080 --> 00:30:01,270
+يعنيإن ال F of X زائد ال A is reducible is
+
+275
+00:30:01,270 --> 00:30:10,110
+reducible على مين؟ على ال Q على .. على .. شغلنا
+
+276
+00:30:10,110 --> 00:30:16,430
+كان في ال F و في ال D reducible على ال Q و على ال
+
+277
+00:30:16,430 --> 00:30:17,850
+F على
+
+278
+00:30:21,380 --> 00:30:26,660
+على F وليس على Q يا عزيزي. يبقى الـ reducible على
+
+279
+00:30:26,660 --> 00:30:36,500
+F. وهذه صنحيلية على F. جل من لا يسكت. يبقى كل
+
+280
+00:30:36,500 --> 00:30:43,640
+شغلنا هذا على F. وهذه كلها على F. لو قلنا على Q صح
+
+281
+00:30:43,640 --> 00:30:49,040
+بسم الله أخدنا حالة خاصة. لأن الـ Q is إيه فيه؟لكن
+
+282
+00:30:49,040 --> 00:30:56,520
+احنا كله شغلنا على مين؟ على F of X كل كيوز حطي
+
+283
+00:30:56,520 --> 00:31:02,480
+مكانها F of X تمام؟ يبقى هذا معناه انه reducible
+
+284
+00:31:02,480 --> 00:31:10,820
+over اللي هو مين؟ over F تناقض؟ اه احنا احنا احنا
+
+285
+00:31:10,820 --> 00:31:16,200
+اقتربناها انها reducible يبقى صار عندنا
+
+286
+00:31:16,200 --> 00:31:17,440
+contradiction
+
+287
+00:31:19,890 --> 00:31:26,230
+يبقى فرضنا اللي فرضناه غلط وعكسه هو الصح يبقى هنا
+
+288
+00:31:26,230 --> 00:31:39,110
+سؤال الـ F of X is irreducible over F وهو المفهوم
+
+289
+00:31:39,110 --> 00:31:47,300
+طيب، الآن هذا نبرسي من السؤالنمرة D من السؤال بده
+
+290
+00:31:47,300 --> 00:31:57,380
+تطبيق عملي على الحالة C فراح قال ليش نمرة D نمرة
+
+291
+00:31:57,380 --> 00:32:08,640
+D من السؤال بيقول use for C استخدم for C to prove
+
+292
+00:32:08,640 --> 00:32:19,220
+to prove thatمش هتروح تثبت أنه التمامية x تكيّب
+
+293
+00:32:19,220 --> 00:32:28,420
+ماقصة 6x زائد الواحد is irreducible على الكيوب is
+
+294
+00:32:28,420 --> 00:32:39,600
+irreducible over الكيوب solution
+
+295
+00:32:44,430 --> 00:32:49,590
+يبقى ال feed اللي عندنا هذا يا بنات صار من؟ صار ال
+
+296
+00:32:49,590 --> 00:32:55,490
+Q، كويس؟ وقال استخدم numeracy هذا اللي استخدمته
+
+297
+00:32:55,490 --> 00:33:01,310
+هنا لإثبات أنه هذه ال function f of x is
+
+298
+00:33:01,310 --> 00:33:06,070
+irreducible على ال Q، بقوله كويس، يبقى احنا عندنا
+
+299
+00:33:06,070 --> 00:33:11,750
+f of x ليه تمانية x تكييف، نعطي ال 6x زايد واحد
+
+300
+00:33:13,340 --> 00:33:21,500
+طبعا بدا بياخدله TA موجودة في ال Q بس بشرط ال A
+
+301
+00:33:21,500 --> 00:33:27,040
+عنصر غير صفي و أبسط الشغلات خد واحد صحيح الواحد
+
+302
+00:33:27,040 --> 00:33:35,140
+موجود في ال Q عادي جدا يبقى أنا لو أخدت ال F of X
+
+303
+00:33:35,140 --> 00:33:43,240
+plus oneيبقى هذا تمانية في X plus one لكل تكييب
+
+304
+00:33:43,240 --> 00:33:50,420
+ناقص ستة في X plus one plus one بدي أفك هذا الهوث
+
+305
+00:33:50,420 --> 00:33:55,840
+يبقى هاي تمانية هذا X تكييب زائد تلاتة X ترمية
+
+306
+00:33:55,840 --> 00:34:05,200
+زائد تلاتة X زائد واحد ناقص ستة X زائد ناقص ستة في
+
+307
+00:34:05,200 --> 00:34:13,220
+Xزائد واحد زائد واحد هم هذه لو فكتها بده يصير f of
+
+308
+00:34:13,220 --> 00:34:21,220
+x زائد واحد يصير تمانية x تكيب زائد أربعة وعشرين x
+
+309
+00:34:21,220 --> 00:34:29,100
+تربيع زائد أربعة وعشرين x زائد تمانية ناقص ستة x
+
+310
+00:34:29,100 --> 00:34:36,940
+ناقص ستة زائد واحد بمعنى آخرصار ال F of X زائد
+
+311
+00:34:36,940 --> 00:34:44,700
+واحد يساوي تمانية X تكايب يااش مشكلة الاربع وعشرين
+
+312
+00:34:44,700 --> 00:34:51,100
+X ترابيع يااش مشكلة طلعولي هنا ناقص ستة X وزائد
+
+313
+00:34:51,100 --> 00:34:57,900
+اربع وعشرين X بضل قدير زائد تمانتاشر X وعندك
+
+314
+00:34:57,900 --> 00:35:04,710
+تمانية واحد تسعة ناقص ستة بضل قدير بضل دلقخير.
+
+315
+00:35:06,230 --> 00:35:15,970
+الآن بتاجر هذه النظرية موجودة في الـ Z6 معاملات
+
+316
+00:35:15,970 --> 00:35:25,530
+كلهم موجودات في Z انتجار صح ولا لا؟ يبقى هذه
+
+317
+00:35:25,530 --> 00:35:34,900
+البرنامج كلها موجودة في Z6 تمام؟ فالعيليللعناصر
+
+318
+00:35:34,900 --> 00:35:41,100
+هذول. التلاتة prime بتسبهم ولا لا؟ ولا يقسم
+
+319
+00:35:41,100 --> 00:35:46,480
+التمانية. والتلاتة تربيع التسعة لا تقسم التلاتة.
+
+320
+00:35:46,500 --> 00:35:53,620
+إيه؟ هذه نظرية كذلك؟ ولا لا؟ يرجعيننا الآن التلاتة
+
+321
+00:35:53,620 --> 00:35:58,980
+لا تقسم التمانية. لكن التلاتة بتقسم الأربعة
+
+322
+00:35:58,980 --> 00:36:05,760
+وعشرين. والتلاتة بتقسم التمنتاشروالتلاتة تقسمي
+
+323
+00:36:05,760 --> 00:36:13,540
+التلاتة أندي التلاتة ترجعي تسعة لتقسمي التلاتة
+
+324
+00:36:13,540 --> 00:36:20,380
+يبقى الدالة هذي إيش؟ R دي و سبب على ال Q يبقى هنا
+
+325
+00:36:20,380 --> 00:36:32,800
+Y previous theorem من نظرية السابقة ال F of X زائد
+
+326
+00:36:32,800 --> 00:36:45,420
+واحدis irreducible over the cube.طب أطلعي هنا لو
+
+327
+00:36:45,420 --> 00:36:50,920
+كانت هذه irreducible على الفيل يبقى الفوبكس من دون
+
+328
+00:36:50,920 --> 00:36:57,960
+ال a irreducible يبقى five excercises
+
+329
+00:36:57,960 --> 00:37:08,280
+خمسة part cالـ F of X اللي هي تمانية X تكييم ناقص
+
+330
+00:37:08,280 --> 00:37:19,940
+ستة X زائد واحد is irreducible over لكي هو المطلوب
+
+331
+00:37:19,940 --> 00:37:27,240
+.طيب ولك في مسائل لسه جاية بتنحل على part B و part
+
+332
+00:37:27,240 --> 00:37:32,140
+A يعني ضروري اتروح اتبرهنيالـ A و الـ B زي ما
+
+333
+00:37:32,140 --> 00:37:37,680
+برهننا الـ C حرفياً كما يعني بدك تاخد polynomial
+
+334
+00:37:37,680 --> 00:37:42,280
+بدياك انت تبقيها irreducible انت فرضها irreducible
+
+335
+00:37:42,280 --> 00:37:48,560
+و تروح اتحللي و نحو ذلك. كان هذا هو المثال أو
+
+336
+00:37:48,560 --> 00:37:54,960
+السؤال رقم خمسة دي. بدنا نروح لسؤال رقم ستة وهو
+
+337
+00:37:54,960 --> 00:38:02,260
+تعميم للحالة اللي خدناها قبل شويةconstruct field
+
+338
+00:38:02,260 --> 00:38:08,740
+ال order له تمانية او ال order له تسعة هذا السؤال
+
+339
+00:38:08,740 --> 00:38:16,220
+اللي هو سؤال ستة سؤال ستة بيقول افترض ان عندنا ال
+
+340
+00:38:16,220 --> 00:38:26,020
+F of X موجودة في ZP وهو هذه irreducible هذه ال F
+
+341
+00:38:26,020 --> 00:38:28,320
+ال F of X is
+
+342
+00:38:32,740 --> 00:38:43,000
+irreducible irreducible over اللي هو there P و
+
+343
+00:38:43,000 --> 00:38:49,780
+ال P is prime و ال degree لل F بده يساوي ال N و ال
+
+344
+00:38:49,780 --> 00:38:58,890
+degree لل F بده يساوي ال Nagain اثبت ان هذا is a
+
+345
+00:38:58,890 --> 00:39:05,950
+field show that نزل
+
+346
+00:39:05,950 --> 00:39:13,850
+P of X modularly principal I P generated by F of X
+
+347
+00:39:13,850 --> 00:39:21,870
+معناه is a field with
+
+348
+00:39:25,340 --> 00:39:26,740
+P⁻⁹
+
+349
+00:40:10,810 --> 00:40:18,090
+خذ فرنوميل F of X من الدرجة النونية موجودة في ZP
+
+350
+00:40:18,090 --> 00:40:24,410
+ZP of X moduloالـ Principle Ideal generated by هذه
+
+351
+00:40:24,410 --> 00:40:30,010
+ال Polynomial SAP وعدد ال عناصر يسوى P to the
+
+352
+00:40:30,010 --> 00:40:37,210
+power N زي المثالين اللي اتوا قبل قليل P أُس درجة
+
+353
+00:40:37,210 --> 00:40:41,590
+ال Polynomial ال Polynomial من الدرجة النونية يبقى
+
+354
+00:40:41,590 --> 00:40:48,910
+أُس L ال P هو ال Prime تبع Main تبع Z P Lيبقى بدنا
+
+355
+00:40:48,910 --> 00:40:54,470
+نيجي نبره صحة هذا الكلام المعلومات اللي عندنا F of
+
+356
+00:40:54,470 --> 00:41:03,410
+X is irreducible على مين؟ على P يبقى هنا let F of
+
+357
+00:41:03,410 --> 00:41:15,050
+X be irreducible polynomial on
+
+358
+00:41:18,430 --> 00:41:27,110
+ZP ما هو معنى هذا الكلام؟ نختصف
+
+359
+00:41:27,110 --> 00:41:31,470
+الدوري على طول الخط يبقى ال principle id
+
+360
+00:41:31,470 --> 00:41:36,310
+الgenerated by F of X هو maximal طبق قليل نظرية
+
+361
+00:41:36,310 --> 00:41:43,890
+يبقى هنا by a previous theorem
+
+362
+00:41:46,270 --> 00:41:58,470
+my previous theorem P of X ال F of X is
+
+363
+00:41:58,470 --> 00:42:06,690
+maximum positive in
+
+364
+00:42:06,690 --> 00:42:11,510
+NZC
+
+365
+00:42:15,830 --> 00:42:23,930
+AX ما ده maximal ideal بالكرولر رقم واحد هذا عبارة
+
+366
+00:42:23,930 --> 00:42:28,130
+عن field يبقى
+
+367
+00:42:28,130 --> 00:42:33,650
+باي انا
+
+368
+00:42:33,650 --> 00:42:44,130
+مش بدنا اثبت ان هذا field صحيح يبقى باي
+
+369
+00:42:47,040 --> 00:42:53,820
+previous quaterly نتيجة
+
+370
+00:42:53,820 --> 00:43:06,580
+السابقة we have ان z هي of x modular principle i
+
+371
+00:43:06,580 --> 00:43:12,340
+.e. generated by f of x is a
+
+372
+00:43:17,770 --> 00:43:25,050
+شو شكله؟ شكله
+
+373
+00:43:25,050 --> 00:43:33,310
+هو Z P of X موديولة ال principle ideal generated
+
+374
+00:43:33,310 --> 00:43:45,910
+by ال F of X بده يساوي مين؟ G of X زائدthe
+
+375
+00:43:45,910 --> 00:43:52,050
+principle ideal generated by f of x such that ان
+
+376
+00:43:52,050 --> 00:43:59,470
+ال g of x موجودة في z في p of x الشكل اللي عامله
+
+377
+00:43:59,470 --> 00:44:06,970
+twice فانا بدي ال g of x دي يمكن الدرجة تبعت أقل
+
+378
+00:44:06,970 --> 00:44:12,830
+من ال f of x ويمكن تكون أكبر من ال f of xإذا أقل
+
+379
+00:44:12,830 --> 00:44:16,530
+من درجة الفوبكس خلاصنا انتهينا من الموضوع لأنه في
+
+380
+00:44:16,530 --> 00:44:21,530
+المثالين اللي قبل قليل ال principle ideal بقينا
+
+381
+00:44:21,530 --> 00:44:28,150
+يقولوا ال remain درجته أقل من درجة اللي هو الدالة
+
+382
+00:44:28,150 --> 00:44:32,250
+اللي ولدتني ال principle ideal صحيح ولا لا؟ إذا
+
+383
+00:44:32,250 --> 00:44:38,510
+هذه النقطة تكون أقل وقد تكون أكبر يبقى بعمل ال
+
+384
+00:44:38,510 --> 00:44:43,530
+division algorithmأو long division يبقى بال
+
+385
+00:44:43,530 --> 00:44:50,030
+division algorithm هذه بقدر أقول هي F of X في ال Q
+
+386
+00:44:50,030 --> 00:44:56,410
+of X زائد ال R of X زائد ال principle ideal
+
+387
+00:44:56,410 --> 00:45:04,690
+generated by F of X وبشرط ان ال R of X بدأت سوى 0
+
+388
+00:45:04,690 --> 00:45:14,660
+او ال degree لل R of Xأقل من ال degree لل F of X
+
+389
+00:45:14,660 --> 00:45:22,000
+مظبوط هيك؟ يبقى أنا شيلت الجيب وحطيتها in general
+
+390
+00:45:22,000 --> 00:45:27,880
+السؤال هو هذا ال element موجود في ال ideal هذا؟
+
+391
+00:45:27,880 --> 00:45:34,760
+يبقى صحيح اني اكتب ال R of X زائد ل principle
+
+392
+00:45:34,760 --> 00:45:41,930
+ideal generated by F of Xبحيث ال R of X يسوى Zero
+
+393
+00:45:41,930 --> 00:45:50,550
+أورى ال degree لل R of X أقل من ال degree لمين؟ لل
+
+394
+00:45:50,550 --> 00:45:56,890
+F of X اللي هو يسوى قداش ال degree لل F of X لأن
+
+395
+00:45:56,890 --> 00:46:04,690
+هو معطينيها مش من عندي طيب إذا حط ال general form
+
+396
+00:46:04,690 --> 00:46:15,680
+تبعها ال general form هوالـ A0 زائد A1 X زائد A2 X
+
+397
+00:46:15,680 --> 00:46:23,820
+تربية زائد A N minus ال 1 في X minus ال 1 مظبوط؟
+
+398
+00:46:23,820 --> 00:46:31,740
+زائد لـ Principle ideal generated by F of X بحيث
+
+399
+00:46:31,740 --> 00:46:43,830
+أن الـ A0 والـ A1 والـ A N minus ال 1موجودة في ZP
+
+400
+00:46:43,830 --> 00:46:54,090
+يبقى عناصر في ZP يبقى ملاحظين ان درجة هذه اقل من
+
+401
+00:46:54,090 --> 00:47:00,390
+درجة من من درجة F of X صحيح ولا لا؟ طيب ممتاز جدا
+
+402
+00:47:00,390 --> 00:47:07,110
+يبقى هذا هو الشكل العام للعنصرزي قبل قليل، لمّا كل
+
+403
+00:47:07,110 --> 00:47:13,530
+فرنسي في المدرجة التانية خلّينه المضافل من الدرجة
+
+404
+00:47:13,530 --> 00:47:17,490
+الأولى، لما كل فرنسي بالأيدي المدرجة التالتة،
+
+405
+00:47:17,490 --> 00:47:22,250
+خلّينه المدرجة التالتة، يعني دائما وأبدأ أقل منه،
+
+406
+00:47:22,250 --> 00:47:28,430
+يعني وكأن هذا السؤال هو تعميم للمثالين اللي أخدهم
+
+407
+00:47:28,430 --> 00:47:34,910
+قبل قليل، طب بدأ أعرف أكمانصر فينا،أظن كلكوا
+
+408
+00:47:34,910 --> 00:47:39,950
+خدرستوا احتمالات، مظبوط؟ وكداش عدد العناصر،
+
+409
+00:47:39,950 --> 00:47:46,430
+الإيهات هدول؟ كداش عدد هدول؟ N، ممتاز ده، يبقى
+
+410
+00:47:46,430 --> 00:47:51,750
+هدول عددهم، السؤال هو بكم طريقة بقدر اختار كل
+
+411
+00:47:51,750 --> 00:47:56,170
+عنصر؟ P، لإن هدول العناصر كلهم بيزد فيه، يفتخر
+
+412
+00:47:56,170 --> 00:48:01,150
+Zero، يواحد، يتنين، يتلاتة، يفي ناقص واحد، اللي هو
+
+413
+00:48:01,150 --> 00:48:07,510
+أخر عنصريبقى عدد القلوب اللي بقدر اختاره هو P to
+
+414
+00:48:07,510 --> 00:48:17,610
+the power N يبقى number of
+
+415
+00:48:17,610 --> 00:48:32,840
+elements in this field is P to the power Nبعدد
+
+416
+00:48:32,840 --> 00:48:37,860
+العناصر وفيه التدفارين زي ما كنا بنعمل قبل قليل في
+
+417
+00:48:37,860 --> 00:48:43,900
+المثالين السابقين بدنا نعطي تطبيق مباشر عليه في
+
+418
+00:48:43,900 --> 00:48:48,680
+عندك سؤال سبعة و سؤال تمانى بناخد سؤال ثاني رقم
+
+419
+00:48:48,680 --> 00:48:53,500
+كبير بدناش رقم صغير توا خدنا تمانية و تسعة خدنا
+
+420
+00:48:53,500 --> 00:48:57,740
+رقم تمانية و رقم دوسرة و رقم سبعة و عشرين يبقى
+
+421
+00:48:57,740 --> 00:49:08,050
+باجي بقول its a precise رقم قدررقم تمانية ايه
+
+422
+00:49:08,050 --> 00:49:13,770
+فيه ال .. الفارضة
+
+423
+00:49:13,770 --> 00:49:19,110
+اللي هو السبعة وعشرين طبعا اللي جاله خمسة وعشرين
+
+424
+00:49:19,110 --> 00:49:24,670
+بتجعله يقولي خمسة تربيع هذا
+
+425
+00:49:24,670 --> 00:49:33,520
+تلاتة وستلاتة يعني هذا هذابدي ساوي تلاتة أس تلاتة
+
+426
+00:49:33,520 --> 00:49:40,460
+يعني بدي زي ال D3 نشغل في زي ال D3 و ال Polynomial
+
+427
+00:49:40,460 --> 00:49:44,700
+يعني ندخل بالطريقة التالتة تقول ان شاء الله خلصنا
+
+428
+00:49:44,700 --> 00:49:50,600
+Polynomial اكتر خديلك واحدة منها تمام؟ اذا ما
+
+429
+00:49:50,600 --> 00:49:52,800
+زبطتش اللولة ممكن تروح الدورة على التالت اذا
+
+430
+00:49:52,800 --> 00:49:55,520
+مازبطتش اللولة دوري على التالت و هكذا يعني انا
+
+431
+00:49:55,520 --> 00:49:59,930
+ممكن اخد Polynomial تظبط معاهوتنتين تلاتة اربعان
+
+432
+00:49:59,930 --> 00:50:03,190
+ياخدوا كلولهم الاخرون تظبط يعني الكلوم اللي افضل
+
+433
+00:50:03,190 --> 00:50:07,310
+اعطيها ليس القرآن نزله بين الاسماع مفيش غيرها لكن
+
+434
+00:50:07,310 --> 00:50:15,430
+لأ ممكن يكون شيء غيرها خديني
+
+435
+00:50:15,430 --> 00:50:24,110
+مثلا ال F of X يسوي X تكييب زي X تربيع زي اتنين اي
+
+436
+00:50:24,110 --> 00:50:34,410
+كلولهم يلمن الدرجة E تالتةبدأي اشتغل on z3 اه يبقى
+
+437
+00:50:34,410 --> 00:50:41,450
+بدي اشتغل على z3 بدي اروح اشوف مين ال F of 0
+
+438
+00:50:41,450 --> 00:50:51,910
+بالنهر و ال F of واحد واحد واحد اتنين اربع في زي
+
+439
+00:50:51,910 --> 00:51:00,010
+التلاتة واحد بدي اخد ال F of اتنينهذا تمانية من
+
+440
+00:51:00,010 --> 00:51:07,270
+أربعة معاشر اتنين اربعتاشر زدتري باتنين يبقى اتنين
+
+441
+00:51:07,270 --> 00:51:14,230
+يبقى ماعنديش zeros على زدتري يبقى باجي بقول له sir
+
+442
+00:51:14,230 --> 00:51:25,010
+f of x has no zeros on والله over زدتري
+
+443
+00:51:46,210 --> 00:51:55,170
+طبعا يبقى دول ما همش zeros على Z3 كويس؟ إذن بقدر
+
+444
+00:51:55,170 --> 00:52:06,120
+أجيب ال field مباشرة يبقى هنا Z E3 R Tموديولو ال X
+
+445
+00:52:06,120 --> 00:52:19,640
+تكييب زاد X تربيع زائدي اتنين هذا is a field طب
+
+446
+00:52:19,640 --> 00:52:31,580
+مين العناصر تبقى؟ where؟ حيث ال Z3 of X موديولو ال
+
+447
+00:52:31,580 --> 00:52:38,060
+principle idealgenerated by X تكييف زائد X تربيع
+
+448
+00:52:38,060 --> 00:52:46,040
+زائد اتنين بده يساوي اكتربيه اكتربيه
+
+449
+00:52:46,040 --> 00:52:54,840
+اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه
+
+450
+00:52:54,840 --> 00:52:58,560
+اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه
+
+451
+00:52:58,560 --> 00:53:00,300
+اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه
+
+452
+00:53:02,060 --> 00:53:10,420
+وبحيث ان الـA والـB والـC موجودة كلها هذه في Z3
+
+453
+00:53:10,420 --> 00:53:19,240
+هكم عنصر في هذا؟ سبعة وعشرين عنصر تمام؟ بدك ايه؟
+
+454
+00:53:19,240 --> 00:53:22,140
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+455
+00:53:22,140 --> 00:53:22,820
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+456
+00:53:22,820 --> 00:53:24,340
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+457
+00:53:24,340 --> 00:53:24,440
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+458
+00:53:24,440 --> 00:53:24,740
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+459
+00:53:24,740 --> 00:53:28,940
+انا براها ايه
+
+460
+00:53:28,940 --> 00:53:35,960
+في البيت؟ انا بخلاص؟ وضاربهم وجامعهم وطرحهم زي
+
+461
+00:53:35,960 --> 00:53:40,680
+اللي قبل؟ فهي عندنا الآن سؤال عشرة السؤال طبعا
+
+462
+00:53:40,680 --> 00:53:47,540
+عشرة حاطط فيه خمسة مطالب مش هحل الى مطلوبين، مطلوب
+
+463
+00:53:47,540 --> 00:53:52,960
+اليوم ومطلوب المرة الجاية لكن نمره A ونمره C زي
+
+464
+00:53:52,960 --> 00:54:01,410
+بعض يبقى نمره A بتفتخدي اللي هو العدد ثلاثةلا يقسم
+
+465
+00:54:01,410 --> 00:54:05,290
+معامل ال Exos خمسة لكن بيقسم معامل ال Exos أربعة و
+
+466
+00:54:05,290 --> 00:54:09,850
+بيقسم معامل ال Exos أربعة و بيقسم الستة و تلاتة
+
+467
+00:54:09,850 --> 00:54:15,550
+Price يبقى طبقا للنظرية هذه Irreducible نمرا سي
+
+468
+00:54:15,550 --> 00:54:19,230
+نفس الطريقة إيه Exos أربعة زي التلاتة Exos التربية
+
+469
+00:54:19,230 --> 00:54:23,330
+زي التلاتة التلاتة بتقسم أخر معاملة بتقسمش الأول
+
+470
+00:54:23,330 --> 00:54:28,670
+مربعة أعلى يقسم العدد أخر يبقى Irreducibleيبقى
+
+471
+00:54:28,670 --> 00:54:33,750
+الأولى و التالتى زى بعض و حلهم سطر واحد النص
+
+472
+00:54:33,750 --> 00:54:41,190
+النظرية مباشرة لكن لو جيتى لنمرة P نمرة P بيقوللى
+
+473
+00:54:41,190 --> 00:54:50,330
+اللى هى X أُص أربعة زائد X زائد واحد زائد X زائد
+
+474
+00:54:50,330 --> 00:54:56,150
+واحد بدي
+
+475
+00:54:56,150 --> 00:55:04,160
+اشتغلعلى مين؟ على field يبقى بجيب اقوله مثلا ان
+
+476
+00:55:04,160 --> 00:55:09,600
+زيت تويها هذي
+
+477
+00:55:09,600 --> 00:55:15,920
+ال F of X هذي في السؤال تشوفوا هل هذا reduceable
+
+478
+00:55:15,920 --> 00:55:21,380
+والله ايه reduceable على ال Q سؤالي الخمس نقاط كله
+
+479
+00:55:21,380 --> 00:55:26,260
+تشوفوا هل reduceable والله irreducible على اللو
+
+480
+00:55:26,260 --> 00:55:32,460
+جيت لل F bar يا بنات of X ليه ال X وصار بعزاه ال X
+
+481
+00:55:32,460 --> 00:55:37,360
+ده اللي هتتغير؟ هي نفسه يبقى سعر ال degree لل F هي
+
+482
+00:55:37,360 --> 00:55:43,020
+ال degree لمن؟ لل F bar يبقى هذا بدي يعطينا ان ال
+
+483
+00:55:43,020 --> 00:55:49,000
+degree لل F هي نفس ال degree لل F bar ذكرت رحينا
+
+484
+00:55:49,000 --> 00:55:54,440
+نظرية؟ خلاصنا؟ طيب ضلي علينا شغلة بسيطة ناسي احنا
+
+485
+00:55:54,440 --> 00:56:01,690
+بنشتغل ويه؟يبقى ال F of zero يساوي واحد وال F of
+
+486
+00:56:01,690 --> 00:56:10,990
+واحد يساوي واحد يبقى صارت has no zeros يبقى هذا
+
+487
+00:56:10,990 --> 00:56:22,190
+بدي يعطينا ال F bar of X has no zeros on Z two وال
+
+488
+00:56:22,190 --> 00:56:28,000
+degree لل Fبتساوي ال degree لل F bar يبقى صورة ال
+
+489
+00:56:28,000 --> 00:56:39,620
+F bar irreducible على Z2 يبقى الصورة F bar of X is
+
+490
+00:56:39,620 --> 00:56:50,980
+irreducible over Z2 هذا بده يعطي كمان ان F الأصلية
+
+491
+00:56:50,980 --> 00:56:58,430
+is irreducible على Z2هدفة هي يعطيكي ان ال F of X X
+
+492
+00:56:58,430 --> 00:57:09,790
+أُس أربع زي X زي واحد is irreducible over liquid
+
+493
+00:57:09,790 --> 00:57:13,450
+خديني
+
+494
+00:57:13,450 --> 00:57:21,130
+هالمثال باشي طبعانمر يا إيه؟ اللي هو آخر السؤال
+
+495
+00:57:21,130 --> 00:57:27,090
+يعطيناكوا مثال حرفي زيه يبقى بتحلوه بنفس الطريقة،
+
+496
+00:57:27,090 --> 00:57:40,150
+جاري قولي في السؤال 12 وسؤال 14 وسؤال 18 وسؤال
+
+497
+00:57:40,150 --> 00:57:44,870
+23 وسؤال
+
+498
+00:57:44,870 --> 00:57:45,670
+25
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2034f2fcf3db13da501c556754832ef1319052f3
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4575, "start": 20.91, "end": 45.75, "text": "بسم الله الرحمن الرحيم نكمل ما كنا نعمل بيه المرة الماضية في نفس الشفقة. ولمرة اللي فاتت في نهاية المحاضرة أعطيناكوا مثال ولمّا ننتهي منه. يبقى بدنا نعمل عليه مرة سريعة ثم ننهي هذا المثال ثم ننتقل إلى المثال اللي يليه. We will construct a field of order تمام.", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 24793, 1211, 19446, 9122, 8315, 8717, 25957, 1211, 4724, 1829, 3224, 9673, 25720, 9673, 46958, 10632, 8978, 8717, 36178, 25124, 5172, 28671, 13, 4032, 19528, 25720, 13672, 1829, 6156, 9307, 2655, 8978, 8717, 11296, 10632, 9673, 5016, 46958, 25720, 5551, 3615, 9566, 1829, 8315, 4117, 14407, 50113, 6027, 4032, 19528, 11703, 995, 8717, 29399, 3224, 1829, 9154, 3224, 13, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 25957, 1211, 47356, 3714, 25720, 8608, 16572, 27884, 38637, 2304, 8717, 1863, 3224, 1829, 23758, 9673, 12984, 6027, 38637, 2304, 8717, 29399, 4587, 1211, 30731, 9673, 12984, 6027, 13672, 1829, 7251, 20292, 3224, 13, 492, 486, 7690, 257, 2519, 295, 1668, 46811, 10943, 13], "avg_logprob": -0.2033832644628099, "compression_ratio": 1.8024691358024691, "no_speech_prob": 0.0, "words": [{"start": 20.91, "end": 21.19, "word": "بسم", "probability": 0.90771484375}, {"start": 21.19, "end": 21.37, "word": " الله", "probability": 0.95556640625}, {"start": 21.37, "end": 21.77, "word": " الرحمن", "probability": 0.9710286458333334}, {"start": 21.77, "end": 22.35, "word": " الرحيم", "probability": 0.9923502604166666}, {"start": 22.35, "end": 23.85, "word": " نكمل", "probability": 0.8317057291666666}, {"start": 23.85, "end": 24.39, "word": " ما", "probability": 0.94091796875}, {"start": 24.39, "end": 24.75, "word": " كنا", "probability": 0.992919921875}, {"start": 24.75, "end": 25.23, "word": " نعمل", "probability": 0.9718424479166666}, {"start": 25.23, "end": 25.47, "word": " بيه", "probability": 0.7440592447916666}, {"start": 25.47, "end": 25.93, "word": " المرة", "probability": 0.7095947265625}, {"start": 25.93, "end": 26.53, "word": " الماضية", "probability": 0.9928385416666666}, {"start": 26.53, "end": 26.83, "word": " في", "probability": 0.90771484375}, {"start": 26.83, "end": 27.17, "word": " نفس", "probability": 0.99755859375}, {"start": 27.17, "end": 27.85, "word": " الشفقة.", "probability": 0.65966796875}, {"start": 28.47, "end": 28.85, "word": " ولمرة", "probability": 0.7263997395833334}, {"start": 28.85, "end": 29.03, "word": " اللي", "probability": 0.903076171875}, {"start": 29.03, "end": 29.47, "word": " فاتت", "probability": 0.857421875}, {"start": 29.47, "end": 29.61, "word": " في", "probability": 0.87841796875}, {"start": 29.61, "end": 29.95, "word": " نهاية", "probability": 0.984375}, {"start": 29.95, "end": 30.61, "word": " المحاضرة", "probability": 0.990234375}, {"start": 30.61, "end": 31.27, "word": " أعطيناكوا", "probability": 0.7544991629464286}, {"start": 31.27, "end": 31.77, "word": " مثال", "probability": 0.98046875}, {"start": 31.77, "end": 32.39, "word": " ولمّا", "probability": 0.8739013671875}, {"start": 32.39, "end": 33.21, "word": " ننتهي", "probability": 0.947265625}, {"start": 33.21, "end": 33.69, "word": " منه.", "probability": 0.9853515625}, {"start": 34.15, "end": 34.41, "word": " يبقى", "probability": 0.7689208984375}, {"start": 34.41, "end": 34.63, "word": " بدنا", "probability": 0.916259765625}, {"start": 34.63, "end": 34.97, "word": " نعمل", "probability": 0.7849934895833334}, {"start": 34.97, "end": 35.45, "word": " عليه", "probability": 0.248291015625}, {"start": 35.45, "end": 35.79, "word": " مرة", "probability": 0.71240234375}, {"start": 35.79, "end": 36.55, "word": " سريعة", "probability": 0.8776041666666666}, {"start": 36.55, "end": 37.01, "word": " ثم", "probability": 0.887451171875}, {"start": 37.01, "end": 37.43, "word": " ننهي", "probability": 0.9794921875}, {"start": 37.43, "end": 37.61, "word": " هذا", "probability": 0.97314453125}, {"start": 37.61, "end": 38.17, "word": " المثال", "probability": 0.9280598958333334}, {"start": 38.17, "end": 38.75, "word": " ثم", "probability": 0.751220703125}, {"start": 38.75, "end": 39.39, "word": " ننتقل", "probability": 0.9869384765625}, {"start": 39.39, "end": 39.61, "word": " إلى", "probability": 0.7939453125}, {"start": 39.61, "end": 40.39, "word": " المثال", "probability": 0.98486328125}, {"start": 40.39, "end": 41.01, "word": " اللي", "probability": 0.66455078125}, {"start": 41.01, "end": 41.53, "word": " يليه.", "probability": 0.6775716145833334}, {"start": 41.97, "end": 42.07, "word": " We", "probability": 0.256591796875}, {"start": 42.07, "end": 42.27, "word": " will", "probability": 0.720703125}, {"start": 42.27, "end": 43.01, "word": " construct", "probability": 0.9658203125}, {"start": 43.01, "end": 43.45, "word": " a", "probability": 0.98388671875}, {"start": 43.45, "end": 44.07, "word": " field", "probability": 0.89501953125}, {"start": 44.07, "end": 44.51, "word": " of", "probability": 0.966796875}, {"start": 44.51, "end": 45.15, "word": " order", "probability": 0.87548828125}, {"start": 45.15, "end": 45.75, "word": " تمام.", "probability": 0.972900390625}], "temperature": 1.0}, {"id": 2, "seek": 7165, "start": 46.51, "end": 71.65, "text": "باقي 8 ايش ممكن احطها عدد مرفوع ل أس عدد او ال prime مرفوع ل أس يبقى 8 لي عبارة عن مين؟ 2 أس 3 ممتاز جدا يبقى هذه 2 أس 3 ل 2 هو ال prime و 3 هو الأس 7 وكأنه بيقول لي هذه polynomial", "tokens": [3555, 995, 38436, 1649, 1975, 1829, 8592, 3714, 43020, 1975, 5016, 9566, 11296, 6225, 3215, 3215, 3714, 28480, 45367, 5296, 5551, 3794, 6225, 3215, 3215, 1975, 2407, 2423, 5835, 3714, 28480, 45367, 5296, 5551, 3794, 7251, 3555, 4587, 7578, 1649, 32239, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 22807, 568, 5551, 3794, 805, 3714, 2304, 2655, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 29538, 568, 5551, 3794, 805, 5296, 568, 31439, 2423, 5835, 4032, 805, 31439, 16247, 3794, 1614, 4032, 4117, 33456, 3224, 4724, 1829, 39648, 32239, 29538, 26110], "avg_logprob": -0.23125000380807453, "compression_ratio": 1.6101694915254237, "no_speech_prob": 0.0, "words": [{"start": 46.51, "end": 46.99, "word": "باقي", "probability": 0.8053385416666666}, {"start": 46.99, "end": 47.41, "word": " 8", "probability": 0.162109375}, {"start": 47.41, "end": 48.05, "word": " ايش", "probability": 0.7036946614583334}, {"start": 48.05, "end": 48.81, "word": " ممكن", "probability": 0.964599609375}, {"start": 48.81, "end": 49.95, "word": " احطها", "probability": 0.826416015625}, {"start": 49.95, "end": 50.61, "word": " عدد", "probability": 0.9500325520833334}, {"start": 50.61, "end": 51.35, "word": " مرفوع", "probability": 0.9757486979166666}, {"start": 51.35, "end": 51.55, "word": " ل", "probability": 0.87451171875}, {"start": 51.55, "end": 51.81, "word": " أس", "probability": 0.4141845703125}, {"start": 51.81, "end": 52.25, "word": " عدد", "probability": 0.9501953125}, {"start": 52.25, "end": 52.77, "word": " او", "probability": 0.720703125}, {"start": 52.77, "end": 52.97, "word": " ال", "probability": 0.8037109375}, {"start": 52.97, "end": 53.57, "word": " prime", "probability": 0.70654296875}, {"start": 53.57, "end": 54.41, "word": " مرفوع", "probability": 0.96923828125}, {"start": 54.41, "end": 54.61, "word": " ل", "probability": 0.95263671875}, {"start": 54.61, "end": 54.99, "word": " أس", "probability": 0.922607421875}, {"start": 54.99, "end": 56.19, "word": " يبقى", "probability": 0.8692626953125}, {"start": 56.19, "end": 56.59, "word": " 8", "probability": 0.609375}, {"start": 56.59, "end": 56.83, "word": " لي", "probability": 0.27294921875}, {"start": 56.83, "end": 57.15, "word": " عبارة", "probability": 0.88623046875}, {"start": 57.15, "end": 57.31, "word": " عن", "probability": 0.9736328125}, {"start": 57.31, "end": 57.79, "word": " مين؟", "probability": 0.6873372395833334}, {"start": 57.79, "end": 58.45, "word": " 2", "probability": 0.68994140625}, {"start": 58.45, "end": 58.85, "word": " أس", "probability": 0.81787109375}, {"start": 58.85, "end": 59.13, "word": " 3", "probability": 0.96240234375}, {"start": 59.13, "end": 60.19, "word": " ممتاز", "probability": 0.8890380859375}, {"start": 60.19, "end": 60.77, "word": " جدا", "probability": 0.973876953125}, {"start": 60.77, "end": 61.69, "word": " يبقى", "probability": 0.9669189453125}, {"start": 61.69, "end": 62.13, "word": " هذه", "probability": 0.59130859375}, {"start": 62.13, "end": 62.81, "word": " 2", "probability": 0.9384765625}, {"start": 62.81, "end": 63.33, "word": " أس", "probability": 0.97900390625}, {"start": 63.33, "end": 64.11, "word": " 3", "probability": 0.97705078125}, {"start": 64.11, "end": 64.73, "word": " ل", "probability": 0.67529296875}, {"start": 64.73, "end": 65.29, "word": " 2", "probability": 0.432373046875}, {"start": 65.29, "end": 65.73, "word": " هو", "probability": 0.96240234375}, {"start": 65.73, "end": 65.97, "word": " ال", "probability": 0.83544921875}, {"start": 65.97, "end": 66.37, "word": " prime", "probability": 0.8466796875}, {"start": 66.37, "end": 66.89, "word": " و", "probability": 0.841796875}, {"start": 66.89, "end": 67.35, "word": " 3", "probability": 0.591796875}, {"start": 67.35, "end": 67.69, "word": " هو", "probability": 0.96142578125}, {"start": 67.69, "end": 68.23, "word": " الأس", "probability": 0.906005859375}, {"start": 68.23, "end": 68.55, "word": " 7", "probability": 0.67333984375}, {"start": 68.55, "end": 69.65, "word": " وكأنه", "probability": 0.843017578125}, {"start": 69.65, "end": 70.13, "word": " بيقول", "probability": 0.90966796875}, {"start": 70.13, "end": 70.33, "word": " لي", "probability": 0.333984375}, {"start": 70.33, "end": 70.77, "word": " هذه", "probability": 0.88671875}, {"start": 70.77, "end": 71.65, "word": " polynomial", "probability": 0.88818359375}], "temperature": 1.0}, {"id": 3, "seek": 9326, "start": 72.78, "end": 93.26, "text": "من الدرجة التالتة و تكون irreducible على زكوك واضح؟ كأنه بيقوللي ها هذه وسيلة الرقم اللي عندي أحطه prime مرفوع لأسفل ال prime بيكون هو مين؟ هو ال field زد لهذا الرقم بيكون هو ال field", "tokens": [27842, 32748, 47341, 3660, 16712, 6027, 2655, 3660, 4032, 6055, 30544, 16014, 769, 32128, 15844, 30767, 4117, 2407, 4117, 4032, 46958, 5016, 22807, 9122, 33456, 3224, 4724, 1829, 39648, 20292, 8032, 995, 29538, 46952, 26895, 3660, 34892, 4587, 2304, 13672, 1829, 18871, 16254, 5551, 5016, 9566, 3224, 5835, 3714, 28480, 45367, 5296, 10721, 3794, 5172, 1211, 2423, 5835, 4724, 1829, 30544, 31439, 3714, 9957, 22807, 31439, 2423, 2519, 30767, 3215, 46740, 15730, 34892, 4587, 2304, 4724, 1829, 30544, 31439, 2423, 2519], "avg_logprob": -0.27991617016675996, "compression_ratio": 1.639344262295082, "no_speech_prob": 0.0, "words": [{"start": 72.78, "end": 73.18, "word": "من", "probability": 0.432373046875}, {"start": 73.18, "end": 74.24, "word": " الدرجة", "probability": 0.8885091145833334}, {"start": 74.24, "end": 75.3, "word": " التالتة", "probability": 0.926025390625}, {"start": 75.3, "end": 75.5, "word": " و", "probability": 0.37744140625}, {"start": 75.5, "end": 76.04, "word": " تكون", "probability": 0.82275390625}, {"start": 76.04, "end": 77.2, "word": " irreducible", "probability": 0.7540690104166666}, {"start": 77.2, "end": 77.56, "word": " على", "probability": 0.8408203125}, {"start": 77.56, "end": 78.38, "word": " زكوك", "probability": 0.47418212890625}, {"start": 78.38, "end": 79.8, "word": " واضح؟", "probability": 0.72479248046875}, {"start": 79.8, "end": 80.64, "word": " كأنه", "probability": 0.8961588541666666}, {"start": 80.64, "end": 81.18, "word": " بيقوللي", "probability": 0.73126220703125}, {"start": 81.18, "end": 81.78, "word": " ها", "probability": 0.611572265625}, {"start": 81.78, "end": 82.12, "word": " هذه", "probability": 0.66455078125}, {"start": 82.12, "end": 82.8, "word": " وسيلة", "probability": 0.9415690104166666}, {"start": 82.8, "end": 83.38, "word": " الرقم", "probability": 0.9521484375}, {"start": 83.38, "end": 83.6, "word": " اللي", "probability": 0.945068359375}, {"start": 83.6, "end": 84.02, "word": " عندي", "probability": 0.821533203125}, {"start": 84.02, "end": 84.88, "word": " أحطه", "probability": 0.76953125}, {"start": 84.88, "end": 85.24, "word": " prime", "probability": 0.6494140625}, {"start": 85.24, "end": 85.82, "word": " مرفوع", "probability": 0.9397786458333334}, {"start": 85.82, "end": 86.46, "word": " لأسفل", "probability": 0.75078125}, {"start": 86.46, "end": 86.94, "word": " ال", "probability": 0.63623046875}, {"start": 86.94, "end": 87.52, "word": " prime", "probability": 0.411865234375}, {"start": 87.52, "end": 88.22, "word": " بيكون", "probability": 0.9501953125}, {"start": 88.22, "end": 88.5, "word": " هو", "probability": 0.95849609375}, {"start": 88.5, "end": 89.14, "word": " مين؟", "probability": 0.5999348958333334}, {"start": 89.14, "end": 89.44, "word": " هو", "probability": 0.97265625}, {"start": 89.44, "end": 89.78, "word": " ال", "probability": 0.57275390625}, {"start": 89.78, "end": 90.24, "word": " field", "probability": 0.93603515625}, {"start": 90.24, "end": 90.88, "word": " زد", "probability": 0.690185546875}, {"start": 90.88, "end": 91.32, "word": " لهذا", "probability": 0.955078125}, {"start": 91.32, "end": 91.78, "word": " الرقم", "probability": 0.98388671875}, {"start": 91.78, "end": 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النظرية يبجي هنا بروح بقولهم فال F of X بده تساوي X تكيب زائد X زائد 1 is irreducible over", "tokens": [15042, 11778, 10943, 2423, 7649, 2407, 26108, 11778, 12610, 7251, 3555, 7435, 1829, 32748, 6027, 3660, 16014, 769, 32128, 15844, 1176, 17, 46599, 6027, 2655, 6027, 1829, 16014, 769, 32128, 15844, 2423, 33580, 37893, 39896, 4117, 1975, 9778, 3215, 8717, 9381, 28239, 19913, 2288, 10632, 7251, 3555, 7435, 1829, 34105, 4724, 32887, 5016, 4724, 39648, 16095, 6156, 6027, 479, 295, 1783, 47525, 3224, 6055, 3794, 995, 45865, 1783, 6055, 4117, 1829, 3555, 30767, 16373, 3215, 1783, 30767, 16373, 3215, 502, 307, 16014, 769, 32128, 670], "avg_logprob": -0.2897892407206602, "compression_ratio": 1.546448087431694, "no_speech_prob": 0.0, "words": [{"start": 198.06, "end": 198.34, "word": "ما", "probability": 0.2237548828125}, {"start": 198.34, "end": 198.64, "word": " دام", "probability": 0.755859375}, {"start": 198.64, "end": 199.26, "word": " الانواج", "probability": 0.75}, {"start": 199.26, 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"probability": 0.5028076171875}, {"start": 216.08, "end": 216.68, "word": " تساوي", "probability": 0.8218994140625}, {"start": 216.68, "end": 217.04, "word": " X", "probability": 0.91552734375}, {"start": 217.04, "end": 217.76, "word": " تكيب", "probability": 0.872802734375}, {"start": 217.76, "end": 218.32, "word": " زائد", "probability": 0.81494140625}, {"start": 218.32, "end": 218.7, "word": " X", "probability": 0.98681640625}, {"start": 218.7, "end": 219.18, "word": " زائد", "probability": 0.9332682291666666}, {"start": 219.18, "end": 219.68, "word": " 1", "probability": 0.6435546875}, {"start": 219.68, "end": 220.72, "word": " is", "probability": 0.865234375}, {"start": 220.72, "end": 223.52, "word": " irreducible", "probability": 0.96728515625}, {"start": 223.52, "end": 225.94, "word": " over", "probability": 0.865234375}], "temperature": 1.0}, {"id": 9, "seek": 25299, "start": 226.83, "end": 252.99, "text": "اللي هو Z2 هذا بدي يعطينا by a previous theorem بدي يكون ال F of X اللي هو X تكييف زي X زي واحد is irreducible over ال Q", "tokens": [6027, 20292, 31439, 1176, 17, 23758, 4724, 16254, 37495, 9566, 1829, 8315, 538, 257, 3894, 20904, 4724, 16254, 7251, 30544, 2423, 479, 295, 1783, 13672, 1829, 31439, 1783, 6055, 4117, 1829, 33911, 30767, 1829, 1783, 30767, 1829, 36764, 24401, 307, 16014, 769, 32128, 670, 2423, 1249], "avg_logprob": -0.2824135739752587, "compression_ratio": 1.2352941176470589, "no_speech_prob": 0.0, "words": [{"start": 226.83, "end": 227.17, "word": "اللي", "probability": 0.66259765625}, {"start": 227.17, "end": 227.33, "word": " هو", "probability": 0.94775390625}, {"start": 227.33, "end": 228.49, "word": " Z2", "probability": 0.5037841796875}, {"start": 228.49, "end": 229.17, "word": " هذا", "probability": 0.5517578125}, {"start": 229.17, "end": 229.55, "word": " بدي", "probability": 0.55859375}, {"start": 229.55, "end": 230.45, "word": " يعطينا", "probability": 0.894287109375}, {"start": 230.45, "end": 232.05, "word": " by", "probability": 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أخدناها على اللي هو النظرية الأخيرة المرضى الماضي", "tokens": [40, 81, 986, 84, 32128, 15844, 2423, 33580, 6225, 6027, 1829, 9122, 45865, 3794, 5296, 15042, 11778, 3224, 2423, 479, 295, 1783, 20328, 9640, 2655, 9151, 986, 84, 32128, 15844, 2423, 33580, 23758, 4724, 1829, 12610, 3215, 20292, 286, 46394, 4032, 286, 46394, 39352, 6674, 8717, 31371, 7435, 3660, 12602, 4587, 2304, 36764, 24401, 5551, 9778, 3215, 8315, 11296, 15844, 13672, 1829, 31439, 28239, 19913, 2288, 10632, 16247, 9778, 48923, 9673, 43042, 7578, 9673, 46958, 1829], "avg_logprob": -0.28997564625430416, "compression_ratio": 1.5222222222222221, "no_speech_prob": 0.0, "words": [{"start": 261.43, "end": 262.47, "word": "Irreducible", "probability": 0.65791015625}, {"start": 262.47, "end": 262.87, "word": " على", "probability": 0.85400390625}, {"start": 262.87, "end": 263.11, "word": " ال", "probability": 0.70556640625}, {"start": 263.11, "end": 263.27, "word": " EQ", "probability": 0.273681640625}, {"start": 263.27, "end": 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0.76318359375}, {"start": 279.89, "end": 280.47, "word": " اللي", "probability": 0.895263671875}, {"start": 280.47, "end": 280.91, "word": " هو", "probability": 0.98681640625}, {"start": 280.91, "end": 282.39, "word": " النظرية", "probability": 0.9229736328125}, {"start": 282.39, "end": 283.23, "word": " الأخيرة", "probability": 0.7505696614583334}, {"start": 283.23, "end": 283.75, "word": " المرضى", "probability": 0.8671875}, {"start": 283.75, "end": 284.25, "word": " الماضي", "probability": 0.7454427083333334}], "temperature": 1.0}, {"id": 11, "seek": 31287, "start": 284.87, "end": 312.87, "text": "يبقى هنا سا اللي هو ال X تكييب زي X زي واحد هذا ال ideal is maximal مدام maximal هذا بده يعطينا ان Z2 of X اه موديون ال principle ideal generated by X تكييب زي X زي واحد is A في الدق", "tokens": [1829, 3555, 4587, 7578, 34105, 8608, 995, 13672, 1829, 31439, 2423, 1783, 6055, 4117, 1829, 1829, 3555, 30767, 1829, 1783, 30767, 1829, 36764, 24401, 23758, 2423, 7157, 307, 49336, 3714, 3215, 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ماقصة 6x زائد الواحد is irreducible على الكيوب is irreducible over الكيوب solution", "tokens": [2304, 8592, 8032, 2655, 32887, 5016, 6055, 12984, 3555, 2655, 14739, 3224, 16712, 2304, 10943, 10632, 2031, 6055, 4117, 1829, 11703, 3555, 19446, 4587, 9381, 3660, 1386, 87, 30767, 16373, 3215, 2423, 14407, 24401, 307, 16014, 769, 32128, 15844, 33251, 1829, 2407, 3555, 307, 16014, 769, 32128, 670, 33251, 1829, 37746, 3827], "avg_logprob": -0.2915683827310238, "compression_ratio": 1.2985074626865671, "no_speech_prob": 0.0, "words": [{"start": 1933.0, "end": 1933.28, "word": "مش", "probability": 0.75244140625}, {"start": 1933.28, "end": 1933.8, "word": " هتروح", "probability": 0.9522705078125}, {"start": 1933.8, "end": 1934.52, "word": " تثبت", "probability": 0.98486328125}, {"start": 1934.52, "end": 1935.3, "word": " أنه", "probability": 0.52978515625}, {"start": 1935.3, "end": 1936.74, "word": " التمامية", "probability": 0.7330322265625}, {"start": 1936.74, "end": 1938.2, "word": " x", 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3348.66, "end": 3349.0, "word": " رحينا", "probability": 0.7242431640625}, {"start": 3349.0, "end": 3350.0, "word": " نظرية؟", "probability": 0.76669921875}, {"start": 3350.0, "end": 3351.78, "word": " خلاصنا؟", "probability": 0.77724609375}, {"start": 3351.78, "end": 3352.04, "word": " طيب", "probability": 0.9547526041666666}, {"start": 3352.04, "end": 3352.32, "word": " ضلي", "probability": 0.3902587890625}, {"start": 3352.32, "end": 3352.64, "word": " علينا", "probability": 0.935791015625}, {"start": 3352.64, "end": 3353.02, "word": " شغلة", "probability": 0.8767903645833334}, {"start": 3353.02, "end": 3353.66, "word": " بسيطة", "probability": 0.978515625}, {"start": 3353.66, "end": 3354.2, "word": " ناسي", "probability": 0.6365559895833334}, {"start": 3354.2, "end": 3354.44, "word": " احنا", "probability": 0.8294270833333334}, {"start": 3354.44, "end": 3354.96, "word": " بنشتغل", "probability": 0.94189453125}, {"start": 3354.96, "end": 3355.44, "word": " ويه؟", "probability": 0.4017333984375}], "temperature": 1.0}, {"id": 118, "seek": 338319, "start": 3356.15, "end": 3383.19, "text": "يبقى ال F of zero يساوي واحد وال F of واحد يساوي واحد يبقى صارت has no zeros يبقى هذا بدي يعطينا ال F bar of X has no zeros on Z two وال degree لل F", "tokens": [1829, 3555, 4587, 7578, 2423, 479, 295, 4018, 7251, 3794, 995, 45865, 36764, 24401, 16070, 479, 295, 36764, 24401, 7251, 3794, 995, 45865, 36764, 24401, 7251, 3555, 4587, 7578, 20328, 9640, 2655, 575, 572, 35193, 7251, 3555, 4587, 7578, 23758, 4724, 16254, 37495, 9566, 1829, 8315, 2423, 479, 2159, 295, 1783, 575, 572, 35193, 322, 1176, 732, 16070, 4314, 24976, 479], "avg_logprob": -0.1851058405253195, "compression_ratio": 1.5671641791044777, "no_speech_prob": 0.0, "words": [{"start": 3356.15, "end": 3357.01, "word": "يبقى", "probability": 0.91845703125}, {"start": 3357.01, "end": 3357.21, "word": " ال", "probability": 0.69921875}, {"start": 3357.21, "end": 3357.77, "word": " F", "probability": 0.76318359375}, {"start": 3357.77, "end": 3358.29, "word": " of", "probability": 0.71044921875}, {"start": 3358.29, "end": 3358.77, "word": " zero", "probability": 0.326904296875}, {"start": 3358.77, "end": 3359.45, "word": " يساوي", "probability": 0.84222412109375}, {"start": 3359.45, "end": 3359.93, "word": " واحد", "probability": 0.987060546875}, {"start": 3359.93, "end": 3360.79, "word": " وال", "probability": 0.58349609375}, {"start": 3360.79, "end": 3361.31, "word": " F", "probability": 0.896484375}, {"start": 3361.31, "end": 3361.69, "word": " of", "probability": 0.94189453125}, {"start": 3361.69, "end": 3362.33, "word": " واحد", "probability": 0.99462890625}, {"start": 3362.33, "end": 3363.63, "word": " يساوي", "probability": 0.989013671875}, {"start": 3363.63, "end": 3364.57, "word": " واحد", "probability": 0.985595703125}, {"start": 3364.57, "end": 3366.11, "word": " يبقى", "probability": 0.943603515625}, {"start": 3366.11, "end": 3366.89, "word": " صارت", "probability": 0.97021484375}, {"start": 3366.89, "end": 3367.69, "word": " has", "probability": 0.693359375}, {"start": 3367.69, "end": 3368.21, "word": " no", "probability": 0.9560546875}, {"start": 3368.21, "end": 3369.39, "word": " zeros", "probability": 0.84033203125}, {"start": 3369.39, "end": 3370.61, "word": " يبقى", "probability": 0.97509765625}, {"start": 3370.61, "end": 3370.99, "word": " هذا", "probability": 0.86572265625}, {"start": 3370.99, "end": 3371.49, "word": " بدي", "probability": 0.4156494140625}, {"start": 3371.49, "end": 3371.99, "word": " يعطينا", "probability": 0.8148193359375}, {"start": 3371.99, "end": 3372.21, "word": " ال", "probability": 0.78955078125}, {"start": 3372.21, "end": 3372.57, "word": " F", "probability": 0.9521484375}, {"start": 3372.57, "end": 3373.37, "word": " bar", "probability": 0.8154296875}, {"start": 3373.37, "end": 3373.83, "word": " of", "probability": 0.9765625}, {"start": 3373.83, "end": 3374.35, "word": " X", "probability": 0.8662109375}, {"start": 3374.35, "end": 3375.59, "word": " has", "probability": 0.87158203125}, {"start": 3375.59, "end": 3376.59, "word": " no", "probability": 0.93701171875}, {"start": 3376.59, "end": 3378.05, "word": " zeros", "probability": 0.916015625}, {"start": 3378.05, "end": 3379.61, "word": " on", "probability": 0.92431640625}, {"start": 3379.61, "end": 3380.81, "word": " Z", "probability": 0.798828125}, {"start": 3380.81, "end": 3381.63, "word": " two", "probability": 0.414794921875}, {"start": 3381.63, "end": 3382.19, "word": " وال", "probability": 0.611328125}, {"start": 3382.19, "end": 3382.47, "word": " degree", "probability": 0.83349609375}, {"start": 3382.47, "end": 3382.85, "word": " لل", "probability": 0.90673828125}, {"start": 3382.85, "end": 3383.19, "word": " F", "probability": 0.7900390625}], "temperature": 1.0}, {"id": 119, "seek": 341310, "start": 3383.44, "end": 3413.1, "text": "بتساوي ال degree لل F bar يبقى صورة ال F bar irreducible على Z2 يبقى الصورة F bar of X is irreducible over Z2 هذا بده يعطي كمان ان F الأصلية is irreducible على Z2", "tokens": [3555, 2655, 3794, 995, 45865, 2423, 4314, 24976, 479, 2159, 7251, 3555, 4587, 7578, 20328, 13063, 3660, 2423, 479, 2159, 16014, 769, 32128, 15844, 1176, 17, 7251, 3555, 4587, 7578, 31767, 13063, 3660, 479, 2159, 295, 1783, 307, 16014, 769, 32128, 670, 1176, 17, 23758, 47525, 3224, 37495, 9566, 1829, 9122, 2304, 7649, 16472, 479, 16247, 36520, 10632, 307, 16014, 769, 32128, 15844, 1176, 17], "avg_logprob": -0.31439393532998633, "compression_ratio": 1.483221476510067, "no_speech_prob": 0.0, "words": [{"start": 3383.44, "end": 3384.22, "word": "بتساوي", "probability": 0.5235107421875}, {"start": 3384.22, "end": 3384.4, "word": " ال", "probability": 0.59521484375}, {"start": 3384.4, "end": 3384.62, "word": " degree", "probability": 0.9853515625}, {"start": 3384.62, "end": 3384.96, "word": " لل", "probability": 0.65673828125}, {"start": 3384.96, "end": 3385.52, "word": " F", "probability": 0.71142578125}, {"start": 3385.52, "end": 3386.16, "word": " bar", "probability": 0.52880859375}, {"start": 3386.16, "end": 3387.16, "word": " يبقى", "probability": 0.9315185546875}, {"start": 3387.16, "end": 3387.7, "word": " صورة", "probability": 0.76123046875}, {"start": 3387.7, "end": 3388.0, "word": " ال", "probability": 0.82080078125}, {"start": 3388.0, "end": 3388.36, "word": " F", "probability": 0.939453125}, {"start": 3388.36, "end": 3389.1, "word": " bar", "probability": 0.89453125}, {"start": 3389.1, "end": 3391.18, "word": " irreducible", "probability": 0.7980143229166666}, {"start": 3391.18, "end": 3392.28, "word": " على", "probability": 0.79052734375}, {"start": 3392.28, "end": 3393.34, "word": " Z2", "probability": 0.38348388671875}, {"start": 3393.34, "end": 3394.92, "word": " يبقى", "probability": 0.9073486328125}, {"start": 3394.92, "end": 3396.16, "word": " الصورة", "probability": 0.7532552083333334}, {"start": 3396.16, "end": 3396.58, "word": " F", "probability": 0.5576171875}, {"start": 3396.58, "end": 3397.44, "word": " bar", "probability": 0.896484375}, {"start": 3397.44, "end": 3398.3, "word": " of", "probability": 0.87109375}, {"start": 3398.3, "end": 3398.9, "word": " X", "probability": 0.95361328125}, {"start": 3398.9, "end": 3399.62, "word": " is", "probability": 0.71044921875}, {"start": 3399.62, "end": 3402.58, "word": " irreducible", "probability": 0.9381510416666666}, {"start": 3402.58, "end": 3403.92, "word": " over", "probability": 0.751953125}, {"start": 3403.92, "end": 3406.72, "word": " Z2", "probability": 0.958251953125}, {"start": 3406.72, "end": 3407.12, "word": " هذا", "probability": 0.853515625}, {"start": 3407.12, "end": 3407.56, "word": " بده", "probability": 0.481689453125}, {"start": 3407.56, "end": 3408.06, "word": " يعطي", "probability": 0.9420572916666666}, {"start": 3408.06, "end": 3408.64, "word": " كمان", "probability": 0.84423828125}, {"start": 3408.64, "end": 3409.36, "word": " ان", "probability": 0.5380859375}, {"start": 3409.36, "end": 3409.96, "word": " F", "probability": 0.48193359375}, {"start": 3409.96, "end": 3410.98, "word": " الأصلية", "probability": 0.71923828125}, {"start": 3410.98, "end": 3411.3, "word": " is", "probability": 0.8984375}, {"start": 3411.3, "end": 3412.28, "word": " irreducible", "probability": 0.9638671875}, {"start": 3412.28, "end": 3412.58, "word": " على", "probability": 0.88720703125}, {"start": 3412.58, "end": 3413.1, "word": " Z2", "probability": 0.812744140625}], "temperature": 1.0}, {"id": 120, "seek": 343775, "start": 3413.51, "end": 3437.75, "text": "هدفة هي يعطيكي ان ال F of X X أُس أربع زي X زي واحد is irreducible over liquid خديني هالمثال باشي طبعا", "tokens": [3224, 3215, 5172, 3660, 39896, 37495, 9566, 1829, 4117, 1829, 16472, 2423, 479, 295, 1783, 1783, 5551, 10859, 3794, 5551, 25513, 3615, 30767, 1829, 1783, 30767, 1829, 36764, 24401, 307, 16014, 769, 32128, 670, 6553, 16490, 3215, 9957, 1829, 8032, 45340, 12984, 6027, 4724, 33599, 1829, 23032, 3555, 3615, 995], "avg_logprob": -0.37622548201504874, "compression_ratio": 1.1590909090909092, "no_speech_prob": 0.0, "words": [{"start": 3413.51, "end": 3414.29, "word": "هدفة", "probability": 0.71844482421875}, {"start": 3414.29, "end": 3414.51, "word": " هي", "probability": 0.87646484375}, {"start": 3414.51, "end": 3415.41, "word": " يعطيكي", "probability": 0.834326171875}, {"start": 3415.41, "end": 3415.91, "word": " ان", "probability": 0.65234375}, {"start": 3415.91, "end": 3416.33, "word": " ال", "probability": 0.48583984375}, {"start": 3416.33, "end": 3416.69, "word": " F", "probability": 0.5380859375}, {"start": 3416.69, "end": 3417.21, "word": " of", "probability": 0.75048828125}, {"start": 3417.21, "end": 3417.73, "word": " X", "probability": 0.91357421875}, {"start": 3417.73, "end": 3418.43, "word": " X", "probability": 0.72119140625}, {"start": 3418.43, "end": 3418.83, "word": " أُس", "probability": 0.5244140625}, {"start": 3418.83, "end": 3419.57, "word": " أربع", "probability": 0.6288248697916666}, {"start": 3419.57, "end": 3420.37, "word": " زي", "probability": 0.731201171875}, {"start": 3420.37, "end": 3420.79, "word": " X", "probability": 0.90576171875}, {"start": 3420.79, "end": 3421.17, "word": " زي", "probability": 0.990234375}, {"start": 3421.17, "end": 3421.91, "word": " واحد", "probability": 0.934326171875}, {"start": 3421.91, "end": 3422.85, "word": " is", "probability": 0.75537109375}, {"start": 3422.85, "end": 3425.47, "word": " irreducible", "probability": 0.8673502604166666}, {"start": 3425.47, "end": 3427.87, "word": " over", "probability": 0.7138671875}, {"start": 3427.87, "end": 3429.79, "word": " liquid", "probability": 0.216064453125}, {"start": 3429.79, "end": 3433.45, "word": " خديني", "probability": 0.61602783203125}, {"start": 3433.45, "end": 3434.19, "word": " هالمثال", "probability": 0.6201171875}, {"start": 3434.19, "end": 3435.71, "word": " باشي", "probability": 0.7815755208333334}, {"start": 3435.71, "end": 3437.75, "word": " طبعا", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 121, "seek": 346567, "start": 3438.41, "end": 3465.67, "text": "نمر يا إيه؟ اللي هو آخر السؤال يعطيناكوا مثال حرفي زيه يبقى بتحلوه بنفس الطريقة، جاري قولي في السؤال 12 وسؤال 14 وسؤال 18 وسؤال 23 وسؤال 25", "tokens": [1863, 29973, 35186, 11933, 1829, 3224, 22807, 13672, 1829, 31439, 19753, 34740, 21136, 33604, 6027, 7251, 3615, 9566, 1829, 8315, 4117, 14407, 50113, 6027, 11331, 28480, 1829, 30767, 1829, 3224, 7251, 3555, 4587, 7578, 39894, 5016, 1211, 2407, 3224, 44945, 36178, 41950, 16572, 28671, 12399, 10874, 9640, 1829, 12174, 12610, 1829, 8978, 21136, 33604, 6027, 2272, 4032, 3794, 33604, 6027, 3499, 4032, 3794, 33604, 6027, 2443, 4032, 3794, 33604, 6027, 6673, 4032, 3794, 33604, 6027, 3552], "avg_logprob": -0.24168019944971258, "compression_ratio": 1.6506849315068493, "no_speech_prob": 0.0, "words": [{"start": 3438.41, "end": 3438.93, "word": "نمر", "probability": 0.606689453125}, {"start": 3438.93, "end": 3439.29, "word": " يا", "probability": 0.07958984375}, {"start": 3439.29, "end": 3439.65, "word": " إيه؟", "probability": 0.72479248046875}, {"start": 3439.65, "end": 3439.75, "word": " اللي", "probability": 0.754638671875}, {"start": 3439.75, "end": 3439.89, "word": " هو", "probability": 0.9931640625}, {"start": 3439.89, "end": 3440.57, "word": " آخر", "probability": 0.885986328125}, {"start": 3440.57, "end": 3441.13, "word": " السؤال", "probability": 0.9562174479166666}, {"start": 3441.13, "end": 3441.83, "word": " يعطيناكوا", "probability": 0.7359095982142857}, {"start": 3441.83, "end": 3442.31, "word": " مثال", "probability": 0.99365234375}, {"start": 3442.31, "end": 3443.05, "word": " حرفي", "probability": 0.9611002604166666}, {"start": 3443.05, "end": 3443.79, "word": " زيه", "probability": 0.96142578125}, {"start": 3443.79, "end": 3445.07, "word": " يبقى", "probability": 0.807861328125}, {"start": 3445.07, "end": 3445.69, "word": " بتحلوه", "probability": 0.88857421875}, {"start": 3445.69, "end": 3446.27, "word": " بنفس", "probability": 0.985107421875}, {"start": 3446.27, "end": 3447.09, "word": " الطريقة،", "probability": 0.80560302734375}, {"start": 3447.09, "end": 3447.33, "word": " جاري", "probability": 0.647705078125}, {"start": 3447.33, "end": 3447.57, "word": " قولي", "probability": 0.8943684895833334}, {"start": 3447.57, "end": 3447.73, "word": " في", "probability": 0.486328125}, {"start": 3447.73, "end": 3448.01, "word": " السؤال", "probability": 0.8699544270833334}, {"start": 3448.01, "end": 3448.69, "word": " 12", "probability": 0.298583984375}, {"start": 3448.69, "end": 3450.73, "word": " وسؤال", "probability": 0.7423095703125}, {"start": 3450.73, "end": 3452.01, "word": " 14", "probability": 0.98193359375}, {"start": 3452.01, "end": 3455.01, "word": " وسؤال", "probability": 0.9345703125}, {"start": 3455.01, "end": 3456.23, "word": " 18", "probability": 0.97802734375}, {"start": 3456.23, "end": 3460.15, "word": " وسؤال", "probability": 0.927001953125}, {"start": 3460.15, "end": 3461.79, "word": " 23", "probability": 0.9814453125}, {"start": 3461.79, "end": 3464.87, "word": " وسؤال", "probability": 0.93408203125}, {"start": 3464.87, "end": 3465.67, "word": " 25", "probability": 0.9892578125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3467.598375, "duration_after_vad": 3353.461874999981}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..04e24a8e6a5382f6ea44a14e034478a61fb685ef
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ_raw.srt
@@ -0,0 +1,1996 @@
+1
+00:00:20,910 --> 00:00:25,930
+بسم الله الرحمن الرحيم نكمل ما كنا نعمل بيه المرة
+
+2
+00:00:25,930 --> 00:00:29,950
+الماضية في نفس الشفقة. ولمرة اللي فاتت في نهاية
+
+3
+00:00:29,950 --> 00:00:34,630
+المحاضرة أعطيناكوا مثال ولمّا ننتهي منه. يبقى بدنا
+
+4
+00:00:34,630 --> 00:00:39,390
+نعمل عليه مرة سريعة ثم ننهي هذا المثال ثم ننتقل
+
+5
+00:00:39,390 --> 00:00:44,510
+إلى المثال اللي يليه. We will construct a field of
+
+6
+00:00:44,510 --> 00:00:51,810
+order تمام.باقي 8 ايش ممكن احطها عدد مرفوع ل أس
+
+7
+00:00:51,810 --> 00:00:57,790
+عدد او ال prime مرفوع ل أس يبقى 8 لي عبارة عن مين؟
+
+8
+00:00:57,790 --> 00:01:06,890
+2 أس 3 ممتاز جدا يبقى هذه 2 أس 3 ل 2 هو ال prime و
+
+9
+00:01:06,890 --> 00:01:14,240
+3 هو الأس 7 وكأنه بيقول لي هذه polynomialمن الدرجة
+
+10
+00:01:14,240 --> 00:01:20,640
+التالتة و تكون irreducible على زكوك واضح؟ كأنه
+
+11
+00:01:20,640 --> 00:01:25,240
+بيقوللي ها هذه وسيلة الرقم اللي عندي أحطه prime
+
+12
+00:01:25,240 --> 00:01:30,880
+مرفوع لأسفل ال prime بيكون هو مين؟ هو ال field زد
+
+13
+00:01:30,880 --> 00:01:36,320
+لهذا الرقم بيكون هو ال fieldوالقصد اللى فوق بيكون
+
+14
+00:01:36,320 --> 00:01:40,320
+هو درجتي ال follow on هو نفسه كأنه مغششني بيقول
+
+15
+00:01:40,320 --> 00:01:46,380
+اتفضل خد اللى هو السؤال هذا اقوله تفضل طيب يبقى
+
+16
+00:01:46,380 --> 00:01:53,780
+احنا جينا للحل المرة اللى فاتت وقلنا let ال F of X
+
+17
+00:01:53,780 --> 00:02:02,100
+تساوي قداشر X تكيب زيديش أخدنا X زي واحد زي X زي
+
+18
+00:02:02,100 --> 00:02:10,220
+واحد مش هيكطيب تلقاه بدي اجي على ZP قولنا on ZP
+
+19
+00:02:10,220 --> 00:02:15,940
+مين P عندنا قولنا هنا بقراه اتنين على Z اتنين we
+
+20
+00:02:15,940 --> 00:02:21,760
+have بدنا نحسب قيمة الدالة عند Zero العنصر الأول
+
+21
+00:02:21,760 --> 00:02:28,060
+من Z2 يبقى بيعطيني جداش واحد بدنا نحسب قيمة الدالة
+
+22
+00:02:28,060 --> 00:02:34,290
+عند F of واحدواحد زي واحد زي واحد تلاتة في زيته
+
+23
+00:02:34,290 --> 00:02:40,150
+جديد معناته ان الدل هذه مالهاش zeros على زيت دي
+
+24
+00:02:40,150 --> 00:02:49,990
+اتنين يبقى هنا Sir ال F of X has no zeros on زيت
+
+25
+00:02:49,990 --> 00:02:55,190
+دي اتنين فهيبقى معاه no zeros على زيت دي اتنين
+
+26
+00:02:55,190 --> 00:02:59,550
+اتفجر مافيش ولا حاجة ولا واحدايه بيساويها؟ طيب ال
+
+27
+00:02:59,550 --> 00:03:09,010
+degree تبعت ال F جدت؟ تلاتة و ال degree على ال F
+
+28
+00:03:09,010 --> 00:03:13,790
+بده يساوي تلاتة طبعا أخدنا ال degree على ال F
+
+29
+00:03:13,790 --> 00:03:17,990
+اتنين او تلاتة او النظرية معانا مشكلة صحيح ولا لا؟
+
+30
+00:03:18,060 --> 00:03:23,560
+ما دام الانواج دول يبجي الدالة irreducible على Z2
+
+31
+00:03:23,560 --> 00:03:27,300
+وبالتالي irreducible على ال EQ مش هيك اخد نص
+
+32
+00:03:27,300 --> 00:03:36,680
+النظرية يبجي هنا بروح بقولهم فال F of X بده تساوي
+
+33
+00:03:36,680 --> 00:03:45,940
+X تكيب زائد X زائد 1 is irreducible over
+
+34
+00:03:46,830 --> 00:03:56,530
+اللي هو Z2 هذا بدي يعطينا by a previous theorem
+
+35
+00:03:56,530 --> 00:04:06,070
+بدي يكون ال F of X اللي هو X تكييف زي X زي واحد is
+
+36
+00:04:06,070 --> 00:04:12,990
+irreducible over ال Q
+
+37
+00:04:21,430 --> 00:04:27,470
+Irreducible على ال EQ عالي كويس لما ده ال F of X
+
+38
+00:04:27,470 --> 00:04:33,850
+صارت Irreducible على ال EQ هذا بيولدلي Ideal و
+
+39
+00:04:33,850 --> 00:04:39,890
+Ideal Value maximum نتيجة رقم واحد أخدناها على
+
+40
+00:04:39,890 --> 00:04:47,250
+اللي هو النظرية الأخيرة المرضى الماضييبقى هنا سا
+
+41
+00:04:47,250 --> 00:04:53,970
+اللي هو ال X تكييب زي X زي واحد هذا ال ideal is
+
+42
+00:04:53,970 --> 00:05:02,750
+maximal مدام maximal هذا بده يعطينا ان Z2 of X اه
+
+43
+00:05:02,750 --> 00:05:08,710
+موديون ال principle ideal generated by X تكييب زي
+
+44
+00:05:08,710 --> 00:05:17,380
+X زي واحد is A في الدقهذا ال field زعمنا انه يحتوي
+
+45
+00:05:17,380 --> 00:05:25,180
+على ثمانية عناصر وقلنا شكله على الشكل التالي Z2 of
+
+46
+00:05:25,180 --> 00:05:31,960
+X modulo principle ideal generated by X تكييف زائد
+
+47
+00:05:31,960 --> 00:05:38,180
+واحد بالدوي ساعة ها ال ideal من الدرجة التالتة
+
+48
+00:05:38,180 --> 00:05:43,100
+يبقى اللي قبله من الدرجة التالتةالثانية او الاولى
+
+49
+00:05:43,100 --> 00:05:48,060
+او الصفرية يعني اقل من الدرجة الثالثة يبقى هذا
+
+50
+00:05:48,060 --> 00:05:54,600
+بيكون على الشكل ax زائد bx زائد c زائد ال
+
+51
+00:05:54,600 --> 00:06:00,240
+principle ideal generated by x تكييب زائد واحد
+
+52
+00:06:00,240 --> 00:06:06,890
+وبحيث ان ال a و ال b و ال c كلها موجودة وينموجودة
+
+53
+00:06:06,890 --> 00:06:14,030
+في Z2 يعني يا إما صفر يا إما .. يا إما واحد. إحنا
+
+54
+00:06:14,030 --> 00:06:20,350
+زعمنا إنه هدف يتمانية عناصر. بدنا نعرف ما هي هذه
+
+55
+00:06:20,350 --> 00:06:25,530
+تمانية عناصر وقلنا لكوا يلا حضروها للمرة القادمة
+
+56
+00:06:25,530 --> 00:06:32,460
+وها قد حضرت المرة القادمة وصارت المرة الحالية.يبقى
+
+57
+00:06:32,460 --> 00:06:39,000
+هذه العناصر عبارة عن مين انا انا انا انا انا انا
+
+58
+00:06:39,000 --> 00:06:39,640
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+59
+00:06:39,640 --> 00:06:39,900
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+60
+00:06:39,900 --> 00:06:40,300
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+61
+00:06:40,300 --> 00:06:40,820
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+62
+00:06:40,820 --> 00:06:41,580
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+63
+00:06:41,580 --> 00:06:45,700
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+64
+00:06:45,700 --> 00:06:49,460
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+65
+00:06:49,460 --> 00:06:51,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+66
+00:06:51,260 --> 00:06:59,520
+انا
+
+67
+00:06:59,520 --> 00:07:05,610
+اناطيب ماذا؟ و X تربيه زائد واحد و X تربيه زائد X
+
+68
+00:07:05,610 --> 00:07:11,050
+و X تربيها زائد X زائد واحد واحد اتنين، تلاتة،
+
+69
+00:07:11,050 --> 00:07:16,010
+اربعة، خمسة، ستة، سبعة، تمانية هدول على كل واحد
+
+70
+00:07:16,010 --> 00:07:20,750
+فيهم بدي اضيف ال principle ideal generated by X
+
+71
+00:07:20,750 --> 00:07:27,590
+تكييف زائد X زائد واحد هاي جميع العناصر هدول كلهم
+
+72
+00:07:27,590 --> 00:07:32,500
+تمانية عناصريعني يا بنات عندنا zero زي ده ده left
+
+73
+00:07:32,500 --> 00:07:37,860
+coset عندنا الواحد زي ال principle ID left coset
+
+74
+00:07:37,860 --> 00:07:42,260
+تانية X زي ال principle left coset تالتة وهكذا
+
+75
+00:07:42,260 --> 00:07:48,780
+بالنسبة لمن للباقي هاي العناصر يبقى هدول ثمانية
+
+76
+00:07:48,780 --> 00:07:57,420
+عناصر يبقى لما أكتب هيك كأنه أنا بغششك جداشاللي هو
+
+77
+00:07:57,420 --> 00:08:01,880
+ال ZP بدي يكون مين هو ال prime اللي بدك تاخديه
+
+78
+00:08:01,880 --> 00:08:06,700
+وقدش درجة ال polynomial اللي لازم تاخديها مشان
+
+79
+00:08:06,700 --> 00:08:13,380
+يطلع كلامك صحيح وسنثبت أيه لك كذا كمان بمثال بعده
+
+80
+00:08:13,380 --> 00:08:17,280
+المثال اللي بعده .. اه قبل المثال اللي بعده لو
+
+81
+00:08:17,280 --> 00:08:24,370
+بدنا نضرب عنصرين في بعض من هذا ال fieldالنسج بدي
+
+82
+00:08:24,370 --> 00:08:29,430
+يطلع داخل ولا برا؟ طب تعالى نضرب ونشوف يطلع داخل
+
+83
+00:08:29,430 --> 00:08:34,670
+ولا برا؟ مش احنا بنزعو انه في ال و close under
+
+84
+00:08:34,670 --> 00:08:37,550
+multiplication و close under الجامعة وغيرها
+
+85
+00:08:37,550 --> 00:08:41,630
+الجامعة مش هيرايا للدرجة، يبقى مافيش فيه مشكلة،
+
+86
+00:08:41,630 --> 00:08:47,070
+المشكلة في الضرب، يبقى لو جينا نضرب على ضرب داخل
+
+87
+00:08:47,070 --> 00:08:52,410
+هدفي، مثلا لو رحت أخدعلى سبيل المثال X تربيه زايد
+
+88
+00:08:52,410 --> 00:08:58,090
+واحد مع هذا مع الاول principle ideal يبقى لو بدى
+
+89
+00:08:58,090 --> 00:09:02,830
+اضرب على ضرب العناصر داخل هذا الفيلم بدى اخد X
+
+90
+00:09:02,830 --> 00:09:09,970
+تربيه زايد واحد زايد principle ideal بدى اضربه في
+
+91
+00:09:09,970 --> 00:09:15,870
+من؟ في العنصر التاني X تربيه زايد X زايد واحد زايد
+
+92
+00:09:15,870 --> 00:09:24,010
+principle idealx تكيب زائد x زائد واحد اشوف النتج
+
+93
+00:09:24,010 --> 00:09:29,410
+جديش بده يساوي يبقى x تربيه في x تربيه في جديه اش؟
+
+94
+00:09:29,410 --> 00:09:37,110
+x أقصر اربعة وهنا زائد x تكيب وهنا زائد x تربيه
+
+95
+00:09:37,110 --> 00:09:46,390
+وزائد كمان x تربيه وزائد x زائد واحد زائد ل
+
+96
+00:09:46,390 --> 00:09:53,350
+principle idealgenerated by ال X تكييف زايد X زايد
+
+97
+00:09:53,350 --> 00:09:59,550
+واحد طلعوني هدول مع بعض كده ش بيعطونيه نين X ترويه
+
+98
+00:09:59,550 --> 00:10:04,630
+داخل زيدي اتنين مع السلامة الله سهل عليهم و غير
+
+99
+00:10:04,630 --> 00:10:09,950
+مقصوف عليهم يبقى بقى لعندي بنات ميم بقى لعندي X وص
+
+100
+00:10:09,950 --> 00:10:17,780
+أربع واطلع X تكييف زايد X زايد واحد موجود هنايبقى
+
+101
+00:10:17,780 --> 00:10:24,640
+بدي يطلع نفس الهمصر هذا يبقى x أُص أربع زائد ال x
+
+102
+00:10:24,640 --> 00:10:30,960
+تكيب زائد ال x زائد واحد يبقى طلعت polynomial من
+
+103
+00:10:30,960 --> 00:10:37,160
+الدرجة الرابعة ك left coset مع ال x تكيب زائد x
+
+104
+00:10:37,160 --> 00:10:42,000
+زائد واحد واحنا بنزعم هنا ان هذا بدي يكون من
+
+105
+00:10:42,000 --> 00:10:48,290
+الدرجة مية متربنشوف هل هذا الكلام صحيح، والله مش
+
+106
+00:10:48,290 --> 00:10:52,890
+صحيح، يعني بنخفض الدرجة، بحيث تصير منها الدرجة
+
+107
+00:10:52,890 --> 00:10:58,410
+الثانية، يعني انا لو روحته وخليته تصير شغلة نقص
+
+108
+00:10:58,410 --> 00:11:03,350
+شوية، بننقص درجات، بتكملي بحيث فعلا يكون على
+
+109
+00:11:03,350 --> 00:11:07,930
+الصيغة اللي عندنا هذه، طب كيف بتخفضه؟ هناك
+
+110
+00:11:07,930 --> 00:11:14,490
+طريقتان، الطريقة الأولى long division، إيش يعني؟
+
+111
+00:11:14,850 --> 00:11:20,010
+قسم المطول نقسم قسم المطول عادي ونشوف وين ماتوصل
+
+112
+00:11:20,010 --> 00:11:25,870
+معانا الدنيا إذا لو جيت في الهامش بدي أقسم X أُس
+
+113
+00:11:25,870 --> 00:11:33,470
+أربعة تأسيب ال X تكيب زائد X زائد واحد X أُس أربعة
+
+114
+00:11:33,470 --> 00:11:39,930
+على X تكيب هي أجدد ال X والباقي ملحقة فيها يبقى
+
+115
+00:11:39,930 --> 00:11:48,390
+هاي X أُس أربعة زائد X تربيعزائد X بنغير الإشارات
+
+116
+00:11:48,390 --> 00:11:55,310
+وبنجمع مع السلامة بظل عندي ناقص X تربيع ناقص X لكن
+
+117
+00:11:55,310 --> 00:12:00,230
+احنا بنشتغل وين؟ في Z دي اتنين في Z دي اتنين بدي
+
+118
+00:12:00,230 --> 00:12:08,210
+اضيف هنا اتنين بظل X تربيع وهذه زيها X يبقى صارت
+
+119
+00:12:08,210 --> 00:12:15,500
+ال X أُس أربعة زائد ال principle IDgenerated by
+
+120
+00:12:15,500 --> 00:12:21,560
+هذا ال element بتساوي خارج القسمة اللي هو mean X
+
+121
+00:12:21,560 --> 00:12:28,560
+في X تكييب زائد X زائد واحد زائد خارج القسمة اللي
+
+122
+00:12:28,560 --> 00:12:33,220
+هو X تربيها زائد X زائد ال principle ideal
+
+123
+00:12:33,220 --> 00:12:39,860
+generated by X تكييب زائد X زائد واحد تمام
+
+124
+00:12:42,380 --> 00:12:47,260
+طيب كويس هذا ال element موجود في ال principle ولا
+
+125
+00:12:47,260 --> 00:12:54,660
+لا يبقى على طول الخط هذا بتساوي ال X تربيع زائد X
+
+126
+00:12:54,660 --> 00:13:01,200
+زائد ال principle ideal generated by X تكييب زائد
+
+127
+00:13:01,200 --> 00:13:07,760
+X زائد 1 صرت من أي درجات؟ داليا بهذا يتفق مع
+
+128
+00:13:07,760 --> 00:13:13,670
+الكلام اللي احنا زعمناه قبل قليل تمام؟طبعا زعمناه
+
+129
+00:13:13,670 --> 00:13:19,950
+مش شكاك، زعمناه يعني من ضمانة، ضامنين مية لمية إن
+
+130
+00:13:19,950 --> 00:13:24,370
+هذا الكلام طبعا هذا كلام اللي أنا بقوله مش من
+
+131
+00:13:24,370 --> 00:13:31,090
+عندي، من القرآن الكريم و لما في قصة سيدنا يوسف لما
+
+132
+00:13:31,090 --> 00:13:36,890
+المكيال اللي جال، اللي بيجيب المكيال هذا، إله حمله
+
+133
+00:13:36,890 --> 00:13:41,610
+بعير و أنا به زعيميعني اللي يجيب هو أنا بعطيه حمل
+
+134
+00:13:41,610 --> 00:13:47,390
+بقير زيادة يبقى نضاما من الضمانة وليس للشك يبقى
+
+135
+00:13:47,390 --> 00:13:53,070
+احنا هنا اللي زعمناه قبل قليل هيأكدنا بمين عمليا
+
+136
+00:13:53,070 --> 00:13:58,550
+بهذا الكلام هذه هي الطريقة من الأولى وكأن X أُص
+
+137
+00:13:58,550 --> 00:14:05,430
+أربعة في هذا ال field تكافئ X تربية زائد X لأنه
+
+138
+00:14:05,430 --> 00:14:10,820
+شيلناها وحطينا بدلها X تربيةزايد X ونستطيع أن نؤكد
+
+139
+00:14:10,820 --> 00:14:17,180
+هذا الكلام بطريقة أخرى ما هي الطريقة الأخرى هنشوف
+
+140
+00:14:17,180 --> 00:14:22,100
+احنا عندنا X تكييف زايد X زايد 1 زايد ال principle
+
+141
+00:14:22,100 --> 00:14:27,480
+ideal generated by X تكييف زايد X زايد 1 هو ال
+
+142
+00:14:27,480 --> 00:14:33,120
+principle ideal generated by X تكييف زايد 1 صح
+
+143
+00:14:33,120 --> 00:14:40,760
+يعني هذا بزياد تماميعني هذا بيصير x تكييب زاد ال x
+
+144
+00:14:40,760 --> 00:14:46,720
+زاد واحد بيصير zero يعني ال x تكييب تساوي ناقص x
+
+145
+00:14:46,720 --> 00:14:54,420
+ناقص واحد احنا بيشتغلوا اين؟ في z two في z two هذا
+
+146
+00:14:54,420 --> 00:15:00,880
+معناه ان x زاد واحد in z twoبتنضروا بال X يبقى يصر
+
+147
+00:15:00,880 --> 00:15:06,100
+ان كمان ال X تكيب في الشغل اللي بنشتغله هذا ممكن
+
+148
+00:15:06,100 --> 00:15:11,120
+ابدلها مين؟ X زائد واحد يعني لو مرت في السؤال كان
+
+149
+00:15:11,120 --> 00:15:15,360
+في عندي X تكيب يمكن استبداله ب X زائد واحد يبقى
+
+150
+00:15:15,360 --> 00:15:19,920
+نزلنا الدرجة التالتة إلى الدرجة الأولى زي ما نزلنا
+
+151
+00:15:19,920 --> 00:15:24,890
+الدرجة الرابعة إلى الدرجة الثانيةطب هذه المعادلة
+
+152
+00:15:24,890 --> 00:15:31,470
+لو ضربت الطرفين في X بصير X قص 4 يساوي X في X زائد
+
+153
+00:15:31,470 --> 00:15:38,630
+1 يعني X تربيها زائد X هي اللي فور مظبوط؟ يبقى
+
+154
+00:15:38,630 --> 00:15:44,490
+صارت هي عندك مدى الطريقة طريقتين مشان ننزل الدرجة
+
+155
+00:15:44,490 --> 00:15:48,290
+من الدرجة الرابعة إلى الدرجة الثانية أو الأولى أو
+
+156
+00:15:48,290 --> 00:15:52,540
+الصفرية حسب طبيعة ميم المثلفلو جنا سؤال في
+
+157
+00:15:52,540 --> 00:15:57,060
+الامتحان او قلنا لك اتي لل multiplicative تبع ال
+
+158
+00:15:57,060 --> 00:16:03,360
+two elements ووصلتي الى شغل زى هذا وقول والله حلت
+
+159
+00:16:03,360 --> 00:16:08,380
+صح وجماشى لأ انت حلته نص الحل ضايل عليك النص
+
+160
+00:16:08,380 --> 00:16:13,560
+التانى انه اتنزلت درجة الى درجة مين ا الثانية و
+
+161
+00:16:13,560 --> 00:16:21,000
+هكذا طيب الان فينا كمان مثال اخربس بتغير عدد
+
+162
+00:16:21,000 --> 00:16:27,340
+العناصر كده عدد العناصر هنا تمانية بدي أغير هذه
+
+163
+00:16:27,340 --> 00:16:34,200
+الطريقة المثال اللي بعده هو بيقول
+
+164
+00:16:34,200 --> 00:16:40,120
+بنفس الطريقة example construct
+
+165
+00:16:40,120 --> 00:16:43,260
+a
+
+166
+00:16:43,260 --> 00:16:47,160
+field construct
+
+167
+00:16:47,160 --> 00:17:00,510
+a fieldof order of order تسعة مش تمانع تسعة تانية
+
+168
+00:17:00,510 --> 00:17:04,750
+تلاتة تربية يعني
+
+169
+00:17:04,750 --> 00:17:09,130
+أنا بدي أشغل لبدل ما كنت أشتغل في Z دي اتنين بدي
+
+170
+00:17:09,130 --> 00:17:15,910
+أشتغل في Z ثلاثة ونقل نمية من الدرجة الثانية تمام
+
+171
+00:17:16,310 --> 00:17:21,410
+يبقى اخدي اي polynomial من الدرجة الثانية تناسب
+
+172
+00:17:21,410 --> 00:17:26,450
+اللي هو Z3 انا ممكن اخد polynomial انت تاخد اخر
+
+173
+00:17:26,450 --> 00:17:31,410
+واحدة تاخد التالتة وكله صح ان حقق المطلوب تبع
+
+174
+00:17:31,410 --> 00:17:37,710
+السؤال الجبال يبقى قوله solution بدى
+
+175
+00:17:37,710 --> 00:17:46,070
+افترض ان ال F of X بدها تسوي مثلا X ترابيع زائدة
+
+176
+00:17:48,150 --> 00:17:55,210
+الان ال P بتلاتة يبقى بدي أشتغل في Z D3 فاجي بقوله
+
+177
+00:17:55,210 --> 00:18:06,150
+N Z D3 We have .. بدي أخد F of Zero F of Zero
+
+178
+00:18:06,150 --> 00:18:14,610
+بواحد بدي أخد F of واحد باتنين بدي أخد F of اتنين
+
+179
+00:18:14,610 --> 00:18:20,880
+بواحد بخمسة خمسة اتنينF of اتنين اربعة واحد خمسة
+
+180
+00:18:20,880 --> 00:18:26,260
+فيه زي دي ثلاث اتنين يبقى معناته ايش هذه ال
+
+181
+00:18:26,260 --> 00:18:32,320
+function مالهاش زي رزة وال degree تبعها جد ايش
+
+182
+00:18:32,320 --> 00:18:36,900
+اتنين يبقى طبقة النظرية اللي اشتغلنا عليها في
+
+183
+00:18:36,900 --> 00:18:52,870
+المثال الأول يبقى سواء ال F أتنين زي رزةزي T3 and
+
+184
+00:18:52,870 --> 00:19:03,210
+ال degree لل F بده يساوي كده؟ بده يساوي اتنى معنى
+
+185
+00:19:03,210 --> 00:19:09,630
+هذا الكلام ان ال F of X is ال reduce وعلى Z تلت
+
+186
+00:19:09,630 --> 00:19:20,430
+يبقى صح ال F of X تساوي ال X ترابيعترابية زائد
+
+187
+00:19:20,430 --> 00:19:28,930
+واحد is irreducible irreducible
+
+188
+00:19:28,930 --> 00:19:32,930
+over
+
+189
+00:19:32,930 --> 00:19:42,930
+Z3 هذا بده يعطينا ان ال F of X ال F X ترابية زائد
+
+190
+00:19:42,930 --> 00:19:47,010
+واحد is irreducible
+
+191
+00:19:48,100 --> 00:20:00,280
+of the cube نفس التكتيك اللي مشيناه Z D3 of X
+
+192
+00:20:00,280 --> 00:20:05,440
+Module ال principle ideals generated by X ترابية
+
+193
+00:20:05,440 --> 00:20:11,760
+زي واحد is a في طبعا استخدمنا ال crawlery واحد
+
+194
+00:20:11,760 --> 00:20:15,040
+اللي عالميا على النظرية المرة اللي فاتة أخدنا two
+
+195
+00:20:15,040 --> 00:20:19,460
+crawleries هذه هي ال crawleryالأول دكتور احنا
+
+196
+00:20:19,460 --> 00:20:24,020
+فرضنا FFX من هنا اه من اللي بتاعك من اللي بتاعك
+
+197
+00:20:24,020 --> 00:20:32,160
+كده اه ايه يعني اي FFX بشرف ترجع إلى تلاتة نزيتش
+
+198
+00:20:32,160 --> 00:20:39,420
+ايه نعم طيب يبقى صار Z تلاتة و FX مضى من X أربع هي
+
+199
+00:20:39,420 --> 00:20:44,960
+عبارة عن field ما هو ما هي شكل العناصر في هذا ال
+
+200
+00:20:44,960 --> 00:20:51,950
+fieldيبقى z تلاتة of x modulo x ترمية زائد واحد
+
+201
+00:20:51,950 --> 00:20:59,070
+شكلها على الشكل التالي هاي ال x ترمية زائد واحد
+
+202
+00:20:59,070 --> 00:21:07,450
+كما يبقى زائد اقل منه في الدرجة بمقدار واحد يومين
+
+203
+00:21:07,450 --> 00:21:15,580
+a x زائد ال bو بحيث ال A و ال B موجودة في Z دي
+
+204
+00:21:15,580 --> 00:21:23,080
+ثلاثة تفضل هاي الشكل جتاش؟ ستة انا بدي اعطيكي
+
+205
+00:21:23,080 --> 00:21:30,540
+التلاتة Zero واحد و اتنين و X و X زيدي واحد و X
+
+206
+00:21:30,540 --> 00:21:35,580
+زيدي اتنين هاي ستة خلطنا؟ طب و اتنين X و اتنين X
+
+207
+00:21:35,580 --> 00:21:39,480
+زيدي واحد و اتنين X زيدي اتنين في غيرهم؟ جتاسعة
+
+208
+00:21:39,480 --> 00:21:43,550
+طالع مظمومتبقى راجع معلوماتك وإلا أخدتي ستة من
+
+209
+00:21:43,550 --> 00:21:51,350
+تسعة. يبقى هذا بتفهمه ولا خلاص؟ بتفهمه؟ خلاص
+
+210
+00:21:51,350 --> 00:22:00,370
+بتفهمه دايما تفهمه. يبقى هذا has nine talents. بعد
+
+211
+00:22:00,370 --> 00:22:04,430
+شوية هكبرتكوا الرقم هذا. بدون تمانية وتسعة بدي
+
+212
+00:22:04,430 --> 00:22:10,890
+أكبره. وشوهش بتسووا فيه؟ اسم الحلال الأسل.طيب،
+
+213
+00:22:10,890 --> 00:22:19,970
+اننا ندل ال exercises على chapter سبعة و عشر Yoga
+
+214
+00:22:19,970 --> 00:22:30,310
+exercises on chapter سبعة و عشر نروح
+
+215
+00:22:30,310 --> 00:22:36,870
+ناخد السؤال الخامس نظرا لإهميته السؤال الخامس
+
+216
+00:22:36,870 --> 00:22:42,160
+عبارة عن أربعة مسائلبتسيبك المطلب الأول والثاني
+
+217
+00:22:42,160 --> 00:22:47,560
+واحد لك التالت والرابع الأول والثاني زي التالت
+
+218
+00:22:47,560 --> 00:22:53,720
+بنفس الطريقة حرفية تمام؟ إذا بدي أروح لنمريا C
+
+219
+00:22:53,720 --> 00:22:59,960
+ونمرادى فبدي أخد نمريا C قبل نمريا C بنحط
+
+220
+00:22:59,960 --> 00:23:07,180
+المعلومات يبقى بقول ال F is a field ال F is a
+
+221
+00:23:07,180 --> 00:23:07,900
+field
+
+222
+00:23:10,410 --> 00:23:18,510
+و ال a non zero element f و ال a لا يساوي zero in
+
+223
+00:23:18,510 --> 00:23:24,790
+f يبقى ال a عنصر غير صفري و موجود في ال f المطموض
+
+224
+00:23:24,790 --> 00:23:33,450
+نمرى c بيقول إذا كان ال f of x زائد a is
+
+225
+00:23:33,450 --> 00:23:35,950
+irreducible
+
+226
+00:23:39,340 --> 00:23:52,140
+الـ Q ثم ال F is او ال F of X is irreducible
+
+227
+00:23:52,140 --> 00:24:00,400
+over الـ Q itself
+
+228
+00:24:00,400 --> 00:24:07,620
+المعلومة
+
+229
+00:24:07,620 --> 00:24:13,120
+اللي عندناإن ال F of X زائد A و ال A موجود في F
+
+230
+00:24:13,120 --> 00:24:18,080
+مين ماكان يكون بشرط ألا يكون العنصر الصفري لو كان
+
+231
+00:24:18,080 --> 00:24:23,140
+unity و الله unit كل ماعناه مش مشكلة يبقى هنا
+
+232
+00:24:23,140 --> 00:24:32,880
+بداجة أقول that ال F of X زائد A be irreducible
+
+233
+00:24:32,880 --> 00:24:42,900
+over liquidإيش بدون أثمة يا بنات؟ إن ال F of X
+
+234
+00:24:42,900 --> 00:24:49,380
+بدون A الرديوسة والعلامين على ال EQ طبعا هذا ال
+
+235
+00:24:49,380 --> 00:24:54,420
+chapter غلبه بالتناقض يبقى حدش يحسن من حد حنبرهن
+
+236
+00:24:54,420 --> 00:25:03,700
+بالتناقض كذلك يبقى باجي بيقول أسيون افترضوا that
+
+237
+00:25:03,700 --> 00:25:17,910
+إن ال F of X isreducible over ال Q فال
+
+238
+00:25:17,910 --> 00:25:26,690
+F of X بقدر اكتبها كحاصل ضارب two polynomials اللي
+
+239
+00:25:26,690 --> 00:25:36,530
+هما مين ال G of X في ال H of X بحيث ال G of Xو ال
+
+240
+00:25:36,530 --> 00:25:44,250
+H of X موجودة وين؟ فال Q of X و التنتين are of
+
+241
+00:25:44,250 --> 00:25:54,970
+lower degree موجودة and of lower degree يعني درجة
+
+242
+00:25:54,970 --> 00:26:02,470
+ال G و درجة ال H أقل من درجة من أقل من درجة اللي
+
+243
+00:26:02,470 --> 00:26:12,000
+هو L طيبالان بدنا نشيل كل X و الحكمة كان X زائد A
+
+244
+00:26:12,000 --> 00:26:19,500
+ونشوف ايش اللي بدي يحصل بلوحة F of X زائد A هتساوي
+
+245
+00:26:19,500 --> 00:26:30,180
+D of X زائد A في H of X زائد A طب استننا شوية خلي
+
+246
+00:26:30,180 --> 00:26:37,040
+المعلومة هنا بدنا نشوف هل هذا معناهإن ال F of X
+
+247
+00:26:37,040 --> 00:26:41,700
+زائد ال A is reduced to a point تعالى نشوف إذا
+
+248
+00:26:41,700 --> 00:26:46,400
+الدرجات جد بعض أه والله بصير مش جد بعض يبقى ليس
+
+249
+00:26:46,400 --> 00:26:51,360
+صحيحة خليني أسألكوا السؤال التالت لو قلتك أنا عندي
+
+250
+00:26:51,360 --> 00:26:58,560
+X تربية وعندي X زائد واحد لكل تربية قداش درجة
+
+251
+00:26:58,560 --> 00:27:05,470
+الأولى والتانية زي بعض لو قلتك عندي الأولى Xتربية
+
+252
+00:27:05,470 --> 00:27:15,290
+زائد واحد وعندي X زائد خمستاشر لكل تربية نفس الشيء
+
+253
+00:27:15,290 --> 00:27:20,430
+يبقى إضافة ال constant لا يغير من درجة ال
+
+254
+00:27:20,430 --> 00:27:25,410
+polynomial بغير من شكلها صحيح لكن لا يغير من درجة
+
+255
+00:27:25,410 --> 00:27:32,350
+ال polynomial يبقى بناء عليه لو بد ال degree لمين؟
+
+256
+00:27:33,280 --> 00:27:43,000
+للـ G of X زائد ال E هل هي ال degree لل G of X؟
+
+257
+00:27:43,000 --> 00:27:48,320
+مطبق تماما، لا بغيرهاش، طب وال degree لل G of X
+
+258
+00:27:48,320 --> 00:27:56,330
+أقل من ال degree لل F of X صحيح ولا لا؟و ال degree
+
+259
+00:27:56,330 --> 00:28:01,270
+لل f of x مش هي نفس ال degree تبع ال f of x زائد
+
+260
+00:28:01,270 --> 00:28:09,010
+ال a يبقى هو هي نفس ال degree تبع ال f of x زائد
+
+261
+00:28:09,010 --> 00:28:17,830
+ال a قريت اعجبتكم بس ان ال degree لل h of x زائد
+
+262
+00:28:17,830 --> 00:28:26,430
+ال a مش هي عبارة عن ال degree لل h of xصح؟ وال
+
+263
+00:28:26,430 --> 00:28:33,210
+degree لل H of X أقل من ال degree لل F of X اللي
+
+264
+00:28:33,210 --> 00:28:41,650
+هي بدها تساوي ال degree لل F of X زائد ال A إذا
+
+265
+00:28:41,650 --> 00:28:48,850
+صارت درجة F of X زائد ال A بده يقابلها درجة G
+
+266
+00:28:48,850 --> 00:28:56,230
+ودرجة ال H اللي هما أقلدرجة g of x زائد a اللي هم
+
+267
+00:28:56,230 --> 00:29:02,950
+اقل من درجة f of x زائد a يبقى صاروا اتنين هذول of
+
+268
+00:29:02,950 --> 00:29:09,630
+lower degree صحيح ولا لأ؟ يبقى صار هذه بتوصف بشكل
+
+269
+00:29:09,630 --> 00:29:18,090
+هذا ال f of x زائد a بتساوي ال g of x زائد a في ال
+
+270
+00:29:18,090 --> 00:29:21,130
+h of x زائد a
+
+271
+00:29:25,380 --> 00:29:35,720
+زائد ال a وال h of x زائد ال a are of lower degree
+
+272
+00:29:35,720 --> 00:29:42,500
+مدام lower degree يبقى هذا principle ولا لا just
+
+273
+00:29:42,500 --> 00:29:52,080
+irreducible ولا لا صحيح يبقى this means that هذا
+
+274
+00:29:52,080 --> 00:30:01,270
+يعنيإن ال F of X زائد ال A is reducible is
+
+275
+00:30:01,270 --> 00:30:10,110
+reducible على مين؟ على ال Q على .. على .. شغلنا
+
+276
+00:30:10,110 --> 00:30:16,430
+كان في ال F و في ال D reducible على ال Q و على ال
+
+277
+00:30:16,430 --> 00:30:17,850
+F على
+
+278
+00:30:21,380 --> 00:30:26,660
+على F وليس على Q يا عزيزي. يبقى الـ reducible على
+
+279
+00:30:26,660 --> 00:30:36,500
+F. وهذه صنحيلية على F. جل من لا يسكت. يبقى كل
+
+280
+00:30:36,500 --> 00:30:43,640
+شغلنا هذا على F. وهذه كلها على F. لو قلنا على Q صح
+
+281
+00:30:43,640 --> 00:30:49,040
+بسم الله أخدنا حالة خاصة. لأن الـ Q is إيه فيه؟لكن
+
+282
+00:30:49,040 --> 00:30:56,520
+احنا كله شغلنا على مين؟ على F of X كل كيوز حطي
+
+283
+00:30:56,520 --> 00:31:02,480
+مكانها F of X تمام؟ يبقى هذا معناه انه reducible
+
+284
+00:31:02,480 --> 00:31:10,820
+over اللي هو مين؟ over F تناقض؟ اه احنا احنا احنا
+
+285
+00:31:10,820 --> 00:31:16,200
+اقتربناها انها reducible يبقى صار عندنا
+
+286
+00:31:16,200 --> 00:31:17,440
+contradiction
+
+287
+00:31:19,890 --> 00:31:26,230
+يبقى فرضنا اللي فرضناه غلط وعكسه هو الصح يبقى هنا
+
+288
+00:31:26,230 --> 00:31:39,110
+سؤال الـ F of X is irreducible over F وهو المفهوم
+
+289
+00:31:39,110 --> 00:31:47,300
+طيب، الآن هذا نبرسي من السؤالنمرة D من السؤال بده
+
+290
+00:31:47,300 --> 00:31:57,380
+تطبيق عملي على الحالة C فراح قال ليش نمرة D نمرة
+
+291
+00:31:57,380 --> 00:32:08,640
+D من السؤال بيقول use for C استخدم for C to prove
+
+292
+00:32:08,640 --> 00:32:19,220
+to prove thatمش هتروح تثبت أنه التمامية x تكيّب
+
+293
+00:32:19,220 --> 00:32:28,420
+ماقصة 6x زائد الواحد is irreducible على الكيوب is
+
+294
+00:32:28,420 --> 00:32:39,600
+irreducible over الكيوب solution
+
+295
+00:32:44,430 --> 00:32:49,590
+يبقى ال feed اللي عندنا هذا يا بنات صار من؟ صار ال
+
+296
+00:32:49,590 --> 00:32:55,490
+Q، كويس؟ وقال استخدم numeracy هذا اللي استخدمته
+
+297
+00:32:55,490 --> 00:33:01,310
+هنا لإثبات أنه هذه ال function f of x is
+
+298
+00:33:01,310 --> 00:33:06,070
+irreducible على ال Q، بقوله كويس، يبقى احنا عندنا
+
+299
+00:33:06,070 --> 00:33:11,750
+f of x ليه تمانية x تكييف، نعطي ال 6x زايد واحد
+
+300
+00:33:13,340 --> 00:33:21,500
+طبعا بدا بياخدله TA موجودة في ال Q بس بشرط ال A
+
+301
+00:33:21,500 --> 00:33:27,040
+عنصر غير صفي و أبسط الشغلات خد واحد صحيح الواحد
+
+302
+00:33:27,040 --> 00:33:35,140
+موجود في ال Q عادي جدا يبقى أنا لو أخدت ال F of X
+
+303
+00:33:35,140 --> 00:33:43,240
+plus oneيبقى هذا تمانية في X plus one لكل تكييب
+
+304
+00:33:43,240 --> 00:33:50,420
+ناقص ستة في X plus one plus one بدي أفك هذا الهوث
+
+305
+00:33:50,420 --> 00:33:55,840
+يبقى هاي تمانية هذا X تكييب زائد تلاتة X ترمية
+
+306
+00:33:55,840 --> 00:34:05,200
+زائد تلاتة X زائد واحد ناقص ستة X زائد ناقص ستة في
+
+307
+00:34:05,200 --> 00:34:13,220
+Xزائد واحد زائد واحد هم هذه لو فكتها بده يصير f of
+
+308
+00:34:13,220 --> 00:34:21,220
+x زائد واحد يصير تمانية x تكيب زائد أربعة وعشرين x
+
+309
+00:34:21,220 --> 00:34:29,100
+تربيع زائد أربعة وعشرين x زائد تمانية ناقص ستة x
+
+310
+00:34:29,100 --> 00:34:36,940
+ناقص ستة زائد واحد بمعنى آخرصار ال F of X زائد
+
+311
+00:34:36,940 --> 00:34:44,700
+واحد يساوي تمانية X تكايب يااش مشكلة الاربع وعشرين
+
+312
+00:34:44,700 --> 00:34:51,100
+X ترابيع يااش مشكلة طلعولي هنا ناقص ستة X وزائد
+
+313
+00:34:51,100 --> 00:34:57,900
+اربع وعشرين X بضل قدير زائد تمانتاشر X وعندك
+
+314
+00:34:57,900 --> 00:35:04,710
+تمانية واحد تسعة ناقص ستة بضل قدير بضل دلقخير.
+
+315
+00:35:06,230 --> 00:35:15,970
+الآن بتاجر هذه النظرية موجودة في الـ Z6 معاملات
+
+316
+00:35:15,970 --> 00:35:25,530
+كلهم موجودات في Z انتجار صح ولا لا؟ يبقى هذه
+
+317
+00:35:25,530 --> 00:35:34,900
+البرنامج كلها موجودة في Z6 تمام؟ فالعيليللعناصر
+
+318
+00:35:34,900 --> 00:35:41,100
+هذول. التلاتة prime بتسبهم ولا لا؟ ولا يقسم
+
+319
+00:35:41,100 --> 00:35:46,480
+التمانية. والتلاتة تربيع التسعة لا تقسم التلاتة.
+
+320
+00:35:46,500 --> 00:35:53,620
+إيه؟ هذه نظرية كذلك؟ ولا لا؟ يرجعيننا الآن التلاتة
+
+321
+00:35:53,620 --> 00:35:58,980
+لا تقسم التمانية. لكن التلاتة بتقسم الأربعة
+
+322
+00:35:58,980 --> 00:36:05,760
+وعشرين. والتلاتة بتقسم التمنتاشروالتلاتة تقسمي
+
+323
+00:36:05,760 --> 00:36:13,540
+التلاتة أندي التلاتة ترجعي تسعة لتقسمي التلاتة
+
+324
+00:36:13,540 --> 00:36:20,380
+يبقى الدالة هذي إيش؟ R دي و سبب على ال Q يبقى هنا
+
+325
+00:36:20,380 --> 00:36:32,800
+Y previous theorem من نظرية السابقة ال F of X زائد
+
+326
+00:36:32,800 --> 00:36:45,420
+واحدis irreducible over the cube.طب أطلعي هنا لو
+
+327
+00:36:45,420 --> 00:36:50,920
+كانت هذه irreducible على الفيل يبقى الفوبكس من دون
+
+328
+00:36:50,920 --> 00:36:57,960
+ال a irreducible يبقى five excercises
+
+329
+00:36:57,960 --> 00:37:08,280
+خمسة part cالـ F of X اللي هي تمانية X تكييم ناقص
+
+330
+00:37:08,280 --> 00:37:19,940
+ستة X زائد واحد is irreducible over لكي هو المطلوب
+
+331
+00:37:19,940 --> 00:37:27,240
+.طيب ولك في مسائل لسه جاية بتنحل على part B و part
+
+332
+00:37:27,240 --> 00:37:32,140
+A يعني ضروري اتروح اتبرهنيالـ A و الـ B زي ما
+
+333
+00:37:32,140 --> 00:37:37,680
+برهننا الـ C حرفياً كما يعني بدك تاخد polynomial
+
+334
+00:37:37,680 --> 00:37:42,280
+بدياك انت تبقيها irreducible انت فرضها irreducible
+
+335
+00:37:42,280 --> 00:37:48,560
+و تروح اتحللي و نحو ذلك. كان هذا هو المثال أو
+
+336
+00:37:48,560 --> 00:37:54,960
+السؤال رقم خمسة دي. بدنا نروح لسؤال رقم ستة وهو
+
+337
+00:37:54,960 --> 00:38:02,260
+تعميم للحالة اللي خدناها قبل شويةconstruct field
+
+338
+00:38:02,260 --> 00:38:08,740
+ال order له تمانية او ال order له تسعة هذا السؤال
+
+339
+00:38:08,740 --> 00:38:16,220
+اللي هو سؤال ستة سؤال ستة بيقول افترض ان عندنا ال
+
+340
+00:38:16,220 --> 00:38:26,020
+F of X موجودة في ZP وهو هذه irreducible هذه ال F
+
+341
+00:38:26,020 --> 00:38:28,320
+ال F of X is
+
+342
+00:38:32,740 --> 00:38:43,000
+irreducible irreducible over اللي هو there P و
+
+343
+00:38:43,000 --> 00:38:49,780
+ال P is prime و ال degree لل F بده يساوي ال N و ال
+
+344
+00:38:49,780 --> 00:38:58,890
+degree لل F بده يساوي ال Nagain اثبت ان هذا is a
+
+345
+00:38:58,890 --> 00:39:05,950
+field show that نزل
+
+346
+00:39:05,950 --> 00:39:13,850
+P of X modularly principal I P generated by F of X
+
+347
+00:39:13,850 --> 00:39:21,870
+معناه is a field with
+
+348
+00:39:25,340 --> 00:39:26,740
+P⁻⁹
+
+349
+00:40:10,810 --> 00:40:18,090
+خذ فرنوميل F of X من الدرجة النونية موجودة في ZP
+
+350
+00:40:18,090 --> 00:40:24,410
+ZP of X moduloالـ Principle Ideal generated by هذه
+
+351
+00:40:24,410 --> 00:40:30,010
+ال Polynomial SAP وعدد ال عناصر يسوى P to the
+
+352
+00:40:30,010 --> 00:40:37,210
+power N زي المثالين اللي اتوا قبل قليل P أُس درجة
+
+353
+00:40:37,210 --> 00:40:41,590
+ال Polynomial ال Polynomial من الدرجة النونية يبقى
+
+354
+00:40:41,590 --> 00:40:48,910
+أُس L ال P هو ال Prime تبع Main تبع Z P Lيبقى بدنا
+
+355
+00:40:48,910 --> 00:40:54,470
+نيجي نبره صحة هذا الكلام المعلومات اللي عندنا F of
+
+356
+00:40:54,470 --> 00:41:03,410
+X is irreducible على مين؟ على P يبقى هنا let F of
+
+357
+00:41:03,410 --> 00:41:15,050
+X be irreducible polynomial on
+
+358
+00:41:18,430 --> 00:41:27,110
+ZP ما هو معنى هذا الكلام؟ نختصف
+
+359
+00:41:27,110 --> 00:41:31,470
+الدوري على طول الخط يبقى ال principle id
+
+360
+00:41:31,470 --> 00:41:36,310
+الgenerated by F of X هو maximal طبق قليل نظرية
+
+361
+00:41:36,310 --> 00:41:43,890
+يبقى هنا by a previous theorem
+
+362
+00:41:46,270 --> 00:41:58,470
+my previous theorem P of X ال F of X is
+
+363
+00:41:58,470 --> 00:42:06,690
+maximum positive in
+
+364
+00:42:06,690 --> 00:42:11,510
+NZC
+
+365
+00:42:15,830 --> 00:42:23,930
+AX ما ده maximal ideal بالكرولر رقم واحد هذا عبارة
+
+366
+00:42:23,930 --> 00:42:28,130
+عن field يبقى
+
+367
+00:42:28,130 --> 00:42:33,650
+باي انا
+
+368
+00:42:33,650 --> 00:42:44,130
+مش بدنا اثبت ان هذا field صحيح يبقى باي
+
+369
+00:42:47,040 --> 00:42:53,820
+previous quaterly نتيجة
+
+370
+00:42:53,820 --> 00:43:06,580
+السابقة we have ان z هي of x modular principle i
+
+371
+00:43:06,580 --> 00:43:12,340
+.e. generated by f of x is a
+
+372
+00:43:17,770 --> 00:43:25,050
+شو شكله؟ شكله
+
+373
+00:43:25,050 --> 00:43:33,310
+هو Z P of X موديولة ال principle ideal generated
+
+374
+00:43:33,310 --> 00:43:45,910
+by ال F of X بده يساوي مين؟ G of X زائدthe
+
+375
+00:43:45,910 --> 00:43:52,050
+principle ideal generated by f of x such that ان
+
+376
+00:43:52,050 --> 00:43:59,470
+ال g of x موجودة في z في p of x الشكل اللي عامله
+
+377
+00:43:59,470 --> 00:44:06,970
+twice فانا بدي ال g of x دي يمكن الدرجة تبعت أقل
+
+378
+00:44:06,970 --> 00:44:12,830
+من ال f of x ويمكن تكون أكبر من ال f of xإذا أقل
+
+379
+00:44:12,830 --> 00:44:16,530
+من درجة الفوبكس خلاصنا انتهينا من الموضوع لأنه في
+
+380
+00:44:16,530 --> 00:44:21,530
+المثالين اللي قبل قليل ال principle ideal بقينا
+
+381
+00:44:21,530 --> 00:44:28,150
+يقولوا ال remain درجته أقل من درجة اللي هو الدالة
+
+382
+00:44:28,150 --> 00:44:32,250
+اللي ولدتني ال principle ideal صحيح ولا لا؟ إذا
+
+383
+00:44:32,250 --> 00:44:38,510
+هذه النقطة تكون أقل وقد تكون أكبر يبقى بعمل ال
+
+384
+00:44:38,510 --> 00:44:43,530
+division algorithmأو long division يبقى بال
+
+385
+00:44:43,530 --> 00:44:50,030
+division algorithm هذه بقدر أقول هي F of X في ال Q
+
+386
+00:44:50,030 --> 00:44:56,410
+of X زائد ال R of X زائد ال principle ideal
+
+387
+00:44:56,410 --> 00:45:04,690
+generated by F of X وبشرط ان ال R of X بدأت سوى 0
+
+388
+00:45:04,690 --> 00:45:14,660
+او ال degree لل R of Xأقل من ال degree لل F of X
+
+389
+00:45:14,660 --> 00:45:22,000
+مظبوط هيك؟ يبقى أنا شيلت الجيب وحطيتها in general
+
+390
+00:45:22,000 --> 00:45:27,880
+السؤال هو هذا ال element موجود في ال ideal هذا؟
+
+391
+00:45:27,880 --> 00:45:34,760
+يبقى صحيح اني اكتب ال R of X زائد ل principle
+
+392
+00:45:34,760 --> 00:45:41,930
+ideal generated by F of Xبحيث ال R of X يسوى Zero
+
+393
+00:45:41,930 --> 00:45:50,550
+أورى ال degree لل R of X أقل من ال degree لمين؟ لل
+
+394
+00:45:50,550 --> 00:45:56,890
+F of X اللي هو يسوى قداش ال degree لل F of X لأن
+
+395
+00:45:56,890 --> 00:46:04,690
+هو معطينيها مش من عندي طيب إذا حط ال general form
+
+396
+00:46:04,690 --> 00:46:15,680
+تبعها ال general form هوالـ A0 زائد A1 X زائد A2 X
+
+397
+00:46:15,680 --> 00:46:23,820
+تربية زائد A N minus ال 1 في X minus ال 1 مظبوط؟
+
+398
+00:46:23,820 --> 00:46:31,740
+زائد لـ Principle ideal generated by F of X بحيث
+
+399
+00:46:31,740 --> 00:46:43,830
+أن الـ A0 والـ A1 والـ A N minus ال 1موجودة في ZP
+
+400
+00:46:43,830 --> 00:46:54,090
+يبقى عناصر في ZP يبقى ملاحظين ان درجة هذه اقل من
+
+401
+00:46:54,090 --> 00:47:00,390
+درجة من من درجة F of X صحيح ولا لا؟ طيب ممتاز جدا
+
+402
+00:47:00,390 --> 00:47:07,110
+يبقى هذا هو الشكل العام للعنصرزي قبل قليل، لمّا كل
+
+403
+00:47:07,110 --> 00:47:13,530
+فرنسي في المدرجة التانية خلّينه المضافل من الدرجة
+
+404
+00:47:13,530 --> 00:47:17,490
+الأولى، لما كل فرنسي بالأيدي المدرجة التالتة،
+
+405
+00:47:17,490 --> 00:47:22,250
+خلّينه المدرجة التالتة، يعني دائما وأبدأ أقل منه،
+
+406
+00:47:22,250 --> 00:47:28,430
+يعني وكأن هذا السؤال هو تعميم للمثالين اللي أخدهم
+
+407
+00:47:28,430 --> 00:47:34,910
+قبل قليل، طب بدأ أعرف أكمانصر فينا،أظن كلكوا
+
+408
+00:47:34,910 --> 00:47:39,950
+خدرستوا احتمالات، مظبوط؟ وكداش عدد العناصر،
+
+409
+00:47:39,950 --> 00:47:46,430
+الإيهات هدول؟ كداش عدد هدول؟ N، ممتاز ده، يبقى
+
+410
+00:47:46,430 --> 00:47:51,750
+هدول عددهم، السؤال هو بكم طريقة بقدر اختار كل
+
+411
+00:47:51,750 --> 00:47:56,170
+عنصر؟ P، لإن هدول العناصر كلهم بيزد فيه، يفتخر
+
+412
+00:47:56,170 --> 00:48:01,150
+Zero، يواحد، يتنين، يتلاتة، يفي ناقص واحد، اللي هو
+
+413
+00:48:01,150 --> 00:48:07,510
+أخر عنصريبقى عدد القلوب اللي بقدر اختاره هو P to
+
+414
+00:48:07,510 --> 00:48:17,610
+the power N يبقى number of
+
+415
+00:48:17,610 --> 00:48:32,840
+elements in this field is P to the power Nبعدد
+
+416
+00:48:32,840 --> 00:48:37,860
+العناصر وفيه التدفارين زي ما كنا بنعمل قبل قليل في
+
+417
+00:48:37,860 --> 00:48:43,900
+المثالين السابقين بدنا نعطي تطبيق مباشر عليه في
+
+418
+00:48:43,900 --> 00:48:48,680
+عندك سؤال سبعة و سؤال تمانى بناخد سؤال ثاني رقم
+
+419
+00:48:48,680 --> 00:48:53,500
+كبير بدناش رقم صغير توا خدنا تمانية و تسعة خدنا
+
+420
+00:48:53,500 --> 00:48:57,740
+رقم تمانية و رقم دوسرة و رقم سبعة و عشرين يبقى
+
+421
+00:48:57,740 --> 00:49:08,050
+باجي بقول its a precise رقم قدررقم تمانية ايه
+
+422
+00:49:08,050 --> 00:49:13,770
+فيه ال .. الفارضة
+
+423
+00:49:13,770 --> 00:49:19,110
+اللي هو السبعة وعشرين طبعا اللي جاله خمسة وعشرين
+
+424
+00:49:19,110 --> 00:49:24,670
+بتجعله يقولي خمسة تربيع هذا
+
+425
+00:49:24,670 --> 00:49:33,520
+تلاتة وستلاتة يعني هذا هذابدي ساوي تلاتة أس تلاتة
+
+426
+00:49:33,520 --> 00:49:40,460
+يعني بدي زي ال D3 نشغل في زي ال D3 و ال Polynomial
+
+427
+00:49:40,460 --> 00:49:44,700
+يعني ندخل بالطريقة التالتة تقول ان شاء الله خلصنا
+
+428
+00:49:44,700 --> 00:49:50,600
+Polynomial اكتر خديلك واحدة منها تمام؟ اذا ما
+
+429
+00:49:50,600 --> 00:49:52,800
+زبطتش اللولة ممكن تروح الدورة على التالت اذا
+
+430
+00:49:52,800 --> 00:49:55,520
+مازبطتش اللولة دوري على التالت و هكذا يعني انا
+
+431
+00:49:55,520 --> 00:49:59,930
+ممكن اخد Polynomial تظبط معاهوتنتين تلاتة اربعان
+
+432
+00:49:59,930 --> 00:50:03,190
+ياخدوا كلولهم الاخرون تظبط يعني الكلوم اللي افضل
+
+433
+00:50:03,190 --> 00:50:07,310
+اعطيها ليس القرآن نزله بين الاسماع مفيش غيرها لكن
+
+434
+00:50:07,310 --> 00:50:15,430
+لأ ممكن يكون شيء غيرها خديني
+
+435
+00:50:15,430 --> 00:50:24,110
+مثلا ال F of X يسوي X تكييب زي X تربيع زي اتنين اي
+
+436
+00:50:24,110 --> 00:50:34,410
+كلولهم يلمن الدرجة E تالتةبدأي اشتغل on z3 اه يبقى
+
+437
+00:50:34,410 --> 00:50:41,450
+بدي اشتغل على z3 بدي اروح اشوف مين ال F of 0
+
+438
+00:50:41,450 --> 00:50:51,910
+بالنهر و ال F of واحد واحد واحد اتنين اربع في زي
+
+439
+00:50:51,910 --> 00:51:00,010
+التلاتة واحد بدي اخد ال F of اتنينهذا تمانية من
+
+440
+00:51:00,010 --> 00:51:07,270
+أربعة معاشر اتنين اربعتاشر زدتري باتنين يبقى اتنين
+
+441
+00:51:07,270 --> 00:51:14,230
+يبقى ماعنديش zeros على زدتري يبقى باجي بقول له sir
+
+442
+00:51:14,230 --> 00:51:25,010
+f of x has no zeros on والله over زدتري
+
+443
+00:51:46,210 --> 00:51:55,170
+طبعا يبقى دول ما همش zeros على Z3 كويس؟ إذن بقدر
+
+444
+00:51:55,170 --> 00:52:06,120
+أجيب ال field مباشرة يبقى هنا Z E3 R Tموديولو ال X
+
+445
+00:52:06,120 --> 00:52:19,640
+تكييب زاد X تربيع زائدي اتنين هذا is a field طب
+
+446
+00:52:19,640 --> 00:52:31,580
+مين العناصر تبقى؟ where؟ حيث ال Z3 of X موديولو ال
+
+447
+00:52:31,580 --> 00:52:38,060
+principle idealgenerated by X تكييف زائد X تربيع
+
+448
+00:52:38,060 --> 00:52:46,040
+زائد اتنين بده يساوي اكتربيه اكتربيه
+
+449
+00:52:46,040 --> 00:52:54,840
+اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه
+
+450
+00:52:54,840 --> 00:52:58,560
+اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه
+
+451
+00:52:58,560 --> 00:53:00,300
+اكتربيه اكتربيه اكتربيه اكتربيه اكتربيه
+
+452
+00:53:02,060 --> 00:53:10,420
+وبحيث ان الـA والـB والـC موجودة كلها هذه في Z3
+
+453
+00:53:10,420 --> 00:53:19,240
+هكم عنصر في هذا؟ سبعة وعشرين عنصر تمام؟ بدك ايه؟
+
+454
+00:53:19,240 --> 00:53:22,140
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+455
+00:53:22,140 --> 00:53:22,820
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+456
+00:53:22,820 --> 00:53:24,340
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+457
+00:53:24,340 --> 00:53:24,440
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+458
+00:53:24,440 --> 00:53:24,740
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+459
+00:53:24,740 --> 00:53:24,740
+انا براها ايه في البيت؟ انا براها ايه في البيت؟
+
+460
+00:53:24,740 --> 00:53:28,940
+انا براها ايه
+
+461
+00:53:28,940 --> 00:53:35,960
+في البيت؟ انا بخلاص؟ وضاربهم وجامعهم وطرحهم زي
+
+462
+00:53:35,960 --> 00:53:40,680
+اللي قبل؟ فهي عندنا الآن سؤال عشرة السؤال طبعا
+
+463
+00:53:40,680 --> 00:53:47,540
+عشرة حاطط فيه خمسة مطالب مش هحل الى مطلوبين، مطلوب
+
+464
+00:53:47,540 --> 00:53:52,960
+اليوم ومطلوب المرة الجاية لكن نمره A ونمره C زي
+
+465
+00:53:52,960 --> 00:54:01,410
+بعض يبقى نمره A بتفتخدي اللي هو العدد ثلاثةلا يقسم
+
+466
+00:54:01,410 --> 00:54:05,290
+معامل ال Exos خمسة لكن بيقسم معامل ال Exos أربعة و
+
+467
+00:54:05,290 --> 00:54:09,850
+بيقسم معامل ال Exos أربعة و بيقسم الستة و تلاتة
+
+468
+00:54:09,850 --> 00:54:15,550
+Price يبقى طبقا للنظرية هذه Irreducible نمرا سي
+
+469
+00:54:15,550 --> 00:54:19,230
+نفس الطريقة إيه Exos أربعة زي التلاتة Exos التربية
+
+470
+00:54:19,230 --> 00:54:23,330
+زي التلاتة التلاتة بتقسم أخر معاملة بتقسمش الأول
+
+471
+00:54:23,330 --> 00:54:28,670
+مربعة أعلى يقسم العدد أخر يبقى Irreducibleيبقى
+
+472
+00:54:28,670 --> 00:54:33,750
+الأولى و التالتى زى بعض و حلهم سطر واحد النص
+
+473
+00:54:33,750 --> 00:54:41,190
+النظرية مباشرة لكن لو جيتى لنمرة P نمرة P بيقوللى
+
+474
+00:54:41,190 --> 00:54:50,330
+اللى هى X أُص أربعة زائد X زائد واحد زائد X زائد
+
+475
+00:54:50,330 --> 00:54:56,150
+واحد بدي
+
+476
+00:54:56,150 --> 00:55:04,160
+اشتغلعلى مين؟ على field يبقى بجيب اقوله مثلا ان
+
+477
+00:55:04,160 --> 00:55:09,600
+زيت تويها هذي
+
+478
+00:55:09,600 --> 00:55:15,920
+ال F of X هذي في السؤال تشوفوا هل هذا reduceable
+
+479
+00:55:15,920 --> 00:55:21,380
+والله ايه reduceable على ال Q سؤالي الخمس نقاط كله
+
+480
+00:55:21,380 --> 00:55:26,260
+تشوفوا هل reduceable والله irreducible على اللو
+
+481
+00:55:26,260 --> 00:55:32,460
+جيت لل F bar يا بنات of X ليه ال X وصار بعزاه ال X
+
+482
+00:55:32,460 --> 00:55:37,360
+ده اللي هتتغير؟ هي نفسه يبقى سعر ال degree لل F هي
+
+483
+00:55:37,360 --> 00:55:43,020
+ال degree لمن؟ لل F bar يبقى هذا بدي يعطينا ان ال
+
+484
+00:55:43,020 --> 00:55:49,000
+degree لل F هي نفس ال degree لل F bar ذكرت رحينا
+
+485
+00:55:49,000 --> 00:55:54,440
+نظرية؟ خلاصنا؟ طيب ضلي علينا شغلة بسيطة ناسي احنا
+
+486
+00:55:54,440 --> 00:56:01,690
+بنشتغل ويه؟يبقى ال F of zero يساوي واحد وال F of
+
+487
+00:56:01,690 --> 00:56:10,990
+واحد يساوي واحد يبقى صارت has no zeros يبقى هذا
+
+488
+00:56:10,990 --> 00:56:22,190
+بدي يعطينا ال F bar of X has no zeros on Z two وال
+
+489
+00:56:22,190 --> 00:56:28,000
+degree لل Fبتساوي ال degree لل F bar يبقى صورة ال
+
+490
+00:56:28,000 --> 00:56:39,620
+F bar irreducible على Z2 يبقى الصورة F bar of X is
+
+491
+00:56:39,620 --> 00:56:50,980
+irreducible over Z2 هذا بده يعطي كمان ان F الأصلية
+
+492
+00:56:50,980 --> 00:56:58,430
+is irreducible على Z2هدفة هي يعطيكي ان ال F of X X
+
+493
+00:56:58,430 --> 00:57:09,790
+أُس أربع زي X زي واحد is irreducible over liquid
+
+494
+00:57:09,790 --> 00:57:13,450
+خديني
+
+495
+00:57:13,450 --> 00:57:21,130
+هالمثال باشي طبعانمر يا إيه؟ اللي هو آخر السؤال
+
+496
+00:57:21,130 --> 00:57:27,090
+يعطيناكوا مثال حرفي زيه يبقى بتحلوه بنفس الطريقة،
+
+497
+00:57:27,090 --> 00:57:40,150
+جاري قولي في السؤال 12 وسؤال 14 وسؤال 18 وسؤال
+
+498
+00:57:40,150 --> 00:57:44,870
+23 وسؤال
+
+499
+00:57:44,870 --> 00:57:45,670
+25
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8d45356875823a6720a369835332dea29d531986
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_postprocess.srt
@@ -0,0 +1,1572 @@
+1
+00:00:21,010 --> 00:00:25,770
+بسم الله الرحمن الرحيم في المحاضرة الماضية تكلمنا
+
+2
+00:00:25,770 --> 00:00:32,210
+حول الخطوط الرئيسية أو العريضة لموضوع جبر حديث
+
+3
+00:00:32,210 --> 00:00:39,870
+اتنين وقلنا سنعطي سبعة sections سنده بال section
+
+4
+00:00:39,870 --> 00:00:44,870
+الأول اللي هو introduction tourings وننتهي بال
+
+5
+00:00:44,870 --> 00:00:50,900
+extension fields اليومحسب ما وعدناه كل مرة الماضية
+
+6
+00:00:50,900 --> 00:00:55,300
+بدنا نبدأ في أول section في مقرر جبر حديثة name
+
+7
+00:00:55,300 --> 00:01:00,860
+وهو introduction to ring في هذا ال section بدنا
+
+8
+00:01:00,860 --> 00:01:06,760
+نعطي تعريف ال ring بعض الخواص لهذا ال ring بعض
+
+9
+00:01:06,760 --> 00:01:12,860
+النظريات البسيطة المتعلقة بهذه الخواص زائد بعض
+
+10
+00:01:12,860 --> 00:01:18,570
+الأمثلة لأن كل ما يتعلق بال sectionو سنبدأ منذ
+
+11
+00:01:18,570 --> 00:01:24,530
+البداية إذا بدنا نعطي تعريف لل ring و نقارن ما
+
+12
+00:01:24,530 --> 00:01:28,970
+بينه و بين تعريف ال group اللي درسها في جبر حديث
+
+13
+00:01:28,970 --> 00:01:34,070
+واحد إذا بقول ال ring R هي set with two binary
+
+14
+00:01:34,070 --> 00:01:38,890
+operations في ال group بجينا نقول إيش؟ one binary
+
+15
+00:01:38,890 --> 00:01:43,450
+operation لكن هنا two binary operations واحدة
+
+16
+00:01:43,450 --> 00:01:48,370
+عملية جمع والتانية عملية ضربيبقى with two binary
+
+17
+00:01:48,370 --> 00:01:52,870
+operations addition بالـ A زائد الـ B والـ
+
+18
+00:01:52,870 --> 00:01:57,250
+multiplication اللي هي ضرب A في B such that for
+
+19
+00:01:57,250 --> 00:02:04,630
+all A وB وC اللي موجودة في R وEها يبقى ال 6R عليها
+
+20
+00:02:04,630 --> 00:02:11,010
+two binary operations بتتحقق ليه ستة شروط بتعرف ما
+
+21
+00:02:11,010 --> 00:02:17,870
+هي هذه الشروط الستة ونقارن فيما بينهاالطلاعين إلى
+
+22
+00:02:17,870 --> 00:02:23,390
+الشروط من واحد لغاية أربعة هل لهم علاقة بعملية
+
+23
+00:02:23,390 --> 00:02:30,150
+الضرب؟ يبقى أول أربعة شروط متعلقة بعملية الجمع فقط
+
+24
+00:02:30,150 --> 00:02:38,770
+لغاية الشرط الأول ان a زائد b بده يسوى b زائد a في
+
+25
+00:02:38,770 --> 00:02:43,790
+حالة ال group بجينا نقول ان هذه ال group ايش
+
+26
+00:02:43,790 --> 00:02:49,580
+نسميها؟Abelian group تحت عملية الجامعة هنا مش
+
+27
+00:02:49,580 --> 00:02:55,420
+هنقول abelian هنقول abelian group تحت عملية
+
+28
+00:02:55,420 --> 00:02:58,780
+الجامعة يبقى abelian ring تحت عملية الجامعة بس
+
+29
+00:02:58,780 --> 00:03:02,780
+كلمة abelian في ال rings مش هتمر معانا أبدا
+
+30
+00:03:02,780 --> 00:03:08,480
+سنستبدل كلمة abelian في ال group ب commutative في
+
+31
+00:03:08,480 --> 00:03:14,000
+حالة ال ring وهذا ما سنشير إليه في الملاحظة الأولى
+
+32
+00:03:14,360 --> 00:03:19,060
+يبقى بالنسبة للجامعة a زائد b يسوى b زائد a عملية
+
+33
+00:03:19,060 --> 00:03:24,440
+الجامعة عملية إبدالية الشرط التاني a زائد b زائد c
+
+34
+00:03:24,440 --> 00:03:29,140
+يسوى a زائد b زائد c زي ما تشاهدونه وهو ما نسميه
+
+35
+00:03:29,140 --> 00:03:38,140
+خاصية ندمج العناصر بعد انطلاق عنصر جديد بمعنىلو
+
+36
+00:03:38,140 --> 00:03:45,860
+جمعت a زائد b أولا ثم جمعت النتج مع c تماما كما لو
+
+37
+00:03:45,860 --> 00:03:51,980
+جمعت b زائد c أولا ثم جمعت a للعنصر النتج هيعطيني
+
+38
+00:03:51,980 --> 00:03:57,340
+نفس الإجابة الشرط التالت ال third condition there
+
+39
+00:03:57,340 --> 00:04:03,720
+is an element zero بسميه additive identity يبقى
+
+40
+00:04:03,720 --> 00:04:09,230
+عنصر الوحدة بالنسبة لعملية الجمعاللي هو man is
+
+41
+00:04:09,230 --> 00:04:14,730
+zero يبقى additive identity عنصر الوحدة بالنسبة
+
+42
+00:04:14,730 --> 00:04:21,530
+لعملية الجامعة صدش ده a زائد zero بده يساوي ال a
+
+43
+00:04:21,530 --> 00:04:27,150
+يعني وجود هذا العنصر تحت هذه العملية لن يغير
+
+44
+00:04:27,150 --> 00:04:32,030
+العنصر الأصلي اللي موجود ف a زائد هذا zero بده
+
+45
+00:04:32,030 --> 00:04:37,230
+يعطينا ال a itselfإن حدث ذلك يبقى الـ zero بسميه
+
+46
+00:04:37,230 --> 00:04:42,970
+ال identity element بالنسبة لعملية الجامعة طب
+
+47
+00:04:42,970 --> 00:04:48,910
+خليني أسأل ليش ما قلتش a زائد zero يسوي zero زائد
+
+48
+00:04:48,910 --> 00:04:55,050
+a يسوى ال a بيصير تكرار ممل لأن أنا جاي في ال
+
+49
+00:04:55,050 --> 00:04:59,130
+condition الأول ان ال a زائد ال b بيبقى سوى ال b
+
+50
+00:04:59,130 --> 00:05:04,410
+زائد ال a لأي عنصرين a وb موجودة في ال set Aيبقى
+
+51
+00:05:04,410 --> 00:05:09,150
+بصير هدأ تكرار مهم اللي يبقى كفي أخات واحدة منهم
+
+52
+00:05:09,150 --> 00:05:13,830
+وهي تساوي الثانية من ال first condition تمام؟ يبقى
+
+53
+00:05:13,830 --> 00:05:17,730
+بقول هنا ال a زايد ال zero بده يساوي ال a لكل ال a
+
+54
+00:05:17,730 --> 00:05:22,890
+اللي موجود في ال R بعدين قال يوجد عنصر سالب a
+
+55
+00:05:22,890 --> 00:05:28,490
+there is an element minus ال a في أرسلت R such
+
+56
+00:05:28,490 --> 00:05:34,720
+that بحيث أن ال a زايد ناقص ال a بده يساوي zeroقبل
+
+57
+00:05:34,720 --> 00:05:38,760
+ما اكمل الشروط بدأ استنى يبقى الأربعة شروط هذه
+
+58
+00:05:38,760 --> 00:05:43,700
+تتعلق بعمليات الجامعة اللحظة ان هذه اللي كنا نقول
+
+59
+00:05:43,700 --> 00:05:48,860
+عليها abelian group هاي شرط ال abelia هاي شرط ال
+
+60
+00:05:48,860 --> 00:05:53,420
+associativity ال identity element معكوس ال element
+
+61
+00:05:53,420 --> 00:05:57,640
+مظبوط يبقى هذه اللي كنا نقول عليها group حطينا
+
+62
+00:05:57,640 --> 00:06:00,760
+عليها الشرط لو ان صارت abelian group بالنسبة
+
+63
+00:06:00,760 --> 00:06:05,160
+لعملية الجامعةبعد ان نخرج من ال group نذهب الى ال
+
+64
+00:06:05,160 --> 00:06:09,760
+ring يبقى نذهب ناخد ايضا ال two conditions الاتنين
+
+65
+00:06:09,760 --> 00:06:18,180
+هذول a في b في c يعني لو ضربت ال b في ال c هينتج
+
+66
+00:06:18,180 --> 00:06:24,220
+عنصر جديد بدي اضرب فيه من جهة الشمال a تماما كما
+
+67
+00:06:24,220 --> 00:06:28,620
+لو ضربت a في b و اللي نتف ضربته في main في c وهذه
+
+68
+00:06:28,620 --> 00:06:33,910
+خاصية ال associated بالنسبة لعملياتيبقى خاصية الـ
+
+69
+00:06:33,910 --> 00:06:37,450
+Associated بالنسبة لعملية الجمع وبالنسبة لعملية
+
+70
+00:06:37,450 --> 00:06:44,690
+الضرب R exists موجودة فبالشرط الأخير يجمع عملية
+
+71
+00:06:44,690 --> 00:06:50,050
+الجمع مع عملية الضرب في آن واحد وهذا بنسميها بنات
+
+72
+00:06:50,050 --> 00:06:55,750
+الـ distributive law قانون التوزيع يبقى قانون
+
+73
+00:06:55,750 --> 00:07:00,800
+التوزيع اللي عندنا A في B زائد الـCبدي ساوي a في b
+
+74
+00:07:00,800 --> 00:07:06,060
+زي a في c اللي بنسميه left distributive law عملية
+
+75
+00:07:06,060 --> 00:07:10,900
+الضرب من جهة الشمال بدي ساوي b في a زي c في a بدي
+
+76
+00:07:10,900 --> 00:07:15,220
+ساوي b في a زي c في a بدي ساوي b في a زي c في a
+
+77
+00:07:15,220 --> 00:07:16,560
+بدي ساوي b في a زي c في a بدي ساوي b في a زي c في
+
+78
+00:07:16,560 --> 00:07:19,420
+زي c في a بدي ساوي b في a زي c في a بدي ساوي b في
+
+79
+00:07:19,420 --> 00:07:28,720
+a زي c في a بدي ساوي b في a زي c في a بدي ساوي
+
+80
+00:07:28,720 --> 00:07:33,170
+bوبالتالي بجدك اتراعي الترتيب مش ع كيفك تضربي لأ
+
+81
+00:07:33,170 --> 00:07:37,150
+انت مقيدة الضرب من الشمال بتخلي الضرب ماشي من جهة
+
+82
+00:07:37,150 --> 00:07:41,030
+الشمال الضرب من جهة اليمين بيبقى ضرب ماشي من جهة
+
+83
+00:07:41,030 --> 00:07:45,130
+اليمين مش هتبدل وغير على كيفي بنفعش هذا الكلام
+
+84
+00:07:45,130 --> 00:07:49,430
+وانت واخدته هذا في ال abstract algebra one يبقى لا
+
+85
+00:07:49,430 --> 00:07:56,470
+يزال هو هو وسيبقى هو هو بعد ذلك ان شاء الله تعالى
+
+86
+00:07:56,470 --> 00:08:02,440
+في أن ملاحظات الآنعلى تعريف ال ring بنقول لو حصل
+
+87
+00:08:02,440 --> 00:08:08,080
+بالنسبة لعملية الضرب ان ال a في ال b كانت تسوى b
+
+88
+00:08:08,080 --> 00:08:14,700
+في a لكل ال a و ال b اللي موجودات في ال set R او
+
+89
+00:08:14,700 --> 00:08:18,660
+في ال ring R يبقى في هذه الحالة بقول ال ring is
+
+90
+00:08:18,660 --> 00:08:24,720
+commutative يبقى ال ring افضلية بدل appealing
+
+91
+00:08:24,720 --> 00:08:29,330
+group بدأ يقول commutative ringيبقى ال ring هذه
+
+92
+00:08:29,330 --> 00:08:36,690
+تتحقق فيها خاصية الإبدال لجميع
+
+93
+00:08:36,690 --> 00:08:42,630
+عناصر a و b اللي موجودة في R لكل ال a و ال b اللي
+
+94
+00:08:42,630 --> 00:08:47,570
+موجودة في R بدون استثناء مش ان اتحققت العنصر ال
+
+95
+00:08:47,570 --> 00:08:53,350
+commutative لأ اتحقق لجميع عناصر R بدون استثناء
+
+96
+00:08:53,350 --> 00:08:58,660
+طيب نقطة ثانيةلو كانت ال R فيها ال identity
+
+97
+00:08:58,660 --> 00:09:02,920
+element with respect to multiplication يبقى في
+
+98
+00:09:02,920 --> 00:09:07,440
+عندي عنصر واحدة بالنسبة لعملية الضرب طبعا هنا في
+
+99
+00:09:07,440 --> 00:09:11,620
+ال zero بالنسبة لعملية الجبهة لأ انا بد ال
+
+100
+00:09:11,620 --> 00:09:16,400
+identity element بالنسبة لعملية الضرب ان وجد ال
+
+101
+00:09:16,400 --> 00:09:21,260
+identity element بالنسبة لعملية الضرب في R بنروح
+
+102
+00:09:21,260 --> 00:09:27,350
+نقولها دي عشان نسميها ring with unityيعني ممكن يا
+
+103
+00:09:27,350 --> 00:09:31,970
+بنات ال ring يكون فيها unity وممكن مايكونش فيها
+
+104
+00:09:31,970 --> 00:09:35,990
+unity إذا فيها ال unity بسميها ring with unity إذا
+
+105
+00:09:35,990 --> 00:09:42,070
+فيهاش بسميها ring without unity كما سنرى بعد قليل
+
+106
+00:09:42,070 --> 00:09:46,330
+من خلال الأمثلة إن بعض ال rings فيها unity و بعض
+
+107
+00:09:46,330 --> 00:09:51,390
+الأخر مافيهش فيها unity و قد يكون ال unity هو
+
+108
+00:09:51,390 --> 00:09:57,960
+الواحد الصحيح و قد لا يكونحسب ال operation المعرفة
+
+109
+00:09:57,960 --> 00:10:04,080
+على ال ring R النقطة التالتة او الملاحظة التالتة
+
+110
+00:10:04,080 --> 00:10:09,520
+لو كانت R ring with unity واخدت عنصر موجود في R
+
+111
+00:10:09,520 --> 00:10:15,280
+وهذا العنصر لا يساوي الصفر يبقى ال A هذا بقول ال
+
+112
+00:10:15,280 --> 00:10:21,540
+multiplicative inverse ان حدث ذلكيبقى ال A هاد ..
+
+113
+00:10:21,540 --> 00:10:27,780
+يبقى هذا ال A بسمي unit في ال ring آه يبقى أصلا
+
+114
+00:10:27,780 --> 00:10:33,540
+عندي كلمتين في unit و في unity ال unity هو ال
+
+115
+00:10:33,540 --> 00:10:37,920
+identity element بالنسبة لعملية الضرب هذا ال unity
+
+116
+00:10:37,920 --> 00:10:42,460
+يبقى هو ال identity element بالنسبة لعملية الضرب
+
+117
+00:10:42,460 --> 00:10:48,720
+ال unitهو العنصر غير الصفري اللي موجود في ال ring
+
+118
+00:10:48,720 --> 00:10:54,980
+R و اللي له معكوس بالنسبة لعملية الضرب يعني إيش
+
+119
+00:10:54,980 --> 00:10:59,480
+بجينا نقول A في ال group إيش معكوس لو أنا A
+
+120
+00:10:59,480 --> 00:11:05,040
+inverse A و بحط فوقها سلب واحد لكنها ليست A أس سلب
+
+121
+00:11:05,040 --> 00:11:11,990
+واحد لكن هو رمز يدل على معكوس العنصر Aيبقى إذا حدث
+
+122
+00:11:11,990 --> 00:11:18,590
+أن للعنصر A معكوس بدي أسميه A inverse يبقى ال A
+
+123
+00:11:18,590 --> 00:11:27,910
+بسميه unit تمام؟ طيب ال ring فيهم مليلات unit و
+
+124
+00:11:27,910 --> 00:11:32,830
+الله يمكن أه ويمكن لا كل احتمالات و أرضها ممكن
+
+125
+00:11:32,830 --> 00:11:38,550
+يكون العناصر كلها غير الصفرية units ويمكن مالجيش
+
+126
+00:11:38,550 --> 00:11:44,270
+فيها units في المغربويمكن نلاقي بعض اليونس فقط
+
+127
+00:11:44,270 --> 00:11:50,430
+عنصرين اربع ستة تمانية لأنه بيكون عدد زوجي عنصر
+
+128
+00:11:50,430 --> 00:11:56,390
+ومعكوسه إذا هدول بيلاقيهم زوجي وما إلى ذلك يبقى
+
+129
+00:11:56,390 --> 00:12:02,210
+اليونس قد يكون موجودة في ال ring وقد لا تكون هذا
+
+130
+00:12:02,210 --> 00:12:07,070
+النقطة اللي هي التالتة يبقى العنصر إن وجدت له
+
+131
+00:12:07,070 --> 00:12:14,070
+معكوس بده يسميهUnity طب خليني أسأل شوية لو عندى
+
+132
+00:12:14,070 --> 00:12:21,370
+unity لا يساوي ال zero تمام unity لا يساوي ال zero
+
+133
+00:12:21,370 --> 00:12:27,390
+ال unity هذا بقدر أقول عليه unit ال
+
+134
+00:12:27,390 --> 00:12:32,630
+unity نفسه بقدر أقول عليه unit اه لأن لو ضربته في
+
+135
+00:12:32,630 --> 00:12:37,490
+نفسه بطلع ال unity صحيح ولا ..فال unity في ال
+
+136
+00:12:37,490 --> 00:12:42,550
+unity بتعطينا ال unity وبقى بناء عليه any unity is
+
+137
+00:12:42,550 --> 00:12:49,430
+a unit but the converse المعكوز is not necessarily
+
+138
+00:12:49,430 --> 00:12:56,490
+true ليس بضرورة صحيحة طيب وصلنا للنقطة الرابعة F
+
+139
+00:12:56,490 --> 00:13:01,150
+ال A و ال B موجودة في R و ال R is commutative و ال
+
+140
+00:13:01,150 --> 00:13:08,580
+A لا تساوي Zeroبنقول ال a تقسم ال b a divide ال b
+
+141
+00:13:08,580 --> 00:13:13,900
+هنكتبها بالشكل هذا زي ما كتبهالكوا في جبر حديث
+
+142
+00:13:13,900 --> 00:13:18,460
+واحد قبل ما بدأت ال group في مقدمة اعطوكوا هذه
+
+143
+00:13:18,460 --> 00:13:24,160
+المقدمة ال a تقسم ال b كنا بنعبر عنها بصيغة اللي
+
+144
+00:13:24,160 --> 00:13:30,220
+قدامنا هذا يبقى بقول a تقسم ال b إذا جدرتألاقي
+
+145
+00:13:30,220 --> 00:13:38,400
+element آخر في R سميته C بحيث ال B يساوي من A في C
+
+146
+00:13:38,400 --> 00:13:45,660
+يبقى ال A تقسم ال B إذا قدرت ألاقي عنصر آخر في R
+
+147
+00:13:45,660 --> 00:13:51,500
+بحيث لو ضربته في A يعطيني من يعطيني ال B طيب لو
+
+148
+00:13:51,500 --> 00:13:56,240
+كان ال A لا تقسم ال B بروح بكتبها بالشكل لأن هذا
+
+149
+00:13:56,590 --> 00:14:04,770
+يبقى a لتقسيم ال b مين بتحب تسأل أي سؤال على هذه
+
+150
+00:14:04,770 --> 00:14:11,130
+المقدمة قبل أن نأخذه الأمثلة؟
+
+151
+00:14:11,130 --> 00:14:16,470
+هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم
+
+152
+00:14:16,470 --> 00:14:16,730
+.. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم ..
+
+153
+00:14:16,730 --> 00:14:17,530
+هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم
+
+154
+00:14:17,530 --> 00:14:22,610
+هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم
+
+155
+00:14:22,610 --> 00:14:32,180
+.. همانتجار وعليها عملية الجمع العادى وعملية الضرب
+
+156
+00:14:32,180 --> 00:14:45,800
+العادى where حيث ال plus and الضغط are usual
+
+157
+00:14:45,800 --> 00:14:52,560
+addition and
+
+158
+00:14:52,560 --> 00:14:54,420
+multiplication
+
+159
+00:15:14,050 --> 00:15:19,370
+multiplication يبقى أخذت ال 6 زر و علينا عملية
+
+160
+00:15:19,370 --> 00:15:22,810
+الجمعة العادية و عملية الضرب العادية هذول two
+
+161
+00:15:22,810 --> 00:15:26,210
+binary operation ليش؟ لأنه لو جمعت two integers
+
+162
+00:15:26,210 --> 00:15:30,610
+الناتج integer يبقى عملية الجمعة binary operation
+
+163
+00:15:30,960 --> 00:15:35,520
+لو ضربت any two integers بيطلع main integer كذلك
+
+164
+00:15:35,520 --> 00:15:40,620
+يرجع يقول ضرب is a binary operation الان لو جينا
+
+165
+00:15:40,620 --> 00:15:46,480
+على هذا بيلاقي الشروط الستة كلها محققة بلا استثناء
+
+166
+00:15:46,480 --> 00:15:52,340
+فمثلا اتنين زي التلاتة هو تلاتة زي اتنين اتنين زي
+
+167
+00:15:52,340 --> 00:15:57,500
+التلاتة زي الخمسة هو اتنين زي التلاتة زي الخمسة
+
+168
+00:15:57,500 --> 00:16:02,900
+بالضبط تماماو هكذا ال zero L مانضفيه لأي رقم
+
+169
+00:16:02,900 --> 00:16:07,600
+بيعطيك نفس الرقم اللي هو الصحيح و هكذا إذا كل
+
+170
+00:16:07,600 --> 00:16:12,780
+الشروط محقق على مين؟ على هذه ال ring هل هذه ال
+
+171
+00:16:12,780 --> 00:16:16,920
+ring commutative؟ بمعنى اتنين في تلاتة هي تلاتة في
+
+172
+00:16:16,920 --> 00:16:24,020
+اتنين صحيح يبقى هذه commutative ring with unity ال
+
+173
+00:16:24,020 --> 00:16:28,180
+unity هي اللي
+
+174
+00:16:28,180 --> 00:16:32,550
+هو مين؟الواحد الواحد اللي ضربيه في أي عنصر من عصر
+
+175
+00:16:32,550 --> 00:16:40,670
+و ذات بطلع نفس العنصر يبقى هذه مالة is commutative
+
+176
+00:16:40,670 --> 00:16:44,090
+ring
+
+177
+00:16:44,090 --> 00:16:54,490
+with unity one طب
+
+178
+00:16:54,490 --> 00:16:57,610
+السؤال فيه units هذي يا بنات؟
+
+179
+00:17:08,120 --> 00:17:13,480
+الواحد هو ال unity في غيره؟ ليش؟ لأن الواحد في
+
+180
+00:17:13,480 --> 00:17:21,960
+واحد يساوي واحد فمش سالب واحد مش سالب واحد مش سالب
+
+181
+00:17:21,960 --> 00:17:26,390
+واحد بواحد بواحد لأن سالب واحد كمان is a unitthe
+
+182
+00:17:26,390 --> 00:17:30,930
+only units is one and minus one فقط لا غيره مافيش
+
+183
+00:17:30,930 --> 00:17:36,350
+غيرهم طبعا يبقى هدول units و لا يوجد غيرهم في الـ
+
+184
+00:17:36,350 --> 00:17:41,610
+z طب اتنين is a unit اه في نص في اتنين و واحد لكن
+
+185
+00:17:41,610 --> 00:17:47,030
+هل النص عدد صحيح لأ يبقى فانفعش اجيب من ستة ليرجع
+
+186
+00:17:47,030 --> 00:17:51,610
+ترجية مافيش هدا حاجة تسمى ترجية هنا طبعا يبقى لا
+
+187
+00:17:51,610 --> 00:17:57,320
+يوجد عند ال units الا الواحد والسالب واحديبقى هنا
+
+188
+00:17:57,320 --> 00:18:12,240
+the only units in the are ال one and سالق واحد
+
+189
+00:18:12,240 --> 00:18:17,180
+لماذا؟ لأن واحد في واحد يساوي واحد سالق واحد في
+
+190
+00:18:17,180 --> 00:18:22,900
+سالق واحد يساوي مين؟ واحد يبقى سالق واحد is a unit
+
+191
+00:18:23,350 --> 00:18:29,230
+و الواحد unity و احنا اتفقنا قبل قليل ان any unity
+
+192
+00:18:29,230 --> 00:18:34,210
+is a unit لكن العكس ليس بضروري يعني مثال و ظاهر
+
+193
+00:18:34,210 --> 00:18:42,290
+هذا unit لكن هل هو unity؟ لا مش صحيح طيب ايش رأيك
+
+194
+00:18:42,290 --> 00:18:49,310
+لو قلتلك also ال set of rational number ال EQ تحت
+
+195
+00:18:49,310 --> 00:18:55,900
+عملية الجمعةوالضرب العادية and ال set of real
+
+196
+00:18:55,900 --> 00:19:00,940
+number تحت عملية الجامعة وتحت عملية الضرب هدول
+
+197
+00:19:00,940 --> 00:19:08,660
+rings ولا لا؟ و communicative؟ وفي community؟
+
+198
+00:19:08,660 --> 00:19:15,980
+community؟ وفي communites كمان تمام؟ يبقى هدول are
+
+199
+00:19:15,980 --> 00:19:19,020
+communicative؟
+
+200
+00:19:40,320 --> 00:19:47,000
+إتناء الرشول النمبر صح؟ إتناء الرشول النمبر، هل هو
+
+201
+00:19:47,000 --> 00:19:53,510
+unit في الـQ؟أه لأن النص موجود في ال Q و نص في
+
+202
+00:19:53,510 --> 00:19:58,050
+اتنين بساوي جدار يبقى واحد صحيح اللي هو ال unity
+
+203
+00:19:58,050 --> 00:20:06,030
+إذا بناء عليه أي non zero element in a cube is a
+
+204
+00:20:06,030 --> 00:20:14,710
+unit صح؟ لأن مقلوبه هو المعكوس تبعه فاتنين مقلبها
+
+205
+00:20:14,710 --> 00:20:20,410
+نص صار النص هو المعكوس تبع اتنينالمية مقلبها واحد
+
+206
+00:20:20,410 --> 00:20:25,430
+عالمية الواحد عالمية هي المعقوزة بعلمية هو قس
+
+207
+00:20:25,430 --> 00:20:31,510
+عليها ما شيتيه طب و الست و ال real number ازايها
+
+208
+00:20:31,510 --> 00:20:37,190
+لان any rational number is a real number يبقى من
+
+209
+00:20:37,190 --> 00:20:42,530
+هنا صارت هذه ازايها طب خلينا نسأل كمان سؤال اتنين
+
+210
+00:20:42,530 --> 00:20:53,410
+زد رنجwith unity و الله without unity بس ولكن
+
+211
+00:20:53,410 --> 00:20:56,710
+اتنين
+
+212
+00:20:56,710 --> 00:21:03,090
+زده اللي هي مين نقطة سالب ستة سالب اربعة سالب
+
+213
+00:21:03,090 --> 00:21:08,470
+اتنين زيرتين اربعة ستة وطلق ماشية الى ما شاء الله
+
+214
+00:21:08,470 --> 00:21:14,070
+من هنا ل infinity و من هنا لسلب infinity رينقولها
+
+215
+00:21:15,240 --> 00:21:22,840
+بتحقق الشروط الستة ولا بتحققهم طيب commutative؟ اه
+
+216
+00:21:22,840 --> 00:21:28,680
+صحيح commutative فيها unity؟ لا ليهاش unity و احنا
+
+217
+00:21:28,680 --> 00:21:32,000
+المرة اللي فاتت قولنا لكوا ال ring و اليوم قولنا
+
+218
+00:21:32,000 --> 00:21:35,240
+ممكن ال ring يكون فيها unity و ممكن مايكونش فيها
+
+219
+00:21:35,240 --> 00:21:40,440
+unity يبقى هذه commutative without unity ماعنديش
+
+220
+00:21:40,440 --> 00:21:43,560
+unity فيها بالمرة يبقى هذه
+
+221
+00:21:47,400 --> 00:22:01,560
+communitative ring without unity يبقى
+
+222
+00:22:01,560 --> 00:22:06,120
+هذه communicative ring و unity مافيهاش يبعت الله
+
+223
+00:22:32,930 --> 00:22:43,270
+مش ممكنش .. مش ممكنش .. مش ممكنش
+
+224
+00:23:30,710 --> 00:23:38,490
+طبعا عدد العناصر يساوي N زد عشرة في عشر عناصر زد
+
+225
+00:23:38,490 --> 00:23:43,670
+ستة في ستة عناصر و هكذا تمام under addition of
+
+226
+00:23:43,670 --> 00:23:49,410
+multiplication modulo Nmodular in نفس الكلام اللي
+
+227
+00:23:49,410 --> 00:23:55,330
+أخدته في جابرة حديث واحد ايش يعني modular in زي
+
+228
+00:23:55,330 --> 00:23:59,110
+الساعة على يدك مثلا تمشي لساعة الساعة اتناشر بعد
+
+229
+00:23:59,110 --> 00:24:03,090
+اتناشر مايقوليش تلاتاشر بنبدأ واحدة تنتين تلاتة
+
+230
+00:24:03,090 --> 00:24:07,590
+لما نوصل الاتناشر وهكذا كل اتناشر ساعة بنعيد
+
+231
+00:24:07,590 --> 00:24:12,270
+الدورة من جديد هذه كل ان من العناصر بنبدأ نعيد
+
+232
+00:24:12,270 --> 00:24:19,290
+الدورة من جديد هي المقصود فيهايبقى تحت عملية الجمع
+
+233
+00:24:19,290 --> 00:24:24,610
+والضرب module in is a commutative ring with unity
+
+234
+00:24:24,610 --> 00:24:31,050
+one طبعا ال one modulo in اتنين modulo in التلاتة
+
+235
+00:24:31,050 --> 00:24:35,290
+modulo in هي المقصود فيها بالشكل اللي قدامها الأن
+
+236
+00:24:35,290 --> 00:24:41,990
+ندور عالمين على ال set of unitsالعناصر اللي ممكن
+
+237
+00:24:41,990 --> 00:24:46,610
+يكون in it's يعني اللي لهم معكوز موجودة في هذه ال
+
+238
+00:24:46,610 --> 00:24:58,750
+ring is UN مين UN هذه يا بنات؟ تذكرين؟ مين هي هذه؟
+
+239
+00:24:58,750 --> 00:25:05,470
+يبقى هذه العناصر اللي موجودة في ZN واللي بتكون
+
+240
+00:25:05,470 --> 00:25:11,210
+relatively prime بالنسبة لمن؟للعدد n مثلا for
+
+241
+00:25:11,210 --> 00:25:14,810
+example
+
+242
+00:25:14,810 --> 00:25:24,870
+for example لو أخدت z عشرة مثلا هي عبارة عن مين؟
+
+243
+00:25:24,870 --> 00:25:33,670
+zero واحد اتنين تلاتة اربع خمسة ستة سابعة تمانية
+
+244
+00:25:33,670 --> 00:25:40,160
+تسعة في عشرة عشرة تاني zeroيبقى هذه العناصر تبعتها
+
+245
+00:25:40,160 --> 00:25:50,360
+بدي أدور على ال units the units is
+
+246
+00:25:50,360 --> 00:25:58,840
+the set U عشرة مين عناصر ال U عشرة بدي أدور على
+
+247
+00:25:58,840 --> 00:26:04,650
+العناصر relatively prime مع مين مع العشرةيعني
+
+248
+00:26:04,650 --> 00:26:10,610
+الأعداد اللي بتقسمش إلا على نفسها وعلى الواحد
+
+249
+00:26:10,610 --> 00:26:17,610
+الصحيح من خلال هذه ال ring همين يا بنات؟ واحد،
+
+250
+00:26:17,610 --> 00:26:27,290
+تلاتة، سبعة، تسعة تمام، هدول ال units فقط، يبقى
+
+251
+00:26:27,290 --> 00:26:32,190
+هدول أربعة، وهي فيها عشرة عناصر، إذا ستة ليسوا
+
+252
+00:26:32,190 --> 00:26:37,020
+unitsمش شرطين من الأول ممنوع يكونوا صفر يبقى بنشيل
+
+253
+00:26:37,020 --> 00:26:43,640
+الصفر منهم بظل خمسة ماهياش units و أربعة فقط هي ال
+
+254
+00:26:43,640 --> 00:26:50,580
+units صحيح؟ يعني كل واحد من هدول بيدلا يجي عنصر
+
+255
+00:26:50,580 --> 00:26:55,560
+أضرب فيه يطلع ناتج ال unit اللي هو واحد الواحد في
+
+256
+00:26:55,560 --> 00:27:00,840
+واحد في واحد خلصنا منه طب الستلاتة ستلاتة في سبعة
+
+257
+00:27:01,130 --> 00:27:05,450
+بواحد وعشر ينشيلي عشرتين بيظل ال unit اللي هو واحد
+
+258
+00:27:05,450 --> 00:27:11,110
+يبقى التلاتة معكوسه من؟ السبعة بيظل عندنا من؟ بيظل
+
+259
+00:27:11,110 --> 00:27:15,810
+عندنا التسعة معكوسه اللي نفسه من تسعة تسعة بواحد و
+
+260
+00:27:15,810 --> 00:27:19,490
+تمانين ينشيلي تمان عشرات بيظل من؟ بيظل ال unit
+
+261
+00:27:19,490 --> 00:27:23,490
+اللي هو واحد يبقى تسعة معكوسه اللي نفسهوالواحد
+
+262
+00:27:23,490 --> 00:27:27,990
+معكسه لنفسه والثلاثة معكسة السبعة أو السبعة معكسة
+
+263
+00:27:27,990 --> 00:27:32,430
+مين التلاتة يبقى هدول هم ال units اللي موجودة وين
+
+264
+00:27:32,430 --> 00:27:40,710
+اللي موجودة في هذه ال group طيب
+
+265
+00:27:40,710 --> 00:27:49,570
+لو جيت Goldslug also شغلة تانية that's it اللي هي
+
+266
+00:27:49,570 --> 00:27:59,110
+zeroاربع ست تمانى رنج
+
+267
+00:27:59,110 --> 00:28:07,210
+طبعا هذه تحت عملية الجمع والضرب موديولو عشرة يبقى
+
+268
+00:28:07,210 --> 00:28:11,690
+هذه under addition
+
+269
+00:28:11,690 --> 00:28:16,990
+and multiplication
+
+270
+00:28:22,800 --> 00:28:34,320
+مدينو عشر is a commutative ring
+
+271
+00:28:34,320 --> 00:28:39,760
+فيها unity يا بنات؟ لا، لا، لا، لا، لا، لا، لا،
+
+272
+00:28:39,760 --> 00:28:42,660
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+273
+00:28:42,660 --> 00:28:46,020
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+274
+00:28:46,020 --> 00:28:50,420
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+275
+00:28:50,420 --> 00:28:50,440
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+276
+00:28:50,440 --> 00:28:50,480
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+277
+00:28:50,480 --> 00:28:53,770
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،مين هي
+
+278
+00:28:53,770 --> 00:28:59,490
+ال unity بده اروح ادور عليها موديوله عشرة ها يلا
+
+279
+00:28:59,490 --> 00:29:07,170
+زيله مالحطاه شكل تمام اتنين ماهو الرقم اللي لو
+
+280
+00:29:07,170 --> 00:29:14,050
+ضربته في اتنين بده يطلع نتجه اتنين ستة ستة في
+
+281
+00:29:14,050 --> 00:29:19,610
+اتنين باثنين موديوله عشرة اتنين تبقى ستة في اتنين
+
+282
+00:29:19,610 --> 00:29:26,010
+يساوي اتنين بعدين اربعأربعة في ستة؟ أربعة وعشرين،
+
+283
+00:29:26,010 --> 00:29:32,050
+شيله عشرتين، يبقى أربعة في ستة يسوي كده؟ أربعة،
+
+284
+00:29:32,050 --> 00:29:39,390
+تمام، ستة في ستة يسوي ستة، ستة في تمانية يسوي
+
+285
+00:29:39,390 --> 00:29:44,410
+تمانية، يبقى صار من ال identity element؟ الستة،
+
+286
+00:29:44,410 --> 00:29:48,110
+يبقى صار الستة identity، وليس الواحد اللي مطبوع في
+
+287
+00:29:48,110 --> 00:29:53,010
+المغقق بمجرد النظريبقى هذا يحتاج إلى تفكير هذا أحد
+
+288
+00:29:53,010 --> 00:29:57,450
+أسئلة الكتابة من سؤال اتنين أو أربعة هذا أحد أسئلة
+
+289
+00:29:57,450 --> 00:30:04,370
+الكتابة يبقى will unity ستة ليش؟ لأن أضرب اتنين في
+
+290
+00:30:04,370 --> 00:30:08,490
+ستة بطلع اتنين أربعة في ستة بطلع أربعة ستة في ستة
+
+291
+00:30:08,490 --> 00:30:12,770
+بطلع ستة تمانية في ستة بطلع تمانية يبقى الناتج كله
+
+292
+00:30:12,770 --> 00:30:19,430
+يعني بيعطيني نفس الرقم بصار ستة will unity تمام؟
+
+293
+00:30:19,830 --> 00:30:25,850
+أيوة يبقى خد بالك واطنع حالك كويس على البحث عن ال
+
+294
+00:30:25,850 --> 00:30:33,510
+unity تلاتة plus it z
+
+295
+00:30:33,510 --> 00:30:47,010
+of x شكل أنها of all polynomials plus it of all
+
+296
+00:30:47,010 --> 00:30:48,070
+polynomials
+
+297
+00:30:50,160 --> 00:31:10,720
+the variable x with integer coefficients معاملات
+
+298
+00:31:10,720 --> 00:31:17,340
+صحيحة under ordinary
+
+299
+00:31:19,860 --> 00:31:26,460
+under ordinary addition and
+
+300
+00:31:26,460 --> 00:31:35,220
+multiplication تحت
+
+301
+00:31:35,220 --> 00:31:45,240
+عملية ضرب وجم العادية is a commutative
+
+302
+00:32:11,090 --> 00:32:21,880
+Z of X المقصود فيهامكونة كل عنصر فيها عبارة عن
+
+303
+00:32:21,880 --> 00:32:28,200
+كثيرة حدود إذا مكونة من كثيرات حدود المعاملات
+
+304
+00:32:28,200 --> 00:32:33,080
+تبعات الحدود كلهم أعداد صحية سواء كانت بالموجب أو
+
+305
+00:32:33,080 --> 00:32:38,160
+بالسالب أو حتى الصفر يبقى هي المقصود هي يبقى the
+
+306
+00:32:38,160 --> 00:32:44,260
+set of all polynomial وحيث كلها دالة في المتغير X
+
+307
+00:32:44,260 --> 00:32:50,650
+زي ايه؟ زي F of X يساوي X تربيةنقص تلاتة X زي 15
+
+308
+00:32:50,650 --> 00:32:58,090
+مثلا زي F of X سوى X أُص أربعة وبدّيش أجيب فيها X
+
+309
+00:32:58,090 --> 00:33:04,890
+تربية زائد تلاتة X تكيب زائد X ناقص واحد يبقى هاي
+
+310
+00:33:04,890 --> 00:33:09,730
+المعامل صفر راح تبع ال X تربية مظبوط؟ بقى المعامل
+
+311
+00:33:09,730 --> 00:33:16,850
+X أُص أربعة ومعامل X تكيب ومعامل X أرقام صحيةبديش
+
+312
+00:33:16,850 --> 00:33:21,690
+ولا كسر يكون فيهم لكن سالب أو موجب القام صحيح
+
+313
+00:33:21,690 --> 00:33:26,970
+ماعناه مشكلة يبقى هذه كل كثيرات الحدود اللي
+
+314
+00:33:26,970 --> 00:33:32,690
+المعاملة تبعتها أعداد صحية هذه بتكون ال
+
+315
+00:33:32,690 --> 00:33:37,050
+commutative ring with unity حد عارف مين مين ال
+
+316
+00:33:37,050 --> 00:33:43,830
+unity؟ اه ممتاز ال unity هي دالة ثابتة بس مش اي
+
+317
+00:33:43,830 --> 00:33:50,050
+دالة ثابتةالدالة ثابتة f of x يساوي واحد يبقى with
+
+318
+00:33:50,050 --> 00:33:56,610
+unity f of x يساوي واحد لإن لو ضربت الواحد في أي
+
+319
+00:33:56,610 --> 00:34:01,010
+polynomial بطلع نفس ال polynomial يبقى هذا هو ال
+
+320
+00:34:01,010 --> 00:34:05,830
+unity اتنين commutative ليش؟ لإن ال polynomial لما
+
+321
+00:34:05,830 --> 00:34:10,570
+تعوضلها برقم بطلع real number برقم ثاني بطلع real
+
+322
+00:34:10,570 --> 00:34:15,090
+number فنضربهم من اليمين و الله من الشمال سياليبقى
+
+323
+00:34:15,090 --> 00:34:19,270
+الاتنين our community bring with unity f of x
+
+324
+00:34:19,270 --> 00:34:29,350
+يساوي واحد صحيح طيب الان ننتقل الى set أخرى يبقى
+
+325
+00:34:29,350 --> 00:34:37,130
+رقم أربع the set m2
+
+326
+00:34:37,130 --> 00:34:50,060
+of z of twoby two matrices with
+
+327
+00:34:50,060 --> 00:34:54,320
+integer
+
+328
+00:34:54,320 --> 00:34:57,780
+interest
+
+329
+00:34:57,780 --> 00:35:01,720
+بعناصر
+
+330
+00:35:01,720 --> 00:35:08,720
+أعداد صحيحة is a non commutative ring
+
+331
+00:35:15,140 --> 00:35:21,540
+non commutative ring with
+
+332
+00:35:21,540 --> 00:35:24,940
+unity
+
+333
+00:35:24,940 --> 00:35:33,940
+اللي هي واحد زيرو زيرو واحد اخدت
+
+334
+00:35:33,940 --> 00:35:40,610
+هذا في الجبرا الخطي لينير الجبراالمصفوفات في
+
+335
+00:35:40,610 --> 00:35:46,410
+الجبهة الخاطية والمحددات معها و ال vector spaces و
+
+336
+00:35:46,410 --> 00:35:50,190
+ال linear transformations كل هذا في الجبهة الخاطية
+
+337
+00:35:50,190 --> 00:35:58,790
+نجي هنا لو أقول يا بنات into z يبقى كل المصفوفات
+
+338
+00:35:58,790 --> 00:36:02,950
+اللي نظامها اتنين في اتنين يعني فيها صفين و فيها
+
+339
+00:36:02,950 --> 00:36:08,590
+عمودين of z العناصر اللي داخل المصفوفة كلهم أعداد
+
+340
+00:36:08,590 --> 00:36:14,770
+صحيحةماعنديش كسر بالمرة M to Z يبقى العناصر اللى
+
+341
+00:36:14,770 --> 00:36:20,710
+جوا مأخودة من ال set of integer Z طيب with integer
+
+342
+00:36:20,710 --> 00:36:26,190
+interest كل معدات صحيحة عبارة عن non commutative
+
+343
+00:36:26,190 --> 00:36:31,890
+ring لإن عملية ضرب المصوفات ليس إبداليا يعني ال A
+
+344
+00:36:31,890 --> 00:36:37,130
+في ال B لأ تسوي ال B في ال A in general لما أقول
+
+345
+00:36:37,130 --> 00:36:42,040
+in general يعني ممكنحالة حالتين تلاتة تشد عنها بس
+
+346
+00:36:42,040 --> 00:36:46,680
+in general ماهياش commutative ال unity تبعتها
+
+347
+00:36:46,680 --> 00:36:52,920
+لمصفوفة الوحدة يبقى ال identity matrix هي عنصر
+
+348
+00:36:52,920 --> 00:36:58,060
+الوحدة بالنسبة لهذه المصفوفة طب ماهو عنصر الصفرية
+
+349
+00:36:58,060 --> 00:37:05,420
+المصفوفة الصفرية 00000 يبقى هذه المصفوفة الصفرية
+
+350
+00:37:05,420 --> 00:37:14,730
+طيبالمعكوس الجامعي لمن؟ للمصوفة A,B,C,D السالب
+
+351
+00:37:14,730 --> 00:37:21,230
+بتاعتها يبقى سالب A هو سالب A سالب B سالب C سالب D
+
+352
+00:37:21,230 --> 00:37:26,890
+يبقى هذا هو العنصر السالب تبعتها طيب بتقدروا
+
+353
+00:37:26,890 --> 00:37:33,170
+تجيبولنا unit في مجموعة المصوفات هذه أبسط حاجة
+
+354
+00:37:33,170 --> 00:37:37,130
+اللي هي ال unity لكن ممكن نجيب غيرهالنجيب غيرها
+
+355
+00:37:37,130 --> 00:37:42,410
+يعني بدي أجيب مصفوفة و المصفوفة هاد يكونلها معكوسة
+
+356
+00:37:42,410 --> 00:37:47,230
+قبل ما نقول منهي بدي أسأل كيف بنجيب معكوسة
+
+357
+00:37:47,230 --> 00:37:50,870
+المصفوفة اللي نضامها اتنين في اتنين نفرضه أنه
+
+358
+00:37:50,870 --> 00:37:56,130
+موجود و بقدره عشان أجيب المصفوفة الوحدة و لأ ما
+
+359
+00:37:56,130 --> 00:37:58,970
+أفهمتش لأ ما أفهمتش ولا حاجة
+
+360
+00:38:03,190 --> 00:38:08,270
+Quiz واحد علي قيمة المحدد تبع هذه المصوفة مضروبا
+
+361
+00:38:08,270 --> 00:38:14,950
+فيه وبنقل إشارات
+
+362
+00:38:14,950 --> 00:38:19,450
+عناصر قتل الذنب يبقى ليه السهولة لما بنتجيب معكوس
+
+363
+00:38:19,450 --> 00:38:24,610
+المصوفة لنضامها 2×2 فقط 3×3 التفكير كله مش صحيح
+
+364
+00:38:24,610 --> 00:38:31,510
+تمام يبقى 2×2 فقط تمام إيش بنعمل؟نعمل ما ياتي بروح
+
+365
+00:38:31,510 --> 00:38:36,330
+بجيب محدد المصوفة جداش قيمته والشرط أساسي ممنوع
+
+366
+00:38:36,330 --> 00:38:41,110
+يساوي الصفر عشان كل المصوفة معكوس المحدد ممنوع
+
+367
+00:38:41,110 --> 00:38:45,870
+يساوي الصفر هاي واحدة الثانية بقول واحد على قيمة
+
+368
+00:38:45,870 --> 00:38:51,290
+المحدد بجي على المصوفة اللي عندي ببدل عناصر القطة
+
+369
+00:38:51,290 --> 00:38:55,790
+الرئيسية مكان بعض و بغير إشارات عناصر القطر الثاني
+
+370
+00:38:55,790 --> 00:39:03,300
+نعطي Coordinate يبغى هناطيب يا بنات لو أخدت مصفوفة
+
+371
+00:39:03,300 --> 00:39:08,940
+وطلع محددها اتنين، تلاتة، اربع، عشرة، اي رقم غير
+
+372
+00:39:08,940 --> 00:39:15,460
+الواحد وغير السالب واحد بنفع يكون unit هذا؟ بنفع؟
+
+373
+00:39:15,460 --> 00:39:19,920
+يعني لو جيت مصفوفة وطلع محددها تلاتة مثلها، بدي
+
+374
+00:39:19,920 --> 00:39:25,820
+اجيب المعقول سبعة طولت في كذا، بنفع؟ احنا في M2Z
+
+375
+00:39:27,430 --> 00:39:33,090
+يبقى بنفع؟ لأ بنفعش ليش بدي يكون أعداد صحيحة مش
+
+376
+00:39:33,090 --> 00:39:36,590
+كسرية هتلاقى ال six real numbers أو ال six
+
+377
+00:39:36,590 --> 00:39:40,330
+rational numbers ماشي ماعنده مشكلة لكن احنا بدنا M
+
+378
+00:39:40,330 --> 00:39:46,090
+to Z يعني أعداد صحية إذا يجب أن يكون قيمة المحدد
+
+379
+00:39:46,090 --> 00:39:51,850
+إما واحد صحيح وإما سالف واحد صحيح حتى يكون unit
+
+380
+00:39:51,850 --> 00:39:54,610
+for example
+
+381
+00:39:59,130 --> 00:40:03,410
+the element الانصف
+
+382
+00:40:03,410 --> 00:40:12,930
+اننا ناخد مصفوفة مثلا اتنين خمسة واحد تلت هذه كدهش
+
+383
+00:40:12,930 --> 00:40:20,110
+محددها واحد صحيح اتنين في تلت او ستة نقص خمس او
+
+384
+00:40:20,110 --> 00:40:26,910
+واحد هذا is a unit because
+
+385
+00:40:29,880 --> 00:40:37,740
+اللي هو اتنين واحد خمسة ثلاثة inverse المعتوذ تبعه
+
+386
+00:40:37,740 --> 00:40:43,860
+المحدد بواحد خلصنا منه يفجأ ده ببدل عناصر القطر
+
+387
+00:40:43,860 --> 00:40:47,820
+الرئيسي ده المكان التلاتة والتلاتة مكان اتنين
+
+388
+00:40:47,820 --> 00:40:54,080
+والخمسة والواحد بخليهم زي ما هم بس بغير اشارات
+
+389
+00:40:54,080 --> 00:41:00,750
+عناصرهم او تغير اشارات عناصر قطر السنةالان لو مسكت
+
+390
+00:41:00,750 --> 00:41:04,630
+المصوفة هذه ضربتنا المصوفة هذه من اليمين و لا من
+
+391
+00:41:04,630 --> 00:41:09,650
+الشمال النتج بدي اعطيني مين ال identity element
+
+392
+00:41:09,650 --> 00:41:14,890
+اللي عندنا يالا بنكمل المرة الجاية ماشي اعطيك
+
+393
+00:41:14,890 --> 00:41:15,330
+العكس
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d0c58ff12b9a95516d599f1488d4593a1142e989
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4859, "start": 21.01, "end": 48.59, "text": "بسم الله الرحمن الرحيم في المحاضرة الماضية تكلمنا حول الخطوط الرئيسية أو العريضة لموضوع جبر حديث اتنين وقلنا سنعطي سبعة sections سنده بال section الأول اللي هو introduction tourings وننتهي بال extension fields اليوم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8978, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 6055, 4117, 19528, 8315, 11331, 12610, 33962, 9566, 2407, 9566, 34892, 19986, 1829, 3794, 10632, 34051, 18863, 16572, 11242, 3660, 32767, 2407, 11242, 45367, 10874, 26890, 11331, 16254, 12984, 1975, 2655, 1863, 9957, 4032, 4587, 1211, 8315, 8608, 1863, 3615, 9566, 1829, 8608, 3555, 27884, 10863, 8608, 41260, 3224, 20666, 3541, 16247, 12610, 13672, 1829, 31439, 9339, 3512, 1109, 4032, 1863, 29399, 3224, 1829, 20666, 10320, 7909, 45595, 20498], "avg_logprob": -0.15948276101857767, "compression_ratio": 1.6602870813397128, "no_speech_prob": 5.960464477539063e-08, "words": 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لهذا ال ring بعض النظريات البسيطة المتعلقة بهذه الخواص زائد بعض الأمثلة لأن كل ما يتعلق بال section", "tokens": [5016, 35457, 19446, 4032, 22488, 8315, 3224, 28242, 3714, 25720, 9673, 46958, 10632, 47525, 8315, 8717, 44510, 10721, 8978, 5551, 12610, 3541, 8978, 3714, 4587, 2288, 2288, 10874, 26890, 11331, 16254, 12984, 3660, 1315, 37037, 2407, 9339, 281, 4875, 8978, 23758, 2423, 3541, 47525, 8315, 8717, 3615, 9566, 1829, 37279, 16572, 5172, 2423, 4875, 45030, 11242, 33962, 14407, 9381, 46740, 15730, 2423, 4875, 45030, 11242, 28239, 19913, 16572, 9307, 29739, 3794, 1829, 9566, 3660, 9673, 2655, 30241, 28671, 39627, 24192, 33962, 14407, 9381, 30767, 16373, 3215, 45030, 11242, 16247, 2304, 12984, 37977, 5296, 33456, 28242, 19446, 7251, 2655, 30241, 4587, 20666, 3541], "avg_logprob": -0.140549145566607, "compression_ratio": 1.8590909090909091, "no_speech_prob": 0.0, "words": [{"start": 48.8, "end": 49.18, "word": "حسب", "probability": 0.893798828125}, {"start": 49.18, "end": 49.38, "word": 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1.0}, {"id": 11, "seek": 33381, "start": 304.05, "end": 333.81, "text": "يبقى بصير هدأ تكرار مهم اللي يبقى كفي أخات واحدة منهم وهي تساوي الثانية من ال first condition تمام؟ يبقى بقول هنا ال a زايد ال zero بده يساوي ال a لكل ال a اللي موجود في ال R بعدين قال يوجد عنصر سالب a there is an element minus ال a في أرسلت R such that بحيث أن ال a زايد ناقص ال a بده يساوي zero", "tokens": [1829, 3555, 4587, 7578, 4724, 9381, 13546, 8032, 3215, 10721, 6055, 37983, 9640, 3714, 16095, 13672, 1829, 7251, 3555, 4587, 7578, 9122, 41185, 5551, 9778, 9307, 36764, 24401, 3660, 9154, 16095, 37037, 1829, 6055, 3794, 995, 45865, 6024, 104, 7649, 10632, 9154, 2423, 700, 4188, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 4724, 39648, 34105, 2423, 257, 30767, 995, 25708, 2423, 4018, 47525, 3224, 7251, 3794, 995, 45865, 2423, 257, 5296, 28820, 2423, 257, 13672, 1829, 3714, 29245, 23328, 8978, 2423, 497, 39182, 9957, 50239, 7251, 29245, 3215, 18871, 9381, 2288, 8608, 6027, 3555, 257, 456, 307, 364, 4478, 3175, 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ان وجد ال identity element بالنسبة لعملية الضرب في R بنروح نقولها دي عشان نسميها ring with unity", "tokens": [1211, 2407, 25961, 2655, 2423, 497, 8978, 11296, 2423, 6575, 4478, 365, 3104, 281, 27290, 7251, 3555, 4587, 7578, 8978, 18871, 16254, 18871, 9381, 2288, 36764, 24401, 3660, 20666, 1863, 35457, 3660, 5296, 25957, 1211, 10632, 6024, 114, 25513, 23032, 3555, 3615, 995, 34105, 8978, 2423, 4018, 20666, 1863, 35457, 3660, 5296, 25957, 1211, 10632, 25724, 3555, 3224, 3660, 5296, 10721, 1975, 8315, 47525, 2423, 6575, 4478, 20666, 1863, 35457, 3660, 5296, 25957, 1211, 10632, 6024, 114, 25513, 16472, 49610, 3215, 2423, 6575, 4478, 20666, 1863, 35457, 3660, 5296, 25957, 1211, 10632, 6024, 114, 25513, 8978, 497, 44945, 32887, 5016, 8717, 39648, 11296, 11778, 1829, 6225, 8592, 7649, 8717, 38251, 1829, 11296, 4875, 365, 18205], "avg_logprob": -0.17322198134557953, "compression_ratio": 2.048888888888889, "no_speech_prob": 0.0, "words": [{"start": 536.24, "end": 536.6, "word": "لو", 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لأن الواحد في واحد يساوي واحد فمش سالب واحد مش سالب واحد مش سالب واحد بواحد بواحد لأن سالب واحد كمان is a unit", "tokens": [6027, 14407, 24401, 31439, 2423, 18205, 8978, 32771, 13546, 3224, 22807, 32239, 8592, 22807, 5296, 33456, 2423, 14407, 24401, 8978, 36764, 24401, 7251, 3794, 995, 45865, 36764, 24401, 6156, 2304, 8592, 8608, 6027, 3555, 36764, 24401, 37893, 8608, 6027, 3555, 36764, 24401, 37893, 8608, 6027, 3555, 36764, 24401, 4724, 14407, 24401, 4724, 14407, 24401, 5296, 33456, 8608, 6027, 3555, 36764, 24401, 9122, 2304, 7649, 307, 257, 4985], "avg_logprob": -0.24954044950359008, "compression_ratio": 2.103448275862069, "no_speech_prob": 0.0, "words": [{"start": 1028.1200000000001, "end": 1028.88, "word": "الواحد", "probability": 0.64459228515625}, {"start": 1028.88, "end": 1029.04, "word": " هو", "probability": 0.9658203125}, {"start": 1029.04, "end": 1029.24, "word": " ال", "probability": 0.93896484375}, {"start": 1029.24, "end": 1029.66, "word": " unity", "probability": 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0.8583984375}, {"start": 1048.09, "end": 1048.45, "word": " one", "probability": 0.748046875}, {"start": 1048.45, "end": 1048.77, "word": " and", "probability": 0.92333984375}, {"start": 1048.77, "end": 1049.03, "word": " minus", "probability": 0.14990234375}, {"start": 1049.03, "end": 1049.35, "word": " one", "probability": 0.923828125}, {"start": 1049.35, "end": 1049.93, "word": " فقط", "probability": 0.945556640625}, {"start": 1049.93, "end": 1050.19, "word": " لا", "probability": 0.552734375}, {"start": 1050.19, "end": 1050.51, "word": " غيره", "probability": 0.71044921875}, {"start": 1050.51, "end": 1050.93, "word": " مافيش", "probability": 0.8206380208333334}, {"start": 1050.93, "end": 1051.93, "word": " غيرهم", "probability": 0.9127604166666666}, {"start": 1051.93, "end": 1052.41, "word": " طبعا", "probability": 0.769989013671875}, {"start": 1052.41, "end": 1053.53, "word": " يبقى", "probability": 0.9324951171875}, {"start": 1053.53, "end": 1053.91, "word": " هدول", "probability": 0.7911783854166666}, {"start": 1053.91, "end": 1054.35, "word": " units", "probability": 0.9306640625}, {"start": 1054.35, "end": 1054.61, "word": " و", "probability": 0.41845703125}, {"start": 1054.61, "end": 1054.73, "word": " لا", "probability": 0.81689453125}, {"start": 1054.73, "end": 1055.15, "word": " يوجد", "probability": 0.947265625}, {"start": 1055.15, "end": 1055.65, "word": " غيرهم", "probability": 0.9765625}, {"start": 1055.65, "end": 1055.97, "word": " في", "probability": 0.80810546875}, {"start": 1055.97, "end": 1056.35, "word": " الـ", "probability": 0.552490234375}, {"start": 1056.35, "end": 1056.41, "word": " z", "probability": 0.298583984375}, {"start": 1056.41, "end": 1056.81, "word": " طب", "probability": 0.6287841796875}, {"start": 1056.81, "end": 1057.47, "word": " اتنين", "probability": 0.8662109375}, {"start": 1057.47, "end": 1057.83, "word": " is", "probability": 0.6748046875}, {"start": 1057.83, "end": 1058.07, "word": " a", "probability": 0.9140625}, {"start": 1058.07, "end": 1058.53, "word": " unit", "probability": 0.974609375}, {"start": 1058.53, "end": 1060.13, "word": " اه", "probability": 0.4871826171875}, {"start": 1060.13, "end": 1060.27, "word": " في", "probability": 0.896484375}, {"start": 1060.27, "end": 1060.65, "word": " نص", "probability": 0.7724609375}, {"start": 1060.65, "end": 1060.81, "word": " في", "probability": 0.1510009765625}, {"start": 1060.81, "end": 1061.09, "word": " اتنين", "probability": 0.9586181640625}, {"start": 1061.09, "end": 1061.19, "word": " و", "probability": 0.896484375}, {"start": 1061.19, "end": 1061.39, "word": " واحد", "probability": 0.937744140625}, {"start": 1061.39, "end": 1061.61, "word": " لكن", "probability": 0.7958984375}, {"start": 1061.61, "end": 1061.91, "word": " هل", "probability": 0.967529296875}, {"start": 1061.91, "end": 1062.47, "word": " النص", "probability": 0.949951171875}, {"start": 1062.47, "end": 1062.93, "word": " عدد", "probability": 0.8702799479166666}, {"start": 1062.93, "end": 1063.91, "word": " صحيح", "probability": 0.972900390625}, {"start": 1063.91, "end": 1064.33, "word": " لأ", "probability": 0.6673583984375}, {"start": 1064.33, "end": 1064.53, "word": " يبقى", "probability": 0.908447265625}, {"start": 1064.53, "end": 1065.19, "word": " فانفعش", "probability": 0.7414794921875}, {"start": 1065.19, "end": 1065.55, "word": " اجيب", "probability": 0.9171142578125}, {"start": 1065.55, "end": 1065.77, "word": " من", "probability": 0.98681640625}, {"start": 1065.77, "end": 1066.45, "word": " ستة", "probability": 0.9119466145833334}, {"start": 1066.45, "end": 1067.03, "word": " ليرجع", "probability": 0.818603515625}, {"start": 1067.03, "end": 1067.57, "word": " ترجية", "probability": 0.7828776041666666}, {"start": 1067.57, "end": 1068.09, "word": " مافيش", "probability": 0.7985026041666666}, {"start": 1068.09, "end": 1068.25, "word": " هدا", "probability": 0.3192138671875}, {"start": 1068.25, "end": 1068.59, "word": " حاجة", "probability": 0.9104817708333334}, {"start": 1068.59, "end": 1068.83, "word": " تسمى", "probability": 0.7400716145833334}, {"start": 1068.83, "end": 1069.25, "word": " ترجية", "probability": 0.9835611979166666}, {"start": 1069.25, "end": 1069.59, "word": " هنا", "probability": 0.509765625}, {"start": 1069.59, "end": 1070.67, "word": " طبعا", "probability": 0.896728515625}, {"start": 1070.67, "end": 1071.45, "word": " يبقى", "probability": 0.9840087890625}, {"start": 1071.45, "end": 1071.61, "word": " لا", "probability": 0.9169921875}, {"start": 1071.61, "end": 1072.15, "word": " يوجد", "probability": 0.92724609375}, {"start": 1072.15, "end": 1072.51, "word": " عند", "probability": 0.90576171875}, {"start": 1072.51, "end": 1072.75, "word": " ال", "probability": 0.7529296875}, {"start": 1072.75, "end": 1073.23, "word": " units", "probability": 0.96484375}, {"start": 1073.23, "end": 1073.67, "word": " الا", "probability": 0.54541015625}, {"start": 1073.67, "end": 1074.39, "word": " الواحد", "probability": 0.9816080729166666}, {"start": 1074.39, "end": 1075.17, "word": " والسالب", "probability": 0.726171875}, {"start": 1075.17, "end": 1075.63, "word": " واحد", "probability": 0.969970703125}], "temperature": 1.0}, {"id": 38, "seek": 110290, "start": 1076.0, "end": 1102.9, "text": "يبقى هنا the only units in the are ال one and سالق واحد لماذا؟ لأن واحد في واحد يساوي واحد سالق واحد في سالق واحد يساوي مين؟ واحد يبقى سالق واحد is a unit", "tokens": [1829, 3555, 4587, 7578, 34105, 264, 787, 6815, 294, 264, 366, 2423, 472, 293, 8608, 6027, 4587, 36764, 24401, 32767, 45636, 995, 22807, 5296, 33456, 36764, 24401, 8978, 36764, 24401, 7251, 3794, 995, 45865, 36764, 24401, 8608, 6027, 4587, 36764, 24401, 8978, 8608, 6027, 4587, 36764, 24401, 7251, 3794, 995, 45865, 3714, 9957, 22807, 36764, 24401, 7251, 3555, 4587, 7578, 8608, 6027, 4587, 36764, 24401, 307, 257, 4985], "avg_logprob": -0.20142662611560544, "compression_ratio": 1.8615384615384616, "no_speech_prob": 0.0, "words": [{"start": 1076.0, "end": 1076.76, "word": "يبقى", "probability": 0.87451171875}, {"start": 1076.76, "end": 1077.32, "word": " هنا", "probability": 0.98828125}, {"start": 1077.32, "end": 1078.02, "word": " the", "probability": 0.6123046875}, {"start": 1078.02, "end": 1080.64, "word": " only", "probability": 0.908203125}, {"start": 1080.64, "end": 1082.64, "word": " units", "probability": 0.880859375}, {"start": 1082.64, "end": 1084.96, "word": " in", "probability": 0.94091796875}, {"start": 1084.96, "end": 1086.7, "word": " the", "probability": 0.779296875}, {"start": 1086.7, "end": 1088.12, "word": " are", "probability": 0.6591796875}, {"start": 1088.12, "end": 1089.06, "word": " ال", "probability": 0.49365234375}, {"start": 1089.06, "end": 1089.6, "word": " one", "probability": 0.51318359375}, {"start": 1089.6, "end": 1090.88, "word": " and", "probability": 0.95849609375}, {"start": 1090.88, "end": 1091.92, "word": " سالق", "probability": 0.4791666666666667}, {"start": 1091.92, "end": 1092.24, "word": " واحد", "probability": 0.94189453125}, {"start": 1092.24, "end": 1093.54, "word": " لماذا؟", "probability": 0.5814208984375}, {"start": 1093.54, "end": 1093.86, "word": " لأن", "probability": 0.806884765625}, {"start": 1093.86, "end": 1094.28, "word": " واحد", "probability": 0.98291015625}, {"start": 1094.28, "end": 1094.44, "word": " في", "probability": 0.97802734375}, {"start": 1094.44, "end": 1094.76, "word": " واحد", "probability": 0.994384765625}, {"start": 1094.76, "end": 1095.18, "word": " يساوي", "probability": 0.74786376953125}, {"start": 1095.18, "end": 1095.56, "word": " واحد", "probability": 0.9951171875}, {"start": 1095.56, "end": 1096.62, "word": " سالق", "probability": 0.8282877604166666}, {"start": 1096.62, "end": 1096.98, "word": " واحد", "probability": 0.988037109375}, {"start": 1096.98, "end": 1097.18, "word": " في", "probability": 0.97900390625}, {"start": 1097.18, "end": 1097.66, "word": " سالق", "probability": 0.9920247395833334}, {"start": 1097.66, "end": 1097.98, "word": " واحد", "probability": 0.99365234375}, {"start": 1097.98, "end": 1098.42, "word": " يساوي", "probability": 0.9764404296875}, {"start": 1098.42, "end": 1099.2, "word": " مين؟", "probability": 0.6346842447916666}, {"start": 1099.2, "end": 1099.78, "word": " واحد", "probability": 0.950927734375}, {"start": 1099.78, "end": 1100.1, "word": " يبقى", "probability": 0.955322265625}, {"start": 1100.1, "end": 1100.6, "word": " سالق", "probability": 0.9459635416666666}, {"start": 1100.6, "end": 1101.08, "word": " واحد", "probability": 0.98974609375}, {"start": 1101.08, "end": 1101.84, "word": " is", "probability": 0.88623046875}, {"start": 1101.84, "end": 1102.36, "word": " a", "probability": 0.9609375}, {"start": 1102.36, "end": 1102.9, "word": " unit", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 39, "seek": 113077, "start": 1103.35, "end": 1130.77, "text": "و الواحد unity و احنا اتفقنا قبل قليل ان any unity is a unit لكن العكس ليس بضروري يعني مثال و ظاهر هذا unit لكن هل هو unity؟ لا مش صحيح طيب ايش رأيك لو قلتلك also ال set of rational number ال EQ تحت عملية الجمعة", "tokens": [2407, 2423, 14407, 24401, 18205, 4032, 1975, 5016, 8315, 1975, 2655, 5172, 4587, 8315, 12174, 36150, 12174, 20292, 1211, 16472, 604, 18205, 307, 257, 4985, 44381, 18863, 4117, 3794, 32239, 3794, 4724, 11242, 2288, 13063, 1829, 37495, 22653, 50113, 6027, 4032, 1357, 116, 40294, 2288, 23758, 4985, 44381, 8032, 1211, 31439, 18205, 22807, 20193, 37893, 20328, 5016, 1829, 5016, 23032, 1829, 3555, 1975, 1829, 8592, 12602, 10721, 1829, 4117, 45164, 12174, 1211, 2655, 23275, 611, 2423, 992, 295, 15090, 1230, 2423, 33580, 6055, 33753, 6225, 42213, 10632, 25724, 2304, 27884], "avg_logprob": -0.22905219059724075, "compression_ratio": 1.4770642201834863, "no_speech_prob": 0.0, "words": [{"start": 1103.35, "end": 1103.63, "word": "و", "probability": 0.6611328125}, {"start": 1103.63, "end": 1104.37, "word": " الواحد", "probability": 0.748046875}, {"start": 1104.37, "end": 1104.87, "word": " unity", "probability": 0.89306640625}, {"start": 1104.87, "end": 1105.07, "word": " و", "probability": 0.61669921875}, {"start": 1105.07, "end": 1105.21, "word": " احنا", "probability": 0.80029296875}, {"start": 1105.21, "end": 1105.87, "word": " اتفقنا", "probability": 0.856005859375}, {"start": 1105.87, "end": 1106.57, "word": " قبل", "probability": 0.975830078125}, {"start": 1106.57, "end": 1107.19, "word": " قليل", "probability": 0.9938151041666666}, {"start": 1107.19, "end": 1107.53, "word": " ان", "probability": 0.93017578125}, {"start": 1107.53, "end": 1108.35, "word": " any", "probability": 0.55224609375}, {"start": 1108.35, "end": 1109.23, "word": " unity", "probability": 0.96826171875}, {"start": 1109.23, "end": 1109.85, "word": " is", "probability": 0.92333984375}, {"start": 1109.85, "end": 1110.23, "word": " a", "probability": 0.951171875}, {"start": 1110.23, "end": 1110.59, "word": " unit", "probability": 0.95556640625}, {"start": 1110.59, "end": 1111.21, "word": " لكن", "probability": 0.88427734375}, {"start": 1111.21, "end": 1111.91, "word": " العكس", "probability": 0.9230143229166666}, {"start": 1111.91, "end": 1112.73, "word": " ليس", "probability": 0.841064453125}, {"start": 1112.73, "end": 1113.15, "word": " بضروري", "probability": 0.6152587890625}, {"start": 1113.15, "end": 1113.51, "word": " يعني", "probability": 0.89501953125}, {"start": 1113.51, "end": 1113.87, "word": " مثال", "probability": 0.7427978515625}, {"start": 1113.87, "end": 1114.03, "word": " و", "probability": 0.98388671875}, {"start": 1114.03, "end": 1114.21, "word": " ظاهر", "probability": 0.728515625}, {"start": 1114.21, "end": 1115.07, "word": " هذا", "probability": 0.54736328125}, {"start": 1115.07, "end": 1115.59, "word": " unit", "probability": 0.92041015625}, {"start": 1115.59, "end": 1116.17, "word": " لكن", "probability": 0.8583984375}, {"start": 1116.17, "end": 1116.45, "word": " هل", "probability": 0.96484375}, {"start": 1116.45, "end": 1116.71, "word": " هو", "probability": 0.9951171875}, {"start": 1116.71, "end": 1117.57, "word": " unity؟", "probability": 0.708984375}, {"start": 1117.57, "end": 1118.01, "word": " لا", "probability": 0.544921875}, {"start": 1118.01, "end": 1118.27, "word": " مش", "probability": 0.86572265625}, {"start": 1118.27, "end": 1119.21, "word": " صحيح", "probability": 0.9947509765625}, {"start": 1119.21, "end": 1121.03, "word": " طيب", "probability": 0.8058268229166666}, {"start": 1121.03, "end": 1121.81, "word": " ايش", "probability": 0.822265625}, {"start": 1121.81, "end": 1122.29, "word": " رأيك", "probability": 0.8707275390625}, {"start": 1122.29, "end": 1122.55, "word": " لو", "probability": 0.98779296875}, {"start": 1122.55, "end": 1123.23, "word": " قلتلك", "probability": 0.9451904296875}, {"start": 1123.23, "end": 1124.13, "word": " also", "probability": 0.39599609375}, {"start": 1124.13, "end": 1125.43, "word": " ال", "probability": 0.6328125}, {"start": 1125.43, "end": 1125.83, "word": " set", "probability": 0.8125}, {"start": 1125.83, "end": 1126.21, "word": " of", "probability": 0.97509765625}, {"start": 1126.21, "end": 1126.73, "word": " rational", "probability": 0.9091796875}, {"start": 1126.73, "end": 1127.59, "word": " number", "probability": 0.85302734375}, {"start": 1127.59, "end": 1127.93, "word": " ال", "probability": 0.436279296875}, {"start": 1127.93, "end": 1128.31, "word": " EQ", "probability": 0.287109375}, {"start": 1128.31, "end": 1129.31, "word": " تحت", "probability": 0.990234375}, {"start": 1129.31, "end": 1129.99, "word": " عملية", "probability": 0.9900716145833334}, {"start": 1129.99, "end": 1130.77, "word": " الجمعة", "probability": 0.8273111979166666}], "temperature": 1.0}, {"id": 40, "seek": 115902, "start": 1130.94, "end": 1159.02, "text": "والضرب العادية and ال set of real number تحت عملية الجامعة وتحت عملية الضرب هدول rings ولا لا؟ و communicative؟ وفي community؟ community؟ وفي communites كمان تمام؟ يبقى 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"seek": 242691, "start": 2399.13, "end": 2426.91, "text": "the element الانصف اننا ناخد مصفوفة مثلا اتنين خمسة واحد تلت هذه كدهش محددها واحد صحيح اتنين في تلت او ستة نقص خمس او واحد هذا is a unit because", "tokens": [3322, 4478, 2423, 7649, 9381, 5172, 16472, 8315, 8717, 47283, 3215, 3714, 9381, 5172, 38688, 3660, 50113, 15040, 1975, 2655, 1863, 9957, 16490, 2304, 3794, 3660, 36764, 24401, 6055, 1211, 2655, 29538, 9122, 3215, 3224, 8592, 3714, 24401, 3215, 11296, 36764, 24401, 20328, 5016, 1829, 5016, 1975, 2655, 1863, 9957, 8978, 6055, 1211, 2655, 1975, 2407, 8608, 2655, 3660, 8717, 4587, 9381, 16490, 2304, 3794, 1975, 2407, 36764, 24401, 23758, 307, 257, 4985, 570], "avg_logprob": -0.2966666809717814, "compression_ratio": 1.5460526315789473, "no_speech_prob": 0.0, "words": [{"start": 2399.13, "end": 2399.43, "word": "the", "probability": 0.1041259765625}, {"start": 2399.43, "end": 2400.07, "word": " element", "probability": 0.77734375}, {"start": 2400.07, "end": 2403.41, "word": " 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2416.75, "word": " واحد", "probability": 0.734375}, {"start": 2416.75, "end": 2417.35, "word": " صحيح", "probability": 0.93603515625}, {"start": 2417.35, "end": 2418.03, "word": " اتنين", "probability": 0.83636474609375}, {"start": 2418.03, "end": 2418.15, "word": " في", "probability": 0.72265625}, {"start": 2418.15, "end": 2418.61, "word": " تلت", "probability": 0.9659830729166666}, {"start": 2418.61, "end": 2418.77, "word": " او", "probability": 0.27655029296875}, {"start": 2418.77, "end": 2419.21, "word": " ستة", "probability": 0.8479817708333334}, {"start": 2419.21, "end": 2419.53, "word": " نقص", "probability": 0.80419921875}, {"start": 2419.53, "end": 2419.91, "word": " خمس", "probability": 0.94140625}, {"start": 2419.91, "end": 2420.11, "word": " او", "probability": 0.70703125}, {"start": 2420.11, "end": 2420.45, "word": " واحد", "probability": 0.9814453125}, {"start": 2420.45, "end": 2421.59, "word": " هذا", "probability": 0.83349609375}, {"start": 2421.59, "end": 2423.07, "word": " is", "probability": 0.8349609375}, {"start": 2423.07, "end": 2424.43, "word": " a", "probability": 0.77978515625}, {"start": 2424.43, "end": 2425.09, "word": " unit", "probability": 0.94775390625}, {"start": 2425.09, "end": 2426.91, "word": " because", "probability": 0.9140625}], "temperature": 1.0}, {"id": 84, "seek": 245912, "start": 2429.88, "end": 2459.12, "text": "اللي هو اتنين واحد خمسة ثلاثة inverse المعتوذ تبعه المحدد بواحد خلصنا منه يفجأ ده ببدل عناصر القطر الرئيسي ده المكان التلاتة والتلاتة مكان اتنين والخمسة والواحد بخليهم زي ما هم بس بغير اشارات عناصرهم او تغير اشارات عناصر قطر السنة", "tokens": [6027, 20292, 31439, 1975, 2655, 1863, 9957, 36764, 24401, 16490, 2304, 3794, 3660, 38637, 1211, 5718, 104, 3660, 17340, 9673, 34268, 2407, 8848, 6055, 3555, 3615, 3224, 9673, 24401, 3215, 4724, 14407, 24401, 16490, 1211, 9381, 8315, 9154, 3224, 7251, 5172, 7435, 10721, 11778, 3224, 4724, 44510, 1211, 18871, 33546, 2288, 25062, 9566, 2288, 34892, 19986, 1829, 3794, 1829, 11778, 3224, 9673, 41361, 16712, 1211, 9307, 3660, 16070, 2655, 1211, 9307, 3660, 3714, 41361, 1975, 2655, 1863, 9957, 16070, 9778, 2304, 3794, 3660, 16070, 14407, 24401, 4724, 9778, 20292, 16095, 30767, 1829, 19446, 8032, 2304, 4724, 3794, 4724, 17082, 13546, 1975, 8592, 9640, 9307, 18871, 33546, 2288, 16095, 1975, 2407, 6055, 17082, 13546, 1975, 8592, 9640, 9307, 18871, 33546, 2288, 12174, 9566, 2288, 21136, 1863, 3660], "avg_logprob": -0.19808070701876962, "compression_ratio": 1.9855769230769231, "no_speech_prob": 0.0, "words": [{"start": 2429.8799999999997, "end": 2431.16, "word": "اللي", "probability": 0.22979736328125}, {"start": 2431.16, "end": 2431.36, "word": " هو", "probability": 0.9140625}, {"start": 2431.36, "end": 2432.0, "word": " اتنين", "probability": 0.860595703125}, {"start": 2432.0, "end": 2432.86, "word": " واحد", "probability": 0.82861328125}, {"start": 2432.86, "end": 2433.84, "word": " خمسة", "probability": 0.951171875}, {"start": 2433.84, "end": 2434.98, "word": " ثلاثة", "probability": 0.9673828125}, {"start": 2434.98, "end": 2435.54, "word": " inverse", "probability": 0.408935546875}, {"start": 2435.54, "end": 2436.7, "word": " المعتوذ", "probability": 0.67669677734375}, {"start": 2436.7, "end": 2437.74, "word": " تبعه", "probability": 0.734619140625}, {"start": 2437.74, "end": 2438.32, "word": " المحدد", "probability": 0.8800455729166666}, {"start": 2438.32, "end": 2438.66, "word": " بواحد", "probability": 0.92041015625}, {"start": 2438.66, "end": 2439.32, "word": " خلصنا", "probability": 0.902587890625}, {"start": 2439.32, "end": 2439.7, "word": " منه", "probability": 0.90673828125}, {"start": 2439.7, "end": 2440.82, "word": " يفجأ", "probability": 0.5482177734375}, {"start": 2440.82, "end": 2441.32, "word": " ده", "probability": 0.6480712890625}, {"start": 2441.32, "end": 2442.14, "word": " ببدل", "probability": 0.9103190104166666}, {"start": 2442.14, "end": 2442.98, "word": " عناصر", "probability": 0.9895833333333334}, {"start": 2442.98, "end": 2443.86, "word": " القطر", "probability": 0.8986002604166666}, {"start": 2443.86, "end": 2444.82, "word": " الرئيسي", "probability": 0.97119140625}, {"start": 2444.82, "end": 2445.24, "word": " ده", "probability": 0.893310546875}, {"start": 2445.24, "end": 2445.68, "word": " المكان", "probability": 0.6463623046875}, {"start": 2445.68, "end": 2446.3, "word": " التلاتة", "probability": 0.7484130859375}, {"start": 2446.3, "end": 2446.92, "word": " والتلاتة", "probability": 0.89189453125}, {"start": 2446.92, "end": 2447.26, "word": " مكان", "probability": 0.890625}, {"start": 2447.26, "end": 2447.82, "word": " اتنين", "probability": 0.9586181640625}, {"start": 2447.82, "end": 2449.38, "word": " والخمسة", "probability": 0.87880859375}, {"start": 2449.38, "end": 2450.06, "word": " والواحد", "probability": 0.94482421875}, {"start": 2450.06, "end": 2450.88, "word": " بخليهم", "probability": 0.9044189453125}, {"start": 2450.88, "end": 2451.28, "word": " زي", "probability": 0.991455078125}, {"start": 2451.28, "end": 2451.44, "word": " ما", "probability": 0.87548828125}, {"start": 2451.44, "end": 2451.72, "word": " هم", "probability": 0.80078125}, {"start": 2451.72, "end": 2452.58, "word": " بس", "probability": 0.780029296875}, {"start": 2452.58, "end": 2453.16, "word": " بغير", "probability": 0.9860026041666666}, {"start": 2453.16, "end": 2454.08, "word": " اشارات", "probability": 0.848876953125}, {"start": 2454.08, "end": 2455.6, "word": " عناصرهم", "probability": 0.9881591796875}, {"start": 2455.6, "end": 2456.4, "word": " او", "probability": 0.831298828125}, {"start": 2456.4, "end": 2456.9, "word": " تغير", "probability": 0.8572591145833334}, {"start": 2456.9, "end": 2457.72, "word": " اشارات", "probability": 0.9765625}, {"start": 2457.72, "end": 2458.2, "word": " عناصر", "probability": 0.99267578125}, {"start": 2458.2, "end": 2458.58, "word": " قطر", "probability": 0.8377278645833334}, {"start": 2458.58, "end": 2459.12, "word": " السنة", "probability": 0.643798828125}], "temperature": 1.0}, {"id": 85, "seek": 247533, "start": 2459.51, "end": 2475.33, "text": "الان لو مسكت المصوفة هذه ضربتنا المصوفة هذه من اليمين و لا من الشمال النتج بدي اعطيني مين ال identity element اللي عندنا يالا بنكمل المرة الجاية ماشي اعطيك العكس", "tokens": [6027, 7649, 45164, 47524, 4117, 2655, 9673, 9381, 38688, 3660, 29538, 48812, 25513, 2655, 8315, 9673, 9381, 38688, 3660, 29538, 9154, 2423, 32640, 9957, 4032, 20193, 9154, 25124, 2304, 6027, 28239, 2655, 7435, 4724, 16254, 1975, 3615, 9566, 9957, 1829, 3714, 9957, 2423, 6575, 4478, 13672, 1829, 43242, 8315, 7251, 6027, 995, 44945, 24793, 1211, 9673, 25720, 25724, 995, 10632, 3714, 33599, 1829, 1975, 3615, 9566, 1829, 4117, 18863, 4117, 3794], "avg_logprob": -0.3370225706862079, "compression_ratio": 1.6746987951807228, "no_speech_prob": 0.0, "words": [{"start": 2459.51, "end": 2460.01, "word": "الان", "probability": 0.6351318359375}, {"start": 2460.01, "end": 2460.25, "word": " لو", "probability": 0.96923828125}, {"start": 2460.25, "end": 2460.75, "word": " مسكت", "probability": 0.9007161458333334}, {"start": 2460.75, "end": 2461.59, "word": " المصوفة", "probability": 0.730804443359375}, {"start": 2461.59, "end": 2461.93, "word": " هذه", "probability": 0.36865234375}, {"start": 2461.93, "end": 2462.69, "word": " ضربتنا", "probability": 0.7745361328125}, {"start": 2462.69, "end": 2463.45, "word": " المصوفة", "probability": 0.923583984375}, {"start": 2463.45, "end": 2463.61, "word": " هذه", "probability": 0.73779296875}, {"start": 2463.61, "end": 2463.77, "word": " من", "probability": 0.9599609375}, {"start": 2463.77, "end": 2464.19, "word": " اليمين", "probability": 0.6807454427083334}, {"start": 2464.19, "end": 2464.33, "word": " و", "probability": 0.58935546875}, {"start": 2464.33, "end": 2464.43, "word": " لا", "probability": 0.46728515625}, {"start": 2464.43, "end": 2464.63, "word": " من", "probability": 0.9013671875}, {"start": 2464.63, "end": 2465.17, "word": " الشمال", "probability": 0.9890950520833334}, {"start": 2465.17, "end": 2465.95, "word": " النتج", "probability": 0.8076171875}, {"start": 2465.95, "end": 2466.19, "word": " بدي", "probability": 0.5220947265625}, {"start": 2466.19, "end": 2466.59, "word": " اعطيني", "probability": 0.76171875}, {"start": 2466.59, "end": 2466.89, "word": " مين", "probability": 0.45904541015625}, {"start": 2466.89, "end": 2467.45, "word": " ال", "probability": 0.779296875}, {"start": 2467.45, "end": 2468.47, "word": " identity", "probability": 0.79541015625}, {"start": 2468.47, "end": 2469.65, "word": " element", "probability": 0.95654296875}, {"start": 2469.65, "end": 2470.57, "word": " اللي", "probability": 0.910400390625}, {"start": 2470.57, "end": 2471.11, "word": " عندنا", "probability": 0.8974609375}, {"start": 2471.11, "end": 2472.47, "word": " يالا", "probability": 0.6566569010416666}, {"start": 2472.47, "end": 2473.07, "word": " بنكمل", "probability": 0.9134114583333334}, {"start": 2473.07, "end": 2473.47, "word": " المرة", "probability": 0.96923828125}, {"start": 2473.47, "end": 2473.95, "word": " الجاية", "probability": 0.9083658854166666}, {"start": 2473.95, "end": 2474.41, "word": " ماشي", "probability": 0.6751708984375}, {"start": 2474.41, "end": 2474.89, "word": " اعطيك", "probability": 0.758056640625}, {"start": 2474.89, "end": 2475.33, "word": " العكس", "probability": 0.4900716145833333}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2475.9205625, "duration_after_vad": 2339.2712499999907}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6dda4ffa43ed1809313c571161aede8f610cfc70
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/cGJzWLBnsaA_raw.srt
@@ -0,0 +1,1604 @@
+1
+00:00:21,010 --> 00:00:25,770
+بسم الله الرحمن الرحيم في المحاضرة الماضية تكلمنا
+
+2
+00:00:25,770 --> 00:00:32,210
+حول الخطوط الرئيسية أو العريضة لموضوع جبر حديث
+
+3
+00:00:32,210 --> 00:00:39,870
+اتنين وقلنا سنعطي سبعة sections سنده بال section
+
+4
+00:00:39,870 --> 00:00:44,870
+الأول اللي هو introduction tourings وننتهي بال
+
+5
+00:00:44,870 --> 00:00:50,900
+extension fields اليومحسب ما وعدناه كل مرة الماضية
+
+6
+00:00:50,900 --> 00:00:55,300
+بدنا نبدأ في أول section في مقرر جبر حديثة name
+
+7
+00:00:55,300 --> 00:01:00,860
+وهو introduction to ring في هذا ال section بدنا
+
+8
+00:01:00,860 --> 00:01:06,760
+نعطي تعريف ال ring بعض الخواص لهذا ال ring بعض
+
+9
+00:01:06,760 --> 00:01:12,860
+النظريات البسيطة المتعلقة بهذه الخواص زائد بعض
+
+10
+00:01:12,860 --> 00:01:18,570
+الأمثلة لأن كل ما يتعلق بال sectionو سنبدأ منذ
+
+11
+00:01:18,570 --> 00:01:24,530
+البداية إذا بدنا نعطي تعريف لل ring و نقارن ما
+
+12
+00:01:24,530 --> 00:01:28,970
+بينه و بين تعريف ال group اللي درسها في جبر حديث
+
+13
+00:01:28,970 --> 00:01:34,070
+واحد إذا بقول ال ring R هي set with two binary
+
+14
+00:01:34,070 --> 00:01:38,890
+operations في ال group بجينا نقول إيش؟ one binary
+
+15
+00:01:38,890 --> 00:01:43,450
+operation لكن هنا two binary operations واحدة
+
+16
+00:01:43,450 --> 00:01:48,370
+عملية جمع والتانية عملية ضربيبقى with two binary
+
+17
+00:01:48,370 --> 00:01:52,870
+operations addition بالـ A زائد الـ B والـ
+
+18
+00:01:52,870 --> 00:01:57,250
+multiplication اللي هي ضرب A في B such that for
+
+19
+00:01:57,250 --> 00:02:04,630
+all A وB وC اللي موجودة في R وEها يبقى ال 6R عليها
+
+20
+00:02:04,630 --> 00:02:11,010
+two binary operations بتتحقق ليه ستة شروط بتعرف ما
+
+21
+00:02:11,010 --> 00:02:17,870
+هي هذه الشروط الستة ونقارن فيما بينهاالطلاعين إلى
+
+22
+00:02:17,870 --> 00:02:23,390
+الشروط من واحد لغاية أربعة هل لهم علاقة بعملية
+
+23
+00:02:23,390 --> 00:02:30,150
+الضرب؟ يبقى أول أربعة شروط متعلقة بعملية الجمع فقط
+
+24
+00:02:30,150 --> 00:02:38,770
+لغاية الشرط الأول ان a زائد b بده يسوى b زائد a في
+
+25
+00:02:38,770 --> 00:02:43,790
+حالة ال group بجينا نقول ان هذه ال group ايش
+
+26
+00:02:43,790 --> 00:02:49,580
+نسميها؟Abelian group تحت عملية الجامعة هنا مش
+
+27
+00:02:49,580 --> 00:02:55,420
+هنقول abelian هنقول abelian group تحت عملية
+
+28
+00:02:55,420 --> 00:02:58,780
+الجامعة يبقى abelian ring تحت عملية الجامعة بس
+
+29
+00:02:58,780 --> 00:03:02,780
+كلمة abelian في ال rings مش هتمر معانا أبدا
+
+30
+00:03:02,780 --> 00:03:08,480
+سنستبدل كلمة abelian في ال group ب commutative في
+
+31
+00:03:08,480 --> 00:03:14,000
+حالة ال ring وهذا ما سنشير إليه في الملاحظة الأولى
+
+32
+00:03:14,360 --> 00:03:19,060
+يبقى بالنسبة للجامعة a زائد b يسوى b زائد a عملية
+
+33
+00:03:19,060 --> 00:03:24,440
+الجامعة عملية إبدالية الشرط التاني a زائد b زائد c
+
+34
+00:03:24,440 --> 00:03:29,140
+يسوى a زائد b زائد c زي ما تشاهدونه وهو ما نسميه
+
+35
+00:03:29,140 --> 00:03:38,140
+خاصية ندمج العناصر بعد انطلاق عنصر جديد بمعنىلو
+
+36
+00:03:38,140 --> 00:03:45,860
+جمعت a زائد b أولا ثم جمعت النتج مع c تماما كما لو
+
+37
+00:03:45,860 --> 00:03:51,980
+جمعت b زائد c أولا ثم جمعت a للعنصر النتج هيعطيني
+
+38
+00:03:51,980 --> 00:03:57,340
+نفس الإجابة الشرط التالت ال third condition there
+
+39
+00:03:57,340 --> 00:04:03,720
+is an element zero بسميه additive identity يبقى
+
+40
+00:04:03,720 --> 00:04:09,230
+عنصر الوحدة بالنسبة لعملية الجمعاللي هو man is
+
+41
+00:04:09,230 --> 00:04:14,730
+zero يبقى additive identity عنصر الوحدة بالنسبة
+
+42
+00:04:14,730 --> 00:04:21,530
+لعملية الجامعة صدش ده a زائد zero بده يساوي ال a
+
+43
+00:04:21,530 --> 00:04:27,150
+يعني وجود هذا العنصر تحت هذه العملية لن يغير
+
+44
+00:04:27,150 --> 00:04:32,030
+العنصر الأصلي اللي موجود ف a زائد هذا zero بده
+
+45
+00:04:32,030 --> 00:04:37,230
+يعطينا ال a itselfإن حدث ذلك يبقى الـ zero بسميه
+
+46
+00:04:37,230 --> 00:04:42,970
+ال identity element بالنسبة لعملية الجامعة طب
+
+47
+00:04:42,970 --> 00:04:48,910
+خليني أسأل ليش ما قلتش a زائد zero يسوي zero زائد
+
+48
+00:04:48,910 --> 00:04:55,050
+a يسوى ال a بيصير تكرار ممل لأن أنا جاي في ال
+
+49
+00:04:55,050 --> 00:04:59,130
+condition الأول ان ال a زائد ال b بيبقى سوى ال b
+
+50
+00:04:59,130 --> 00:05:04,410
+زائد ال a لأي عنصرين a وb موجودة في ال set Aيبقى
+
+51
+00:05:04,410 --> 00:05:09,150
+بصير هدأ تكرار مهم اللي يبقى كفي أخات واحدة منهم
+
+52
+00:05:09,150 --> 00:05:13,830
+وهي تساوي الثانية من ال first condition تمام؟ يبقى
+
+53
+00:05:13,830 --> 00:05:17,730
+بقول هنا ال a زايد ال zero بده يساوي ال a لكل ال a
+
+54
+00:05:17,730 --> 00:05:22,890
+اللي موجود في ال R بعدين قال يوجد عنصر سالب a
+
+55
+00:05:22,890 --> 00:05:28,490
+there is an element minus ال a في أرسلت R such
+
+56
+00:05:28,490 --> 00:05:34,720
+that بحيث أن ال a زايد ناقص ال a بده يساوي zeroقبل
+
+57
+00:05:34,720 --> 00:05:38,760
+ما اكمل الشروط بدأ استنى يبقى الأربعة شروط هذه
+
+58
+00:05:38,760 --> 00:05:43,700
+تتعلق بعمليات الجامعة اللحظة ان هذه اللي كنا نقول
+
+59
+00:05:43,700 --> 00:05:48,860
+عليها abelian group هاي شرط ال abelia هاي شرط ال
+
+60
+00:05:48,860 --> 00:05:53,420
+associativity ال identity element معكوس ال element
+
+61
+00:05:53,420 --> 00:05:57,640
+مظبوط يبقى هذه اللي كنا نقول عليها group حطينا
+
+62
+00:05:57,640 --> 00:06:00,760
+عليها الشرط لو ان صارت abelian group بالنسبة
+
+63
+00:06:00,760 --> 00:06:05,160
+لعملية الجامعةبعد ان نخرج من ال group نذهب الى ال
+
+64
+00:06:05,160 --> 00:06:09,760
+ring يبقى نذهب ناخد ايضا ال two conditions الاتنين
+
+65
+00:06:09,760 --> 00:06:18,180
+هذول a في b في c يعني لو ضربت ال b في ال c هينتج
+
+66
+00:06:18,180 --> 00:06:24,220
+عنصر جديد بدي اضرب فيه من جهة الشمال a تماما كما
+
+67
+00:06:24,220 --> 00:06:28,620
+لو ضربت a في b و اللي نتف ضربته في main في c وهذه
+
+68
+00:06:28,620 --> 00:06:33,910
+خاصية ال associated بالنسبة لعملياتيبقى خاصية الـ
+
+69
+00:06:33,910 --> 00:06:37,450
+Associated بالنسبة لعملية الجمع وبالنسبة لعملية
+
+70
+00:06:37,450 --> 00:06:44,690
+الضرب R exists موجودة فبالشرط الأخير يجمع عملية
+
+71
+00:06:44,690 --> 00:06:50,050
+الجمع مع عملية الضرب في آن واحد وهذا بنسميها بنات
+
+72
+00:06:50,050 --> 00:06:55,750
+الـ distributive law قانون التوزيع يبقى قانون
+
+73
+00:06:55,750 --> 00:07:00,800
+التوزيع اللي عندنا A في B زائد الـCبدي ساوي a في b
+
+74
+00:07:00,800 --> 00:07:06,060
+زي a في c اللي بنسميه left distributive law عملية
+
+75
+00:07:06,060 --> 00:07:10,900
+الضرب من جهة الشمال بدي ساوي b في a زي c في a بدي
+
+76
+00:07:10,900 --> 00:07:15,220
+ساوي b في a زي c في a بدي ساوي b في a زي c في a
+
+77
+00:07:15,220 --> 00:07:16,560
+بدي ساوي b في a زي c في a بدي ساوي b في a زي c في
+
+78
+00:07:16,560 --> 00:07:16,560
+a بدي ساوي b في a زي c في a بدي ساوي b في a زي c
+
+79
+00:07:16,560 --> 00:07:16,560
+في a بدي ساوي b في a زي c في a بدي ساوي b في a زي
+
+80
+00:07:16,560 --> 00:07:16,560
+c في a بدي ساوي b في a زي c في a بدي ساوي b في a
+
+81
+00:07:16,560 --> 00:07:19,420
+زي c في a بدي ساوي b في a زي c في a بدي ساوي b في
+
+82
+00:07:19,420 --> 00:07:28,720
+a زي c في a بدي ساوي b في a زي c في a بدي ساوي
+
+83
+00:07:28,720 --> 00:07:33,170
+bوبالتالي بجدك اتراعي الترتيب مش ع كيفك تضربي لأ
+
+84
+00:07:33,170 --> 00:07:37,150
+انت مقيدة الضرب من الشمال بتخلي الضرب ماشي من جهة
+
+85
+00:07:37,150 --> 00:07:41,030
+الشمال الضرب من جهة اليمين بيبقى ضرب ماشي من جهة
+
+86
+00:07:41,030 --> 00:07:45,130
+اليمين مش هتبدل وغير على كيفي بنفعش هذا الكلام
+
+87
+00:07:45,130 --> 00:07:49,430
+وانت واخدته هذا في ال abstract algebra one يبقى لا
+
+88
+00:07:49,430 --> 00:07:56,470
+يزال هو هو وسيبقى هو هو بعد ذلك ان شاء الله تعالى
+
+89
+00:07:56,470 --> 00:08:02,440
+في أن ملاحظات الآنعلى تعريف ال ring بنقول لو حصل
+
+90
+00:08:02,440 --> 00:08:08,080
+بالنسبة لعملية الضرب ان ال a في ال b كانت تسوى b
+
+91
+00:08:08,080 --> 00:08:14,700
+في a لكل ال a و ال b اللي موجودات في ال set R او
+
+92
+00:08:14,700 --> 00:08:18,660
+في ال ring R يبقى في هذه الحالة بقول ال ring is
+
+93
+00:08:18,660 --> 00:08:24,720
+commutative يبقى ال ring افضلية بدل appealing
+
+94
+00:08:24,720 --> 00:08:29,330
+group بدأ يقول commutative ringيبقى ال ring هذه
+
+95
+00:08:29,330 --> 00:08:36,690
+تتحقق فيها خاصية الإبدال لجميع
+
+96
+00:08:36,690 --> 00:08:42,630
+عناصر a و b اللي موجودة في R لكل ال a و ال b اللي
+
+97
+00:08:42,630 --> 00:08:47,570
+موجودة في R بدون استثناء مش ان اتحققت العنصر ال
+
+98
+00:08:47,570 --> 00:08:53,350
+commutative لأ اتحقق لجميع عناصر R بدون استثناء
+
+99
+00:08:53,350 --> 00:08:58,660
+طيب نقطة ثانيةلو كانت ال R فيها ال identity
+
+100
+00:08:58,660 --> 00:09:02,920
+element with respect to multiplication يبقى في
+
+101
+00:09:02,920 --> 00:09:07,440
+عندي عنصر واحدة بالنسبة لعملية الضرب طبعا هنا في
+
+102
+00:09:07,440 --> 00:09:11,620
+ال zero بالنسبة لعملية الجبهة لأ انا بد ال
+
+103
+00:09:11,620 --> 00:09:16,400
+identity element بالنسبة لعملية الضرب ان وجد ال
+
+104
+00:09:16,400 --> 00:09:21,260
+identity element بالنسبة لعملية الضرب في R بنروح
+
+105
+00:09:21,260 --> 00:09:27,350
+نقولها دي عشان نسميها ring with unityيعني ممكن يا
+
+106
+00:09:27,350 --> 00:09:31,970
+بنات ال ring يكون فيها unity وممكن مايكونش فيها
+
+107
+00:09:31,970 --> 00:09:35,990
+unity إذا فيها ال unity بسميها ring with unity إذا
+
+108
+00:09:35,990 --> 00:09:42,070
+فيهاش بسميها ring without unity كما سنرى بعد قليل
+
+109
+00:09:42,070 --> 00:09:46,330
+من خلال الأمثلة إن بعض ال rings فيها unity و بعض
+
+110
+00:09:46,330 --> 00:09:51,390
+الأخر مافيهش فيها unity و قد يكون ال unity هو
+
+111
+00:09:51,390 --> 00:09:57,960
+الواحد الصحيح و قد لا يكونحسب ال operation المعرفة
+
+112
+00:09:57,960 --> 00:10:04,080
+على ال ring R النقطة التالتة او الملاحظة التالتة
+
+113
+00:10:04,080 --> 00:10:09,520
+لو كانت R ring with unity واخدت عنصر موجود في R
+
+114
+00:10:09,520 --> 00:10:15,280
+وهذا العنصر لا يساوي الصفر يبقى ال A هذا بقول ال
+
+115
+00:10:15,280 --> 00:10:21,540
+multiplicative inverse ان حدث ذلكيبقى ال A هاد ..
+
+116
+00:10:21,540 --> 00:10:27,780
+يبقى هذا ال A بسمي unit في ال ring آه يبقى أصلا
+
+117
+00:10:27,780 --> 00:10:33,540
+عندي كلمتين في unit و في unity ال unity هو ال
+
+118
+00:10:33,540 --> 00:10:37,920
+identity element بالنسبة لعملية الضرب هذا ال unity
+
+119
+00:10:37,920 --> 00:10:42,460
+يبقى هو ال identity element بالنسبة لعملية الضرب
+
+120
+00:10:42,460 --> 00:10:48,720
+ال unitهو العنصر غير الصفري اللي موجود في ال ring
+
+121
+00:10:48,720 --> 00:10:54,980
+R و اللي له معكوس بالنسبة لعملية الضرب يعني إيش
+
+122
+00:10:54,980 --> 00:10:59,480
+بجينا نقول A في ال group إيش معكوس لو أنا A
+
+123
+00:10:59,480 --> 00:11:05,040
+inverse A و بحط فوقها سلب واحد لكنها ليست A أس سلب
+
+124
+00:11:05,040 --> 00:11:11,990
+واحد لكن هو رمز يدل على معكوس العنصر Aيبقى إذا حدث
+
+125
+00:11:11,990 --> 00:11:18,590
+أن للعنصر A معكوس بدي أسميه A inverse يبقى ال A
+
+126
+00:11:18,590 --> 00:11:27,910
+بسميه unit تمام؟ طيب ال ring فيهم مليلات unit و
+
+127
+00:11:27,910 --> 00:11:32,830
+الله يمكن أه ويمكن لا كل احتمالات و أرضها ممكن
+
+128
+00:11:32,830 --> 00:11:38,550
+يكون العناصر كلها غير الصفرية units ويمكن مالجيش
+
+129
+00:11:38,550 --> 00:11:44,270
+فيها units في المغربويمكن نلاقي بعض اليونس فقط
+
+130
+00:11:44,270 --> 00:11:50,430
+عنصرين اربع ستة تمانية لأنه بيكون عدد زوجي عنصر
+
+131
+00:11:50,430 --> 00:11:56,390
+ومعكوسه إذا هدول بيلاقيهم زوجي وما إلى ذلك يبقى
+
+132
+00:11:56,390 --> 00:12:02,210
+اليونس قد يكون موجودة في ال ring وقد لا تكون هذا
+
+133
+00:12:02,210 --> 00:12:07,070
+النقطة اللي هي التالتة يبقى العنصر إن وجدت له
+
+134
+00:12:07,070 --> 00:12:14,070
+معكوس بده يسميهUnity طب خليني أسأل شوية لو عندى
+
+135
+00:12:14,070 --> 00:12:21,370
+unity لا يساوي ال zero تمام unity لا يساوي ال zero
+
+136
+00:12:21,370 --> 00:12:27,390
+ال unity هذا بقدر أقول عليه unit ال
+
+137
+00:12:27,390 --> 00:12:32,630
+unity نفسه بقدر أقول عليه unit اه لأن لو ضربته في
+
+138
+00:12:32,630 --> 00:12:37,490
+نفسه بطلع ال unity صحيح ولا ..فال unity في ال
+
+139
+00:12:37,490 --> 00:12:42,550
+unity بتعطينا ال unity وبقى بناء عليه any unity is
+
+140
+00:12:42,550 --> 00:12:49,430
+a unit but the converse المعكوز is not necessarily
+
+141
+00:12:49,430 --> 00:12:56,490
+true ليس بضرورة صحيحة طيب وصلنا للنقطة الرابعة F
+
+142
+00:12:56,490 --> 00:13:01,150
+ال A و ال B موجودة في R و ال R is commutative و ال
+
+143
+00:13:01,150 --> 00:13:08,580
+A لا تساوي Zeroبنقول ال a تقسم ال b a divide ال b
+
+144
+00:13:08,580 --> 00:13:13,900
+هنكتبها بالشكل هذا زي ما كتبهالكوا في جبر حديث
+
+145
+00:13:13,900 --> 00:13:18,460
+واحد قبل ما بدأت ال group في مقدمة اعطوكوا هذه
+
+146
+00:13:18,460 --> 00:13:24,160
+المقدمة ال a تقسم ال b كنا بنعبر عنها بصيغة اللي
+
+147
+00:13:24,160 --> 00:13:30,220
+قدامنا هذا يبقى بقول a تقسم ال b إذا جدرتألاقي
+
+148
+00:13:30,220 --> 00:13:38,400
+element آخر في R سميته C بحيث ال B يساوي من A في C
+
+149
+00:13:38,400 --> 00:13:45,660
+يبقى ال A تقسم ال B إذا قدرت ألاقي عنصر آخر في R
+
+150
+00:13:45,660 --> 00:13:51,500
+بحيث لو ضربته في A يعطيني من يعطيني ال B طيب لو
+
+151
+00:13:51,500 --> 00:13:56,240
+كان ال A لا تقسم ال B بروح بكتبها بالشكل لأن هذا
+
+152
+00:13:56,590 --> 00:14:04,770
+يبقى a لتقسيم ال b مين بتحب تسأل أي سؤال على هذه
+
+153
+00:14:04,770 --> 00:14:11,130
+المقدمة قبل أن نأخذه الأمثلة؟
+
+154
+00:14:11,130 --> 00:14:16,470
+هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم
+
+155
+00:14:16,470 --> 00:14:16,470
+.. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم ..
+
+156
+00:14:16,470 --> 00:14:16,470
+هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم
+
+157
+00:14:16,470 --> 00:14:16,730
+.. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم ..
+
+158
+00:14:16,730 --> 00:14:17,530
+هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم
+
+159
+00:14:17,530 --> 00:14:17,530
+.. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم ..
+
+160
+00:14:17,530 --> 00:14:22,610
+هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم .. هم
+
+161
+00:14:22,610 --> 00:14:32,180
+.. همانتجار وعليها عملية الجمع العادى وعملية الضرب
+
+162
+00:14:32,180 --> 00:14:45,800
+العادى where حيث ال plus and الضغط are usual
+
+163
+00:14:45,800 --> 00:14:52,560
+addition and
+
+164
+00:14:52,560 --> 00:14:54,420
+multiplication
+
+165
+00:15:14,050 --> 00:15:19,370
+multiplication يبقى أخذت ال 6 زر و علينا عملية
+
+166
+00:15:19,370 --> 00:15:22,810
+الجمعة العادية و عملية الضرب العادية هذول two
+
+167
+00:15:22,810 --> 00:15:26,210
+binary operation ليش؟ لأنه لو جمعت two integers
+
+168
+00:15:26,210 --> 00:15:30,610
+الناتج integer يبقى عملية الجمعة binary operation
+
+169
+00:15:30,960 --> 00:15:35,520
+لو ضربت any two integers بيطلع main integer كذلك
+
+170
+00:15:35,520 --> 00:15:40,620
+يرجع يقول ضرب is a binary operation الان لو جينا
+
+171
+00:15:40,620 --> 00:15:46,480
+على هذا بيلاقي الشروط الستة كلها محققة بلا استثناء
+
+172
+00:15:46,480 --> 00:15:52,340
+فمثلا اتنين زي التلاتة هو تلاتة زي اتنين اتنين زي
+
+173
+00:15:52,340 --> 00:15:57,500
+التلاتة زي الخمسة هو اتنين زي التلاتة زي الخمسة
+
+174
+00:15:57,500 --> 00:16:02,900
+بالضبط تماماو هكذا ال zero L مانضفيه لأي رقم
+
+175
+00:16:02,900 --> 00:16:07,600
+بيعطيك نفس الرقم اللي هو الصحيح و هكذا إذا كل
+
+176
+00:16:07,600 --> 00:16:12,780
+الشروط محقق على مين؟ على هذه ال ring هل هذه ال
+
+177
+00:16:12,780 --> 00:16:16,920
+ring commutative؟ بمعنى اتنين في تلاتة هي تلاتة في
+
+178
+00:16:16,920 --> 00:16:24,020
+اتنين صحيح يبقى هذه commutative ring with unity ال
+
+179
+00:16:24,020 --> 00:16:28,180
+unity هي اللي
+
+180
+00:16:28,180 --> 00:16:32,550
+هو مين؟الواحد الواحد اللي ضربيه في أي عنصر من عصر
+
+181
+00:16:32,550 --> 00:16:40,670
+و ذات بطلع نفس العنصر يبقى هذه مالة is commutative
+
+182
+00:16:40,670 --> 00:16:44,090
+ring
+
+183
+00:16:44,090 --> 00:16:54,490
+with unity one طب
+
+184
+00:16:54,490 --> 00:16:57,610
+السؤال فيه units هذي يا بنات؟
+
+185
+00:17:08,120 --> 00:17:13,480
+الواحد هو ال unity في غيره؟ ليش؟ لأن الواحد في
+
+186
+00:17:13,480 --> 00:17:21,960
+واحد يساوي واحد فمش سالب واحد مش سالب واحد مش سالب
+
+187
+00:17:21,960 --> 00:17:26,390
+واحد بواحد بواحد لأن سالب واحد كمان is a unitthe
+
+188
+00:17:26,390 --> 00:17:30,930
+only units is one and minus one فقط لا غيره مافيش
+
+189
+00:17:30,930 --> 00:17:36,350
+غيرهم طبعا يبقى هدول units و لا يوجد غيرهم في الـ
+
+190
+00:17:36,350 --> 00:17:41,610
+z طب اتنين is a unit اه في نص في اتنين و واحد لكن
+
+191
+00:17:41,610 --> 00:17:47,030
+هل النص عدد صحيح لأ يبقى فانفعش اجيب من ستة ليرجع
+
+192
+00:17:47,030 --> 00:17:51,610
+ترجية مافيش هدا حاجة تسمى ترجية هنا طبعا يبقى لا
+
+193
+00:17:51,610 --> 00:17:57,320
+يوجد عند ال units الا الواحد والسالب واحديبقى هنا
+
+194
+00:17:57,320 --> 00:18:12,240
+the only units in the are ال one and سالق واحد
+
+195
+00:18:12,240 --> 00:18:17,180
+لماذا؟ لأن واحد في واحد يساوي واحد سالق واحد في
+
+196
+00:18:17,180 --> 00:18:22,900
+سالق واحد يساوي مين؟ واحد يبقى سالق واحد is a unit
+
+197
+00:18:23,350 --> 00:18:29,230
+و الواحد unity و احنا اتفقنا قبل قليل ان any unity
+
+198
+00:18:29,230 --> 00:18:34,210
+is a unit لكن العكس ليس بضروري يعني مثال و ظاهر
+
+199
+00:18:34,210 --> 00:18:42,290
+هذا unit لكن هل هو unity؟ لا مش صحيح طيب ايش رأيك
+
+200
+00:18:42,290 --> 00:18:49,310
+لو قلتلك also ال set of rational number ال EQ تحت
+
+201
+00:18:49,310 --> 00:18:55,900
+عملية الجمعةوالضرب العادية and ال set of real
+
+202
+00:18:55,900 --> 00:19:00,940
+number تحت عملية الجامعة وتحت عملية الضرب هدول
+
+203
+00:19:00,940 --> 00:19:08,660
+rings ولا لا؟ و communicative؟ وفي community؟
+
+204
+00:19:08,660 --> 00:19:15,980
+community؟ وفي communites كمان تمام؟ يبقى هدول are
+
+205
+00:19:15,980 --> 00:19:19,020
+communicative؟
+
+206
+00:19:40,320 --> 00:19:47,000
+إتناء الرشول النمبر صح؟ إتناء الرشول النمبر، هل هو
+
+207
+00:19:47,000 --> 00:19:53,510
+unit في الـQ؟أه لأن النص موجود في ال Q و نص في
+
+208
+00:19:53,510 --> 00:19:58,050
+اتنين بساوي جدار يبقى واحد صحيح اللي هو ال unity
+
+209
+00:19:58,050 --> 00:20:06,030
+إذا بناء عليه أي non zero element in a cube is a
+
+210
+00:20:06,030 --> 00:20:14,710
+unit صح؟ لأن مقلوبه هو المعكوس تبعه فاتنين مقلبها
+
+211
+00:20:14,710 --> 00:20:20,410
+نص صار النص هو المعكوس تبع اتنينالمية مقلبها واحد
+
+212
+00:20:20,410 --> 00:20:25,430
+عالمية الواحد عالمية هي المعقوزة بعلمية هو قس
+
+213
+00:20:25,430 --> 00:20:31,510
+عليها ما شيتيه طب و الست و ال real number ازايها
+
+214
+00:20:31,510 --> 00:20:37,190
+لان any rational number is a real number يبقى من
+
+215
+00:20:37,190 --> 00:20:42,530
+هنا صارت هذه ازايها طب خلينا نسأل كمان سؤال اتنين
+
+216
+00:20:42,530 --> 00:20:53,410
+زد رنجwith unity و الله without unity بس ولكن
+
+217
+00:20:53,410 --> 00:20:56,710
+اتنين
+
+218
+00:20:56,710 --> 00:21:03,090
+زده اللي هي مين نقطة سالب ستة سالب اربعة سالب
+
+219
+00:21:03,090 --> 00:21:08,470
+اتنين زيرتين اربعة ستة وطلق ماشية الى ما شاء الله
+
+220
+00:21:08,470 --> 00:21:14,070
+من هنا ل infinity و من هنا لسلب infinity رينقولها
+
+221
+00:21:15,240 --> 00:21:22,840
+بتحقق الشروط الستة ولا بتحققهم طيب commutative؟ اه
+
+222
+00:21:22,840 --> 00:21:28,680
+صحيح commutative فيها unity؟ لا ليهاش unity و احنا
+
+223
+00:21:28,680 --> 00:21:32,000
+المرة اللي فاتت قولنا لكوا ال ring و اليوم قولنا
+
+224
+00:21:32,000 --> 00:21:35,240
+ممكن ال ring يكون فيها unity و ممكن مايكونش فيها
+
+225
+00:21:35,240 --> 00:21:40,440
+unity يبقى هذه commutative without unity ماعنديش
+
+226
+00:21:40,440 --> 00:21:43,560
+unity فيها بالمرة يبقى هذه
+
+227
+00:21:47,400 --> 00:22:01,560
+communitative ring without unity يبقى
+
+228
+00:22:01,560 --> 00:22:06,120
+هذه communicative ring و unity مافيهاش يبعت الله
+
+229
+00:22:32,930 --> 00:22:43,270
+مش ممكنش .. مش ممكنش .. مش ممكنش
+
+230
+00:23:30,710 --> 00:23:38,490
+طبعا عدد العناصر يساوي N زد عشرة في عشر عناصر زد
+
+231
+00:23:38,490 --> 00:23:43,670
+ستة في ستة عناصر و هكذا تمام under addition of
+
+232
+00:23:43,670 --> 00:23:49,410
+multiplication modulo Nmodular in نفس الكلام اللي
+
+233
+00:23:49,410 --> 00:23:55,330
+أخدته في جابرة حديث واحد ايش يعني modular in زي
+
+234
+00:23:55,330 --> 00:23:59,110
+الساعة على يدك مثلا تمشي لساعة الساعة اتناشر بعد
+
+235
+00:23:59,110 --> 00:24:03,090
+اتناشر مايقوليش تلاتاشر بنبدأ واحدة تنتين تلاتة
+
+236
+00:24:03,090 --> 00:24:07,590
+لما نوصل الاتناشر وهكذا كل اتناشر ساعة بنعيد
+
+237
+00:24:07,590 --> 00:24:12,270
+الدورة من جديد هذه كل ان من العناصر بنبدأ نعيد
+
+238
+00:24:12,270 --> 00:24:19,290
+الدورة من جديد هي المقصود فيهايبقى تحت عملية الجمع
+
+239
+00:24:19,290 --> 00:24:24,610
+والضرب module in is a commutative ring with unity
+
+240
+00:24:24,610 --> 00:24:31,050
+one طبعا ال one modulo in اتنين modulo in التلاتة
+
+241
+00:24:31,050 --> 00:24:35,290
+modulo in هي المقصود فيها بالشكل اللي قدامها الأن
+
+242
+00:24:35,290 --> 00:24:41,990
+ندور عالمين على ال set of unitsالعناصر اللي ممكن
+
+243
+00:24:41,990 --> 00:24:46,610
+يكون in it's يعني اللي لهم معكوز موجودة في هذه ال
+
+244
+00:24:46,610 --> 00:24:58,750
+ring is UN مين UN هذه يا بنات؟ تذكرين؟ مين هي هذه؟
+
+245
+00:24:58,750 --> 00:25:05,470
+يبقى هذه العناصر اللي موجودة في ZN واللي بتكون
+
+246
+00:25:05,470 --> 00:25:11,210
+relatively prime بالنسبة لمن؟للعدد n مثلا for
+
+247
+00:25:11,210 --> 00:25:14,810
+example
+
+248
+00:25:14,810 --> 00:25:24,870
+for example لو أخدت z عشرة مثلا هي عبارة عن مين؟
+
+249
+00:25:24,870 --> 00:25:33,670
+zero واحد اتنين تلاتة اربع خمسة ستة سابعة تمانية
+
+250
+00:25:33,670 --> 00:25:40,160
+تسعة في عشرة عشرة تاني zeroيبقى هذه العناصر تبعتها
+
+251
+00:25:40,160 --> 00:25:50,360
+بدي أدور على ال units the units is
+
+252
+00:25:50,360 --> 00:25:58,840
+the set U عشرة مين عناصر ال U عشرة بدي أدور على
+
+253
+00:25:58,840 --> 00:26:04,650
+العناصر relatively prime مع مين مع العشرةيعني
+
+254
+00:26:04,650 --> 00:26:10,610
+الأعداد اللي بتقسمش إلا على نفسها وعلى الواحد
+
+255
+00:26:10,610 --> 00:26:17,610
+الصحيح من خلال هذه ال ring همين يا بنات؟ واحد،
+
+256
+00:26:17,610 --> 00:26:27,290
+تلاتة، سبعة، تسعة تمام، هدول ال units فقط، يبقى
+
+257
+00:26:27,290 --> 00:26:32,190
+هدول أربعة، وهي فيها عشرة عناصر، إذا ستة ليسوا
+
+258
+00:26:32,190 --> 00:26:37,020
+unitsمش شرطين من الأول ممنوع يكونوا صفر يبقى بنشيل
+
+259
+00:26:37,020 --> 00:26:43,640
+الصفر منهم بظل خمسة ماهياش units و أربعة فقط هي ال
+
+260
+00:26:43,640 --> 00:26:50,580
+units صحيح؟ يعني كل واحد من هدول بيدلا يجي عنصر
+
+261
+00:26:50,580 --> 00:26:55,560
+أضرب فيه يطلع ناتج ال unit اللي هو واحد الواحد في
+
+262
+00:26:55,560 --> 00:27:00,840
+واحد في واحد خلصنا منه طب الستلاتة ستلاتة في سبعة
+
+263
+00:27:01,130 --> 00:27:05,450
+بواحد وعشر ينشيلي عشرتين بيظل ال unit اللي هو واحد
+
+264
+00:27:05,450 --> 00:27:11,110
+يبقى التلاتة معكوسه من؟ السبعة بيظل عندنا من؟ بيظل
+
+265
+00:27:11,110 --> 00:27:15,810
+عندنا التسعة معكوسه اللي نفسه من تسعة تسعة بواحد و
+
+266
+00:27:15,810 --> 00:27:19,490
+تمانين ينشيلي تمان عشرات بيظل من؟ بيظل ال unit
+
+267
+00:27:19,490 --> 00:27:23,490
+اللي هو واحد يبقى تسعة معكوسه اللي نفسهوالواحد
+
+268
+00:27:23,490 --> 00:27:27,990
+معكسه لنفسه والثلاثة معكسة السبعة أو السبعة معكسة
+
+269
+00:27:27,990 --> 00:27:32,430
+مين التلاتة يبقى هدول هم ال units اللي موجودة وين
+
+270
+00:27:32,430 --> 00:27:40,710
+اللي موجودة في هذه ال group طيب
+
+271
+00:27:40,710 --> 00:27:49,570
+لو جيت Goldslug also شغلة تانية that's it اللي هي
+
+272
+00:27:49,570 --> 00:27:59,110
+zeroاربع ست تمانى رنج
+
+273
+00:27:59,110 --> 00:28:07,210
+طبعا هذه تحت عملية الجمع والضرب موديولو عشرة يبقى
+
+274
+00:28:07,210 --> 00:28:11,690
+هذه under addition
+
+275
+00:28:11,690 --> 00:28:16,990
+and multiplication
+
+276
+00:28:22,800 --> 00:28:34,320
+مدينو عشر is a commutative ring
+
+277
+00:28:34,320 --> 00:28:39,760
+فيها unity يا بنات؟ لا، لا، لا، لا، لا، لا، لا،
+
+278
+00:28:39,760 --> 00:28:42,660
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+279
+00:28:42,660 --> 00:28:46,020
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+280
+00:28:46,020 --> 00:28:50,420
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+281
+00:28:50,420 --> 00:28:50,440
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+282
+00:28:50,440 --> 00:28:50,480
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+283
+00:28:50,480 --> 00:28:50,480
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+284
+00:28:50,480 --> 00:28:50,480
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+285
+00:28:50,480 --> 00:28:53,770
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،مين هي
+
+286
+00:28:53,770 --> 00:28:59,490
+ال unity بده اروح ادور عليها موديوله عشرة ها يلا
+
+287
+00:28:59,490 --> 00:29:07,170
+زيله مالحطاه شكل تمام اتنين ماهو الرقم اللي لو
+
+288
+00:29:07,170 --> 00:29:14,050
+ضربته في اتنين بده يطلع نتجه اتنين ستة ستة في
+
+289
+00:29:14,050 --> 00:29:19,610
+اتنين باثنين موديوله عشرة اتنين تبقى ستة في اتنين
+
+290
+00:29:19,610 --> 00:29:26,010
+يساوي اتنين بعدين اربعأربعة في ستة؟ أربعة وعشرين،
+
+291
+00:29:26,010 --> 00:29:32,050
+شيله عشرتين، يبقى أربعة في ستة يسوي كده؟ أربعة،
+
+292
+00:29:32,050 --> 00:29:39,390
+تمام، ستة في ستة يسوي ستة، ستة في تمانية يسوي
+
+293
+00:29:39,390 --> 00:29:44,410
+تمانية، يبقى صار من ال identity element؟ الستة،
+
+294
+00:29:44,410 --> 00:29:48,110
+يبقى صار الستة identity، وليس الواحد اللي مطبوع في
+
+295
+00:29:48,110 --> 00:29:53,010
+المغقق بمجرد النظريبقى هذا يحتاج إلى تفكير هذا أحد
+
+296
+00:29:53,010 --> 00:29:57,450
+أسئلة الكتابة من سؤال اتنين أو أربعة هذا أحد أسئلة
+
+297
+00:29:57,450 --> 00:30:04,370
+الكتابة يبقى will unity ستة ليش؟ لأن أضرب اتنين في
+
+298
+00:30:04,370 --> 00:30:08,490
+ستة بطلع اتنين أربعة في ستة بطلع أربعة ستة في ستة
+
+299
+00:30:08,490 --> 00:30:12,770
+بطلع ستة تمانية في ستة بطلع تمانية يبقى الناتج كله
+
+300
+00:30:12,770 --> 00:30:19,430
+يعني بيعطيني نفس الرقم بصار ستة will unity تمام؟
+
+301
+00:30:19,830 --> 00:30:25,850
+أيوة يبقى خد بالك واطنع حالك كويس على البحث عن ال
+
+302
+00:30:25,850 --> 00:30:33,510
+unity تلاتة plus it z
+
+303
+00:30:33,510 --> 00:30:47,010
+of x شكل أنها of all polynomials plus it of all
+
+304
+00:30:47,010 --> 00:30:48,070
+polynomials
+
+305
+00:30:50,160 --> 00:31:10,720
+the variable x with integer coefficients معاملات
+
+306
+00:31:10,720 --> 00:31:17,340
+صحيحة under ordinary
+
+307
+00:31:19,860 --> 00:31:26,460
+under ordinary addition and
+
+308
+00:31:26,460 --> 00:31:35,220
+multiplication تحت
+
+309
+00:31:35,220 --> 00:31:45,240
+عملية ضرب وجم العادية is a commutative
+
+310
+00:32:11,090 --> 00:32:21,880
+Z of X المقصود فيهامكونة كل عنصر فيها عبارة عن
+
+311
+00:32:21,880 --> 00:32:28,200
+كثيرة حدود إذا مكونة من كثيرات حدود المعاملات
+
+312
+00:32:28,200 --> 00:32:33,080
+تبعات الحدود كلهم أعداد صحية سواء كانت بالموجب أو
+
+313
+00:32:33,080 --> 00:32:38,160
+بالسالب أو حتى الصفر يبقى هي المقصود هي يبقى the
+
+314
+00:32:38,160 --> 00:32:44,260
+set of all polynomial وحيث كلها دالة في المتغير X
+
+315
+00:32:44,260 --> 00:32:50,650
+زي ايه؟ زي F of X يساوي X تربيةنقص تلاتة X زي 15
+
+316
+00:32:50,650 --> 00:32:58,090
+مثلا زي F of X سوى X أُص أربعة وبدّيش أجيب فيها X
+
+317
+00:32:58,090 --> 00:33:04,890
+تربية زائد تلاتة X تكيب زائد X ناقص واحد يبقى هاي
+
+318
+00:33:04,890 --> 00:33:09,730
+المعامل صفر راح تبع ال X تربية مظبوط؟ بقى المعامل
+
+319
+00:33:09,730 --> 00:33:16,850
+X أُص أربعة ومعامل X تكيب ومعامل X أرقام صحيةبديش
+
+320
+00:33:16,850 --> 00:33:21,690
+ولا كسر يكون فيهم لكن سالب أو موجب القام صحيح
+
+321
+00:33:21,690 --> 00:33:26,970
+ماعناه مشكلة يبقى هذه كل كثيرات الحدود اللي
+
+322
+00:33:26,970 --> 00:33:32,690
+المعاملة تبعتها أعداد صحية هذه بتكون ال
+
+323
+00:33:32,690 --> 00:33:37,050
+commutative ring with unity حد عارف مين مين ال
+
+324
+00:33:37,050 --> 00:33:43,830
+unity؟ اه ممتاز ال unity هي دالة ثابتة بس مش اي
+
+325
+00:33:43,830 --> 00:33:50,050
+دالة ثابتةالدالة ثابتة f of x يساوي واحد يبقى with
+
+326
+00:33:50,050 --> 00:33:56,610
+unity f of x يساوي واحد لإن لو ضربت الواحد في أي
+
+327
+00:33:56,610 --> 00:34:01,010
+polynomial بطلع نفس ال polynomial يبقى هذا هو ال
+
+328
+00:34:01,010 --> 00:34:05,830
+unity اتنين commutative ليش؟ لإن ال polynomial لما
+
+329
+00:34:05,830 --> 00:34:10,570
+تعوضلها برقم بطلع real number برقم ثاني بطلع real
+
+330
+00:34:10,570 --> 00:34:15,090
+number فنضربهم من اليمين و الله من الشمال سياليبقى
+
+331
+00:34:15,090 --> 00:34:19,270
+الاتنين our community bring with unity f of x
+
+332
+00:34:19,270 --> 00:34:29,350
+يساوي واحد صحيح طيب الان ننتقل الى set أخرى يبقى
+
+333
+00:34:29,350 --> 00:34:37,130
+رقم أربع the set m2
+
+334
+00:34:37,130 --> 00:34:50,060
+of z of twoby two matrices with
+
+335
+00:34:50,060 --> 00:34:54,320
+integer
+
+336
+00:34:54,320 --> 00:34:57,780
+interest
+
+337
+00:34:57,780 --> 00:35:01,720
+بعناصر
+
+338
+00:35:01,720 --> 00:35:08,720
+أعداد صحيحة is a non commutative ring
+
+339
+00:35:15,140 --> 00:35:21,540
+non commutative ring with
+
+340
+00:35:21,540 --> 00:35:24,940
+unity
+
+341
+00:35:24,940 --> 00:35:33,940
+اللي هي واحد زيرو زيرو واحد اخدت
+
+342
+00:35:33,940 --> 00:35:40,610
+هذا في الجبرا الخطي لينير الجبراالمصفوفات في
+
+343
+00:35:40,610 --> 00:35:46,410
+الجبهة الخاطية والمحددات معها و ال vector spaces و
+
+344
+00:35:46,410 --> 00:35:50,190
+ال linear transformations كل هذا في الجبهة الخاطية
+
+345
+00:35:50,190 --> 00:35:58,790
+نجي هنا لو أقول يا بنات into z يبقى كل المصفوفات
+
+346
+00:35:58,790 --> 00:36:02,950
+اللي نظامها اتنين في اتنين يعني فيها صفين و فيها
+
+347
+00:36:02,950 --> 00:36:08,590
+عمودين of z العناصر اللي داخل المصفوفة كلهم أعداد
+
+348
+00:36:08,590 --> 00:36:14,770
+صحيحةماعنديش كسر بالمرة M to Z يبقى العناصر اللى
+
+349
+00:36:14,770 --> 00:36:20,710
+جوا مأخودة من ال set of integer Z طيب with integer
+
+350
+00:36:20,710 --> 00:36:26,190
+interest كل معدات صحيحة عبارة عن non commutative
+
+351
+00:36:26,190 --> 00:36:31,890
+ring لإن عملية ضرب المصوفات ليس إبداليا يعني ال A
+
+352
+00:36:31,890 --> 00:36:37,130
+في ال B لأ تسوي ال B في ال A in general لما أقول
+
+353
+00:36:37,130 --> 00:36:42,040
+in general يعني ممكنحالة حالتين تلاتة تشد عنها بس
+
+354
+00:36:42,040 --> 00:36:46,680
+in general ماهياش commutative ال unity تبعتها
+
+355
+00:36:46,680 --> 00:36:52,920
+لمصفوفة الوحدة يبقى ال identity matrix هي عنصر
+
+356
+00:36:52,920 --> 00:36:58,060
+الوحدة بالنسبة لهذه المصفوفة طب ماهو عنصر الصفرية
+
+357
+00:36:58,060 --> 00:37:05,420
+المصفوفة الصفرية 00000 يبقى هذه المصفوفة الصفرية
+
+358
+00:37:05,420 --> 00:37:14,730
+طيبالمعكوس الجامعي لمن؟ للمصوفة A,B,C,D السالب
+
+359
+00:37:14,730 --> 00:37:21,230
+بتاعتها يبقى سالب A هو سالب A سالب B سالب C سالب D
+
+360
+00:37:21,230 --> 00:37:26,890
+يبقى هذا هو العنصر السالب تبعتها طيب بتقدروا
+
+361
+00:37:26,890 --> 00:37:33,170
+تجيبولنا unit في مجموعة المصوفات هذه أبسط حاجة
+
+362
+00:37:33,170 --> 00:37:37,130
+اللي هي ال unity لكن ممكن نجيب غيرهالنجيب غيرها
+
+363
+00:37:37,130 --> 00:37:42,410
+يعني بدي أجيب مصفوفة و المصفوفة هاد يكونلها معكوسة
+
+364
+00:37:42,410 --> 00:37:47,230
+قبل ما نقول منهي بدي أسأل كيف بنجيب معكوسة
+
+365
+00:37:47,230 --> 00:37:50,870
+المصفوفة اللي نضامها اتنين في اتنين نفرضه أنه
+
+366
+00:37:50,870 --> 00:37:56,130
+موجود و بقدره عشان أجيب المصفوفة الوحدة و لأ ما
+
+367
+00:37:56,130 --> 00:37:58,970
+أفهمتش لأ ما أفهمتش ولا حاجة
+
+368
+00:38:03,190 --> 00:38:08,270
+Quiz واحد علي قيمة المحدد تبع هذه المصوفة مضروبا
+
+369
+00:38:08,270 --> 00:38:14,950
+فيه وبنقل إشارات
+
+370
+00:38:14,950 --> 00:38:19,450
+عناصر قتل الذنب يبقى ليه السهولة لما بنتجيب معكوس
+
+371
+00:38:19,450 --> 00:38:24,610
+المصوفة لنضامها 2×2 فقط 3×3 التفكير كله مش صحيح
+
+372
+00:38:24,610 --> 00:38:31,510
+تمام يبقى 2×2 فقط تمام إيش بنعمل؟نعمل ما ياتي بروح
+
+373
+00:38:31,510 --> 00:38:36,330
+بجيب محدد المصوفة جداش قيمته والشرط أساسي ممنوع
+
+374
+00:38:36,330 --> 00:38:41,110
+يساوي الصفر عشان كل المصوفة معكوس المحدد ممنوع
+
+375
+00:38:41,110 --> 00:38:45,870
+يساوي الصفر هاي واحدة الثانية بقول واحد على قيمة
+
+376
+00:38:45,870 --> 00:38:51,290
+المحدد بجي على المصوفة اللي عندي ببدل عناصر القطة
+
+377
+00:38:51,290 --> 00:38:55,790
+الرئيسية مكان بعض و بغير إشارات عناصر القطر الثاني
+
+378
+00:38:55,790 --> 00:39:03,300
+نعطي Coordinate يبغى هناطيب يا بنات لو أخدت مصفوفة
+
+379
+00:39:03,300 --> 00:39:08,940
+وطلع محددها اتنين، تلاتة، اربع، عشرة، اي رقم غير
+
+380
+00:39:08,940 --> 00:39:15,460
+الواحد وغير السالب واحد بنفع يكون unit هذا؟ بنفع؟
+
+381
+00:39:15,460 --> 00:39:19,920
+يعني لو جيت مصفوفة وطلع محددها تلاتة مثلها، بدي
+
+382
+00:39:19,920 --> 00:39:25,820
+اجيب المعقول سبعة طولت في كذا، بنفع؟ احنا في M2Z
+
+383
+00:39:27,430 --> 00:39:33,090
+يبقى بنفع؟ لأ بنفعش ليش بدي يكون أعداد صحيحة مش
+
+384
+00:39:33,090 --> 00:39:36,590
+كسرية هتلاقى ال six real numbers أو ال six
+
+385
+00:39:36,590 --> 00:39:40,330
+rational numbers ماشي ماعنده مشكلة لكن احنا بدنا M
+
+386
+00:39:40,330 --> 00:39:46,090
+to Z يعني أعداد صحية إذا يجب أن يكون قيمة المحدد
+
+387
+00:39:46,090 --> 00:39:51,850
+إما واحد صحيح وإما سالف واحد صحيح حتى يكون unit
+
+388
+00:39:51,850 --> 00:39:54,610
+for example
+
+389
+00:39:59,130 --> 00:40:03,410
+the element الانصف
+
+390
+00:40:03,410 --> 00:40:12,930
+اننا ناخد مصفوفة مثلا اتنين خمسة واحد تلت هذه كدهش
+
+391
+00:40:12,930 --> 00:40:20,110
+محددها واحد صحيح اتنين في تلت او ستة نقص خمس او
+
+392
+00:40:20,110 --> 00:40:26,910
+واحد هذا is a unit because
+
+393
+00:40:29,880 --> 00:40:37,740
+اللي هو اتنين واحد خمسة ثلاثة inverse المعتوذ تبعه
+
+394
+00:40:37,740 --> 00:40:43,860
+المحدد بواحد خلصنا منه يفجأ ده ببدل عناصر القطر
+
+395
+00:40:43,860 --> 00:40:47,820
+الرئيسي ده المكان التلاتة والتلاتة مكان اتنين
+
+396
+00:40:47,820 --> 00:40:54,080
+والخمسة والواحد بخليهم زي ما هم بس بغير اشارات
+
+397
+00:40:54,080 --> 00:41:00,750
+عناصرهم او تغير اشارات عناصر قطر السنةالان لو مسكت
+
+398
+00:41:00,750 --> 00:41:04,630
+المصوفة هذه ضربتنا المصوفة هذه من اليمين و لا من
+
+399
+00:41:04,630 --> 00:41:09,650
+الشمال النتج بدي اعطيني مين ال identity element
+
+400
+00:41:09,650 --> 00:41:14,890
+اللي عندنا يالا بنكمل المرة الجاية ماشي اعطيك
+
+401
+00:41:14,890 --> 00:41:15,330
+العكس
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7cc23561c327e555b1ca10cf71011d512872b48a
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo.srt
@@ -0,0 +1,1470 @@
+1
+00:00:20,860 --> 00:00:26,000
+بسم الله الرحمن الرحيم. المرة اللي فاتت ابتدأنا في
+
+2
+00:00:26,000 --> 00:00:33,680
+حل exercises على chapter 16 ووصلنا إلى السؤال رقم
+
+3
+00:00:33,680 --> 00:00:40,980
+السؤال رقم 12، أنا ما أذكر يعني، مظلوم؟ وقلنا
+
+4
+00:00:40,980 --> 00:00:46,720
+هذا بدنا فيه good exercises، تمرنوا أيديكم فيه
+
+5
+00:00:46,720 --> 00:00:53,670
+وزي سؤال 11 اللي قبله، أدري حلته ولا لا، ممتازة
+
+6
+00:00:53,670 --> 00:00:58,050
+يبقى بدي أقول الفكرة الشفوية اللي ما عرفتش أتحل ثم
+
+7
+00:00:58,050 --> 00:01:03,130
+ننتقل إلى السؤال اللي بعده، طبعا احنا بدنا نقسم في
+
+8
+00:01:03,130 --> 00:01:09,290
+سؤال اثني عشر: خمسة اكس أس أربعة على ثلاثة اكس تربيع
+
+9
+00:01:09,290 --> 00:01:18,250
+احنا بنشتغل وين؟ في Z سبعة of X، مظبوط؟ يبقى في Z
+
+10
+00:01:18,250 --> 00:01:24,760
+سبعة of X، في Z7، لما أجي أجسم خمسة على ثلاثة، يبقى
+
+11
+00:01:24,760 --> 00:01:29,560
+فيش حاجة اسمها الخمسة على ثلاثة، هذا كسر مش موجود في
+
+12
+00:01:29,560 --> 00:01:36,840
+Z، فماذا نعمل؟ بنروح، بنضيف لخمسة مضاعفات السبعة
+
+13
+00:01:36,840 --> 00:01:42,280
+لغاية ما تقسم على ثلاثة، يبقى أنا عندي خمسة،
+
+14
+00:01:42,280 --> 00:01:46,280
+أضيف لها سبعة، سبعة ثانية، صفر في Z7، يعني كأني
+
+15
+00:01:46,280 --> 00:01:51,710
+ما عملتش حاجة، فبيصير سبعة وخمسة، اثنا عشر، و بتقسم على مين؟
+
+16
+00:01:51,710 --> 00:01:57,490
+على ثلاثة، لو ما قسمت، بأضيف كمان سبعة، بضل أضيف
+
+17
+00:01:57,490 --> 00:02:02,770
+سبعة لما تقسم، بيكون هي النتيجة المطلوبة، فأنت سبعة
+
+18
+00:02:02,770 --> 00:02:08,110
+وخمسة، اثنا عشر، بس اثنا عشر على ثلاثة، أربعة اكس تربيع
+
+19
+00:02:08,110 --> 00:02:13,250
+وهكذا بكمل مثل القسمة العادية، وأنا أعطيتكم قبل ذلك
+
+20
+00:02:13,430 --> 00:02:17,930
+مثال قسمة، بس ما كانش، كان المعامل هنا واحد، والمعامل
+
+21
+00:02:17,930 --> 00:02:22,290
+هنا واحد، وبالتالي لم تظهر المشكلة، لكن لما كانوا
+
+22
+00:02:22,290 --> 00:02:28,270
+أرقام مختلفة هنا، ظهرت المشكلة، وحلها: بضيف مضاعفات
+
+23
+00:02:28,270 --> 00:02:33,950
+السبعة بحيث تتم القسمة، طبعا. إذا سؤال اثني عشر، very
+
+24
+00:02:33,950 --> 00:02:41,260
+easy، بروح لأقل سؤال، سؤال سبعة عشر، هذا سؤال سبعة عشر، أخذنا
+
+25
+00:02:41,260 --> 00:02:46,240
+لأنه لازم لي في chapter سبعة عشر، ولازم لي أي chapter طبعا
+
+26
+00:02:46,240 --> 00:02:52,620
+تحت، إذن هذا يجب أن نحله لأنه لازم لي قدام، يبقى بالي
+
+27
+00:02:52,620 --> 00:02:59,140
+لمين؟ لسؤال سبعة عشر، سؤال سبعة عشر بيقول: دي integral
+
+28
+00:02:59,140 --> 00:03:06,260
+domain، يبقى دي is an integral domain
+
+29
+00:03:08,690 --> 00:03:15,110
+وعندنا الـ F of X والـ G of X موجودة في D، والـ F
+
+30
+00:03:15,110 --> 00:03:25,610
+of X والـ G of X عناصر موجودة في الـ D of X، بيقول لي بعدين: اثبت أن الـ degree لحاصل الضرب تساوي الـ
+
+31
+00:03:25,610 --> 00:03:29,290
+degree للجمع، يفى المطلوب الأول، النقطة الأولى، إن
+
+32
+00:03:29,290 --> 00:03:38,250
+الـ degree لمن؟ للـ F of X مضروبا في الـ G of X تساوي الـ
+
+33
+00:03:38,250 --> 00:03:46,210
+degree للـ F مضافا إليها الـ degree للـ G، هذا المطلوب
+
+34
+00:03:46,210 --> 00:03:53,330
+الأول، المطلوب الثاني بيقول: هذه commutative ring
+
+35
+00:03:53,330 --> 00:03:58,650
+بحيث هذه تكون مش صحيحة، كيف يعني مش صحيحة؟ يعني يكون
+
+36
+00:03:58,650 --> 00:04:03,470
+الـ degree لحاصل الضرب أقل من الـ degree لمن؟ للجمع
+
+37
+00:04:03,470 --> 00:04:10,910
+بس مش في الـ integral domain، الـ integral domain ده
+
+38
+00:04:10,910 --> 00:04:14,510
+كلام صحيح دائما، أبدا قلت لأ، في commutative ring
+
+39
+00:04:14,510 --> 00:04:18,970
+ليس بالضرورة أن تكون integral domain، طيب خلي
+
+40
+00:04:18,970 --> 00:04:25,390
+المطلوب الثاني بعد ما نخلص المطلوب الأول، يبدأ أنا
+
+41
+00:04:25,390 --> 00:04:29,770
+بدي آخذ الـ two polynomials الموجودة في D of X، يبقى الـ
+
+42
+00:04:29,770 --> 00:04:35,700
+solution على الوجه التالي، نقطة واحدة بداية، أقول
+
+43
+00:04:35,700 --> 00:04:42,680
+افترضوا أن الـ f of x هي a n x to the power n، a
+
+44
+00:04:42,680 --> 00:04:50,280
+n-1 x أس n-1 زائد زائد إلى
+
+45
+00:04:50,280 --> 00:04:57,920
+a1 x زائد ال a0، وفي المقابل الـ a n does
+
+46
+00:04:57,920 --> 00:05:07,060
+not equal to zero، مشان أضمن أن أعلى degree عندي
+
+47
+00:05:07,060 --> 00:05:12,840
+جديدة اللي هو m، وفي نفس الوقت الـ g of x بدي يساوي b
+
+48
+00:05:12,840 --> 00:05:20,640
+m x to the power m، b m-1 x to the power m-1
+
+49
+00:05:20,640 --> 00:05:26,840
+زائد b1 x زائد ال b0، والـ bm
+
+50
+00:05:26,840 --> 00:05:33,460
+كذلك لا تساوي 0، والاثنتين هدول كلهم موجودات في مين؟
+
+51
+00:05:33,460 --> 00:05:40,880
+في الـ integral domain D of X، الآن بدي آخذ حاصل
+
+52
+00:05:40,880 --> 00:05:47,800
+ضربهما، يبقى بدي آخذ الـ F of X في الـ G of X، يبقى
+
+53
+00:05:47,800 --> 00:05:55,940
+لما أبدأ أضربهم، هقول: an bm في X أس n زائد ال m
+
+54
+00:05:55,940 --> 00:06:04,450
+تمام، زائد ونظل ماشيين لغاية ما نوصل لمين؟ للـ a0
+
+55
+00:06:04,450 --> 00:06:12,430
+b1 زائد a1 b0 في الـ X زائد الـ a0 b0
+
+56
+00:06:12,430 --> 00:06:21,310
+يبقى هذا حاصل الضرب، الآن أنا بتهمني الـ
+
+57
+00:06:21,310 --> 00:06:29,070
+degree، هذه الـ an bm، ممكن تكون بصفر؟ لأ لأ لأ لأ
+
+58
+00:06:29,070 --> 00:06:37,180
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+59
+00:06:37,180 --> 00:06:40,420
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+60
+00:06:40,420 --> 00:06:40,920
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+61
+00:06:40,920 --> 00:06:41,040
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+62
+00:06:41,040 --> 00:06:41,920
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+63
+00:06:41,920 --> 00:06:42,100
+لأ لأ لأ لأ لأ لأ لأ
+
+64
+00:06:42,100 --> 00:06:47,980
+لأ لأ لأ لأ لأ لأ لأ
+
+65
+00:06:47,980 --> 00:06:52,260
+لأ لأ لأ لأ لأ
+
+66
+00:06:52,260 --> 00:06:58,140
+لأ
+
+67
+00:06:58,140 --> 00:07:04,850
+لأ، هدف صفر، ولا هدف صفر، يعني بنفع لما الهدف
+
+68
+00:07:04,850 --> 00:07:09,630
+ماهيش بصفر، وهدف ماهيش بصفر، حاصل درجة ما يكونش
+
+69
+00:07:09,630 --> 00:07:15,990
+صفر، فهي احتمال أن يكون صفر، بس لما كان Integral
+
+70
+00:07:15,990 --> 00:07:22,310
+domain، يبقى لا يمكن أن يساوي صفر، يبقى هدف لا
+
+71
+00:07:22,310 --> 00:07:27,550
+يساوي صفر لسببين، السبب الأول: ولا واحدة فيهم بـ
+
+72
+00:07:27,550 --> 00:07:38,460
+صفر، والسبب الثاني: الـ D is an integral domain
+
+73
+00:07:38,460 --> 00:07:43,240
+تمام؟
+
+74
+00:07:43,240 --> 00:07:47,580
+لأن في الـ integral domain ما فيش عندي zero divisors
+
+75
+00:07:47,580 --> 00:07:52,680
+تمام؟ لكن لو ما كانش integral domain، ممكن هذه
+
+76
+00:07:52,680 --> 00:07:58,580
+لا تساوي صفر، وهذه لا تساوي صفر، وحاصل ضربهما ما يساوي
+
+77
+00:07:58,580 --> 00:08:02,610
+صفر، يعني في احتمال يكون واحد فيهم Zero divisor
+
+78
+00:08:02,610 --> 00:08:08,690
+وبالتالي هذا الكلام ليس صحيحا، إذا هذا لا يكون
+
+79
+00:08:08,690 --> 00:08:13,810
+يساوي صفر لسببين، ولا واحد فيهم صفر، الاثنين دي
+
+80
+00:08:13,810 --> 00:08:21,630
+integral domain، مدام هيك، جداش الـ degree لهذه m زائد m
+
+81
+00:08:21,630 --> 00:08:30,980
+يبقى هنا، ساعة الـ degree للـ F of X في الـ G of X هي
+
+82
+00:08:30,980 --> 00:08:37,340
+عند استبعاد هذه بـ صفر، يبقى هذا بده يساوي الـ n
+
+83
+00:08:37,340 --> 00:08:47,240
+زائد الـ m، والـ degree لمن؟ للـ F زائد الـ degree
+
+84
+00:08:47,240 --> 00:08:53,420
+للـ G، كده إيش بده يساوي؟ الأولى هي الـ degree تبعها n
+
+85
+00:08:53,420 --> 00:09:00,370
+لأنه اشترطنا أن الـ a n لا تساوي صفر، والثانية m، لأن
+
+86
+00:09:00,370 --> 00:09:05,850
+اشترطنا الـ bm لا تساوي صفر، يبقى الـ degree تبعها
+
+87
+00:09:05,850 --> 00:09:11,450
+m، والـ degree تبعها n، من الاثنين هدول، يبقى الـ
+
+88
+00:09:11,450 --> 00:09:19,810
+degree للـ F of X في الـ G of X يساوي الـ degree للـ F
+
+89
+00:09:19,810 --> 00:09:27,770
+of X زائد الـ degree للـ G of X، هذا المطلوب الأول
+
+90
+00:09:27,770 --> 00:09:35,430
+مطلوب الثاني قال لي: هذه commutative ring، بدي أجيب
+
+91
+00:09:35,430 --> 00:09:38,890
+الـ polynomial في الأولى، والـ polynomial في الثانية
+
+92
+00:09:38,890 --> 00:09:44,290
+و الـ degree لحاصل الضرب يكون أقل من الـ degree
+
+93
+00:09:44,290 --> 00:09:49,230
+للأولى، للـ degree للثانية، المطلوب الأول، أجيب
+
+94
+00:09:49,230 --> 00:09:56,850
+commutative ring، حد فيكم أجابتها؟ Z6، ممتاز، زد ستة
+
+95
+00:09:56,850 --> 00:10:02,390
+ما هيش integral domain، لكنها commutative ring، لأن
+
+96
+00:10:02,390 --> 00:10:05,910
+اثنين في ثلاثة تساوي صفر، وبالتالي اثنين وثلاثة
+
+97
+00:10:05,910 --> 00:10:11,130
+zero divisor، يبقى هذه not integral domain، ولكنها
+
+98
+00:10:11,130 --> 00:10:20,250
+ring، يبقى هنا بعدين بقول زد ستة هذه is a
+
+99
+00:10:20,250 --> 00:10:22,210
+commutative
+
+100
+00:10:25,490 --> 00:10:33,250
+ring but not an
+
+101
+00:10:33,250 --> 00:10:42,310
+integral domain، لأنها ليست انتجرال دومان، طيب أدور
+
+102
+00:10:42,310 --> 00:10:47,870
+على two polynomials فيه، وأجيب degree الأولى، و
+
+103
+00:10:47,870 --> 00:10:52,270
+degree الثانية، ونضرب، ويطلع الـ degree لحاصل
+
+104
+00:10:52,270 --> 00:10:58,320
+الضرب أقل من مجموع الـ two degrees، يبقى فكري ممكن
+
+105
+00:10:58,320 --> 00:11:04,140
+two polynomials، ولا ممكن عشرات، مش يعني واحدة
+
+106
+00:11:04,140 --> 00:11:08,940
+والله شيء كثير جدا، ما بدك غير الأرقام زي ما بدك
+
+107
+00:11:08,940 --> 00:11:19,040
+بأحد الأرقام تكون في Z6، فمثلا لو أخذنا take مثلا
+
+108
+00:11:19,040 --> 00:11:29,460
+الـ F of X يساوي 2X أس 4 على سبيل المثال، والـ G
+
+109
+00:11:29,460 --> 00:11:33,420
+of X تساوي، شوفوا يا بني كيف بدنا نجيب الـ G of X،
+
+110
+00:11:33,420 --> 00:11:44,340
+هذه 2X أس 4، بدي آخذ هنا رقم في X، في X تربيع، في
+
+111
+00:11:44,340 --> 00:11:49,260
+X تكعيب، اللي بدك إياه، حيث حاصل ضربهما يطلع صفر
+
+112
+00:11:49,980 --> 00:11:55,840
+وبالتالي الـ degree بتنزل، طبيعي، يبقى لما قلت اثنين
+
+113
+00:11:55,840 --> 00:12:00,680
+اكس تربيع، هذه، اليوم، بدأ آخذها ثلاثة، لأن ثلاثة في
+
+114
+00:12:00,680 --> 00:12:05,760
+اثنين هي صفر، يبقى الـ degree نزلت ثلاثة، إيش؟ ثلاثة
+
+115
+00:12:05,760 --> 00:12:12,160
+مثلا اكس تربيع زائد خمسة، على سبيل المثال، هي عندك
+
+116
+00:12:12,160 --> 00:12:17,080
+اثنين وثلاثة وخمسة موجودة في Z6
+
+117
+00:12:20,980 --> 00:12:25,540
+سبعة تعني واحد، ثمانية تعني اثنين، يبقى لها هذه
+
+118
+00:12:25,540 --> 00:12:29,880
+الأرقام، عندي، أحط الرقم اللي بدك إياه من صفر لغاية
+
+119
+00:12:29,880 --> 00:12:38,940
+خمسة، كله موجود وين؟ في Z6، طيب then بدي
+
+120
+00:12:38,940 --> 00:12:48,060
+آخذ الـ degree لمن؟ للـ F زائد الـ degree للـ G، كده إيش؟ الـ
+
+121
+00:12:48,060 --> 00:12:58,140
+degree للأولى والثانية 3، يبقى 4 زائد 2 ويساوي كده؟
+
+122
+00:12:58,140 --> 00:13:04,620
+ويساوي 6، طب بدي أجي أضربهم في بعض، بدي أجي آخذ الـ F of
+
+123
+00:13:04,620 --> 00:13:14,560
+X في الـ G of X، يبقى 2 X أس 4 في 3 X تربيع زائد 5
+
+124
+00:13:14,560 --> 00:13:24,310
+ويساوي 3 في 2، ستة تعني صفر، صفر في X أس ستة، يبقى
+
+125
+00:13:24,310 --> 00:13:31,630
+صفر في X أس ستة، هنا، زائد اثنين في خمسة، في عشرة
+
+126
+00:13:31,630 --> 00:13:41,910
+عشرة في زد ستة تعني أربعة، يبقى أربعة X أس أربعة، مرة
+
+127
+00:13:41,910 --> 00:13:48,520
+ثانية، اثنين في ثلاثة، بالزد في ستة، X أس ستة، الستة
+
+128
+00:13:48,520 --> 00:13:56,580
+الأولى بـ 0، يبقى X أس 6، الثانية 2 × 5 بـ 10، X أس 4
+
+129
+00:13:56,580 --> 00:14:04,720
+العشرة هذه، ثانياً، 4 في Z6، يبقى 4 في Z6 النتيجة تساوي
+
+130
+00:14:04,720 --> 00:14:14,460
+4 X أس 4، هذا بدي يعطينا أن الـ degree للـ F of X في
+
+131
+00:14:14,460 --> 00:14:23,830
+الـ G of X بيساوي كده إيش؟ أربعة، والأربعة أقل من الستة
+
+132
+00:14:23,830 --> 00:14:29,270
+نفرض هي جيبنا له two polynomials، الـ degree للأولى
+
+133
+00:14:29,270 --> 00:14:33,970
+والـ degree للثانية ستة، وحاصل ضربهما ما طلع الـ degree
+
+134
+00:14:33,970 --> 00:14:38,690
+يساوي أربعة، وبالتالي الأربعة أقل من الستة، يبقى الـ
+
+135
+00:14:38,690 --> 00:14:43,750
+degree اللي حصل ضرب أقل من الـ degree للجمع، لما
+
+136
+00:14:43,750 --> 00:14:50,850
+شيلنا من المثال كلمة integral domain، طبعا، يبقى يكون
+
+137
+00:14:50,850 --> 00:14:54,790
+شغلنا دقيقة، احنا بنشتغل في ring، في integral domain
+
+138
+00:14:54,790 --> 00:14:59,210
+في field، إلى آخره، يبقى هذا المطلوب الثاني من
+
+139
+00:14:59,210 --> 00:15:06,270
+السؤال رقم سبعة عشر، رقم ثمانية عشر بيقول: اثبت لي أن الـ
+
+140
+00:15:06,270 --> 00:15:11,150
+principle ideal generated by X هو maximum ideal في
+
+141
+00:15:11,150 --> 00:15:15,370
+الـ Q of X، سؤال ثمانية عشر
+
+142
+00:15:17,020 --> 00:15:23,100
+that أن الـ principle ideal generated by X is
+
+143
+00:15:23,100 --> 00:15:30,440
+maximal in الـ Q of X
+
+144
+00:15:30,440 --> 00:15:35,960
+و X solution
+
+145
+00:15:35,960 --> 00:15:42,860
+طيب
+
+146
+00:15:42,860 --> 00:15:46,860
+نروي على موضوعنا، احنا بدنا نثبت أن الـ principle
+
+147
+00:15:46,860 --> 00:15:53,540
+ideal generated by X هو maximum ideal في الـ Q of X
+
+148
+00:15:53,540 --> 00:15:58,880
+نقول: كويس، لو رجعنا يا بنات للـ isomorphism theorem
+
+149
+00:15:58,880 --> 00:16:05,320
+إذا قدرنا نثبت إن الـ Q of X modulo الـ principle
+
+150
+00:16:05,320 --> 00:16:13,140
+ideal generated by X هذا عبارة عن field، يبقى بسيط
+
+151
+00:16:13,420 --> 00:16:16,660
+الـ principle ideal generated by X is maximal
+
+152
+00:16:16,660 --> 00:16:22,380
+وبيكون خلصنا من هذا الشغل هذا، مظبوط؟ يبقى الفكرة إني
+
+153
+00:16:22,380 --> 00:16:26,480
+أثبت أن الـ Q of X modulo principle ideal
+
+154
+00:16:26,480 --> 00:16:31,140
+generated by X is a field، وعطاني ما عجبتنيش الفكرة
+
+155
+00:16:31,140 --> 00:16:36,260
+التبعتها، قالت لأ، أنا بدي أدور على ideal ثاني ويكون
+
+156
+00:16:36,260 --> 00:16:39,880
+subset منه وهذا بيساوي هذه، أنا بدي أثبت أنه
+
+157
+00:16:39,880 --> 00:16:44,650
+بيساوي الـ ring، هي طرق ثانية غيرها، إذا عارفين غيرها
+
+158
+00:16:44,650 --> 00:16:48,370
+دلوني عليهم، فإما الطريق هذه أو الطريق هذه، لكي
+
+159
+00:16:48,370 --> 00:16:54,810
+أثبت الـ maximum لهذا الـ ideal، نقول بسيطة، طيب بدنا
+
+160
+00:16:54,810 --> 00:17:00,190
+نشتغل جهود جامد شوية، فدققوا معنا، بروح أعرف
+
+161
+00:17:00,190 --> 00:17:09,350
+function من الـ Q of X إلى الـ Q، طب ليش الـ Q؟ يعني ما
+
+162
+00:17:09,350 --> 00:17:15,670
+هي السؤال، الحين بنجاوبه قبل، هقول: define a
+
+163
+00:17:15,670 --> 00:17:22,730
+function، والله mapping اللي بدك إياه، فاي من الـ q of
+
+164
+00:17:22,730 --> 00:17:31,070
+x إلى الـ q، set of rational numbers، باي اللي هو
+
+165
+00:17:31,070 --> 00:17:41,500
+الـ فاي of f of x بدي يساوي الـ a0، where حيث الـ F
+
+166
+00:17:41,500 --> 00:17:48,480
+of X هي a n x to the power n، a n-1 x to
+
+167
+00:17:48,480 --> 00:17:53,880
+the power n-1 زائد a1 x زائد ال a0
+
+168
+00:17:53,880 --> 00:17:59,720
+يبقى عرفنا مين هي الـ a0، عرفنا مين هي
+
+169
+00:17:59,720 --> 00:18:06,800
+الجزء الثابت من الـ polynomial، يبقى phi of a0
+
+170
+00:18:06,800 --> 00:
+
+223
+00:24:17,080 --> 00:24:21,920
+الـQ؟ يبقى الـQ  variable و لا constant
+
+224
+00:24:24,390 --> 00:24:29,210
+يبقى then لكيو
+
+225
+00:24:29,210 --> 00:24:40,790
+as لكيو as constant يعني إذا ممكن أعتبره هو الconstant
+
+226
+00:24:40,790 --> 00:24:51,210
+تبع أي polynomial صح ولا لأ، يبقى then ال
+
+227
+00:24:51,210 --> 00:24:59,450
+f of x بده تساوي اللي هو مثلا أو ليش و ليش يقول
+
+228
+00:24:59,450 --> 00:25:11,450
+خلاص constant هذا يساوي constant، then لكيو is a
+
+229
+00:25:11,450 --> 00:25:21,110
+constant of a polynomial of polynomial f of x for
+
+230
+00:25:21,110 --> 00:25:22,570
+some
+
+231
+00:25:24,490 --> 00:25:36,710
+f of x اللي موجودة في الـ Q[x] that is ال
+
+232
+00:25:36,710 --> 00:25:45,750
+Q[x] هذا بدي يساوي φ(f of x) تبقى من هنا صارت onto
+
+233
+00:25:45,750 --> 00:25:52,930
+الآن بقوله by the first
+
+234
+00:25:55,660 --> 00:26:05,700
+isomorphism theorem we have أن الـ Q[x] module
+
+235
+00:26:05,700 --> 00:26:17,060
+الكرنل للـ φ isomorphic لمن؟ للـ φ(Q[x])  مش هيك
+
+236
+00:26:17,060 --> 00:26:21,800
+نص الـ first isomorphism theorem، طيب الـ φ أثبتناها
+
+237
+00:26:21,800 --> 00:26:28,940
+أنها onto، يبقى هذه كلها مين هين؟ φ(cubics)
+
+238
+00:26:28,940 --> 00:26:35,500
+عبارة عن مين؟ عبارة عن الـQ. يبقى هذه اللي هي الـQ
+
+239
+00:26:35,500 --> 00:26:42,660
+itself. ضلت علينا واحدة بس. إذا قدرنا نثبت أن
+
+240
+00:26:42,660 --> 00:26:46,900
+الكرنل للـφ هو الـ principal ideal generated by X،
+
+241
+00:26:46,900 --> 00:26:54,230
+بيقول خلصنا. خلصنا خلاص. يبقى الآن one to show
+
+242
+00:26:54,230 --> 00:27:00,850
+to show أن الـ principal ideal generated by X هو
+
+243
+00:27:00,850 --> 00:27:09,210
+الكرنل للفعل، سمّي العلاقة هذه رقم واحد، إذا
+
+244
+00:27:09,210 --> 00:27:16,530
+بدأ أقول خذ الـ f of x موجودة في الكرنل للفعل
+
+245
+00:27:16,530 --> 00:27:20,230
+تمام؟ then
+
+246
+00:27:22,730 --> 00:27:30,630
+الـ φ(f of x) بده يساوي صفر لأنها موجودة وين؟
+
+247
+00:27:30,630 --> 00:27:36,310
+في الكرنل، طب الـ φ(f of x) يبقى هذا سميناه a
+
+248
+00:27:36,310 --> 00:27:42,410
+nought، يبقى هذا بده يعطيك أن الـ a nought بده يساوي
+
+249
+00:27:42,410 --> 00:27:48,350
+صفر تمام؟ يبقى هذا إذا كانت a nought تساوي صفر
+
+250
+00:27:48,720 --> 00:27:54,080
+يبقى شكل الـ f of x اللي موجودة في الكرنل بدي
+
+251
+00:27:54,080 --> 00:28:01,160
+يكون على الشكل التالي، الـ f of x بدي يساوي a n x n +
+
+252
+00:28:01,160 --> 00:28:07,460
+a n-1 x n-1 + ... + a 1 x
+
+253
+00:28:07,460 --> 00:28:14,320
++ a 1 x فقط، لغير عندي a nought لأنه a
+
+254
+00:28:14,320 --> 00:28:20,040
+nought بصفر، طيب شو رأيك؟ بدك تكتب هذه بطريقة ثانية
+
+255
+00:28:20,040 --> 00:28:28,880
+شو الطريقة الثانية؟ a n x n-1 + a n-1 x n-2 + ... + a 1 x
+
+256
+00:28:28,880 --> 00:28:37,720
+بإمكاننا استخدام قانون التوزيع، طيب هذا ال
+
+257
+00:28:37,720 --> 00:28:45,250
+element وين موجود؟ في الـ principal ideal generated by
+
+258
+00:28:45,250 --> 00:28:49,950
+X لأنه حسب تعريف الـ principal ideal هو الـ X مضروب
+
+259
+00:28:49,950 --> 00:28:54,510
+في polynomial، هي الـ polynomial الموجودة، هي الـ X
+
+260
+00:28:54,510 --> 00:28:58,510
+إذا هذا موجود في الـ principal ideal generated by X
+
+261
+00:28:58,510 --> 00:29:04,290
+إذا هذا موجود في الـ principal ideal generated by X
+
+262
+00:29:04,290 --> 00:29:11,410
+يبقى أصبح أن الكرنل للـ φ هو subset من الـ
+
+263
+00:29:11,410 --> 00:29:15,340
+principal ideal generated by X، إذا نمشي للعملية
+
+264
+00:29:15,340 --> 00:29:21,600
+العكسية، يبقى بالطبع أقول أن افترض أن الـ f of x
+
+265
+00:29:21,600 --> 00:29:26,940
+موجودة في الـ principal ideal generated by X، then
+
+266
+00:29:26,940 --> 00:29:36,400
+إيش شكل الـ f of x؟ بده يكون الـ X نفسها مضروبة في
+
+267
+00:29:36,400 --> 00:29:45,680
+polynomial، ولتكن g of x، صحيح؟ يعني هذه بدها تكون X
+
+268
+00:29:45,680 --> 00:29:54,860
+في مين؟ في الـ b m x m + b m-1 x m-1
+
+269
+00:29:54,860 --> 00:30:05,560
++ ... + b 1 x + b 0، طيب  ضرب هذه
+
+270
+00:30:05,560 --> 00:30:16,380
+بيصير b m x m+1 + b m-1 x m + ... + b 1 x^2 + b 0 x، يبقى
+
+271
+00:30:16,380 --> 00:30:26,040
+الحد الثابت  كم؟ بصفر، يبقى هذه موجودة في
+
+272
+00:30:26,040 --> 00:30:31,040
+الكرنل، يبقى هذه موجودة في الكرنل للـ φ
+
+273
+00:30:37,180 --> 00:30:43,850
+يبقى الـ f of x اللي أخدتها هنا، هي هذه، امشي امشي
+
+274
+00:30:43,850 --> 00:30:48,750
+وجدتها موجودة وين؟ في الكرنل، يبقى بقدر أقوله
+
+275
+00:30:48,750 --> 00:30:53,590
+الـ principal ideal generated by X subset من الـ
+
+276
+00:30:53,590 --> 00:31:00,490
+كرنل للـ φ، يبقى ذات، وهكذا الكرنل للـ φ
+
+277
+00:31:00,490 --> 00:31:06,510
+بالضبط هو الـ principal ideal generated by X، ناخذ
+
+278
+00:31:06,510 --> 00:31:12,030
+هذه المعلومة و نعود في العلاقة رقم واحد
+
+279
+00:31:12,030 --> 00:31:18,810
+يبقى باجي بقوله هنا Substitute
+
+280
+00:31:18,810 --> 00:31:25,930
+(repeated word removed)
+
+281
+00:31:25,930 --> 00:31:29,010
+(repeated word removed)
+
+282
+00:31:29,010 --> 00:31:29,490
+(repeated word removed)
+
+283
+00:31:29,490 --> 00:31:38,210
+(repeated word removed)
+
+284
+00:31:38,210 --> 00:31:48,380
+هذا isomorphic لمين يا بنات؟ لكيو، لكيو فيه؟ يبقى
+
+285
+00:31:48,380 --> 00:31:52,360
+part لكيو
+
+286
+00:31:52,360 --> 00:32:03,340
+is a field، مدام field هذا بدي يعطيكي أن لكيو of x
+
+287
+00:32:03,340 --> 00:32:11,350
+modulo X is a field، طب مداه فيه يبقى ال
+
+288
+00:32:11,350 --> 00:32:18,310
+ideal هذا ما له؟ maximum، يبقى هذا بدي يعطيكي ال
+
+289
+00:32:18,310 --> 00:32:27,570
+maximum ideal في اللي هو الـ ring اللي عندك هذا فيكم
+
+290
+00:32:27,570 --> 00:32:35,330
+أي تساؤل؟ حلت المشكلة؟  خلاص؟ يبقى أنا كان بدي
+
+291
+00:32:35,330 --> 00:32:39,330
+الفكرة الأساسية، يقول الفكرة كلمة في الشرح، إما
+
+292
+00:32:39,330 --> 00:32:43,510
+استخدام الـ first isomorphism theorem يا إما نستخدم
+
+293
+00:32:43,510 --> 00:32:48,030
+التعريف تبع الـ maximal ideal، بأي طريقة، بهذه أو
+
+294
+00:32:48,030 --> 00:32:53,490
+بهذه، نوصل، ما عندنا مشكلة، هذا كان سؤال 17 من
+
+295
+00:32:53,490 --> 00:32:57,850
+التدريبات، قبل ما أنا، لأن سؤال 24
+
+296
+00:32:57,850 --> 00:33:01,850
+qualitative theory of Z[x] is not a principal
+
+297
+00:33:01,850 --> 00:33:14,700
+ideal domain، سؤال 24 بيقول that Z[x] is
+
+298
+00:33:14,700 --> 00:33:28,840
+not a principal ideal domain، وإيش
+
+299
+00:33:28,840 --> 00:33:34,040
+معنى principal ideal domain؟ لكل ideal يكون
+
+300
+00:33:34,040 --> 00:33:39,480
+principal، صح ولا لأ؟ يعني احنا لو جيبنا ideal واحد
+
+301
+00:33:39,480 --> 00:33:44,480
+وأثبتنا أنه هذا not a principle، خلاص بتصير مش
+
+302
+00:33:44,480 --> 00:33:48,700
+principal ID domain، مش هي الفكرة؟ يعني جيبنا
+
+303
+00:33:48,700 --> 00:33:53,880
+counter example ضد أنها تكون principal ID domain
+
+304
+00:33:53,880 --> 00:33:59,880
+بيكون حلّنا الإشكالية، أعتقد، ولا واحدة حلت السؤال؟
+
+305
+00:33:59,880 --> 00:34:02,840
+طيب، هي الفكرة بس هال... بس هال... بس هال...
+
+306
+00:34:02,840 --> 00:34:05,380
+(repeated phrase removed)
+
+307
+00:34:05,380 --> 00:34:05,900
+(repeated phrase removed)
+
+308
+00:34:05,900 --> 00:34:09,640
+(repeated phrase removed)
+
+309
+00:34:09,640 --> 00:34:14,820
+الآن بدنا نبدأ بشيء أنتم
+
+310
+00:34:09,640 --> 00:34:14,820
+أخذتوه قبل ذلك، ideal أخذتوه، عارفينه، واشتغلنا
+
+311
+00:34:14,820 --> 00:34:20,720
+عليه قبل ذلك في أمثلة سابقة، الآن لو جأت بنات لمن؟
+
+312
+00:34:20,720 --> 00:34:29,200
+ل ideal اللي هو الـ (x, 2) اللي كل عناصر x في
+
+313
+00:34:29,200 --> 00:34:36,220
+f of x زائد 2 في g of x بحيث أن f of x و g
+
+314
+00:34:36,220 --> 00:34:46,620
+of x موجود في Z[x]، موجود في Z[x]، شفناها قبل
+
+315
+00:34:46,620 --> 00:34:50,280
+ذلك، وقبل ذلك، ولا لأ؟ شفناها وكتبناها و
+
+316
+00:34:50,280 --> 00:34:55,800
+اشتغلناها وحلّيناها بعدد مسائل، طيب إذا قدرت أُثبت أن
+
+317
+00:34:55,800 --> 00:35:01,280
+هذا ليس principal، خلاص، بصير Z[x] is not a
+
+318
+00:35:01,280 --> 00:35:13,230
+principal، صحيح؟ طيب if we show that أن ال... ال...
+
+319
+00:35:13,230 --> 00:35:21,990
+الـ ideal (x, 2) is not principal then
+
+320
+00:35:21,990 --> 00:35:30,050
+Z[x] is not
+
+321
+00:35:33,300 --> 00:35:39,800
+a principal is not a principal ideal domain، خلاص
+
+322
+00:35:39,800 --> 00:35:47,740
+بقي
+
+323
+00:35:47,740 --> 00:35:53,480
+مرة ثانية، أنا أخذت ideal موجود في Z[x] وبدي
+
+324
+00:35:53,480 --> 00:35:58,900
+أحاول أثبت هذا أنه is not a principal، يعني إيش؟ يعني
+
+325
+00:35:58,900 --> 00:36:04,380
+بدي أثبت أن هذا الـ ideal لا يمكن أن يولد بعنصر واحد
+
+326
+00:36:04,380 --> 00:36:10,140
+لا يمكن أن يولد بـ polynomial لأن العنصر هنا polynomial
+
+327
+00:36:10,140 --> 00:36:14,580
+بمعاملات أعداد صحيحة اللي هي جاية من وين؟ جاية من
+
+328
+00:36:14,580 --> 00:36:21,840
+هنا، يبقى that is
+
+329
+00:36:21,840 --> 00:36:24,900
+to show
+
+330
+00:36:24,900 --> 00:36:45,800
+that  الـ (x, 2) is not generated but by
+
+331
+00:36:45,800 --> 00:36:54,620
+a single polynomial، then
+
+332
+00:36:54,620 --> 00:36:56,780
+we
+
+333
+00:36:58,660 --> 00:37:09,280
+get the result، يعني
+
+334
+00:37:09,280 --> 00:37:14,880
+إذا قدرنا نثبت أن الـ ideal اللي عندنا لا يمكن أن
+
+335
+00:37:14,880 --> 00:37:20,160
+يولد بـ polynomial واحدة، بيكون حصلنا مين؟ حصلنا على
+
+336
+00:37:20,160 --> 00:37:25,620
+النتيجة، بنثبت بالـ contradiction، assume not، مش
+
+337
+00:37:25,620 --> 00:37:27,540
+صحيح، يبقى
+
+338
+00:37:32,480 --> 00:37:40,720
+not، ليش يعني assume not؟ يعني that is أن الـ
+
+339
+00:37:40,720 --> 00:37:46,340
+principal ideal generated by (x, 2) بدي يولد بـ كثير
+
+340
+00:37:46,340 --> 00:37:56,240
+حدود، ولتكن p of x، حيث الـ p of x هي
+
+341
+00:37:56,240 --> 00:38:01,000
+polynomial موجودة وين؟ في Z[x]
+
+342
+00:38:06,920 --> 00:38:11,860
+إذا أنا بأحاول أثبت بالتناقض، بإن أنا بدي أثبت أن
+
+343
+00:38:11,860 --> 00:38:17,200
+هذا لا يمكن أن يولد بعنصر واحد، وافترض أنه ولد
+
+344
+00:38:17,200 --> 00:38:22,220
+بعنصر واحد اللي هو p of x، بدي أشوف هذا بدي يقودني
+
+345
+00:38:22,220 --> 00:38:26,620
+إلى شيء صحيح، والله إلى شيء خطأ، إذا الله قادني إلى
+
+346
+00:38:26,620 --> 00:38:32,120
+شيء خطأ، يبقى الفرض اللي فرضته غلط، وعكسه هو إيه؟ هو
+
+347
+00:38:32,120 --> 00:38:37,410
+الصحيح، يعني لا يمكن لهذا الـ ideal (x, 2) أن يولد
+
+348
+00:38:37,410 --> 00:38:44,370
+بعنصر واحد، يبقى ذات، فرضنا أنه يولد بالـ p of x
+
+349
+00:38:44,370 --> 00:38:51,870
+السؤال هو، هذول الإثنين يا بنات موجودين في الـ ideal (x, 2)؟
+
+350
+00:38:51,870 --> 00:38:58,830
+موجود، صحيح؟ إيه؟،  x بصفر، و g of x
+
+351
+00:38:58,830 --> 00:39:02,290
+بواحد، أو g of 0 بواحد مثلا، يبقى الإثنين
+
+352
+00:39:02,290 --> 00:39:10,670
+موجود، طيب مدام موجودين then الإثنين موجودين في p of x
+
+353
+00:39:10,670 --> 00:39:20,030
+أو موجودين في الـ principal ideal generated by
+
+354
+00:39:20,030 --> 00:39:28,750
+p of x، مظبوط؟ يعني يعني شو شكله الإثنين هذا بدي
+
+355
+00:39:28,750 --> 00:39:35,460
+يعطينا أن الإثنين بدي يساوي p of x  في
+
+356
+00:39:35,460 --> 00:39:41,740
+polynomial ثانية، p of x مش شوف تعريف الـ principal
+
+357
+00:39:41,740 --> 00:39:48,320
+الـ principal، الـ p of x في polynomial ثانية بده
+
+358
+00:39:48,320 --> 00:39:53,480
+يعطينا الـ element اللي هو اثنين، الآن ما هو تفسير و
+
+359
+00:39:53,480 --> 00:39:59,140
+كنّا لهذه المعادلة الأخيرة، شو علاقة الـ p of x
+
+360
+00:39:59,140 --> 00:40:06,850
+بالإثنين؟  تقسم، تقسم، تمام كلامي كويس، يبقى هدف اللي
+
+361
+00:40:06,850 --> 00:40:17,490
+بده يعطينا أن الـ p of x يقبل القسمة على اثنين، طب ما هي قواسم
+
+362
+00:40:17,490 --> 00:40:23,150
+اثنين؟ واحد وسالب واحد واثنين وسالب اثنين، واحد و
+
+363
+00:40:23,150 --> 00:40:28,030
+سالب واحد مستبعد لأن هذا بيجيبلي عنصر واحد فقط
+
+364
+00:40:28,030 --> 00:40:35,410
+واحد، مش مظبوط، طيب الآن يبقى ما فضلش عندي يا إما
+
+365
+00:40:35,410 --> 00:40:43,350
+اثنين يا إما مين؟ سالب اثنين، يبقى هذا معناته أن الـ
+
+366
+00:40:43,350 --> 00:40:50,390
+p of x يا إما بده يساوي سالب اثنين يا إما الـ p of x
+
+367
+00:40:50,390 --> 00:40:57,030
+بده يساوي كذا؟ بده يساوي اثنين، يجي على كل الأحوال الـ
+
+368
+00:40:57,030 --> 00:41:04,820
+p of x بده يساوي constant، مظبوط؟ يبقى هذا معناته أن
+
+369
+00:41:04,820 --> 00:41:12,920
+الـ p of x بده يساوي k، والـ k يا إما زائد أو ناقص
+
+370
+00:41:12,920 --> 00:41:21,300
+اثنين طبعاً؟ طيب كويس، نجي لصحة هذا الكلام اللي احنا
+
+371
+00:41:21,300 --> 00:41:28,580
+قلنا، يبقى إيش صار عندنا؟ صار عندنا الـ p of x بده
+
+372
+00:41:28,580 --> 00:41:35,580
+يساوي k، يبقى هنا الـ principal ideal (x, 2) هو
+
+373
+00:41:35,580 --> 00:41:40,980
+هو الـ principal ideal generated by x
+
+374
+00:41:40,980 --> 00:41:47,280
+وهو الـ principal ideal generated by k، والـ k هذه
+
+375
+00:41:47,280 --> 00:41:54,680
+زائد أو ناقص اثنين، كمان سؤال، إيش من هنا؟ اثنين
+
+376
+00:41:54,680 --> 00:42:04,490
+موجودة هنا، السؤال هو الـ x موجودة هنا ولا لأ؟  لما؟
+
+377
+00:42:04,490 --> 00:42:15,590
+الـ x بدها تساوي آه، إيش بدها تساوي؟ كذا؟
+
+378
+00:42:15,590 --> 00:42:22,070
+مش عارفة، مش شايفة كل شيء قدامي هنا ولا لأ؟  بقالي بدي
+
+379
+00:42:22,070 --> 00:42:29,090
+أجرب هالأكتر، الـ x موجودة، معناته الـ x موجودة في
+
+380
+00:42:29,090 --> 00:42:34,410
+الـ principal ideal generated by k، مظبوط؟ يعني
+
+381
+00:42:34,410 --> 00:42:44,610
+معناته أن الـ x بده يساوي h of x في k، وكتيش
+
+382
+00:42:44,610 --> 00:42:50,610
+بيكون الكلام هذا صحيح لو كان الـ h of x هي
+
+383
+00:42:50,610 --> 00:42:58,090
+polynomial من الدرجة الأولى، في غير هيك؟ لأ، لأن x
+
+384
+00:42:58,090 --> 00:43:02,790
+polynomial من الدرجة الأولى، يبقى هذا كيفش هذا
+
+385
+00:43:02,790 --> 00:43:08,110
+الكلام صحيح فقط إذا كانت h of x polynomial من
+
+386
+00:43:08,110 --> 00:43:17,890
+الدرجة الأولى، يبقى this is a proof when
+
+387
+00:43:17,890 --> 00:43:21,590
+الـ
+
+388
+00:43:21,590 --> 00:43:29,590
+h of x يساوي ax أو ax + b، ناخذها الأبسط x
+
+389
+00:43:29,590 --> 00:43:38,350
+ونهمل الـ b، طيب هذا بدي يعطينا أن الـ x بدي يساوي
+
+390
+00:43:38,350 --> 00:43:51,190
+ax في k، أو الـ x بدي يساوي ak في x، طب هذول الـ a و الـ
+
+391
+00:43:51,190 --> 00:43:57,770
+k أرقام، والـ x موجودة وين؟ في Z، نشتغل في Z احنا، و
+
+392
+00:43:57,770 --> 00:44:05,330
+Z[x] تمام؟ يبقى هذا معناته أن الـ ak بقداش يا بنات؟
+
+393
+00:44:05,330 --> 00:44:11,270
+بقداش؟ واحد، بواحد، تمام، لكن لو كان ما فيه
+
+394
+00:44:11,270 --> 00:44:16,190
+الواحد، الـ Z بصير كلامنا مش صحيح، لكن الواحد موجود
+
+395
+00:44:16,190 --> 00:44:24,550
+في الـ Z، إذا الـ ak يبقى، السؤال هو
+
+445
+00:50:51,030 --> 00:50:57,230
+معناته؟ معناته أنه zero يساوي واحد، ترفيع ولا واحد
+
+446
+00:50:57,230 --> 00:51:02,370
+تكعيب ولا واحد،  قص مية ولا واحد، قص ألف، كله يقلب واحد
+
+447
+00:51:02,370 --> 00:51:10,330
+يبقى هذا معناه a<sub>n</sub> + a<sub>n-1</sub> + a
+
+448
+00:51:10,330 --> 00:51:16,200
+<sub>1</sub> + a<sub>0</sub> أظن هو المفترض خلاص من اتجاه
+
+449
+00:51:16,200 --> 00:51:23,060
+الأول، من جهة، اتجاه الثانية on the other hand
+
+450
+00:51:23,060 --> 00:51:26,640
+assume
+
+451
+00:51:26,640 --> 00:51:38,740
+نفترض أن ال a<sub>n</sub> + ال a<sub>n-1</sub> +
+
+452
+00:51:38,740 --> 00:51:48,880
+ال a<sub>1</sub> + ال a<sub>0</sub> يساوي صفر، إيش بدي أثبت؟ X ناقص
+
+453
+00:51:48,880 --> 00:51:57,620
+واحد عبارة عن factor للـ polynomial f(x) أو
+
+454
+00:51:57,620 --> 00:52:03,940
+لو قدرت أثبت أن الواحد هو عبارة عن zero لهذه الـ
+
+455
+00:52:03,940 --> 00:52:09,500
+polynomial، بكرة اللي إثنين عندكم، بدي يكون الـ X ناقص
+
+456
+00:52:09,500 --> 00:52:16,060
+واحد هو عبارة عن factor، طيب
+
+457
+00:52:16,060 --> 00:52:21,540
+بدي أحاول المعادلة هذه أكتبها بصيغة أخرى وأشوف
+
+458
+00:52:21,540 --> 00:52:30,820
+أجد أن الـ A<sub>n</sub> في الواحد أس N، أجد أيه أيه أيه A<sub>n</sub>
+
+459
+00:52:30,820 --> 00:52:40,000
+أيه A<sub>n</sub> ما يساوي شيء، تمام. زائد a<sub>n-1</sub> في الواحد أس n-1
+
+460
+00:52:40,000 --> 00:52:48,460
+زائد زائد a<sub>1</sub> في الواحد زائد a<sub>0</sub> ليست ب صفر، طيب إيش
+
+461
+00:52:48,460 --> 00:52:56,600
+تفسيرك لهذه؟ أن الواحد عبارة عن zero، يبقى هنا this
+
+462
+00:52:56,600 --> 00:53:04,200
+means that أن الواحد is
+
+463
+00:53:06,600 --> 00:53:15,520
+a<sub>0</sub> of the polynomial F
+
+464
+00:53:15,520 --> 00:53:22,120
+of X اللي عندنا، هذا الـ F(x) الأساسي، يعني أين
+
+465
+00:53:22,120 --> 00:53:28,280
+راح تقيم؟ يبقى هذا معناته أن واحد حل لمين بهذه
+
+466
+00:53:28,280 --> 00:53:32,460
+المعادلة، مدام حل يبقى
+
+467
+00:53:36,690 --> 00:53:42,330
+إثنين اللي خدناها المرة اللي فاتت، الـ X ناقص الواحد
+
+468
+00:53:42,330 --> 00:53:56,610
+is a factor، is a factor of the polynomial F
+
+469
+00:53:56,610 --> 00:53:57,470
+of X
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..9f8acb69e761a586ef4b528a58d2bb43d0b178c7
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_raw.json
@@ -0,0 +1 @@
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degree لل F مضافا إليها ال degree لل G هذا المطلوب الأول المطلوب الثاني بيقول هذي commutative ring بحيث هذي تكون مش صحية كيف يعني مش صحية يعني يكون ال degree لحاصل الضرب أقل", "tokens": [28814, 1863, 2423, 4314, 5296, 27842, 22807, 24976, 479, 295, 1783, 20666, 460, 295, 1783, 6055, 3794, 995, 45865, 2423, 4314, 24976, 479, 3714, 11242, 31845, 995, 11933, 20292, 11296, 2423, 4314, 24976, 460, 23758, 9673, 9566, 1211, 37746, 16247, 12610, 9673, 9566, 1211, 37746, 6024, 104, 7649, 1829, 4724, 1829, 39648, 8032, 8848, 1829, 800, 325, 1166, 4875, 4724, 5016, 1829, 12984, 8032, 8848, 1829, 6055, 30544, 37893, 20328, 5016, 10632, 9122, 33911, 37495, 22653, 37893, 20328, 5016, 10632, 37495, 22653, 7251, 30544, 2423, 4314, 5296, 5016, 33546, 1211, 6024, 114, 25513, 5551, 4587, 1211], "avg_logprob": -0.22793169611508085, "compression_ratio": 1.8115183246073299, "no_speech_prob": 0.0, "words": [{"start": 217.77, "end": 218.25, "word": "إن", "probability": 0.529937744140625}, {"start": 218.25, 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ring ليس بالضرورة أن تكون integral domain طيب خلّي المطلوب التاني بعد ما نخلص المطلوب الأول يبدأ أنا بدي أخد ال two polynomials موجودة في D of X", "tokens": [27842, 2423, 4314, 5296, 27842, 22807, 24976, 7435, 10943, 27884, 4724, 3794, 37893, 8978, 2423, 11573, 9274, 2423, 11573, 9274, 11778, 3224, 28242, 10943, 20328, 5016, 1829, 5016, 11778, 47302, 15042, 5551, 3555, 28259, 12174, 1211, 2655, 5296, 10721, 8978, 800, 325, 1166, 4875, 32239, 3794, 20666, 11242, 2288, 13063, 3660, 14739, 6055, 30544, 11573, 9274, 23032, 1829, 3555, 16490, 1211, 11703, 1829, 9673, 9566, 1211, 37746, 16712, 7649, 1829, 39182, 19446, 8717, 9778, 1211, 9381, 9673, 9566, 1211, 37746, 16247, 12610, 7251, 44510, 10721, 41850, 4724, 16254, 5551, 9778, 3215, 2423, 732, 22560, 12356, 3714, 29245, 23328, 3660, 8978, 413, 295, 1783], "avg_logprob": -0.25796273866525066, "compression_ratio": 1.6122448979591837, "no_speech_prob": 0.0, "words": [{"start": 246.95, "end": 247.35, "word": "من", "probability": 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1111.43, "end": 1111.93, "word": " لكيو", "probability": 0.80877685546875}, {"start": 1111.93, "end": 1112.97, "word": " فيلد", "probability": 0.7799479166666666}], "temperature": 1.0}, {"id": 39, "seek": 114142, "start": 1113.8, "end": 1141.42, "text": "يبقى بصير الرنج عندنا فيه اللي يبقى ال absolute value يبقى ال principle ideal generated by X is maximal. ويكون خلصنا هذه الشغلات. طب تستعجلش شوية شوية لو سمحت. تعالى نمشي شوية شوية. بدأ نثبت ان هذه في الأول هي homomorphism. فهذه بقوله الـ Phi is a homomorphism. تمام؟", "tokens": [1829, 3555, 4587, 7578, 4724, 9381, 13546, 34892, 1863, 7435, 43242, 8315, 8978, 3224, 13672, 1829, 7251, 3555, 4587, 7578, 2423, 8236, 2158, 7251, 3555, 4587, 7578, 2423, 8665, 7157, 10833, 538, 1783, 307, 49336, 13, 4032, 1829, 30544, 16490, 1211, 9381, 8315, 29538, 25124, 17082, 1211, 9307, 13, 23032, 3555, 6055, 14851, 3615, 7435, 1211, 8592, 13412, 2407, 10632, 13412, 2407, 10632, 45164, 8608, 2304, 33753, 13, 37279, 6027, 7578, 8717, 2304, 8592, 1829, 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Then بدي أخد Phi of ال F of X", "tokens": [11622, 16373, 3215, 4724, 1829, 4032, 1863, 1783, 30767, 16373, 3215, 4724, 1829, 8717, 45367, 37037, 15730, 3714, 8315, 35457, 12399, 4724, 16254, 5551, 39648, 2423, 316, 426, 20193, 7251, 3794, 995, 45865, 17182, 4032, 2423, 363, 376, 20193, 7251, 3794, 995, 45865, 17182, 12399, 16070, 9307, 1863, 9957, 8032, 3215, 12610, 3714, 29245, 23328, 9307, 8978, 2423, 1249, 295, 1783, 13, 1396, 4724, 16254, 5551, 9778, 3215, 41435, 295, 2423, 479, 295, 1783], "avg_logprob": -0.44374998728434245, "compression_ratio": 1.4968944099378882, "no_speech_prob": 0.0, "words": [{"start": 1171.09, "end": 1171.87, "word": "زائد", "probability": 0.688232421875}, {"start": 1171.87, "end": 1172.47, "word": " بي", "probability": 0.5244140625}, {"start": 1172.47, "end": 1172.89, "word": " ون", "probability": 0.75537109375}, {"start": 1172.89, "end": 1173.41, "word": " X", "probability": 0.42529296875}, {"start": 1173.41, "end": 1174.15, "word": " زائد", 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"word": " في", "probability": 0.53466796875}], "temperature": 1.0}, {"id": 49, "seek": 142610, "start": 1401.94, "end": 1426.1, "text": "is a homomorphism طريقة كويسة لو كانت فاي on two بقدر استخدم ال first isomorphism فيرمه باشرة يكفيني ان تكون الفاي is on two وليس بالضرورة ان تكون one to one", "tokens": [271, 257, 3655, 32702, 1434, 23032, 16572, 28671, 9122, 45865, 3794, 3660, 45164, 25961, 2655, 6156, 47302, 322, 732, 4724, 28543, 2288, 44713, 9778, 40448, 2423, 700, 307, 32702, 1434, 6156, 13546, 2304, 3224, 4724, 33599, 25720, 7251, 4117, 41185, 22653, 16472, 6055, 30544, 27188, 47302, 307, 322, 732, 4032, 20292, 3794, 20666, 11242, 2288, 13063, 3660, 16472, 6055, 30544, 472, 281, 472], "avg_logprob": -0.27734374813735485, "compression_ratio": 1.484076433121019, "no_speech_prob": 0.0, "words": [{"start": 1401.94, "end": 1402.66, "word": "is", "probability": 0.60498046875}, {"start": 1402.66, "end": 1403.44, "word": " a", "probability": 0.9033203125}, {"start": 1403.44, "end": 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{"start": 1412.08, "end": 1414.62, "word": " isomorphism", "probability": 0.9365234375}, {"start": 1414.62, "end": 1415.92, "word": " فيرمه", "probability": 0.7027587890625}, {"start": 1415.92, "end": 1416.68, "word": " باشرة", "probability": 0.7228190104166666}, {"start": 1416.68, "end": 1418.3, "word": " يكفيني", "probability": 0.7611083984375}, {"start": 1418.3, "end": 1418.68, "word": " ان", "probability": 0.548828125}, {"start": 1418.68, "end": 1419.18, "word": " تكون", "probability": 0.985595703125}, {"start": 1419.18, "end": 1419.94, "word": " الفاي", "probability": 0.69873046875}, {"start": 1419.94, "end": 1420.32, "word": " is", "probability": 0.68310546875}, {"start": 1420.32, "end": 1420.8, "word": " on", "probability": 0.7861328125}, {"start": 1420.8, "end": 1421.12, "word": " two", "probability": 0.9462890625}, {"start": 1421.12, "end": 1422.08, "word": " وليس", "probability": 0.95263671875}, {"start": 1422.08, "end": 1423.16, "word": " بالضرورة", "probability": 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"probability": 0.698699951171875}, {"start": 1444.66, "end": 1444.96, "word": " بدأ", "probability": 0.5526123046875}, {"start": 1444.96, "end": 1445.26, "word": " أخد", "probability": 0.8986002604166666}, {"start": 1445.26, "end": 1445.7, "word": " عنصر", "probability": 0.9401041666666666}, {"start": 1445.7, "end": 1446.04, "word": " وين", "probability": 0.816162109375}, {"start": 1446.04, "end": 1447.04, "word": " في", "probability": 0.6591796875}, {"start": 1447.04, "end": 1447.72, "word": " الـQ", "probability": 0.7693684895833334}, {"start": 1447.72, "end": 1448.34, "word": " و", "probability": 0.75}, {"start": 1448.34, "end": 1448.72, "word": " أبين", "probability": 0.7322591145833334}, {"start": 1448.72, "end": 1449.24, "word": " إنه", "probability": 0.94189453125}, {"start": 1449.24, "end": 1449.44, "word": " إيه", "probability": 0.68603515625}, {"start": 1449.44, "end": 1449.94, "word": " أصل", "probability": 0.815673828125}, {"start": 1449.94, "end": 1450.16, "word": " في", 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"probability": 0.86767578125}, {"start": 1459.2, "end": 1459.48, "word": " يبقى", "probability": 0.990966796875}, {"start": 1459.48, "end": 1459.86, "word": " الـQ", "probability": 0.978515625}, {"start": 1459.86, "end": 1460.8, "word": " variable", "probability": 0.68359375}, {"start": 1460.8, "end": 1461.06, "word": " و", "probability": 0.436767578125}, {"start": 1461.06, "end": 1461.22, "word": " لا", "probability": 0.57763671875}, {"start": 1461.22, "end": 1461.92, "word": " constant", "probability": 0.6953125}], "temperature": 1.0}, {"id": 51, "seek": 149259, "start": 1464.39, "end": 1492.59, "text": "يبقى then لكيو as لكيو as كونستان يعني إذا ممكن أاخده هو الكنستان تبع أي polynomial صح ولا لأ يبقى then ال f of x", "tokens": [1829, 3555, 4587, 7578, 550, 5296, 4117, 1829, 2407, 382, 5296, 4117, 1829, 2407, 382, 9122, 11536, 14851, 7649, 37495, 22653, 11933, 15730, 3714, 43020, 5551, 47283, 3215, 3224, 31439, 2423, 19452, 14851, 7649, 6055, 3555, 3615, 36632, 26110, 20328, 5016, 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كلامي كويس يبقى هدف اللي بده يعطينا ان ال PRX divide لإتنين طب ما هي قاسم إتنين واحد و سالب واحد و اتنين و سالب اتنين واحد و سالب واحد مستبعد لإن هذا بيجيبلي عنصر واحد فقط واحد مش غير", "tokens": [2407, 6055, 4587, 38251, 6055, 4587, 38251, 46811, 10943, 28242, 10943, 1829, 9122, 45865, 3794, 7251, 3555, 4587, 7578, 8032, 3215, 5172, 13672, 1829, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 2423, 11568, 55, 9845, 5296, 28814, 2655, 1863, 9957, 23032, 3555, 19446, 39896, 12174, 32277, 2304, 11933, 2655, 1863, 9957, 36764, 24401, 4032, 8608, 6027, 3555, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 4032, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 36764, 24401, 4032, 8608, 6027, 3555, 36764, 24401, 3714, 14851, 3555, 22488, 5296, 28814, 1863, 23758, 4724, 1829, 7435, 1829, 3555, 20292, 18871, 9381, 2288, 36764, 24401, 6156, 47432, 36764, 24401, 37893, 32771, 13546], "avg_logprob": -0.2688376045672693, "compression_ratio": 1.9333333333333333, "no_speech_prob": 0.0, "words": [{"start": 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"probability": 0.93603515625}], "temperature": 1.0}, {"id": 96, "seek": 279757, "start": 2772.73, "end": 2797.57, "text": "والإتنين cannot be generated by a single polynomial معناته لا يمكن أن يكون هذا ال principle، that is", "tokens": [2407, 6027, 28814, 2655, 1863, 9957, 2644, 312, 10833, 538, 257, 2167, 26110, 20449, 8315, 47395, 20193, 7251, 43020, 14739, 7251, 30544, 23758, 2423, 8665, 12399, 300, 307], "avg_logprob": -0.34455817732317695, "compression_ratio": 1.0909090909090908, "no_speech_prob": 0.0, "words": [{"start": 2772.73, "end": 2774.21, "word": "والإتنين", "probability": 0.7931722005208334}, {"start": 2774.21, "end": 2775.07, "word": " cannot", "probability": 0.1751708984375}, {"start": 2775.07, "end": 2778.17, "word": " be", "probability": 0.8447265625}, {"start": 2778.17, "end": 2781.35, "word": " generated", "probability": 0.8447265625}, {"start": 2781.35, "end": 2784.03, "word": " by", "probability": 0.9384765625}, {"start": 2784.03, "end": 2785.95, "word": " a", 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كان سؤال اربعة وعشرين الآن بنجي لسؤال تلاتين سؤال تلاتين بقول ال F فيه وزيادة على ذلك ال F of X", "tokens": [1829, 3555, 4587, 7578, 8717, 7435, 1829, 3555, 1863, 6027, 3224, 5682, 1365, 4724, 1829, 4117, 41185, 24976, 28814, 7435, 16758, 3660, 15844, 21136, 33604, 6027, 23758, 25961, 8608, 33604, 6027, 1975, 25513, 27884, 4032, 3615, 46309, 9957, 6024, 48506, 44945, 7435, 1829, 5296, 3794, 33604, 6027, 6055, 1211, 9307, 9957, 8608, 33604, 6027, 6055, 1211, 9307, 9957, 4724, 39648, 2423, 479, 8978, 3224, 4032, 11622, 1829, 18513, 3660, 15844, 29910, 23275, 2423, 479, 295, 1783], "avg_logprob": -0.1955154189815769, "compression_ratio": 1.5757575757575757, "no_speech_prob": 0.0, "words": [{"start": 2828.84, "end": 2829.18, "word": "يبقى", "probability": 0.678680419921875}, {"start": 2829.18, "end": 2829.8, "word": " نجيبناله", "probability": 0.8255440848214286}, {"start": 2829.8, "end": 2830.52, "word": " counter", "probability": 0.447998046875}, {"start": 2830.52, "end": 2831.54, 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{"start": 2910.2, "end": 2910.38, "word": " ال", "probability": 0.95068359375}, {"start": 2910.38, "end": 2910.58, "word": " A", "probability": 0.9755859375}, {"start": 2910.58, "end": 2910.94, "word": " naught", "probability": 0.197998046875}, {"start": 2910.94, "end": 2911.56, "word": " يساوي", "probability": 0.78558349609375}, {"start": 2911.56, "end": 2911.92, "word": " زيو", "probability": 0.5882975260416666}], "temperature": 1.0}, {"id": 101, "seek": 295253, "start": 2923.91, "end": 2952.53, "text": "سؤال مرة تانية نعطينا ال field بطلنا integral domain يبقى كل أنصر له معكوس أخدنا polynomial ring في هذا ال field تمام على الشكل اللي عندنا هذا فجالي اثبت ان ال X ماقص واحد هو factor لل F of X F and all F إذا كان مجموع المعاملات يساوي Z", "tokens": [3794, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 8717, 3615, 9566, 1829, 8315, 2423, 2519, 4724, 9566, 1211, 8315, 11573, 9274, 7251, 3555, 4587, 7578, 28242, 14739, 9381, 2288, 46740, 20449, 4117, 41779, 5551, 9778, 3215, 8315, 26110, 4875, 8978, 23758, 2423, 2519, 46811, 10943, 15844, 25124, 28820, 13672, 1829, 43242, 8315, 23758, 6156, 7435, 6027, 1829, 1975, 12984, 3555, 2655, 16472, 2423, 1783, 3714, 995, 4587, 9381, 36764, 24401, 31439, 5952, 24976, 479, 295, 1783, 479, 293, 439, 479, 11933, 15730, 25961, 3714, 7435, 2304, 45367, 9673, 3615, 10943, 1211, 9307, 7251, 3794, 995, 45865, 1176], "avg_logprob": -0.24362245612606712, "compression_ratio": 1.5062240663900415, "no_speech_prob": 0.0, "words": [{"start": 2923.91, "end": 2924.33, "word": "سؤال", "probability": 0.9542643229166666}, {"start": 2924.33, "end": 2924.65, "word": " مرة", "probability": 0.879638671875}, {"start": 2924.65, "end": 2925.07, "word": " تانية", "probability": 0.7985026041666666}, {"start": 2925.07, "end": 2926.59, "word": " نعطينا", "probability": 0.79033203125}, {"start": 2926.59, "end": 2926.85, "word": " ال", "probability": 0.1341552734375}, {"start": 2926.85, "end": 2927.63, "word": " field", "probability": 0.79443359375}, {"start": 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0.8916015625}, {"start": 2936.67, "end": 2937.39, "word": " هذا", "probability": 0.9765625}, {"start": 2937.39, "end": 2937.91, "word": " ال", "probability": 0.92919921875}, {"start": 2937.91, "end": 2938.49, "word": " field", "probability": 0.93310546875}, {"start": 2938.49, "end": 2939.55, "word": " تمام", "probability": 0.838623046875}, {"start": 2939.55, "end": 2939.93, "word": " على", "probability": 0.435791015625}, {"start": 2939.93, "end": 2940.41, "word": " الشكل", "probability": 0.9814453125}, {"start": 2940.41, "end": 2940.59, "word": " اللي", "probability": 0.921142578125}, {"start": 2940.59, "end": 2941.03, "word": " عندنا", "probability": 0.982666015625}, {"start": 2941.03, "end": 2941.43, "word": " هذا", "probability": 0.96337890625}, {"start": 2941.43, "end": 2942.59, "word": " فجالي", "probability": 0.8369140625}, {"start": 2942.59, "end": 2943.29, "word": " اثبت", "probability": 0.8890380859375}, {"start": 2943.29, "end": 2943.49, "word": " ان", "probability": 0.70947265625}, {"start": 2943.49, "end": 2943.69, "word": " ال", "probability": 0.64794921875}, {"start": 2943.69, "end": 2943.95, "word": " X", "probability": 0.62255859375}, {"start": 2943.95, "end": 2944.47, "word": " ماقص", "probability": 0.653045654296875}, {"start": 2944.47, "end": 2944.83, "word": " واحد", "probability": 0.976806640625}, {"start": 2944.83, "end": 2945.17, "word": " هو", "probability": 0.966796875}, {"start": 2945.17, "end": 2945.99, "word": " factor", "probability": 0.49755859375}, {"start": 2945.99, "end": 2946.43, "word": " لل", "probability": 0.72509765625}, {"start": 2946.43, "end": 2946.79, "word": " F", "probability": 0.82080078125}, {"start": 2946.79, "end": 2947.07, "word": " of", "probability": 0.783203125}, {"start": 2947.07, "end": 2947.35, "word": " X", "probability": 0.98681640625}, {"start": 2947.35, "end": 2948.09, "word": " F", "probability": 0.4765625}, {"start": 2948.09, "end": 2948.43, "word": " and", "probability": 0.76123046875}, {"start": 2948.43, "end": 2948.71, "word": " all", "probability": 0.28857421875}, {"start": 2948.71, "end": 2949.03, "word": " F", "probability": 0.85595703125}, {"start": 2949.03, "end": 2949.39, "word": " إذا", "probability": 0.83349609375}, {"start": 2949.39, "end": 2949.95, "word": " كان", "probability": 0.99462890625}, {"start": 2949.95, "end": 2950.81, "word": " مجموع", "probability": 0.947509765625}, {"start": 2950.81, "end": 2951.73, "word": " المعاملات", "probability": 0.98603515625}, {"start": 2951.73, "end": 2952.33, "word": " يساوي", "probability": 0.7369384765625}, {"start": 2952.33, "end": 2952.53, "word": " Z", "probability": 0.55859375}], "temperature": 1.0}, {"id": 102, "seek": 298183, "start": 2953.11, "end": 2981.83, "text": "كلمة f and o left تعني ان القرآن بيصير اتجاهين يبقى ناخد الاتجاه الأول assume that افترض ان ال x ناقص الواحد is a factor of ال f of x افترض انه 30 طيب", "tokens": [4117, 19528, 3660, 283, 293, 277, 1411, 37279, 22653, 16472, 25062, 2288, 148, 48506, 4724, 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"probability": 0.57666015625}, {"start": 2955.33, "end": 2955.79, "word": " القرآن", "probability": 0.7125244140625}, {"start": 2955.79, "end": 2956.77, "word": " بيصير", "probability": 0.63226318359375}, {"start": 2956.77, "end": 2958.81, "word": " اتجاهين", "probability": 0.84169921875}, {"start": 2958.81, "end": 2959.13, "word": " يبقى", "probability": 0.77789306640625}, {"start": 2959.13, "end": 2959.61, "word": " ناخد", "probability": 0.8658854166666666}, {"start": 2959.61, "end": 2960.43, "word": " الاتجاه", "probability": 0.9266357421875}, {"start": 2960.43, "end": 2961.01, "word": " الأول", "probability": 0.865478515625}, {"start": 2961.01, "end": 2962.49, "word": " assume", "probability": 0.61181640625}, {"start": 2962.49, "end": 2964.53, "word": " that", "probability": 0.82958984375}, {"start": 2964.53, "end": 2965.65, "word": " افترض", "probability": 0.9117431640625}, {"start": 2965.65, "end": 2966.15, "word": " ان", "probability": 0.90625}, {"start": 2966.15, "end": 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"probability": 0.9779052734375}, {"start": 2979.35, "end": 2979.83, "word": " انه", "probability": 0.907958984375}, {"start": 2979.83, "end": 2980.17, "word": " 30", "probability": 0.123291015625}, {"start": 2980.17, "end": 2981.83, "word": " طيب", "probability": 0.9654947916666666}], "temperature": 1.0}, {"id": 103, "seek": 301234, "start": 2982.72, "end": 3012.34, "text": "أخدنا كرولري السابقة بتقول إن هذا لو كان factor يبقى X يساوي واحد هو مين؟ Zero للدالة يعني لو عوضنا بال X بواحد النتج بدي يعطينا جدير يساوي Zero يبقى assume that then ال X يساوي واحد is a zero of F of X", "tokens": [10721, 9778, 3215, 8315, 9122, 2288, 12610, 16572, 21136, 16758, 28671, 39894, 39648, 36145, 23758, 45164, 25961, 5952, 7251, 3555, 4587, 7578, 1783, 7251, 3794, 995, 45865, 36764, 24401, 31439, 3714, 9957, 22807, 17182, 24976, 3215, 6027, 3660, 37495, 22653, 45164, 6225, 2407, 11242, 8315, 20666, 1783, 4724, 14407, 24401, 28239, 2655, 7435, 4724, 16254, 7251, 3615, 9566, 1829, 8315, 10874, 3215, 13546, 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"probability": 0.96875}, {"start": 2994.86, "end": 2995.26, "word": " X", "probability": 0.880859375}, {"start": 2995.26, "end": 2995.82, "word": " بواحد", "probability": 0.9619140625}, {"start": 2995.82, "end": 2996.3, "word": " النتج", "probability": 0.5909830729166666}, {"start": 2996.3, "end": 2996.56, "word": " بدي", "probability": 0.704345703125}, {"start": 2996.56, "end": 2996.94, "word": " يعطينا", "probability": 0.825244140625}, {"start": 2996.94, "end": 2997.56, "word": " جدير", "probability": 0.6432291666666666}, {"start": 2997.56, "end": 2998.54, "word": " يساوي", "probability": 0.9613037109375}, {"start": 2998.54, "end": 2998.98, "word": " Zero", "probability": 0.75244140625}, {"start": 2998.98, "end": 3000.1, "word": " يبقى", "probability": 0.884521484375}, {"start": 3000.1, "end": 3000.68, "word": " assume", "probability": 0.5087890625}, {"start": 3000.68, "end": 3001.34, "word": " that", "probability": 0.88720703125}, {"start": 3001.34, "end": 3002.08, "word": " then", "probability": 0.73095703125}, {"start": 3002.08, "end": 3003.72, "word": " ال", "probability": 0.459716796875}, {"start": 3003.72, "end": 3004.16, "word": " X", "probability": 0.96435546875}, {"start": 3004.16, "end": 3004.9, "word": " يساوي", "probability": 0.971923828125}, {"start": 3004.9, "end": 3005.58, "word": " واحد", "probability": 0.990478515625}, {"start": 3005.58, "end": 3006.54, "word": " is", "probability": 0.9169921875}, {"start": 3006.54, "end": 3007.48, "word": " a", "probability": 0.94921875}, {"start": 3007.48, "end": 3008.68, "word": " zero", "probability": 0.4697265625}, {"start": 3008.68, "end": 3009.92, "word": " of", "probability": 0.94189453125}, {"start": 3009.92, "end": 3011.32, "word": " F", "probability": 0.40625}, {"start": 3011.32, "end": 3011.88, "word": " of", "probability": 0.85302734375}, {"start": 3011.88, "end": 3012.34, "word": " X", "probability": 0.99609375}], "temperature": 1.0}, {"id": 104, "seek": 304229, "start": 3013.27, "end": 3042.29, "text": "that is أي أن ال F of واحد بده يساوي Z طيب هذا معناه وين ال F؟ هاي يبقى Zero بده يساوي ال F of واحد بده يساوي ال A N الواحد to the power N A N minus ال one مرة في واحد أس N minus ال one", "tokens": [6780, 307, 36632, 14739, 2423, 479, 295, 36764, 24401, 47525, 3224, 7251, 3794, 995, 45865, 1176, 23032, 1829, 3555, 23758, 20449, 8315, 3224, 4032, 9957, 2423, 479, 22807, 8032, 47302, 7251, 3555, 4587, 7578, 17182, 47525, 3224, 7251, 3794, 995, 45865, 2423, 479, 295, 36764, 24401, 47525, 3224, 7251, 3794, 995, 45865, 2423, 316, 426, 2423, 14407, 24401, 281, 264, 1347, 426, 316, 426, 3175, 2423, 472, 3714, 25720, 8978, 36764, 24401, 5551, 3794, 426, 3175, 2423, 472], "avg_logprob": -0.2612737402131286, "compression_ratio": 1.7106918238993711, "no_speech_prob": 0.0, "words": [{"start": 3013.27, "end": 3013.75, "word": "that", "probability": 0.6806640625}, {"start": 3013.75, "end": 3014.57, "word": " is", "probability": 0.94384765625}, {"start": 3014.57, "end": 3016.41, "word": " 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..595f483b82a2d24b4b84e3a0605192321e02bd4f
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_raw.srt
@@ -0,0 +1,1888 @@
+1
+00:00:20,860 --> 00:00:26,000
+بسم الله الرحمن الرحيم المرة اللي فاتت إبتدانا في
+
+2
+00:00:26,000 --> 00:00:33,680
+حل exercises على chapter 16 ووصلنا إلى السؤال رقم
+
+3
+00:00:33,680 --> 00:00:40,980
+.. السؤال رقم 12 أنا ما أذكر يعني، مظلوم؟ وقلنا
+
+4
+00:00:40,980 --> 00:00:46,720
+هذا بدنا يأكل good exercises اتمرنوا إيديكوا فيه
+
+5
+00:00:46,720 --> 00:00:53,670
+وزي وزي سؤال 11 اللي قبللا أدري حلته ولا لا ممتازة
+
+6
+00:00:53,670 --> 00:00:58,050
+يبقى بدي أقول الفكرة الشفاوية اللي ماعرفتش أتحل ثم
+
+7
+00:00:58,050 --> 00:01:03,130
+ننتقل إلى السؤال اللي بعد طبعا احنا بدنا نقسم في
+
+8
+00:01:03,130 --> 00:01:09,290
+سؤال اتناشر خمسة اكسوس اربع على تلاتة اكس تربيه
+
+9
+00:01:09,290 --> 00:01:18,250
+احنا بنشتغل وين في Z سبعة of X مظبوط يبقى في Z
+
+10
+00:01:18,250 --> 00:01:24,760
+سبعة of Xفي Z7 لما أجي أجسم خمسة على تلاتة، يبقى
+
+11
+00:01:24,760 --> 00:01:29,560
+فيش حاجة اسم الخمسة على تلاتة، هذا كسر مش موجود في
+
+12
+00:01:29,560 --> 00:01:36,840
+Z، فماذا نعمل؟ بنروح، بنضيف لخمسة مضاعفات السبعة
+
+13
+00:01:36,840 --> 00:01:42,280
+لغاية ما تجسم على تلاتة، يبقى أنا عندي خمسة،
+
+14
+00:01:42,280 --> 00:01:46,280
+أضيفيلها سبعة سبعة تانية، Zero في Z7، يعني كأني
+
+15
+00:01:46,280 --> 00:01:51,710
+ماعملتش حاجة، فبصير سبعة وخمسةأتناشى و بتقسم ع مين
+
+16
+00:01:51,710 --> 00:01:57,490
+على تلاتة لو مانقسمتش باضيف كمان سابعة بضل اضيف
+
+17
+00:01:57,490 --> 00:02:02,770
+سبعت لما تقسم بيكون هى النتيجة المطلوبة فانت سبعة
+
+18
+00:02:02,770 --> 00:02:08,110
+و خمسة اتناش بس اتناش ع تلاتة باربع اكس تربيع
+
+19
+00:02:08,110 --> 00:02:13,250
+وهكذا بكمل مثل القسم العادى وانا اعطيتكوا قبل ذلك
+
+20
+00:02:13,430 --> 00:02:17,930
+مثال قسمة بس ماكانش كان المعامل هنا واحد والمعامل
+
+21
+00:02:17,930 --> 00:02:22,290
+هنا واحد وبالتالي لم تظهر المشكلة لكن لما كانوا
+
+22
+00:02:22,290 --> 00:02:28,270
+أرقام مختلفة هنا ظهرت المشكلة وحلها المضيف مضاعفات
+
+23
+00:02:28,270 --> 00:02:33,950
+السبعة بحيث تتم القسمة طبعا؟ إذا سؤال اتناش very
+
+24
+00:02:33,950 --> 00:02:41,260
+easy بروح الأقل سؤال سبعتاشروهذا سؤال سبعتاش أخدنا
+
+25
+00:02:41,260 --> 00:02:46,240
+لإنه لازملي في شبطر سبعتاش و لازملي أي شبطر طبعا
+
+26
+00:02:46,240 --> 00:02:52,620
+تحت إذن هذا يجب أن نحله لإنه لازملي قدام يبقى بالي
+
+27
+00:02:52,620 --> 00:02:59,140
+لمين لسؤال سبعتاش سؤال سبعتاش بيقول دي integral
+
+28
+00:02:59,140 --> 00:03:06,260
+domain يبقى دي is is integral domain
+
+29
+00:03:08,690 --> 00:03:15,110
+و عندنا ال F of X و ال G of X موجودة في D و ال F
+
+30
+00:03:15,110 --> 00:03:25,610
+of X و ال G of X عناصر موجودة في ال D of X بيقول
+
+31
+00:03:25,610 --> 00:03:29,290
+لي بعدك اثبت ان ال degree لحاصل الضرب تساوي ال
+
+32
+00:03:29,290 --> 00:03:38,250
+degree ل الجمع يفى المطلوب الأول النقطة الأولى شإن
+
+33
+00:03:38,250 --> 00:03:46,210
+ال degree لمن؟ لل F of X بال G of X تساوي ال
+
+34
+00:03:46,210 --> 00:03:53,330
+degree لل F مضافا إليها ال degree لل G هذا المطلوب
+
+35
+00:03:53,330 --> 00:03:58,650
+الأول المطلوب الثاني بيقول هذي commutative ring
+
+36
+00:03:58,650 --> 00:04:03,470
+بحيث هذي تكون مش صحية كيف يعني مش صحية يعني يكون
+
+37
+00:04:03,470 --> 00:04:10,910
+ال degree لحاصل الضرب أقلمن ال degree لمن؟ للجامعة
+
+38
+00:04:10,910 --> 00:04:14,510
+بس مش في ال integral domain ال integral domain ده
+
+39
+00:04:14,510 --> 00:04:18,970
+كلام صحيح دايما أبدا قلت لأ في commutative ring
+
+40
+00:04:18,970 --> 00:04:25,390
+ليس بالضرورة أن تكون integral domain طيب خلّي
+
+41
+00:04:25,390 --> 00:04:29,770
+المطلوب التاني بعد ما نخلص المطلوب الأول يبدأ أنا
+
+42
+00:04:29,770 --> 00:04:35,700
+بدي أخد ال two polynomials موجودة في D of Xيبقى ال
+
+43
+00:04:35,700 --> 00:04:42,680
+solution على الوجه التالي نقطة واحدة بداية اقول
+
+44
+00:04:42,680 --> 00:04:50,280
+افترضوا ان ال f of x هي a n x to the power n a
+
+45
+00:04:50,280 --> 00:04:57,920
+minus ال one لل x أُس n minus ال one زائد زائد إلى
+
+46
+00:04:57,920 --> 00:05:07,060
+a one x زائد ال a naughtوفي المقابل ال a n does
+
+47
+00:05:07,060 --> 00:05:12,840
+not equal to zero مشان أضمن أن أعلى degree عندي
+
+48
+00:05:12,840 --> 00:05:20,640
+جداش اللي هو m وفي نفس الوقت ال g of x بدي يسوي b
+
+49
+00:05:20,640 --> 00:05:26,840
+m x to the power m b minus ال one x to the power m
+
+50
+00:05:26,840 --> 00:05:33,460
+minus ال one زائد b one x زائد ال b nonو ال BM
+
+51
+00:05:33,460 --> 00:05:40,880
+كذلك لا تساوي 0 والتنتين هدول كلهم موجودات في مين؟
+
+52
+00:05:40,880 --> 00:05:47,800
+في ال integral domain D of X الآن بدي أخد حاصل
+
+53
+00:05:47,800 --> 00:05:55,940
+ضربهما يبقى بدي أخد ال F of X في ال G of X يبقى
+
+54
+00:05:55,940 --> 00:06:04,450
+لما أبدأ أضربهم هقول AN BM في X أُس Nزائد ال M
+
+55
+00:06:04,450 --> 00:06:12,430
+تمام زائد ونظل ماشيين لغاية ما نوصل لمين لل A node
+
+56
+00:06:12,430 --> 00:06:21,310
+B1 زائد A1 B node في ال X زائد ال A node B node
+
+57
+00:06:21,310 --> 00:06:29,070
+يبقى هاد هاش هاد حاصل الضرر الآن أنا بتهمني ال
+
+58
+00:06:29,070 --> 00:06:37,180
+degreeهذه الان بي ام ممكن تكون بزيرو لأ لأ لأ لأ
+
+59
+00:06:37,180 --> 00:06:40,420
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+60
+00:06:40,420 --> 00:06:40,920
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+61
+00:06:40,920 --> 00:06:41,040
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+62
+00:06:41,040 --> 00:06:41,920
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+63
+00:06:41,920 --> 00:06:42,100
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+64
+00:06:42,100 --> 00:06:47,980
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+65
+00:06:47,980 --> 00:06:52,260
+لأ لأ لأ لأ لأ
+
+66
+00:06:52,260 --> 00:06:58,140
+لأ
+
+67
+00:06:58,140 --> 00:07:04,850
+لألا هدف Zero ولا هدف Zero يعني بنفع لما الهدف
+
+68
+00:07:04,850 --> 00:07:09,630
+ماهياش ب Zero وهدف ماهياش ب Zero حاصل درجة مايكونش
+
+69
+00:07:09,630 --> 00:07:15,990
+Zero فهي احتمال ان يكون Zero بس لما كان Integral
+
+70
+00:07:15,990 --> 00:07:22,310
+domain يبقى لا يمكن ان يساوي Zero يبقى هدف لا
+
+71
+00:07:22,310 --> 00:07:27,550
+يساوي Zero لسببين السبب الأول ولا واحدة فيهم ب
+
+72
+00:07:27,550 --> 00:07:38,460
+Zero والسبب الثانيالـ D is an integral domain
+
+73
+00:07:38,460 --> 00:07:43,240
+تمام؟
+
+74
+00:07:43,240 --> 00:07:47,580
+لأن في ال integral domain مافيش عندي zero divisors
+
+75
+00:07:47,580 --> 00:07:52,680
+تمام؟ لكن لو ماكنش integral domain ممكن هذه
+
+76
+00:07:52,680 --> 00:07:58,580
+لاتساوي zero وهذه لاتساوي zero وحاصل ضربه مايساوي
+
+77
+00:07:58,580 --> 00:08:02,610
+zeroيعني في احتمال يكون واحد فيهم Zero divisor
+
+78
+00:08:02,610 --> 00:08:08,690
+وبالتالي هذا الكلام ليس صحيحا إذا هذا لا يكون
+
+79
+00:08:08,690 --> 00:08:13,810
+يساوي Zero لسببين ولا واحد فيهم Zero اتنين دي
+
+80
+00:08:13,810 --> 00:08:21,630
+انتجرال دمية مدام هيك جداش ال degree لهذه M زائد M
+
+81
+00:08:21,630 --> 00:08:30,980
+يبقى هنا ساعة ال degree لل F of Xفي الـ G of X هي
+
+82
+00:08:30,980 --> 00:08:37,340
+عند استبعاد تهدي ب Zero يبقى هذا بده ساوي ال N
+
+83
+00:08:37,340 --> 00:08:47,240
+زائد ال F and ال degree لمن؟ لل F زائد ال degree
+
+84
+00:08:47,240 --> 00:08:53,420
+لل G كده ايش بده ساوي؟ الأولى هي ال degree تبعها N
+
+85
+00:08:53,420 --> 00:09:00,370
+لانه اشترقنا ان ال A N لا تساوي Zeroوالتانية M لأن
+
+86
+00:09:00,370 --> 00:09:05,850
+اشتراطنا ال BM لا تساوي Zero يبقى ال degree تبعها
+
+87
+00:09:05,850 --> 00:09:11,450
+M وال degree تبعها N من الاتنين هدول يبقى ال
+
+88
+00:09:11,450 --> 00:09:19,810
+degree لل F of X في ال G of X يساوي ال degree لل F
+
+89
+00:09:19,810 --> 00:09:27,770
+of X زائد ال degree لل G of Xهذا المطلوب الأول
+
+90
+00:09:27,770 --> 00:09:35,430
+مطلوب التاني قال لي هذي commutative ring بحب تجيب
+
+91
+00:09:35,430 --> 00:09:38,890
+ال polynomial في الأول و ال polynomial في التانية
+
+92
+00:09:38,890 --> 00:09:44,290
+و ال degree اللي حصل الدرب يكون أقل من ال degree
+
+93
+00:09:44,290 --> 00:09:49,230
+للأولى لل degree للتانية المطلوب الأول انجيب
+
+94
+00:09:49,230 --> 00:09:56,850
+commutative ring حد فيك أجابتها؟ Z6 ممتاززد ستة
+
+95
+00:09:56,850 --> 00:10:02,390
+ماهياش integral domain لكنها commutative ring لأن
+
+96
+00:10:02,390 --> 00:10:05,910
+اتنين في تلاتة تساوي zero وبالتالي اتنين و تلاتة
+
+97
+00:10:05,910 --> 00:10:11,130
+zero divisor يبقى هذه not integral domain ولكنها
+
+98
+00:10:11,130 --> 00:10:20,250
+ring يبقى هنا بعدين بقول زد ستة هذه is a
+
+99
+00:10:20,250 --> 00:10:22,210
+commutative
+
+100
+00:10:25,490 --> 00:10:33,250
+Ring but not an
+
+101
+00:10:33,250 --> 00:10:42,310
+integral domain لأنها ليست انتجرال دومان طيب ادور
+
+102
+00:10:42,310 --> 00:10:47,870
+على two polynomial فيه واجيب degree الأولى و
+
+103
+00:10:47,870 --> 00:10:52,270
+degree الثانية و نضرب و يطلع ال degree اللي حصل
+
+104
+00:10:52,270 --> 00:10:58,320
+الضربأقل من مجموع الـ two degrees يبقى فكري ممكن
+
+105
+00:10:58,320 --> 00:11:04,140
+two polynomials و لا ممكن عشرات مش يعني واحدة
+
+106
+00:11:04,140 --> 00:11:08,940
+والله اشي كتير جد ما بدك غير الأرقام زي ما بدك
+
+107
+00:11:08,940 --> 00:11:19,040
+باحد الأرقام تكون في Z6 فمثلا لو أخدنا take مثلا
+
+108
+00:11:19,040 --> 00:11:29,460
+ال F of Xيساوي 2X أُص 4 على سبيل المثال and الـG
+
+109
+00:11:29,460 --> 00:11:33,420
+of X تساوي شوفوا يا بني كيف بدنا نجيب الـG of X
+
+110
+00:11:33,420 --> 00:11:44,340
+هذه 2X أُص 4 بدي أخد هنا الرقم في X في X تربية في
+
+111
+00:11:44,340 --> 00:11:49,260
+X تكييب اللي بدك هي في حيث الحاصل ضربهم يطلع Zero
+
+112
+00:11:49,980 --> 00:11:55,840
+وبالتالي ال degree بتنزل طبيعي يبقى لما قلت اتنين
+
+113
+00:11:55,840 --> 00:12:00,680
+اكس تربية هذه اليوم بدأ اخدها تلاتة لان تلاتة في
+
+114
+00:12:00,680 --> 00:12:05,760
+اتنين هي zero يبقى ال degree نزلت تلاتة ايش؟ تلاتة
+
+115
+00:12:05,760 --> 00:12:12,160
+مثلا اكس تربية زيد خمس على سبيل المثال هي عندك
+
+116
+00:12:12,160 --> 00:12:17,080
+اتنين والتلاتة والخمسة موجودة في Z6
+
+117
+00:12:20,980 --> 00:12:25,540
+سبعة تعني واحد تمانية تعني اتنين يبقى لها هذه
+
+118
+00:12:25,540 --> 00:12:29,880
+العقام عندى احط الرقم اللى بدكى ياه من zero لغاية
+
+119
+00:12:29,880 --> 00:12:38,940
+خمسة كله موجود وين في Z6 طيب then بدي
+
+120
+00:12:38,940 --> 00:12:48,060
+اخد ال degree لمن لل F زائد ال degree لل G كدهش ال
+
+121
+00:12:48,060 --> 00:12:58,140
+degree لل أولىوالتانية 3 يبقى 4 زائد 2 ويساوي كده؟
+
+122
+00:12:58,140 --> 00:13:04,620
+ويساوي 6 طب بداجي أضربهم في بعض بداجي أخد ال F of
+
+123
+00:13:04,620 --> 00:13:14,560
+X في ال G of X يبقى 2 X أُص 4 في 3 X تربيع زائد 5
+
+124
+00:13:14,560 --> 00:13:24,310
+ويساوي 3 في 2ستة تعني Zero Zero في X أُس ستة يبقى
+
+125
+00:13:24,310 --> 00:13:31,630
+Zero في X أُس ستة هنا زرع اتنين في خمسة في عشرة
+
+126
+00:13:31,630 --> 00:13:41,910
+عشرة في زيت ستة تعني اربع يبقى اربع X أُس اربع مرة
+
+127
+00:13:41,910 --> 00:13:48,520
+تانية اتنين في دلاتر بالزيت في ستة X أُس ستةالستة
+
+128
+00:13:48,520 --> 00:13:56,580
+الأولى بـ 0 يبقى X أُس 6 التانية 2×5 بـ 10 X أُس 4
+
+129
+00:13:56,580 --> 00:14:04,720
+العشرة هذه تانية 4 في Z6 يبقى 4 في Z6 النتج يزاوي
+
+130
+00:14:04,720 --> 00:14:14,460
+4 X أُس 4 هذا بدي يعطينا أن ال degree لل F of X في
+
+131
+00:14:14,460 --> 00:14:23,830
+ال G of X بيساوي كدهاش؟أربعة والاربعة أقل من الستة
+
+132
+00:14:23,830 --> 00:14:29,270
+نفجر هى جيبناله two pronomials ال degree للأولى
+
+133
+00:14:29,270 --> 00:14:33,970
+وال degree للتانية ستة وحصل ضربه ما طلع ال degree
+
+134
+00:14:33,970 --> 00:14:38,690
+يساوي أربعة وبالتالي الأربعة أقل من الستة يبقى ال
+
+135
+00:14:38,690 --> 00:14:43,750
+degree اللى حصل ضرب أقل من ال degree للجامعة لما
+
+136
+00:14:43,750 --> 00:14:50,850
+شيلنا من المثلة كلمة integraldomain طبعا يبقى يكون
+
+137
+00:14:50,850 --> 00:14:54,790
+شغلنا دقيقه احنا نشغل في ring في integral domain
+
+138
+00:14:54,790 --> 00:14:59,210
+في field إلى اخرى يبقى هذا المطلوب الثاني من
+
+139
+00:14:59,210 --> 00:15:06,270
+السؤال رقم سبعتاشر رقم تمانتاشر بيقول اثبتلي ان ال
+
+140
+00:15:06,270 --> 00:15:11,150
+principle ideal generated by X هو maximum ideal في
+
+141
+00:15:11,150 --> 00:15:15,370
+ال Q of X سؤال تمانتاشر
+
+142
+00:15:17,020 --> 00:15:23,100
+that أن ال principle ideal generated by X is
+
+143
+00:15:23,100 --> 00:15:30,440
+maximal in الهوليكي
+
+144
+00:15:30,440 --> 00:15:35,960
+و X solution
+
+145
+00:15:35,960 --> 00:15:42,860
+طيب
+
+146
+00:15:42,860 --> 00:15:46,860
+نروي على موضوعنا احنا بينا نثبتإن ال principle
+
+147
+00:15:46,860 --> 00:15:53,540
+ideal generated by X هو maximum ideal في ال Q of X
+
+148
+00:15:53,540 --> 00:15:58,880
+نقول كويس لو رجعنا يا بنات لل isomorphism theorem
+
+149
+00:15:58,880 --> 00:16:05,320
+إذا جدرنا نثبت إن ال Q of X موديالو ال principle
+
+150
+00:16:05,320 --> 00:16:13,140
+ideal generated by X هذا عبارة عن field يبقى بسيط
+
+151
+00:16:13,420 --> 00:16:16,660
+ال principle of ideal generated by X is maximal
+
+152
+00:16:16,660 --> 00:16:22,380
+وبيكون خلصا من هالشغل هذا، مظبوط؟ يبقى الفكرة اني
+
+153
+00:16:22,380 --> 00:16:26,480
+أثبت ان ال Q of X modular principle of ideal
+
+154
+00:16:26,480 --> 00:16:31,140
+generated by X is E فيه وعتانى ما عجبتاش الفكرة
+
+155
+00:16:31,140 --> 00:16:36,260
+التبعتي، قالت لأ أنا بدأ أدور على ideal تاني ويكون
+
+156
+00:16:36,260 --> 00:16:39,880
+subset منه وهذا بيسوي الشهده، انا بدأ أثبت انه
+
+157
+00:16:39,880 --> 00:16:44,650
+بيسوي ال ringهي طرق تنفيه غيرهم إذا عارفين غيرهم
+
+158
+00:16:44,650 --> 00:16:48,370
+دلوني عليهم فاش يا الطريق هذي و يا الطريق هذي لكي
+
+159
+00:16:48,370 --> 00:16:54,810
+أثبت ال maximum ل هذا ال ID نقوله بسيطة طيب بدا
+
+160
+00:16:54,810 --> 00:17:00,190
+نشتغل جهود جامد شوية فدققوا معانا بروح أعرف
+
+161
+00:17:00,190 --> 00:17:09,350
+function من ال Q of X إلى ال Q طب ليش ال Q يعني ما
+
+162
+00:17:09,350 --> 00:17:15,670
+هي السؤالالحين بنجاوبه بقبله هقوله define a
+
+163
+00:17:15,670 --> 00:17:22,730
+function والله mapping اللي بدك ايه فاي من ال q of
+
+164
+00:17:22,730 --> 00:17:31,070
+x إلى ال q set of rational number باي اللي هو
+
+165
+00:17:31,070 --> 00:17:41,500
+الفاي of f of x بدي ساوي ال a node where حيثهال F
+
+166
+00:17:41,500 --> 00:17:48,480
+of X هي A N X to the power N A minus ال one X to
+
+167
+00:17:48,480 --> 00:17:53,880
+the power N minus ال one زائد A one X زائد ال A
+
+168
+00:17:53,880 --> 00:17:59,720
+node يبقى عرفنا مين هي ال A node عرفناها مين هي
+
+169
+00:17:59,720 --> 00:18:06,800
+الجزء الثابت من ال polynomial يبقى Phi of X node
+
+170
+00:18:06,800 --> 00:18:13,810
+هي ال A nodeهو جزء ثابت من هذه الـ polynomial إذا
+
+171
+00:18:13,810 --> 00:18:21,030
+قدرت أثبت إنه هذا homomorphism وجبتله
+
+172
+00:18:21,030 --> 00:18:27,230
+ال kernel يبقى بيصير في Q of X موديول الكيرنيل
+
+173
+00:18:27,230 --> 00:18:35,860
+ايزو مورفك لمين؟ للكيو طب لكيو فيلديبقى بصير الرنج
+
+174
+00:18:35,860 --> 00:18:39,220
+عندنا فيه اللي يبقى ال absolute value يبقى ال
+
+175
+00:18:39,220 --> 00:18:44,100
+principle ideal generated by X is maximal. ويكون
+
+176
+00:18:44,100 --> 00:18:48,200
+خلصنا هذه الشغلات. طب تستعجلش شوية شوية لو سمحت.
+
+177
+00:18:48,740 --> 00:18:52,540
+تعالى نمشي شوية شوية. بدأ نثبت ان هذه في الأول هي
+
+178
+00:18:52,540 --> 00:18:58,300
+homomorphism. فهذه بقوله الـ Phi is a
+
+179
+00:18:58,300 --> 00:19:06,640
+homomorphism. تمام؟يبقى بدها خدمة ال F of X بدها
+
+180
+00:19:06,640 --> 00:19:14,560
+تساوي ال A N X N A N minus ال one X N minus ال one
+
+181
+00:19:14,560 --> 00:19:20,140
+زائد زائد اللي هو A one X زائد ال A naught
+
+182
+00:19:20,140 --> 00:19:27,780
+والتانية ال G of X يساوي B M X to the power M B M
+
+183
+00:19:27,780 --> 00:19:34,950
+minus ال one X M minus ال oneزائد بي ون X زائد بي
+
+184
+00:19:34,950 --> 00:19:41,310
+نوع وهذا مناسب، بدي أقول ال A N لا يساوي Zero و ال
+
+185
+00:19:41,310 --> 00:19:48,950
+B M لا يساوي Zero، والاتنين هدول موجودات في ال Q
+
+186
+00:19:48,950 --> 00:20:02,800
+of X. Then بدي أخد Phi of ال F of Xزائد ال G of X
+
+187
+00:20:02,800 --> 00:20:08,780
+هذا الكلام بده يساوي في فاي اوك بده اجمع ال two
+
+188
+00:20:08,780 --> 00:20:14,520
+polynomials اول ما بدأنا هذا ال chapter عرفناكوا
+
+189
+00:20:14,520 --> 00:20:23,120
+كيف نجمع ال polynomials قولنا لك هذا AN زائد او AS
+
+190
+00:20:23,120 --> 00:20:33,820
+زائد BS في X قص Sمين الـ S هذا يا بناه؟ الرقم ليه
+
+191
+00:20:33,820 --> 00:20:39,700
+كبير في M أو N؟ لأن الـ N بيسويش الـ M يمكن الأولى
+
+192
+00:20:39,700 --> 00:20:43,100
+تكون من الدرجة العاشرة والتانية من الدرجة الرابعة
+
+193
+00:20:43,100 --> 00:20:48,000
+مثلا أو الخامسة، يبقى دولة دي كعدد عناصرها فيها
+
+194
+00:20:48,000 --> 00:20:52,640
+عشرة، هذه فيها خمسة، خمستر مجموعة بعض بعض، يبقى
+
+195
+00:20:52,640 --> 00:20:58,380
+واحدة فيهم بتكون بالـ Zero والتانية بتكون بأنصر
+
+196
+00:20:58,380 --> 00:21:07,350
+محدديبقى ال S هو الرقم الكبير في M و N زاد ال A S
+
+197
+00:21:07,350 --> 00:21:13,810
+minus ال one زاد ال B S minus ال one X أُس S minus
+
+198
+00:21:13,810 --> 00:21:22,330
+ال one نيجي زاد زاد A one زاد B one في X زاد ال A
+
+199
+00:21:22,330 --> 00:21:28,810
+naught زاد ال B naught كلهالـ Phi ستؤثر على هذا
+
+200
+00:21:28,810 --> 00:21:36,630
+العنصر تبقى للتعريف اللى احنا عرفناه للـ Phi يبقى
+
+201
+00:21:36,630 --> 00:21:41,650
+هذا بيدى يسوى مين المقدار التابع اللى همين A نوت
+
+202
+00:21:41,650 --> 00:21:48,110
+زائد B نوت يسوى A نوت زائد B نوت طب ال A نوت اللى
+
+203
+00:21:48,110 --> 00:21:56,480
+همين Phi لل F of X وال B نوت اللى هو Phi زائدالـ
+
+204
+00:21:56,480 --> 00:22:07,400
+Phi للـ G of X. انا بدي اقعد اخد Phi للـ F of X في
+
+205
+00:22:07,400 --> 00:22:15,420
+الـ G of X. تمام؟ هذا الكلام بيسوي Phi R. بإنه نجي
+
+206
+00:22:15,420 --> 00:22:20,140
+للضرب. الضرب بتلزمنيش الكلك على كلها. تبعد كل
+
+207
+00:22:20,140 --> 00:22:24,460
+عنصر، ياكفيني أول عنصر و آخر عنصر.يبقى لو جينا
+
+208
+00:22:24,460 --> 00:22:35,060
+ضربناهم في بعض تصير a n b m x أس n زائد ال m زائد
+
+209
+00:22:35,060 --> 00:22:40,540
+زائد لما نوصل لآخر عنصر اللي هو من أو ما قبل
+
+210
+00:22:40,540 --> 00:22:47,000
+الأخير اللي هو a naught b one زائد a one b naught
+
+211
+00:22:47,000 --> 00:22:54,370
+x زائد a naught b naughtيبقى هاي باشتصار حاصل
+
+212
+00:22:54,370 --> 00:22:58,570
+الضرب هذا كله انا مش لازملي النتيجة هي الكون
+
+213
+00:22:58,570 --> 00:23:03,230
+الصحيبي بيهمنا مين ال a naught b naught يبقى هذا
+
+214
+00:23:03,230 --> 00:23:09,970
+الكلام a naught b naught ال a naught اللي في of x
+
+215
+00:23:09,970 --> 00:23:21,090
+و ال b naught اللي هو في of g of x يبقى هنا سا في
+
+216
+00:23:21,940 --> 00:23:30,020
+is a homomorphism طريقة كويسة لو كانت فاي on two
+
+217
+00:23:30,020 --> 00:23:36,680
+بقدر استخدم ال first isomorphism فيرمه باشرة
+
+218
+00:23:36,680 --> 00:23:43,780
+يكفيني ان تكون الفاي is on two وليس بالضرورة ان
+
+219
+00:23:43,780 --> 00:23:46,100
+تكون one to one
+
+220
+00:23:55,760 --> 00:24:04,660
+طيب، بنحاول نثبت إنه Phi is only يبقى
+
+221
+00:24:04,660 --> 00:24:10,160
+بدأ أخد عنصر وين في الـQ و أبين إنه إيه أصل في
+
+222
+00:24:10,160 --> 00:24:17,080
+الـQ of X يبقى لو جيت، قلت، ليه الـEQ موجودة في
+
+223
+00:24:17,080 --> 00:24:21,920
+الـQ؟ يبقى الـQ variable و لا constant
+
+224
+00:24:24,390 --> 00:24:29,210
+يبقى then لكيو
+
+225
+00:24:29,210 --> 00:24:40,790
+as لكيو as كونستان يعني إذا ممكن أاخده هو الكنستان
+
+226
+00:24:40,790 --> 00:24:51,210
+تبع أي polynomial صح ولا لأ يبقى then ال
+
+227
+00:24:51,210 --> 00:24:59,450
+f of xبادها تساوي اللي هو مثلا او ليش و ليش يقول
+
+228
+00:24:59,450 --> 00:25:11,450
+خلاص كونستان هذا يساوي كونستان then ليكيو is a
+
+229
+00:25:11,450 --> 00:25:21,110
+constant of a polynomial of polynomial f of x for
+
+230
+00:25:21,110 --> 00:25:22,570
+some
+
+231
+00:25:24,490 --> 00:25:36,710
+f of x اللي موجودة في ال EQ of x that is ال
+
+232
+00:25:36,710 --> 00:25:45,750
+EQ هذا بدي يسوى فاي لل F of X تبقى من هنا صارت on
+
+233
+00:25:45,750 --> 00:25:52,930
+الان بقوله by then first
+
+234
+00:25:55,660 --> 00:26:05,700
+isomorphism theorem we have ان ال Q of X موديول
+
+235
+00:26:05,700 --> 00:26:17,060
+الكيرن للفاي isomorphic لمن؟ للفاي of Q of X مشيك
+
+236
+00:26:17,060 --> 00:26:21,800
+نص الفيروس isomorphism theorem طيب الفاي أثبتناها
+
+237
+00:26:21,800 --> 00:26:28,940
+أنها ontoيبقى هذه كلها مين هين؟ Phi of cubics
+
+238
+00:26:28,940 --> 00:26:35,500
+عبارة عن مين؟ عبارة عن الـQ. يبقى هذه اللي هي الـQ
+
+239
+00:26:35,500 --> 00:26:42,660
+itself. ضالت علينا واحدة بس. إذا جدرنا نثبت إن
+
+240
+00:26:42,660 --> 00:26:46,900
+الكرن للـPhi هو ال principle ideal generated by X،
+
+241
+00:26:46,900 --> 00:26:54,230
+بيقول خلصنا. خلصنا خلاص. يبقى الآن one to showone
+
+242
+00:26:54,230 --> 00:27:00,850
+two sure ان ال principle ideal generated by X هو
+
+243
+00:27:00,850 --> 00:27:09,210
+الكيرن للفعل سمولي العلاقة هذه رقم واحدة اذا
+
+244
+00:27:09,210 --> 00:27:16,530
+بدأ اقول خدي ال F of X موجودة في الكيرن للفعل
+
+245
+00:27:16,530 --> 00:27:20,230
+تمام؟ then
+
+246
+00:27:22,730 --> 00:27:30,630
+الـ Phi لل F of X بده يساوي Zero لإنها موجودة وين؟
+
+247
+00:27:30,630 --> 00:27:36,310
+في ال curve طب ال Phi لل F of X يبقى ده شبناها A
+
+248
+00:27:36,310 --> 00:27:42,410
+naught يبقى هذا بده يعطيك إن ال A naught بده يساوي
+
+249
+00:27:42,410 --> 00:27:48,350
+Zero تمام؟ يبقى هذا إذا كانت A naught تساوي Zero
+
+250
+00:27:48,720 --> 00:27:54,080
+يبقى شكل ال F of X اللي موجودة في ال kernel بدي
+
+251
+00:27:54,080 --> 00:28:01,160
+يكون على الشكل التالي ال F of X بدي يسوي A N X N A
+
+252
+00:28:01,160 --> 00:28:07,460
+N minus ال one X N minus ال one زائد اللي هو main
+
+253
+00:28:07,460 --> 00:28:14,320
+زائد A one X فقط لغير مش عندي A naught لإنه A
+
+254
+00:28:14,320 --> 00:28:20,040
+naught بزيهطيب شو رأيك؟ بدك تكتب هذه بطريقة ثانية
+
+255
+00:28:20,040 --> 00:28:28,880
+شو الطريقة الثانية؟ a n x أس n minus ال 1 زائد a n
+
+256
+00:28:28,880 --> 00:28:37,720
+minus ال 1 x n minus 2 زائد زائد a 1 كله في x
+
+257
+00:28:37,720 --> 00:28:45,250
+بنفع؟ Distributive law قانون التوزيعطيب هذا ال
+
+258
+00:28:45,250 --> 00:28:49,950
+element وين موجود؟ ال principle ideal generated by
+
+259
+00:28:49,950 --> 00:28:54,510
+X لأنه تحسب تعريف ال principle ideal هو ال X مضروب
+
+260
+00:28:54,510 --> 00:28:58,510
+في polynomial هي ال polynomial الموجودة هي ال X
+
+261
+00:28:58,510 --> 00:29:04,290
+إذا هذا موجود في ال principle ideal generated by X
+
+262
+00:29:04,290 --> 00:29:11,410
+يبقى أصبح ان الكيرن لل Phi هو ال subset من ال
+
+263
+00:29:11,410 --> 00:29:15,340
+principle ideal generated by Xإذا نمشي للعملية
+
+264
+00:29:15,340 --> 00:29:21,600
+العكسية يبقى بالداجة اقول انه افترض ان ال F of X
+
+265
+00:29:21,600 --> 00:29:26,940
+موجودة في ال principle ideal generated by X then
+
+266
+00:29:26,940 --> 00:29:36,400
+ايش شكل ال F of X؟ بده يكون ال X نفسها مضروبة في
+
+267
+00:29:36,400 --> 00:29:45,680
+polynomial والتكن G of X صحيح؟يعني هذه بدها تكون X
+
+268
+00:29:45,680 --> 00:29:54,860
+في مين؟ في الـ B M X M B M minus ال one X M minus
+
+269
+00:29:54,860 --> 00:30:05,560
+ال one زائد ال B one X زائد ال B نقطة طيب تدفك هذه
+
+270
+00:30:05,560 --> 00:30:16,380
+بصير B M X أس M plus one زائدpm-1xm
+
+271
+00:30:16,380 --> 00:30:26,040
+بزائد بزائد b1x ترابيع بزائد b نوت في ال x يبقى
+
+272
+00:30:26,040 --> 00:30:31,040
+الخنصار ال term صرف كم؟ ب zero يبقى هذه موجودة في
+
+273
+00:30:31,040 --> 00:30:37,180
+ال kernel يبقى هذه موجودة في ال kernel لل file
+
+274
+00:30:37,180 --> 00:30:43,850
+يبقى الصرف of x اللي أخدتها هناهي هذه امشي امشي
+
+275
+00:30:43,850 --> 00:30:48,750
+وجدتها موجودة وين؟ في الـ Kernel يبقى بقدر اقوله
+
+276
+00:30:48,750 --> 00:30:53,590
+ال principle ideal generated by X subset من ال
+
+277
+00:30:53,590 --> 00:31:00,490
+Kernel للـ Phi يبقى ذات و هكذا ال Kernel للـ Phi
+
+278
+00:31:00,490 --> 00:31:06,510
+بالضبط هو ال principle ideal generated by X ناخد
+
+279
+00:31:06,510 --> 00:31:12,030
+هذه المعلومة و نعود في Mainفي الولاقة رقم واحد
+
+280
+00:31:12,030 --> 00:31:18,810
+يبقى باجي بقوله هنا Substitute
+
+281
+00:31:18,810 --> 00:31:25,930
+N1 نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+282
+00:31:25,930 --> 00:31:29,010
+نحن
+
+283
+00:31:29,010 --> 00:31:29,490
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+284
+00:31:29,490 --> 00:31:29,490
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+285
+00:31:29,490 --> 00:31:29,490
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+286
+00:31:29,490 --> 00:31:29,490
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+287
+00:31:29,490 --> 00:31:38,210
+نحن نحن نحن نحن نحن
+
+288
+00:31:38,210 --> 00:31:48,380
+نهذا isomorphic لمين يا بنات؟ لكيو لكيو فيه؟ يبقى
+
+289
+00:31:48,380 --> 00:31:52,360
+part لكيو
+
+290
+00:31:52,360 --> 00:32:03,340
+is a field مدام field هذا بدي يعطيكي ان لكيو of x
+
+291
+00:32:03,340 --> 00:32:11,350
+modular principle is a fieldطب مدى فيه يبقى ال
+
+292
+00:32:11,350 --> 00:32:18,310
+ideal هذا ماله؟ maximum يبقى هذا بدي يعطيكي ال
+
+293
+00:32:18,310 --> 00:32:27,570
+maximum ideal في اللي هو الرنجل اللي عندك هذا فيكم
+
+294
+00:32:27,570 --> 00:32:35,330
+اي تساؤل؟ حلت المشكلة؟ بلاص؟ يبقى انا كان بدي
+
+295
+00:32:35,330 --> 00:32:39,330
+الفكرة الاساسية يقول الفكرة كلمة في الشريفيا إما
+
+296
+00:32:39,330 --> 00:32:43,510
+استخدام ال first isomorphism theorem يا إما نستخدم
+
+297
+00:32:43,510 --> 00:32:48,030
+التعريف تبع ال maximal ideal بأي طريقة بهذه أو
+
+298
+00:32:48,030 --> 00:32:53,490
+بهذه نوصل ماعندنا مشكلة هذا كان سؤال تمنتاشر من
+
+299
+00:32:53,490 --> 00:32:57,850
+التدريبين قبل ما أنا لان سؤال أربعة وعشرين
+
+300
+00:32:57,850 --> 00:33:01,850
+qualitative theory of z of x is not a principle
+
+301
+00:33:01,850 --> 00:33:14,700
+ideal domain سؤال أربعة وعشرين شهرthat z of x is
+
+302
+00:33:14,700 --> 00:33:28,840
+not a principal ideal domain وإيش
+
+303
+00:33:28,840 --> 00:33:34,040
+معنى principal ideal domain لكل ideal يكون
+
+304
+00:33:34,040 --> 00:33:39,480
+principal صحيح ولا لأ؟يعني احنا لو جيبنا ID الواحد
+
+305
+00:33:39,480 --> 00:33:44,480
+واثبتنا انه هذا not a principle خلاص بتبطّر أصير
+
+306
+00:33:44,480 --> 00:33:48,700
+principle ID الدومية مش هي الفكرة؟ يعني جيبنا
+
+307
+00:33:48,700 --> 00:33:53,880
+counter example ضد انها تكون principle ID الدومية
+
+308
+00:33:53,880 --> 00:33:59,880
+بيكون حلنا الإشكالية أعتقد ولا واحدة حلت السؤال؟
+
+309
+00:33:59,880 --> 00:34:02,840
+طيب ده الفكرة بس هالكش .. بس هالكش .. بس هالكش ..
+
+310
+00:34:02,840 --> 00:34:05,380
+بس هالكش .. بس هالكش .. بس هالكش .. بس هالكش .. بس
+
+311
+00:34:05,380 --> 00:34:05,900
+هالكش .. بس هالكش .. بس هالكش .. بس هالكش .. بس
+
+312
+00:34:05,900 --> 00:34:09,640
+هالكش .. بس هالكش ..الان بدنا نبدأ بشيء انتوا
+
+313
+00:34:09,640 --> 00:34:14,820
+اخدتهوا قبل ذلك ايديل اخدتهوا عارفينه واشتغلنا
+
+314
+00:34:14,820 --> 00:34:20,720
+عليه قبل ذلك في امتلة سابعة الان لو جاتى بنات لمن؟
+
+315
+00:34:20,720 --> 00:34:29,200
+لال ايديل اللى هو ال X و 2 اللى كل العناصر X في ال
+
+316
+00:34:29,200 --> 00:34:36,220
+F of X زي ال 2 في ال U of Xبحيث ان ال F of X و G
+
+317
+00:34:36,220 --> 00:34:46,620
+of X موجود في Z of X موجود في Z of X شوفناها قبل
+
+318
+00:34:46,620 --> 00:34:50,280
+ايديك و قبل ايديك ولا لا؟ شوفناها و كتبناها و
+
+319
+00:34:50,280 --> 00:34:55,800
+إشتغلناها و حلناها بعدد مسائل طيب إذا كنت أثبت ان
+
+320
+00:34:55,800 --> 00:35:01,280
+هذا مشي principle خلاص بصي Z of X is not a
+
+321
+00:35:01,280 --> 00:35:13,230
+principle صحيح؟طيب if we show that ان ال .. ال ..
+
+322
+00:35:13,230 --> 00:35:21,990
+ال ideal x و 2 is not principal then
+
+323
+00:35:21,990 --> 00:35:30,050
+z of x is not
+
+324
+00:35:33,300 --> 00:35:39,800
+a principle is not a principle ideal domain خلاص
+
+325
+00:35:39,800 --> 00:35:47,740
+بقى
+
+326
+00:35:47,740 --> 00:35:53,480
+مرة تانية أنا خدت ideal موجود في zip of x وبدى
+
+327
+00:35:53,480 --> 00:35:58,900
+أحاول أثبت هذا انه is not a principle يعني ايشيعني
+
+328
+00:35:58,900 --> 00:36:04,380
+بدي اثبت ان هذا ال ID لا يمكن ان يولد بعنصر واحد
+
+329
+00:36:04,380 --> 00:36:10,140
+لا يمكن ان يولد ببولنوميا لان العنصر هنا بولنوميا
+
+330
+00:36:10,140 --> 00:36:14,580
+لمعاملات واعداد صحيحة اللي هي جاية من وين؟ جاية من
+
+331
+00:36:14,580 --> 00:36:21,840
+هنا يبقى that is
+
+332
+00:36:21,840 --> 00:36:24,900
+f
+
+333
+00:36:24,900 --> 00:36:45,800
+vshow that ان الـ X و 2 is not generated but by
+
+334
+00:36:45,800 --> 00:36:54,620
+a single polynomial then
+
+335
+00:36:54,620 --> 00:36:56,780
+we
+
+336
+00:36:58,660 --> 00:37:09,280
+the result يعني
+
+337
+00:37:09,280 --> 00:37:14,880
+إذا قدرنا نثبت إن الـ ideas اللي عندنا لأ يمكن أن
+
+338
+00:37:14,880 --> 00:37:20,160
+يولد ب polynomial واحدة بيكون حصلنا مين حصلنا على
+
+339
+00:37:20,160 --> 00:37:25,620
+النتيجة بتأثبت بال contradiction assume not مش
+
+340
+00:37:25,620 --> 00:37:27,540
+صحيح يبقى
+
+341
+00:37:32,480 --> 00:37:40,720
+not ليش يعني اسيوم not؟ يعني that is ان ال
+
+342
+00:37:40,720 --> 00:37:46,340
+principle id generated by x و 2 بدي يولد بكثير
+
+343
+00:37:46,340 --> 00:37:56,240
+حدود و أنت كون P of x where حيث ال P of x هي
+
+344
+00:37:56,240 --> 00:38:01,000
+polynomial موجودة وين Pz of x
+
+345
+00:38:06,920 --> 00:38:11,860
+إذا أنا بأحاول أثبت بالتناقض بإن أنا بدي أثبت إن
+
+346
+00:38:11,860 --> 00:38:17,200
+هداك لا يمكن أن يولد بعنصر واحد و تفترض أنه ولد
+
+347
+00:38:17,200 --> 00:38:22,220
+بعنصر واحد اللي هو P of X بدي أشوف هذا بدي يقودني
+
+348
+00:38:22,220 --> 00:38:26,620
+إلى شغل صح و الله إلى شغل خطر إذا الله قادي إلى
+
+349
+00:38:26,620 --> 00:38:32,120
+شغل خطر يبقى فرض اللي فرضته غلط و عكسه هو إيه هو
+
+350
+00:38:32,120 --> 00:38:37,410
+الصح يعني لا يمكن لهذا اللي أيديه ال X و 2هنيولد
+
+351
+00:38:37,410 --> 00:38:44,370
+بعمطرين واحد يبقى ذاتس فرقته انه يولد بال P of X
+
+352
+00:38:44,370 --> 00:38:51,870
+السؤال هو هال اتنين يا بنات موجود في ال ID ال X و
+
+353
+00:38:51,870 --> 00:38:58,830
+اتنين ؟ موجود صحيح ايه ؟ خط X بالزيرو و G of X
+
+354
+00:38:58,830 --> 00:39:02,290
+بالواحد او G of Zero بالواحد فلسنا يبقى الاتنين
+
+355
+00:39:02,290 --> 00:39:10,670
+موجود طيب مدان موجودthen الاتنين موجود في P of X
+
+356
+00:39:10,670 --> 00:39:20,030
+او موجود في P of X ال incident ideal generated by
+
+357
+00:39:20,030 --> 00:39:28,750
+P of X مظبوط يعني يعني شو شكلوا الاتنين هذا بدي
+
+358
+00:39:28,750 --> 00:39:35,460
+يعطينا ان الاتنين بدي يساوي P of X تمامفي
+
+359
+00:39:35,460 --> 00:39:41,740
+polynomial تانية P of X مش شيف تعريف ال principle
+
+360
+00:39:41,740 --> 00:39:48,320
+ال principle ال P of X في polynomial تانية بده
+
+361
+00:39:48,320 --> 00:39:53,480
+يعطينا ال element اللي هو اتنين الآن ما هو تفسير و
+
+362
+00:39:53,480 --> 00:39:59,140
+كنا لهذه المعادلة الأخيرة شو علاقة ال P of X
+
+363
+00:39:59,140 --> 00:40:06,850
+بالاتنين؟و تقسم تقسم تمام كلامي كويس يبقى هدف اللي
+
+364
+00:40:06,850 --> 00:40:17,490
+بده يعطينا ان ال PRX divide لإتنين طب ما هي قاسم
+
+365
+00:40:17,490 --> 00:40:23,150
+إتنين واحد و سالب واحد و اتنين و سالب اتنين واحد و
+
+366
+00:40:23,150 --> 00:40:28,030
+سالب واحد مستبعد لإن هذا بيجيبلي عنصر واحد فقط
+
+367
+00:40:28,030 --> 00:40:35,410
+واحد مش غيرمظبوط طيب الان يبقى مفضلش عندي يا إما
+
+368
+00:40:35,410 --> 00:40:43,350
+اتنين يا إما مين سالب اتنين يبقى هذا معناته ان ال
+
+369
+00:40:43,350 --> 00:40:50,390
+P of X يا إما بده يسوي سالب اتنين يا إما ال P of X
+
+370
+00:40:50,390 --> 00:40:57,030
+بده يسوي كده؟ بده يسوي اتنين يجي علي كل الأمرين ال
+
+371
+00:40:57,030 --> 00:41:04,820
+P of X بده يسوي constantمظبوط؟ يبقى هذا معناته ان
+
+372
+00:41:04,820 --> 00:41:12,920
+ال P of X بده يساوي K وال K يا اما زائد او ناقص
+
+373
+00:41:12,920 --> 00:41:21,300
+اتنين طبعا؟ طيب كويس نجي لصحة هذا الكلام اللي احنا
+
+374
+00:41:21,300 --> 00:41:28,580
+ابنه يبقى ايش صار عندنا؟ صار عندنا ال P of X بده
+
+375
+00:41:28,580 --> 00:41:35,580
+يساوي Kيبقى هنا ال principle او ال ideal ال X
+
+376
+00:41:35,580 --> 00:41:40,980
+والإتنين هو ال principle ال ideal generated by X
+
+377
+00:41:40,980 --> 00:41:47,280
+وهو ال principle ال ideal generated by K وال K هذي
+
+378
+00:41:47,280 --> 00:41:54,680
+زائد او لاقص اتنين كمان سؤال ايش من هنا؟ نين
+
+379
+00:41:54,680 --> 00:42:04,490
+موجودة هنا السؤال هو ال X موجودةهنا ولا لا؟ لما؟
+
+380
+00:42:04,490 --> 00:42:15,590
+ال X بدها تساوي آه، إيش بدها تساوي؟ كده؟
+
+381
+00:42:15,590 --> 00:42:22,070
+مش داريه، مش شايف كله قدامي هنا ولا لا؟ بقالي بدي
+
+382
+00:42:22,070 --> 00:42:29,090
+أجرب هالك أكتر، ال X موجودةمعناته ال X موجودة في
+
+383
+00:42:29,090 --> 00:42:34,410
+ال principle ideal generated by K مظبوط يعني
+
+384
+00:42:34,410 --> 00:42:44,610
+معناته ان ال X بده ساوي H of X في K وكتيش
+
+385
+00:42:44,610 --> 00:42:50,610
+بيكون الكلام هذا صحيح لو كان ال H of X هي
+
+386
+00:42:50,610 --> 00:42:58,090
+polynomial من الدرجة الأولىفي غير هيكد؟ لأ لإن X
+
+387
+00:42:58,090 --> 00:43:02,790
+polynomial من الدرجة الأولى يبقى هذا كيفش هذا
+
+388
+00:43:02,790 --> 00:43:08,110
+الكلام صحيح فقط إذا كانت H of X polynomial من
+
+389
+00:43:08,110 --> 00:43:17,890
+الدرجة الأولى يبقى this is a proof when
+
+390
+00:43:17,890 --> 00:43:21,590
+ال
+
+391
+00:43:21,590 --> 00:43:29,590
+H of Xيساوي ax او ax زائد b ناخدها الأبسط اكس
+
+392
+00:43:29,590 --> 00:43:38,350
+ومدناشر ال b طيب هذا بدي يعطينا ان ال x بدي ساوي
+
+393
+00:43:38,350 --> 00:43:51,190
+ax في k او ال x بدي ساوي ak في xطب هدول ال A و ال
+
+394
+00:43:51,190 --> 00:43:57,770
+K أرقام و ال X موجودة وين؟ في Z نشتغل في Z احنا و
+
+395
+00:43:57,770 --> 00:44:05,330
+Z X تمام؟ يبقى هذا معناته ان ال A K بقداش يا بنات؟
+
+396
+00:44:05,330 --> 00:44:11,270
+بقداش؟ واحد، بواحد، تمام، لكن لو كان فيش فيها
+
+397
+00:44:11,270 --> 00:44:16,190
+الواحد ال Z بصير كلامنا مش صحيح، لكن الواحد موجود
+
+398
+00:44:16,190 --> 00:44:24,550
+في ال Zإذا الـ A K يبقى أحد السؤال هو واجتيش من
+
+399
+00:44:24,550 --> 00:44:30,010
+خلال هذه المعادلة لأن K معروفة أنها مجدد شبنات
+
+400
+00:44:30,010 --> 00:44:38,410
+اتنين و سالب اتنين إذا هذا الكلام ليس صحيحا إلا
+
+401
+00:44:38,410 --> 00:44:46,510
+إذا كانت A مرة بسالب نص و مرة نص مظبوط يبقى هنا
+
+402
+00:44:48,470 --> 00:44:56,510
+فالـ K تساوي سالب اتنين ثم ال A تساوي سالب نصر،
+
+403
+00:44:56,510 --> 00:45:05,070
+مظبوط؟ طيب لو كانت ال K تساوي اتنين ثم ال A تساوي
+
+404
+00:45:05,070 --> 00:45:11,270
+نصر، حاصل ضربهما بالواحد اللي هناك، حاصل ضربهما
+
+405
+00:45:11,270 --> 00:45:19,030
+بالواحد اللي هناك السؤال هذا موجود في Zلأ لأ هذا
+
+406
+00:45:19,030 --> 00:45:26,270
+موجود في Z لأ طب احنا لما نجينا خدنا ال H of X ال
+
+407
+00:45:26,270 --> 00:45:32,970
+A هذه وين موجودة يا بناها Z ولا لأ Z لإن احنا مش
+
+408
+00:45:32,970 --> 00:45:41,570
+خالع Z و ZX يبقى هذه موجودة في Z أصلا تمام طب هنا
+
+409
+00:45:41,570 --> 00:45:48,820
+A موجودة في Zقطلة A تصير موجودة في Z يبقى إيش هذا
+
+410
+00:45:48,820 --> 00:45:55,860
+بيعطينا هذا contradiction to
+
+411
+00:45:55,860 --> 00:46:02,860
+ال A موجودة في Z مدام تناقض يبقى شو جاب التناقض
+
+412
+00:46:02,860 --> 00:46:11,880
+جاب الخرض الغلط بظبط يبقى هنا أساس اللي هو ال X
+
+413
+00:46:12,730 --> 00:46:18,170
+والإتنين cannot be
+
+414
+00:46:18,170 --> 00:46:21,350
+generated
+
+415
+00:46:21,350 --> 00:46:33,670
+by a single polynomial معناته
+
+416
+00:46:33,670 --> 00:46:40,500
+لا يمكن أن يكون هذا ال principle، that isالـ X و
+
+417
+00:46:40,500 --> 00:46:48,280
+الأتنين is not a principal ID
+
+418
+00:46:48,280 --> 00:46:54,520
+مدى ما هوش principal ID، هاي جيبناله ك example
+
+419
+00:46:54,520 --> 00:47:03,760
+يبقى Z of X is not a principal ID
+
+420
+00:47:08,840 --> 00:47:15,360
+يبقى نجيبناله counter example بيكفي للإجابة على
+
+421
+00:47:15,360 --> 00:47:20,560
+السؤال هذا كان سؤال اربعة وعشرين الآن بنجي لسؤال
+
+422
+00:47:20,560 --> 00:47:25,480
+تلاتين سؤال
+
+423
+00:47:25,480 --> 00:47:32,800
+تلاتين بقول ال F فيه وزيادة
+
+424
+00:47:32,800 --> 00:47:42,060
+على ذلك ال F of Xبدي أساوي a n x to the power n
+
+425
+00:47:42,060 --> 00:47:48,380
+minus ال one x to the power n minus ال one a one x
+
+426
+00:47:48,380 --> 00:47:57,200
+زائد ال a naught موجود وموجود في كتاب تبقى full
+
+427
+00:47:57,200 --> 00:48:06,080
+text بيقول لما ياتي المطلوب prove that prove that
+
+428
+00:48:07,140 --> 00:48:17,160
+من ال X ناقص الواحد is a factor of F of X if and
+
+429
+00:48:17,160 --> 00:48:25,960
+only if F and only if ال A N زائد ال A N minus ال
+
+430
+00:48:25,960 --> 00:48:31,920
+one زائد ال A one زائد ال A naught يساوي زيو
+
+431
+00:48:43,910 --> 00:48:49,570
+سؤال مرة تانية نعطينا ال field بطلنا integral
+
+432
+00:48:49,570 --> 00:48:55,850
+domain يبقى كل أنصر له معكوس أخدنا polynomial ring
+
+433
+00:48:55,850 --> 00:49:01,430
+في هذا ال field تمام على الشكل اللي عندنا هذا
+
+434
+00:49:01,430 --> 00:49:08,090
+فجالي اثبت ان ال X ماقص واحد هو factor لل F of X F
+
+435
+00:49:08,090 --> 00:49:13,990
+and all F إذا كان مجموع المعاملات يساوي Zكلمة f
+
+436
+00:49:13,990 --> 00:49:19,610
+and o left تعني ان القرآن بيصير اتجاهين يبقى ناخد
+
+437
+00:49:19,610 --> 00:49:28,150
+الاتجاه الأول assume that افترض ان ال x ناقص
+
+438
+00:49:28,150 --> 00:49:41,830
+الواحد is a factor of ال f of x افترض انه 30 طيب
+
+439
+00:49:42,720 --> 00:49:47,520
+أخدنا كرولري السابقة بتقول إن هذا لو كان factor
+
+440
+00:49:47,520 --> 00:49:53,660
+يبقى X يساوي واحد هو مين؟ Zero للدالة يعني لو
+
+441
+00:49:53,660 --> 00:49:58,980
+عوضنا بال X بواحد النتج بدي يعطينا جدير يساوي Zero
+
+442
+00:49:58,980 --> 00:50:09,920
+يبقى assume that then ال X يساوي واحد is a zero of
+
+443
+00:50:09,920 --> 00:50:22,530
+F of Xthat is أي أن ال F of واحد بده يساوي Z طيب
+
+444
+00:50:22,530 --> 00:50:29,970
+هذا معناه وين ال F؟ هاي يبقى Zero بده يساوي ال F
+
+445
+00:50:29,970 --> 00:50:37,690
+of واحد بده يساوي ال A N الواحد to the power N A N
+
+446
+00:50:37,690 --> 00:50:43,530
+minus ال one مرة في واحد أس N minus ال oneزائد
+
+447
+00:50:43,530 --> 00:50:51,030
+زائد a one في واحد زائد ال a nine طب هذا ايش
+
+448
+00:50:51,030 --> 00:50:57,230
+معناته؟ معناته انه zero يساوي واحد ترفيع ولا واحد
+
+449
+00:50:57,230 --> 00:51:02,370
+تكيب ولا واحد قص مية ولا واحد قص الف كله يقلب واحد
+
+450
+00:51:02,370 --> 00:51:10,330
+يبقى هذا معناه a n زائد a n minus ال one زائد a
+
+451
+00:51:10,330 --> 00:51:16,200
+oneزائد ال a نوت اظنوا هو المفترض خلاص من اتجاه
+
+452
+00:51:16,200 --> 00:51:23,060
+الاول من جهة اتجاه التانية on the other hand
+
+453
+00:51:23,060 --> 00:51:26,640
+assume
+
+454
+00:51:26,640 --> 00:51:38,740
+ترضوا that ان ال a n زائد ال a n minus ال one زائد
+
+455
+00:51:38,740 --> 00:51:48,880
+ال a oneزائد ال a0 يساوي زيه ايش بدى اثبت X ناقص
+
+456
+00:51:48,880 --> 00:51:57,620
+واحد عبارة عن factor لمن ل ال polynomial f of X او
+
+457
+00:51:57,620 --> 00:52:03,940
+لو جدرت اثبت ان الواحد هو عبارة عن zero لهذه ال
+
+458
+00:52:03,940 --> 00:52:09,500
+polynomial بكره اللي اثنين عندكمبدي يكون ال X ناقص
+
+459
+00:52:09,500 --> 00:52:16,060
+واحد هو عبارة عن factor طيب
+
+460
+00:52:16,060 --> 00:52:21,540
+بدي أحاول المعادلة هذه أكتبها بصيغة أخرى و أشوف
+
+461
+00:52:21,540 --> 00:52:30,820
+يبجد ان ال A N في الواحد أس N يبجد ايه ايه ايه A N
+
+462
+00:52:30,820 --> 00:52:40,000
+ايه A N ماساويش شي تمام زادan-1 في الواحد أس n-1
+
+463
+00:52:40,000 --> 00:52:48,460
+زاد زاد a1 في الواحد زاد a0 ليست ب zero طب ايش
+
+464
+00:52:48,460 --> 00:52:56,600
+تفسيرك لهذه ان الواحد عبارة عن zero يبقى هنا this
+
+465
+00:52:56,600 --> 00:53:04,200
+means that ان الواحد is
+
+466
+00:53:06,600 --> 00:53:15,520
+A0 of the polynomial F
+
+467
+00:53:15,520 --> 00:53:22,120
+of X اللي عندنا هذا الـ F of X الأساسي يعني أين
+
+468
+00:53:22,120 --> 00:53:28,280
+راح تقيم يبقى هذا معناته أن واحد حل لمين بهذه
+
+469
+00:53:28,280 --> 00:53:32,460
+المثل مدام حل يبقى Pi
+
+470
+00:53:36,690 --> 00:53:42,330
+إتنين اللي خدناها المرة اللي فاتت ال X ناقص الواحد
+
+471
+00:53:42,330 --> 00:53:56,610
+is a factor is a factor of the polynomial F
+
+472
+00:53:56,610 --> 00:53:57,470
+of X
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/iH5Kjc7tIXA.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/iH5Kjc7tIXA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1f3c90a8b02212da92cd029496c7aae7fd649ffa
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/iH5Kjc7tIXA.srt
@@ -0,0 +1,1290 @@
+1
+00:00:20,740 --> 00:00:24,140
+بسم الله الرحمن الرحيم، ابتدأنا المرة اللي فاتت في
+
+2
+00:00:24,140 --> 00:00:27,900
+شهر خمسة عشر، اللي هو Ring Homomorphism، أعطينا
+
+3
+00:00:27,900 --> 00:00:31,260
+تعريفًا للـ Ring Homomorphism، وأخذنا على ذلك، اللي
+
+4
+00:00:31,260 --> 00:00:36,480
+هو خمسة أمثلة، مضبوط؟ نعم، صح. طيب، بدي أسألك سؤالي
+
+5
+00:00:36,480 --> 00:00:37,140
+ثاني،
+
+6
+00:00:49,940 --> 00:00:58,800
+لِمَن؟ للـ Z الاثنين. هل الـ Z متشابه (isomorphic) للـ Z الاثنين؟
+
+7
+00:00:58,800 --> 00:01:02,960
+حلقة؟ آه، آه، حلقة لأن هذا الـ U نفسه هو الواحد،
+
+8
+00:01:02,960 --> 00:01:07,420
+هذا الشيء يعني مئة بالمئة، بقول two rings  مشان يكون
+
+9
+00:01:07,420 --> 00:01:11,060
+بينهم isomorphism يكون جميع الخواص الرياضية للـ
+
+10
+00:01:11,060 --> 00:01:16,040
+rings الأولى، لو الثانية لهم نفس الخواص الرياضية،
+
+11
+00:01:16,040 --> 00:01:23,500
+two rings لهم نفس الـ properties من ناحية الرياضية. Z
+
+12
+00:01:23,500 --> 00:01:27,260
+فيها الـ unity،  بس Z الاثنين ما فيه unity  بجهته اللي
+
+13
+00:01:27,260 --> 00:01:36,900
+يمكن أن يكون isomorphic لبعضهما. يبقى الـ answer Z
+
+14
+00:01:36,900 --> 00:01:46,880
+is not isomorphic لـ Z الاثنين. السبب because Z
+
+15
+00:01:50,700 --> 00:02:05,940
+unity unity but  Z الاثنين ليس به unity.
+
+16
+00:02:05,940 --> 00:02:11,540
+طيب
+
+17
+00:02:11,540 --> 00:02:13,780
+نواصل example 6
+
+18
+00:02:19,610 --> 00:02:26,570
+مثال 6 بيقول determine حدد
+
+19
+00:02:26,570 --> 00:02:33,430
+all ring homomorphisms
+
+20
+00:02:33,430 --> 00:02:42,930
+from Z12 to Z30
+
+21
+00:03:02,200 --> 00:03:08,120
+السؤال مرة ثانية يقول حدد لي كم homomorphism من
+
+22
+00:03:08,120 --> 00:03:14,800
+Z12 إلى Z30. يمكن يطلع أكثر ويمكن يطلع اثنين بيساوا
+
+23
+00:03:14,800 --> 00:03:18,900
+بعض، يمكن ثلاثة بيساوا بعض، هذول الثلاثة اللي بيساوا
+
+24
+00:03:18,900 --> 00:03:22,560
+بعض أو اثنين بيساوا بعض يعتبر واحد. homomorphism
+
+25
+00:03:22,560 --> 00:03:27,800
+واحد فقط، إذا بدنا نحدد مين هم الـ discrete
+
+26
+00:03:27,800 --> 00:03:31,730
+homomorphism أو الـ destined homomorphism. مين الـ
+
+27
+00:03:31,730 --> 00:03:35,670
+homomorphism اللي ولا واحد زي الثاني، تعالوا نشوف.
+
+28
+00:03:35,670 --> 00:03:46,790
+كتب، نحلل مثلًا، بدي بقول له any homomorphism Φ من Z
+
+29
+00:03:46,790 --> 00:03:59,310
+12 إلى Z 30 is defined by. بروح نعرفه بالشكل الثاني.
+
+30
+00:03:59,910 --> 00:04:13,410
+Φ(x) بده يساوي x modulo 30. طيب
+
+31
+00:04:13,410 --> 00:04:21,590
+الآن لو جيت لـ Φ(x)، Φ(x) الـ x وين موجودة
+
+32
+00:04:21,590 --> 00:04:25,350
+هذه يا بنات؟ Z اثنا عشر، يعني ممكن يكون صفر، واحد،
+
+33
+00:04:25,350 --> 00:04:31,620
+اثنين، ثلاثة لغاية أحد عشر. تمام؟ إذا بقدر أقول هي  Φ
+
+34
+00:04:31,620 --> 00:04:39,260
+of واحد + واحد + واحد + ...  كم مرة؟ x times
+
+35
+00:04:39,260 --> 00:04:44,660
+يعني x من المرات. يعني لو كانت Φ of ثلاثة، بدي يكون
+
+36
+00:04:44,660 --> 00:04:48,180
+واحد + واحد + واحد. كانت Φ of سبعة، بدي أحط
+
+37
+00:04:48,180 --> 00:04:51,960
+واحد + واحد سبع مرات. Φ of عشرين، بيجي واحد
+
+38
+00:04:51,960 --> 00:04:57,740
++ واحد عشرين مرة وهكذا. طيب، الآن فيجي لي
+
+39
+00:04:57,740 --> 00:05:04,460
+homomorphism، تمام؟ إذا هذا بيبقى يساوي Φ of one
+
+40
+00:05:04,460 --> 00:05:13,620
++ Φ of one + Φ of one. كم مرة حتقولي؟ x، يبقى
+
+41
+00:05:13,620 --> 00:05:22,140
+هذا الكلام بيبقى يساوي x في Φ of one، تمام؟ وهذا
+
+42
+00:05:22,140 --> 00:05:29,910
+الكلام لكل الـ x اللي موجودة في Z12. إذا صار Φ of x
+
+43
+00:05:29,910 --> 00:05:36,210
+اللي عندنا يساوي x في Φ of 1، تمام؟ يبقى إيش اللي
+
+44
+00:05:36,210 --> 00:05:45,810
+صار عندنا؟ صار عندنا Φ(x) يساوي x في Φ(1).
+
+45
+00:05:45,810 --> 00:05:53,450
+بهذا الشكل، طيب لو جيت لـ Φ(1)، هذا element
+
+46
+00:05:53,450 --> 00:05:59,880
+وين؟ في Z الثلاثين. بدي اسميه a مثلًا، على سبيل المثال.
+
+47
+00:05:59,880 --> 00:06:07,260
+يبقى هنا بحتاج أقول له put Φ(1) يساوي a و
+
+48
+00:06:07,260 --> 00:06:12,360
+بعدين نبحث إيش الشكل الـ a ممكن يكون. إذا هذا بدي
+
+49
+00:06:12,360 --> 00:06:23,900
+يكون x في a، تمام؟ اللي ممكن اسميه لسه هو Φ(a) of x.
+
+50
+00:06:25,690 --> 00:06:32,530
+يبقى Φ(x) والله Φ(a)(x) هو نفس الشيء ويساوي حاصل
+
+51
+00:06:32,530 --> 00:06:38,310
+ضرب الـ x في من؟ في الـ a. سيبقى لي هذه المعلومة
+
+52
+00:06:38,310 --> 00:06:48,210
+ونرجع لها إن شاء الله بعد قليل. نجي للـ a، الـ a بده
+
+53
+00:06:48,210 --> 00:06:54,620
+يساوي Φ(1)، احنا فرضناه. يبقى بيصير الـ order للـ
+
+54
+00:06:54,620 --> 00:07:02,320
+a بيساوي الـ order لـ Φ(1) مضبوط؟ إيش الـ
+
+55
+00:07:02,320 --> 00:07:09,600
+order؟ أصغر عدد صحيح موجب بحطه أس الـ a بتعطيني
+
+56
+00:07:09,600 --> 00:07:17,100
+الـ identity أو الـ unity عندنا. طيب، الآن الـ order
+
+57
+00:07:17,100 --> 00:07:22,720
+لـ a بيقول يساوي الـ order لـ Φ(1). لو راجعنا
+
+58
+00:07:22,720 --> 00:07:27,080
+للـ groups، لو
+
+59
+00:07:27,080 --> 00:07:31,780
+كان الـ Φ isomorphism، يبقى الـ order لـ Φ(a)
+
+60
+00:07:31,780 --> 00:07:37,000
+هو الـ order للـ a. لكن لما يكون الـ Φ homomorphism،
+
+61
+00:07:37,000 --> 00:07:42,980
+فالـ order لـ Φ(a) بيقسم الـ order للـ a. يبقى الـ
+
+62
+00:07:42,980 --> 00:07:51,310
+order لـ Φ(1) بيقسم الـ order للـ 1. يبقى هذا
+
+63
+00:07:51,310 --> 00:07:58,710
+بده يقسم الـ order لـ what. تعالوا نفهم إيش هذا
+
+64
+00:07:58,710 --> 00:08:06,110
+الكلام. هذا بده يعطينا الـ order للـ a بده يساوي الـ
+
+65
+00:08:06,110 --> 00:08:12,130
+order لـ Φ(1). يبقى الـ order للـ a بده يساوي
+
+66
+00:08:12,130 --> 00:08:13,670
+هو الـ a، وإيش الموجود
+
+67
+00:08:20,260 --> 00:08:26,980
+يبقى الـ order اللي بدّه يقسم الثلاثين، صح ولا لأ؟
+
+68
+00:08:26,980 --> 00:08:34,160
+يبقى هذا الـ order اللي بده يقسم الثلاثين implies
+
+69
+00:08:34,160 --> 00:08:40,180
+أن الـ order للـ a ممكن يكون واحد وممكن يكون اثنين،
+
+70
+00:08:40,180 --> 00:08:46,100
+وثلاثة، وأربعة، بتقسم الثلاثين. ممكن يكون خمسة، ممكن
+
+71
+00:08:46,100 --> 00:08:53,400
+يكون ستة، ممكن عشرة، ممكن خمسة، عشرة، ممكن ثلاثين،
+
+72
+00:08:53,400 --> 00:08:58,780
+كل الاحتمالات هذه وارد. تمام؟ الحين بنقول الـ order
+
+73
+00:08:58,780 --> 00:09:04,340
+لـ Φ بيقسم الـ order للواحد. الواحد هذا وين موجود؟
+
+74
+00:09:04,340 --> 00:09:12,160
+في الـ Z12، الـ Φ(1)، يبقى الواحد هذا تبع الـ Z12.
+
+75
+00:09:12,860 --> 00:09:21,860
+يبقى الـ order للـ a اللي هو هذا بده يقسم اللي هو
+
+76
+00:09:21,860 --> 00:09:29,680
+الـ 12. بده يقسم الـ order للواحد. بده يقسم الـ order
+
+77
+00:09:29,680 --> 00:09:34,080
+للواحد اللي هو بده يساوي 12. هذا معناه أن الـ
+
+78
+00:09:34,080 --> 00:09:40,460
+order للـ a ممكن يكون واحد أو اثنين أو ثلاثة أو
+
+79
+00:09:40,460 --> 00:09:48,480
+أربعة، بيقسم الاثنا عشر، أو ستة، أو اثنا عشر. في غير هذول؟ لا،
+
+80
+00:09:48,480 --> 00:09:51,460
+يبقى هذه الاحتمالات الواردة، بدي أشوف مين
+
+81
+00:09:51,460 --> 00:09:56,400
+الاحتمالات الصحيحة منهم، وبالتالي بروح بقول يبقى
+
+82
+00:09:56,400 --> 00:10:03,680
+من الاثنين هذول مع بعض، بدل ما أستنتج ما يأتي، أن الـ
+
+83
+00:10:03,680 --> 00:10:07,960
+order للـ a يا إما واحد، يا اثنين،
+
+84
+00:10:11,680 --> 00:10:15,660
+لأ، لأنه الخمسة موجودة فوق ومش موجودة تحت. والأربعة
+
+85
+00:10:15,660 --> 00:10:20,880
+موجودة تحت ومش موجودة فوق. يبقى ستة. في غير هذول؟ لأ.
+
+86
+00:10:20,880 --> 00:10:29,660
+طيب، إذا بدي أدور على الـ a، إيش ممكن تكون الـ a؟ هي الـ
+
+87
+00:10:29,660 --> 00:10:32,860
+order يا واحد، يا اثنين، يا ثلاثة، يا ستة، بدي أروح
+
+88
+00:10:32,860 --> 00:10:39,340
+أدور على العناصر اللي في Z ثلاثين لأن الـ a في Z
+
+89
+00:10:39,340 --> 00:10:44,260
+ثلاثين. مين العناصر اللي في Z الثلاثين الـ order لها
+
+90
+00:10:44,260 --> 00:10:48,340
+يساوي واحد أو اثنين أو ثلاثة أو ستة؟ طب الـ order
+
+91
+00:10:48,340 --> 00:10:53,500
+يساوي واحد لمين؟ للصفر. صفر أس واحد يساوي صفر،
+
+92
+00:10:53,500 --> 00:11:01,720
+يبقى الـ a ممكن يكون صفر، طيب الـ order يساوي اثنين،
+
+93
+00:11:01,720 --> 00:11:07,260
+خمسة عشر. خمسة عشر × اثنين ثلاثين. اثنين
+
+94
+00:11:07,260 --> 00:11:14,800
+ثلاثة، عشرة، عشرين، بينفع، بينفع. يبقى عشرة أو
+
+95
+00:11:14,800 --> 00:11:19,980
+عشرين، العشرة والعشرين اللي الـ order تبعهم ثلاثة.
+
+96
+00:11:19,980 --> 00:11:24,220
+ثلاثة في عشرين ستين تعني صفر. ثلاثة في عشرة
+
+97
+00:11:24,220 --> 00:11:28,280
+ثلاثين تعني صفر. في غير هذول بالنسبة
+
+98
+00:11:28,280 --> 00:11:35,080
+لثلاثة؟ لا. طيب اللي الـ order إلها يساوي ستة زي مين؟
+
+99
+00:11:35,080 --> 00:11:41,990
+خمسة، وخمسة وعشرين. خمسة وعشرين × ستة
+
+100
+00:11:41,990 --> 00:11:47,830
+مئة وخمسين أو ما يعني، والمئة وخمسين تعني صفر بالنسبة للثلاثين.
+
+101
+00:11:47,830 --> 00:11:53,330
+يبقى خمسة وعشرين مظبوط، تمام؟ يبقى هذه كل العناصر
+
+102
+00:12:00,270 --> 00:12:06,930
+اللي ممكن ناخدها من Z الثلاثين والتي تحقق Φ of
+
+103
+00:12:06,930 --> 00:12:11,630
+one يساوي a. يبقى هذا بيصير الصفر، والخمسة، وعشرة،
+
+104
+00:12:11,630 --> 00:12:16,010
+والعشرة، والعشرين، والخمسة، والخمسة والعشرين. يعني أفهم
+
+105
+00:12:16,010 --> 00:12:22,890
+من هذا الكلام أنه أنا أقول Φ(a)(x)، يعني بده يطلع
+
+106
+00:12:22,890 --> 00:12:30,830
+عندي ستة homomorphisms. قد يكون وقد لا يكون. طب بدي
+
+107
+00:12:30,830 --> 00:12:37,190
+أحصيهم بالضبط كم هم؟ ستة، والله أقل من ستة، بقول اه،
+
+108
+00:12:37,190 --> 00:12:42,480
+استنى شوية. تعالوا نشوفهم هم ستة بالضبط مئة بالمئة
+
+109
+00:12:42,480 --> 00:12:47,680
+والله أقل من ذلك. الحين لو جينا سألناكم يا أبطالي،
+
+110
+00:12:47,680 --> 00:12:52,360
+قلنا لكم إيه؟ قلنا لكم إن الواحد في الواحد يساوي
+
+111
+00:12:52,360 --> 00:12:58,060
+كده؟ واحد. طيب إذا Φ(1) في واحد يبقى Φ
+
+112
+00:12:58,060 --> 00:13:06,260
+(1) في واحد يبقى Φ(1) مضبوط؟ طيب هذا الكلام
+
+113
+00:13:06,260 --> 00:13:14,470
+Φ(1) في Φ(1) يساوي Φ(1). طب
+
+114
+00:13:14,470 --> 00:13:21,170
+Φ(1)  فرضناه a، يبقى هذا بده يعطينا
+
+115
+00:13:21,170 --> 00:13:29,330
+أن الـ a في الـ a بده يساوي الـ a. وكأن الـ a
+
+116
+00:13:29,330 --> 00:13:35,490
+idempotent element، لأن الـ a تربيع يساوي الـ a. بدي أروح
+
+117
+00:13:35,490 --> 00:13:40,610
+أشوف الأرقام اللي أنا جايبها هل تحقق هذه المعادلة
+
+118
+00:13:40,610 --> 00:13:46,770
+ولا لا؟ يبقى كل واحد بيحقق هذه المعادلة بيكون إيش؟
+
+119
+00:13:46,770 --> 00:13:51,650
+homomorphism. تعالوا نشوف كلامنا هذا صحيح؟ والله فيه
+
+120
+00:13:51,650 --> 00:13:56,690
+يا عليك كلام. نمسك النقطة الأولى: هي عندك صفر في
+
+121
+00:13:56,690 --> 00:14:01,530
+صفر قد إيش بيعطينا؟ صفر. اه ما فيش فيها مشكلة. a في a
+
+122
+00:14:01,530 --> 00:14:07,950
+بده يعطيني a. طب نمسك اللي بعثته خمسة عشر في خمسة عشر
+
+123
+00:14:08,540 --> 00:14:15,340
+ميتين وخمسة وعشرين. سبعة في ثلاثين، ميتين وعشرة. من
+
+124
+00:14:15,340 --> 00:14:19,780
+ميتين و... ميتين و... و... و... وخمسة وعشرين، بيطلعوا
+
+125
+00:14:19,780 --> 00:14:25,140
+الخمسة عشر. يبقى، وهذه كمان تحقق المعادلة اللي
+
+126
+00:14:25,140 --> 00:14:30,320
+عندنا: a في a يساوي a. بعد الخمسة عشر عندنا
+
+127
+00:14:30,320 --> 00:14:37,120
+عشرة في عشرة. كده؟ ثلاثة ثلاثينات في السنة بيطلع
+
+128
+00:14:37,120 --> 00:14:43,620
+عشرة. يبقى وهذه بتحققها، نجي بعد العشرة: عشرين، فيها
+
+129
+00:14:43,620 --> 00:14:48,320
+عشرين؟ أربعمائة، طبعًا ثلاثة وتسعين بتقسمها
+
+130
+00:14:48,320 --> 00:14:54,080
+ثلاثين، فيها ثلاثة عشر، مضبوط؟ يبقى بيضل ثلاثة عشر، عشرة،
+
+131
+00:14:54,080 --> 00:15:01,640
+اه هذه مش مظبوطة، صح؟ هذه ما تحققش أن a في a يساوي
+
+132
+00:15:01,640 --> 00:15:07,960
+الـ a. الآن بعد العشرين، بتاخد خمسة في خمسة، بيطلع
+
+133
+00:15:08,140 --> 00:15:16,860
+خمسة وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة
+
+134
+00:15:16,860 --> 00:15:20,400
+وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة
+
+135
+00:15:20,400 --> 00:15:20,660
+وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة
+
+136
+00:15:20,660 --> 00:15:24,480
+وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة
+
+137
+00:15:24,480 --> 00:15:27,360
+وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة
+
+138
+00:15:27,360 --> 00:15:36,640
+وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة وعشرين
+
+140
+00:15:39,380 --> 00:15:44,840
+ايوا، ما حققوش الـ homomorphism، ما حققوش المعادلة
+
+141
+00:15:44,840 --> 00:15:49,380
+اللي عندي هذه، تمام؟ ما حققوش المعادلة، يبقى هذول
+
+142
+00:15:49,380 --> 00:15:54,480
+بدنا نستثنيهم، لأنهم ما حققوش المعادلة دي، بيبقوا
+
+143
+00:15:54,480 --> 00:16:00,320
+كم عندهم؟ أربعة homomorphisms فقط، لا غير. طب و
+
+144
+00:16:00,320 --> 00:16:05,020
+الاثنين المستثنين هذول، الاثنين المستثنين هيساووا واحد
+
+145
+00:16:05,020 --> 00:16:09,050
+منهم، كل واحد هيساوي واحد. كيف الحين بوريكم.
+
+146
+00:16:09,050 --> 00:16:13,290
+وبالتالي إذا ما يكون اثنين homomorphism بيقدوا نفس
+
+147
+00:16:13,290 --> 00:16:17,270
+النتيجة، بعتبر واحد مش اثنين، يبقى بأستبعد واحد و
+
+148
+00:16:17,270 --> 00:16:28,630
+بيخلي الثاني وهكذا. طيب، يبقى هنا so we have four
+
+149
+00:16:28,630 --> 00:16:35,670
+homomorphisms، تمام؟ مين الأول؟ الأول Φ
+
+150
+00:16:37,410 --> 00:16:45,610
+اللي هو Φ(zero)(x) بده يساوي x في صفر اللي
+
+151
+00:16:45,610 --> 00:16:52,390
+هو بده يساوي صفر. الثاني Φ خمسة عشر (x) هو يساوي
+
+152
+00:16:52,390 --> 00:17:01,650
+خمسة عشر x. الثالث اللي هو Φ (استبعدنا الخمسة عشر)
+
+153
+00:17:01,650 --> 00:17:02,490
+في عشرة.
+
+154
+00:17:16,820 --> 00:17:22,620
+طيب أما لو أنا بدي أحسب Φ خمسة عشر كده
+
+155
+00:17:22,620 --> 00:17:29,380
+تساوي أنا بدي أعرف كده Φ خمسة عشر إيش الـ
+
+156
+00:17:29,380 --> 00:17:35,130
+range تبعها، يبقى خمسة عشر في صفر. بدي أشيل x وأحط
+
+157
+00:17:35,130 --> 00:17:40,170
+صفر، واحد، اثنين، ثلاثة لغاية اثنا عشر. تمام؟ Φ of
+
+158
+00:17:40,170 --> 00:17:46,210
+صفر: صفر. ولما تبقى x بواحد، خمسة عشر في واحد، خمسة عشر.
+
+159
+00:17:46,210 --> 00:17:52,650
+ولما تبقى x باثنين، خمسة عشر في اثنين: ثلاثين تعني صفر. هي
+
+160
+00:17:52,650 --> 00:17:57,710
+طيب بعد اثنين: ثلاثة في خمسة عشر: خمسة وأربعين. أشيل
+
+161
+00:17:57,710 --> 00:18:02,120
+ثلاثين وأبقى خمسة عشر. هي أربعة، خمسة، ستة، اثنا عشر،
+
+162
+00:18:02,120 --> 00:18:06,780
+ما تلاقيش غير العنصرين هذول، ما فيش غيرهم. إذا Φ
+
+163
+00:18:06,780 --> 00:18:12,020
+خمسة عشر of x، هم موجودين في الـ range له two elements
+
+164
+00:18:12,020 --> 00:18:16,620
+فقط. طيب تعالوا نشوف Φ عشرة اللي عندنا، اللي
+
+165
+00:18:16,620 --> 00:18:21,980
+قد إيش: عشرة في صفر: صفر. عشرة في واحد: عشرة.
+
+166
+00:18:21,980 --> 00:18:30,150
+عشرة في اثنين: عشرين. عشرة في ثلاثة: صفر. عشرة
+
+167
+00:18:30,150 --> 00:18:36,150
+في أربعة: أربعين. أشيل ثلاثين بيضل عشرة. عشرة في خمسة:
+
+168
+00:18:36,150 --> 00:18:41,130
+خمسين، أشيل ثلاثين بيصير عشرين. عشرة في ستة: صفر،
+
+169
+00:18:41,130 -->
+
+223
+00:23:41,850 --> 00:23:45,750
+في عشرة تكيب خمسة في عشرة تكيب خمسة في عشرة تكيب
+
+224
+00:23:45,750 --> 00:23:48,350
+خمسة في عشرة تكيب خمسة في عشرة تكيب خمسة في عشرة
+
+225
+00:23:48,350 --> 00:23:54,260
+تكيب خمسة في عشرة قدرت أكتبه على الشكل اللي عندنا
+
+226
+00:23:54,260 --> 00:24:03,180
+هنا، و من هنا بروح بقول له: Sir, any positive integer
+
+227
+00:24:03,180 --> 00:24:13,700
+can be written as
+
+228
+00:24:13,700 --> 00:24:17,980
+(in)
+
+229
+00:24:17,980 --> 00:24:19,600
+itself
+
+230
+00:24:21,240 --> 00:24:33,240
+أي كي عشرة  أوز كي زائد أي كي minus ال one عشرة
+
+231
+00:24:33,240 --> 00:24:39,500
+أوز كي minus ال one زائد نظل ماشيين لغاية أي one في
+
+232
+00:24:39,500 --> 00:24:46,000
+عشرة زائد ال أي نو  لأن نص تلاتة إثنين واحد صفر
+
+233
+00:24:46,000 --> 00:24:53,970
+بظل ينزل، بدأنا بكتابة k-1, k-2, k-3 لغاية ما وصلنا ل 10
+
+234
+00:24:53,970 --> 00:25:01,310
+و نقص واحد زائد آنول يبقى أي إنتاج بقدر أكتبه على
+
+235
+00:25:01,310 --> 00:25:07,590
+شكل كثيرة الحدود اللي عندنا، طيب الآن بدنا نروح
+
+236
+00:25:07,590 --> 00:25:19,380
+لمثال رقم 7. مثال رقم 7 بيقول ما فيه any integer in any
+
+237
+00:25:19,380 --> 00:25:27,960
+integer with decimal representation with
+
+238
+00:25:27,960 --> 00:25:33,280
+decimal representation
+
+239
+00:25:33,280 --> 00:25:42,980
+with
+
+240
+00:25:42,980 --> 00:25:51,740
+decimal representation. A<sub>k</sub>, A<sub>k-1</sub>، ونظر ماشيين لغاية
+
+241
+00:25:51,740 --> 00:26:01,740
+A<sub>1</sub>، الـ A<sub>0</sub> is divisible by
+
+242
+00:26:01,740 --> 00:26:16,620
+9 if and only if if and only if الـ A<sub>k</sub> plus A<sub>k-1</sub>
+
+243
+00:26:16,620 --> 00:26:27,960
+plus plus A<sub>1</sub> plus A<sub>0</sub> is divisible by 9
+
+244
+00:26:53,860 --> 00:26:59,740
+قلب الأرقام بيقول لي أنا عند أي انتجر قدرت أكتبه
+
+245
+00:26:59,740 --> 00:27:06,480
+على الشكل اللي عندنا. دعيني من الشكل بيقول لي هذا ال
+
+246
+00:27:06,480 --> 00:27:12,040
+N بقدر أقول divisible by 9 if and only if مجموعة
+
+247
+00:27:12,040 --> 00:27:17,860
+هدول اللي هو الأرقام is divisible by 9. بقوله بسيطة
+
+248
+00:27:17,860 --> 00:27:34,830
+خالص. الآن let N a positive integer, then N بده
+
+249
+00:27:34,830 --> 00:27:45,130
+يساوي A<sub>k</sub> عشرة أُسّ k زائد A<sub>k-1</sub> مضروب
+
+250
+00:27:45,130 --> 00:27:51,110
+في عشرة أُسّ k-1 زائد زائد A<sub>1</sub> في
+
+251
+00:27:51,110 --> 00:27:58,960
+عشرة زائد A<sub>0</sub>. حسب ما احنا كاتبين هنا تمام، يبقى
+
+252
+00:27:58,960 --> 00:28:05,120
+فرضنا أنه على الشكل اللي عندنا هذا. طيب الآن أنا
+
+253
+00:28:05,120 --> 00:28:08,580
+فرضت هذه as a positive integer وكتبناها بالشكل اللي
+
+254
+00:28:08,580 --> 00:28:19,460
+قلتُه من هذا. الآن define a homomorphism φ من Z
+
+255
+00:28:19,460 --> 00:28:31,340
+إلى Z<sub>9</sub> by φ(x) بده يساوي x modulo 9
+
+256
+00:28:31,340 --> 00:28:35,080
+نيجي
+
+257
+00:28:35,080 --> 00:28:40,760
+للنص اللي جاي. ليه جاي؟ ليه إن الـ N اللي عنها ده is
+
+258
+00:28:40,760 --> 00:28:46,300
+divisible by 9 if and only if هذا divisible by
+
+259
+00:28:46,300 --> 00:28:58,780
+9. يبقى بدي أقول له N is divisible by 9 if and
+
+260
+00:28:58,780 --> 00:29:06,900
+only if. يعني لازم ألاقي رقم أضربه في 9 يطلع لي
+
+261
+00:29:06,900 --> 00:29:20,640
+الـ N. يبقى N يساوي 9M، والـ M موجودة في Z.  مفهوم؟
+
+262
+00:29:20,640 --> 00:29:30,080
+طيب هذا الكلام صحيح if and only if φ(M) بدل
+
+263
+00:29:30,080 --> 00:29:36,920
+ما يساوي φ(9M). هذا
+
+264
+00:29:36,920 --> 00:29:44,460
+الكلام صحيح if and only if φ(M) = 9M
+
+265
+00:29:44,460 --> 00:29:46,840
+modulo 9
+
+266
+00:29:51,440 --> 00:29:59,440
+= 0. ممتاز. يبقى هذا الكلام صحيح if and only if φ
+
+267
+00:29:59,440 --> 00:30:08,780
+(N) بده يساوي 0.  0 تبع الـ Z<sub>9</sub>. طيب هذا الكلام صحيح
+
+268
+00:30:08,780 --> 00:30:15,100
+if and only if φ. وين الـ N هاي؟ هشيلها وأكتب
+
+269
+00:30:15,100 --> 00:30:24,100
+بدالها كثيرة الحدود هذه. يبقى A<sub>k</sub> في عشرة أُسّ k زائد
+
+270
+00:30:24,100 --> 00:30:31,400
+A<sub>k-1</sub> عشرة أُسّ k-1 زائد زائد
+
+271
+00:30:31,400 --> 00:30:40,560
+A<sub>1</sub> في عشرة زائد الـ A<sub>0</sub> كله بده يساوي صفر. طيب
+
+272
+00:30:40,560 --> 00:30:46,680
+هذا الكلام صحيح if and only if  الـ φ  يشغّلين عليه
+
+273
+00:30:46,680 --> 00:30:52,500
+إحنا homomorphism. يبقى بقدر أدخل الـ φ على كل
+
+274
+00:30:52,500 --> 00:31:01,060
+term من هذه الـ terms. يبقى هذا φ(A<sub>k</sub>) في عشرة أُسّ
+
+275
+00:31:01,060 --> 00:31:09,020
+k، φ(A<sub>k-1</sub>) عشرة أُسّ k-1
+
+276
+00:31:09,020 --> 00:31:20,310
+زائد زائد φ(A<sub>1</sub>) في عشرة زائد φ(A<sub>0</sub>). هذا الكلام
+
+277
+00:31:20,310 --> 00:31:25,930
+كله بده يساوي قداش؟ بده يساوي صفر. هذا الكلام صحيح
+
+278
+00:31:25,930 --> 00:31:31,950
+if and only if هذول حاصل ضرب والـ φ homomorphism
+
+279
+00:31:31,950 --> 00:31:37,070
+خاصية ثانية وخاصية بدخل الـ φ على كل واحد من هذه
+
+280
+00:31:37,070 --> 00:31:45,410
+الـ terms. يبقى φ(A<sub>k</sub>) φ(عشرة أُسّ k) زائد φ
+
+281
+00:31:45,410 --> 00:31:53,370
+(A<sub>k-1</sub>) في φ(عشرة أُسّ k-1) زائد
+
+282
+00:31:53,370 --> 00:32:02,310
+الـ one زائد زائد φ(A<sub>1</sub>) في φ(عشرة) زائد
+
+283
+00:32:02,310 --> 00:32:09,130
+φ(A<sub>0</sub>). كل هذا الكلام يساوي صفر. فهيبقى هذا
+
+284
+00:32:09,130 --> 00:32:18,100
+صحيح if and only if.  φ(A<sub>k</sub>) العشرة هذه في Z<sub>9</sub>
+
+285
+00:32:18,100 --> 00:32:24,660
+قداش؟ اعتبرها modulo 9؟ واحد صح؟ إذا ما بقدر أشيلها وأ
+
+286
+00:32:24,660 --> 00:32:30,880
+حط مكانها واحد أُسّ قداش؟ واحد في واحد بقى قداش؟ ما
+
+287
+00:32:30,880 --> 00:32:39,880
+بدي إياه بواحد. يبقى هذه صار φ(1) وهنا φ
+
+288
+00:32:39,880 --> 00:32:49,840
+(A<sub>k-1</sub>) في φ(1) وهنا φ(A<sub>1</sub>) في φ
+
+289
+00:32:49,840 --> 00:32:56,920
+(1) وهنا φ(A<sub>0</sub>). كله سيكون ساوي مين؟ سيكون ساوي
+
+290
+00:32:56,920 --> 00:33:04,680
+صفر. طلعيني للتعريف هنا. φ(1) قداش ساوي؟
+
+291
+00:33:04,680 --> 00:33:06,480
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+292
+00:33:06,480 --> 00:33:07,980
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+293
+00:33:07,980 --> 00:33:12,180
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+294
+00:33:12,180 --> 00:33:12,680
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+295
+00:33:12,680 --> 00:33:12,720
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+296
+00:33:12,720 --> 00:33:13,550
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، وافي
+
+297
+00:33:13,550 --> 00:33:22,410
+φ(A<sub>k</sub>). يبقى if and only if φ(A<sub>k</sub>) زائد
+
+298
+00:33:22,410 --> 00:33:29,850
+φ(A<sub>k-1</sub>) زائد زائد φ(A<sub>1</sub>)
+
+299
+00:33:29,850 --> 00:33:37,130
+زائد φ(A<sub>0</sub>) بده يساوي صفر. هذا الكلام
+
+300
+00:33:37,130 --> 00:33:46,610
+because φ(1) يساوي 1 modulo 9. طيب
+
+301
+00:33:46,610 --> 00:33:54,550
+برجع لنفس المعادلة. φ(A<sub>k</sub>) قداش بتساوي؟ A<sub>k</sub>
+
+302
+00:33:54,550 --> 00:34:01,010
+modulo 9. φ(A<sub>k-1</sub>) = A<sub>k-1</sub> و
+
+303
+00:34:01,010 --> 00:34:08,310
+هكذا.  يفجر هذا الكلام صحيح if and only if A<sub>k</sub>
+
+304
+00:34:08,840 --> 00:34:15,800
+زائد A<sub>k-1</sub> زائد A<sub>1</sub> زائد A
+
+305
+00:34:15,800 --> 00:34:22,740
+<sub>0</sub> كلهم بده يساوي صفر. صحيح؟ طيب هذا الكلام
+
+306
+00:34:22,740 --> 00:34:29,480
+if and only if مجموع هدول كلهم بده
+
+307
+00:34:29,480 --> 00:34:36,390
+يساوي صفر. إيش معنى هذا الكلام؟ إنه هذا ينقسم
+
+308
+00:34:36,390 --> 00:34:43,550
+أو ينقسم على التسعة بدون باقي. يبقى هذا الكلام صحيح if
+
+309
+00:34:43,550 --> 00:34:50,190
+and only if A<sub>k</sub> + A<sub>k-1</sub> + A
+
+310
+00:34:50,190 --> 00:34:55,690
+<sub>1</sub> + A<sub>0</sub> is divisible by
+
+311
+00:35:22,450 --> 00:35:29,550
+بنجي الآن لأول نظرية موجودة في هذا الفصل من
+
+312
+00:35:29,550 --> 00:35:37,930
+العنوان. من عنوانها: Beneficent Properties of Ring
+
+313
+00:35:37,930 --> 00:35:40,950
+Homomorphisms
+
+314
+00:35:40,950 --> 00:35:49,490
+النظرية بتقول، ما يبتدي في إيران: Let
+
+315
+00:35:49,490 --> 00:36:00,380
+φ من R إلى S be a ring homomorphism. be a ring
+
+316
+00:36:00,380 --> 00:36:03,420
+homomorphism
+
+317
+00:36:03,420 --> 00:36:18,180
+let A be a subring. let A be a subring of R and
+
+318
+00:36:18,180 --> 00:36:33,500
+B an ideal of S. then النقطة الأولى. النقطة
+
+319
+00:36:33,500 --> 00:36:45,040
+الأولى: for any or any r belongs to R and any
+
+320
+00:36:45,040 --> 00:36:49,780
+positive integer
+
+321
+00:36:56,010 --> 00:37:01,170
+وانتجر N نحن
+
+322
+00:37:01,170 --> 00:37:04,970
+لدينا
+
+323
+00:37:04,970 --> 00:37:17,450
+φ(nA) يساوي nφ(A). وφ(r<sup>n</sup>)
+
+324
+00:37:17,450 --> 00:37:24,690
+يساوي φ(r)<sup>n</sup>
+
+325
+00:37:24,690 --> 00:37:34,270
+نمرة إثنين: φ(A) كل العناصر φ(A) بحيث ال
+
+326
+00:37:34,270 --> 00:37:46,010
+A موجودة فيها  هي subring of S. يعني صورة ال
+
+327
+00:37:46,010 --> 00:37:59,890
+subring هي subring كذلك. تلاتة: If A is an ideal of
+
+328
+00:37:59,890 --> 00:38:12,210
+A and φ is onto... and φ is onto S...
+
+329
+00:38:12,210 --> 00:38:18,630
+onto S, then
+
+330
+00:38:27,960 --> 00:38:42,780
+then φ(A) is an ideal of S. مفتاح
+
+331
+00:38:42,780 --> 00:38:53,040
+رابع: φ<sup>-1</sup>(B) اللي هو كل الـ r الموجودة
+
+332
+00:38:53,040 --> 00:39:01,700
+في R such that φ(r) موجودة فيه، بيه. if it is an
+
+333
+00:39:01,700 --> 00:39:14,280
+ideal of R is an ideal of R.  نمرة خمسة: if R is
+
+334
+00:39:14,280 --> 00:39:22,280
+commutative. if R is commutative
+
+335
+00:39:24,020 --> 00:39:38,900
+then φ(R) is commutative. نمرة
+
+336
+00:39:38,900 --> 00:39:52,910
+ستة: if R has a unity. if R has a unity as
+
+337
+00:39:52,910 --> 00:40:01,850
+unity one، والاسم لا تساوي صفر، وφ is onto
+
+338
+00:40:01,850 --> 00:40:13,950
+and φ is onto, then φ
+
+339
+00:40:13,950 --> 00:40:20,450
+(1)  φ(1) is the unity and
+
+340
+00:40:22,860 --> 00:40:29,460
+unity of S. نقرأ
+
+341
+00:40:29,460 --> 00:40:37,540
+السابعة: φ is an isomorphism. φ is an
+
+342
+00:40:37,540 --> 00:40:50,420
+isomorphism if and only if φ is onto and
+
+343
+00:40:52,600 --> 00:41:00,760
+الكيرنل للفاي اللي هو كل العناصر r الموجودة في
+
+344
+00:41:00,760 --> 00:41:09,540
+R such that φ(r) بدي يساوي صفر. بدي يساوي صفر
+
+345
+00:41:09,540 --> 00:41:19,080
+هنا. تمانية: φ is an isomorphism. φ is an
+
+346
+00:41:19,080 --> 00:41:21,180
+isomorphism
+
+347
+00:41:22,290 --> 00:41:27,230
+from R
+
+348
+00:41:27,230 --> 00:41:29,730
+onto S
+
+349
+00:42:22,570 --> 00:42:27,910
+طبعا لو نظرنا لهذه الخواص السبعة، يعني بنلاقي نفس
+
+350
+00:42:27,910 --> 00:42:32,270
+الخواص اللي موجودة عالميا على الـ groups مضبوط
+
+351
+00:42:32,270 --> 00:42:38,860
+تماماً. بيقول لو كان φ من R إلى S ring homomorphism with
+
+352
+00:42:38,860 --> 00:42:45,620
+A subring من R والـ B ideal في S، بيقول أي عنصر r
+
+353
+00:42:45,620 --> 00:42:51,120
+موجود في R وأي positive integer n، we have φ(nr)
+
+354
+00:42:51,120 --> 00:42:56,900
+يساوي nφ(r). وφ(r<sup>n</sup>) يساوي
+
+355
+00:42:56,900 --> 00:43:03,310
+φ(r)<sup>n</sup>.  نقطة ثانية: لما تأثر
+
+356
+00:43:03,310 --> 00:43:09,970
+على الـ ideal A بده تبقى صورته هي subring من مين؟
+
+357
+00:43:09,970 --> 00:43:18,010
+من S. الـ A هو subset من R، صورته φ(A) هي subring
+
+358
+00:43:18,010 --> 00:43:23,610
+من مين؟ من الـ S. تلاتة: لو كان A ideal و φ
+
+359
+00:43:23,610 --> 00:43:29,520
+كانت onto، يبقى φ(A) ideal. يبقى خلّينا A ideal والـ φ
+
+360
+00:43:29,520 --> 00:43:35,900
+كانت onto، يبقى صورته بتكون ideal من S. يبقى قلنا
+
+361
+00:43:35,900 --> 00:43:40,660
+φ onto. الـ homomorphism صار onto وفي نفس الوقت الـ
+
+362
+00:43:40,660 --> 00:43:45,680
+A صار ideal، يبقى صورة الـ ideal هي ideal كذلك
+
+363
+00:43:45,680 --> 00:43:51,200
+فاهمين؟ في S. φ<sup>-1</sup>(B) كل العناصر r
+
+364
+00:43:51,200 --> 00:43:55,860
+في R بحيث φ(r) موجودة وين؟ في B. كأننا بنجيب الـ
+
+365
+00:43:55,860 --> 00:44:01,010
+homomorphism المعكوس اللي هو من S إلى R. يبقى كمان
+
+366
+00:44:01,010 --> 00:44:07,250
+هذا ideal. لو كانت R commutative، يبقى صورتها في S
+
+367
+00:44:07,250 --> 00:44:13,930
+كذلك بتكون commutative. النقطة الثالثة: لو كان R
+
+368
+00:44:13,930 --> 00:44:18,830
+فيها الـ unity وS ليس فيها الصفر، وφ is
+
+369
+00:44:18,830 --> 00:44:24,830
+onto، يبقى φ(1) هو الـ unity تبع S.  φ
+
+370
+00:44:24,830 --> 00:44:30,130
+isomorphism if and only if φ is onto والكيرنل
+
+371
+00:44:30,130 --> 00:44:34,850
+كان يساوي صفر نفسها. كانت في حالة الـ group
+
+372
+00:44:34,850 --> 00:44:39,910
+بالضبط تماماً. بس هناك بنجي نقول اللي هو الكيرنل
+
+373
+00:44:39,910 --> 00:44:45,230
+φ بده يساوي identity تماماً. وهذا هو الـ
+
+374
+00:44:45,230 --> 00:44:51,000
+identity بالنسبة لعملية الجمع. النقطة التانية: لو
+
+375
+00:44:51,000 --> 00:44:55,360
+كان φ isomorphism من ring إلى تانية، يبقى
+
+376
+00:44:55,360 --> 00:45:00,700
+φ<sup>-1</sup> بده يكون كذلك isomorphism من S إلى
+
+377
+00:45:00,700 --> 00:45:07,400
+R. المرة القادمة إن شاء الله تعالى يعطيكم العافية.
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a1f8c375dba6a63aa0b40f22cbcc104586458e89
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_postprocess.srt
@@ -0,0 +1,1064 @@
+1
+00:00:20,910 --> 00:00:25,830
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا بيه في ال F
+
+2
+00:00:25,830 --> 00:00:33,530
+of X has a Z NF السؤال اللي بدنا نسأله طب لو غيرنا
+
+3
+00:00:33,530 --> 00:00:38,870
+ال degree تبعت ال F وكان أكبر من تلاتة أربع، خمسة،
+
+4
+00:00:38,870 --> 00:00:44,370
+ستة، اللي بدكي ايه؟ تمام هل تبقى نظرية صحيحة؟
+
+5
+00:00:44,370 --> 00:00:49,570
+الإجابة لا وهذا هو موضوع ال note اللي احنا كاتبينه
+
+6
+00:00:49,570 --> 00:00:53,720
+على اللوحةيبقى الملاحظة اللي عندنا هذه The above
+
+7
+00:00:53,720 --> 00:00:58,940
+theorem تبعت المرة الماضية need not be true ليس
+
+8
+00:00:58,940 --> 00:01:04,980
+بالضرورة صحيحة عندما تكون ضرر ال F أكبر من ثلاثة
+
+9
+00:01:04,980 --> 00:01:11,040
+يعني أربعة ثم فوق for example كمثال على ذلك لو
+
+10
+00:01:11,040 --> 00:01:16,580
+جينا ال Q of X ال Q of X is a field، مظبوط؟ طيب،
+
+11
+00:01:16,580 --> 00:01:22,130
+بدنا نجي ناخد بلانوميل اللي هي mainالـ F of X
+
+12
+00:01:22,130 --> 00:01:28,270
+يساوي X أُص أربعة زائد اتنين X تربية زائد واحد
+
+13
+00:01:28,270 --> 00:01:34,890
+تمام؟ بالنسبالي هل بنقدر نحللها إلى عاملين؟
+
+14
+00:01:34,890 --> 00:01:42,530
+الإجابة نعم وهي ان X تربية زائد واحد في X تربية
+
+15
+00:01:42,530 --> 00:01:49,460
+زائد واحديبقى صارت ال F اللي عندنا Reducible على
+
+16
+00:01:49,460 --> 00:01:57,520
+مين على ال Q يبقى هذا بدي يعطينا ان ال F of X is
+
+17
+00:01:57,520 --> 00:02:08,140
+Reducible over Q طيب ما علينا السؤال هو هل اي
+
+18
+00:02:08,140 --> 00:02:17,480
+واحدة من هدول لها حل في ال QX تربيه زائد واحد يسوى
+
+19
+00:02:17,480 --> 00:02:23,900
+صفر انها حالة اينا but is irreducible but اللي هو
+
+20
+00:02:23,900 --> 00:02:33,080
+مثلا but ال X تربيه زائد واحد تساوي zero أو دور
+
+21
+00:02:33,080 --> 00:02:43,540
+بلاش تساوي zero has no solution in AQ يعني لا يمكن
+
+22
+00:02:44,020 --> 00:02:50,120
+ألاقي الرقم في الـ Q يحقق هذه المعادلة has no
+
+23
+00:02:50,120 --> 00:02:56,120
+solution أو has no zero حسب نص من نص النظرية F
+
+24
+00:02:56,120 --> 00:03:01,880
+فبقول لازم تلاقي Zero لل .. لل .. لل .. لل
+
+25
+00:03:01,880 --> 00:03:06,460
+polynomial F small of X إذا كانت ال degree اتنين
+
+26
+00:03:06,460 --> 00:03:10,800
+أو تلاتة لكن لما انصرت أربعة هي مافيش أنزح حلول
+
+27
+00:03:10,800 --> 00:03:18,230
+تمام؟يبقى has no solution في ليكيوم يبقى هذا يؤكد
+
+28
+00:03:18,230 --> 00:03:22,790
+ان النظرية هذا لو شيلت ال condition اللي عندنا هذا
+
+29
+00:03:22,790 --> 00:03:29,710
+بصير غير صحيحة تمام؟ إذا هذه الملاحظة اللي كنا
+
+30
+00:03:29,710 --> 00:03:33,430
+بنقولها على النظرية المرة اللي فاتت ولم يكن هناك
+
+31
+00:03:33,430 --> 00:03:40,830
+وقت لأن نشيرة إليها نجي ناخد definition جديد
+
+32
+00:03:42,090 --> 00:03:50,210
+definition بيقول ما هي the content of
+
+33
+00:03:50,210 --> 00:04:03,510
+a non zero polynomial of a non zero polynomial a n
+
+34
+00:04:03,510 --> 00:04:09,130
+x to the power n a minus one x to the power n
+
+35
+00:04:09,130 --> 00:04:21,950
+minus oneplus a1x plus a0 where حيث ال a هدول كلهم
+
+36
+00:04:21,950 --> 00:04:31,150
+are integers كلهم أعداد صحيحة is the greatest
+
+37
+00:04:31,150 --> 00:04:38,770
+common divisor اللي هو is that greatest
+
+38
+00:04:45,920 --> 00:04:57,600
+common divisor is
+
+39
+00:04:57,600 --> 00:05:05,460
+the greatest common divisor of
+
+40
+00:05:05,460 --> 00:05:06,460
+the integers
+
+41
+00:05:16,290 --> 00:05:23,570
+هو الـ a n و ال a m minus ال one و ال a one و ال a
+
+42
+00:05:23,570 --> 00:05:31,610
+naught كمان تعريف تاني definition a primitive
+
+43
+00:05:31,610 --> 00:05:38,610
+polynomial a primitive polynomial
+
+44
+00:05:46,640 --> 00:05:53,660
+is an element is
+
+45
+00:05:53,660 --> 00:06:05,560
+an element of capital Z of X capital Z of X with
+
+46
+00:06:05,560 --> 00:06:08,600
+content
+
+47
+00:06:08,600 --> 00:06:18,150
+one لما بنقف هعمل two definitionsنقرأ من جديد و
+
+48
+00:06:18,150 --> 00:06:23,010
+نحاول نفهم ما هو المقصود بكل تعريف من هذين
+
+49
+00:06:23,010 --> 00:06:29,810
+التعريفين نجي مع التعريف الأول ال content of a non
+
+50
+00:06:29,810 --> 00:06:34,830
+-zero polynomial هي قدامي انا عند non-zero
+
+51
+00:06:34,830 --> 00:06:39,170
+polynomial بالشكل هذا ما هو ال content تبعها؟
+
+52
+00:06:39,170 --> 00:06:45,030
+بيقول لي بحيث كل ال إيهات اللي عندي عبارة عن انتجة
+
+53
+00:06:45,390 --> 00:06:54,230
+يبقى AN AN-1 AN-2 لغاية A2 A1 A0 كلهم أعداد صحيحة
+
+54
+00:06:54,230 --> 00:06:59,970
+تمام يبقى ال content للبرنامج الهادي هو ال
+
+55
+00:06:59,970 --> 00:07:07,150
+greatest common divisor لمين لهذه الانتجارة طب ال
+
+56
+00:07:07,150 --> 00:07:11,170
+content يمكن يكون واحد يمكن يكون اتنين يمكن يكون
+
+57
+00:07:11,170 --> 00:07:15,080
+تلاتة يمكن يكون اربع ممكن يكون كثيرلأ لأنه نور
+
+58
+00:07:15,080 --> 00:07:20,000
+انتجاز لأ نور انتجاز مش همكانية تمام اذا يا بنات
+
+59
+00:07:20,000 --> 00:07:24,820
+المعاملات اللي عندى فى هذه ال polynomial كلها عدد
+
+60
+00:07:24,820 --> 00:07:29,920
+صحيح تمام من هو ال content لهذه ال polynomial هو
+
+61
+00:07:29,920 --> 00:07:36,280
+ال grays common divisor يعني اعلى رقم بيقسم كل هذه
+
+62
+00:07:36,280 --> 00:07:41,820
+المعاملة فهمنا التعريف الاول التعريف التانى سيعتمد
+
+63
+00:07:41,820 --> 00:07:47,270
+على التعريف الاولطبعا هي التعريف التاني قال ال
+
+64
+00:07:47,270 --> 00:07:53,470
+primitive polynomial كثيرة الحدود الأولية كلمة
+
+65
+00:07:53,470 --> 00:07:58,890
+primitive جاء من كلمة prime prime عدد أول يبقى
+
+66
+00:07:58,890 --> 00:08:02,790
+primitive أول يبقى ال polynomial كثيرة الحدود
+
+67
+00:08:02,790 --> 00:08:11,950
+الأولية is an element of z of x يبقى هي كثيرة حدود
+
+68
+00:08:11,950 --> 00:08:17,950
+في z of xوالمعاملات تبعتها كلها أعداد صحيحة بحيث
+
+69
+00:08:17,950 --> 00:08:22,430
+ال content إلها يساوي مين؟ يساوي الواحد الصحية
+
+70
+00:08:22,430 --> 00:08:28,790
+يبقى أي polynomial في Z of X اللي طلع للمعاملات
+
+71
+00:08:28,790 --> 00:08:32,190
+تبعت هذه ال polynomial إذا كان الجريسيس common
+
+72
+00:08:32,190 --> 00:08:36,710
+divisor إلها كلها بواحد يبقى على طول الخطب يقول ال
+
+73
+00:08:36,710 --> 00:08:41,340
+polynomial هي primitiveكان اتنين، تلتة، اربعة،
+
+74
+00:08:41,340 --> 00:08:46,000
+خمسة جنة يكوني جنات الـ Primitive يبقى التعريف
+
+75
+00:08:46,000 --> 00:08:50,420
+الثاني يعتمد على التعريف الأول إذا ممكن أنا أصيه
+
+76
+00:08:50,420 --> 00:08:55,180
+التعريف الثاني بقول هي Primitive Polynomial F of X
+
+77
+00:08:55,180 --> 00:09:00,600
+اللي موجودة في Z of X هي Primitive إذا كان ال
+
+78
+00:09:00,600 --> 00:09:06,360
+content اللي هيساوي واحد مجروح؟ اه ال content
+
+79
+00:09:06,360 --> 00:09:13,100
+يساوي واحديبقى any polynomial في z of x ال content
+
+80
+00:09:13,100 --> 00:09:17,720
+لها يساوي واحد بقول عنها primitive polynomial طب
+
+81
+00:09:17,720 --> 00:09:21,560
+كان ال content لها يساوي اتنين يعني ال classes
+
+82
+00:09:21,560 --> 00:09:25,780
+common divisor للمعاملات كلها يساوي اتنين يبقى في
+
+83
+00:09:25,780 --> 00:09:30,260
+هذه الحالة بقدرش اقول عليها primitive polynomial
+
+84
+00:09:30,260 --> 00:09:37,040
+تمام طيب نعطي مثال توضيحي على ذلك يبقى example
+
+85
+00:09:45,140 --> 00:09:46,460
+يبقى ده polynomial.
+
+86
+00:09:50,640 --> 00:10:03,940
+F of X التي تساوي تلاتة X تربيع او تلاتة X تكيب
+
+87
+00:10:03,940 --> 00:10:11,960
+اناقش اربع X زائد خمسة وثلاثين. هل هذه قيمة
+
+88
+00:10:11,960 --> 00:10:20,930
+بيمنعك؟primitive؟ لأ لأ
+
+89
+00:10:20,930 --> 00:10:27,050
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+90
+00:10:27,050 --> 00:10:29,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+91
+00:10:29,790 --> 00:10:29,810
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+92
+00:10:29,810 --> 00:10:36,050
+لأ لأ لأ لأ
+
+93
+00:10:36,050 --> 00:10:44,090
+لأ لأ
+
+94
+00:10:44,420 --> 00:10:50,000
+and الخمسة وتلاتين is one يعني ال content إلها
+
+95
+00:10:50,000 --> 00:10:56,640
+يسوى واحد that is its
+
+96
+00:10:56,640 --> 00:11:02,980
+content is
+
+97
+00:11:02,980 --> 00:11:07,060
+one but the polynomial
+
+98
+00:11:15,250 --> 00:11:28,490
+مثلا Ge of X يساوى 12 X ترابيع زائد ستة X ناقص
+
+99
+00:11:28,490 --> 00:11:40,190
+ثلاثة هل هذه primitive؟ لأ is not primitive السبب
+
+100
+00:11:40,190 --> 00:11:41,550
+because
+
+101
+00:11:44,990 --> 00:11:51,470
+the greatest common divisor of الاطناش، نهيت كمان
+
+102
+00:11:51,470 --> 00:11:56,310
+مرة، تبقى فأقول الآن ال pronominant تاني g of x
+
+103
+00:11:56,310 --> 00:12:01,510
+اللي اتناشر x ثميه زي الستة x ناقص تلاتة is not
+
+104
+00:12:01,510 --> 00:12:05,510
+primitive ما هو السبب؟ لإن ال greatest common
+
+105
+00:12:05,510 --> 00:12:10,190
+divisor للمعاملة الاطناش والستة والناقص تلاتة هو
+
+106
+00:12:10,190 --> 00:12:14,980
+مين؟ هو التلاتةيعني ال content لهذه ال polynomial
+
+107
+00:12:14,980 --> 00:12:22,900
+هو تلاتة ممتاز نيجي الآن يا بنات لحاجة نظرية اسمها
+
+108
+00:12:22,900 --> 00:12:33,080
+Gauss's lemma يبقى بالتالي Gauss's lemma أرضية
+
+109
+00:12:33,080 --> 00:12:40,340
+جاوس تقول ما يعني the product
+
+110
+00:12:42,390 --> 00:12:51,150
+of two primitive polynomials
+
+111
+00:12:51,150 --> 00:12:55,310
+the
+
+112
+00:12:55,310 --> 00:13:00,810
+derivative of two primitive polynomials is a
+
+113
+00:13:00,810 --> 00:13:09,510
+primitive let's
+
+114
+00:13:09,510 --> 00:13:09,730
+hope
+
+115
+00:13:14,030 --> 00:13:19,150
+أنا بدي افترض ان عندي two polynomials وكل واحدة
+
+116
+00:13:19,150 --> 00:13:23,990
+فيهم primitive بعدين بدي احاول اثبت ان حاصل الضرب
+
+117
+00:13:23,990 --> 00:13:34,070
+يكون primitive بدي اقول let f of x و g of x
+
+118
+00:13:34,070 --> 00:13:42,590
+الاتنين are primitive polynomials
+
+119
+00:13:47,480 --> 00:13:54,860
+m z of x I
+
+120
+00:13:54,860 --> 00:13:59,220
+want to show ان
+
+121
+00:13:59,220 --> 00:14:06,400
+احاول ان بيبين ان ال f of x ال g of x is a
+
+122
+00:14:06,400 --> 00:14:11,280
+primitive that
+
+123
+00:14:11,280 --> 00:14:11,660
+is
+
+124
+00:14:16,250 --> 00:14:22,350
+want to show that
+
+125
+00:14:22,350 --> 00:14:29,770
+ان ال content of
+
+126
+00:14:29,770 --> 00:14:42,110
+ال F of X في ال G of X بتساوي كده؟ بتساوي واحد لان
+
+127
+00:14:42,110 --> 00:14:44,410
+اثبت هذا الكلام بالتناقض
+
+128
+00:14:49,910 --> 00:15:02,170
+assume that ان ال content of او نفرض انهم في الأول
+
+129
+00:15:02,170 --> 00:15:07,310
+ال primitive وما إلى ذلك او بيخد أه قلنا أولي ال
+
+130
+00:15:07,310 --> 00:15:11,150
+primitive صحيح one to show حاصر الطربي لبنان that
+
+131
+00:15:11,150 --> 00:15:15,880
+is one to show that هذي ال content assume thatthe
+
+132
+00:15:15,880 --> 00:15:24,160
+content of ال F of X في ال G of X greater than one
+
+133
+00:15:24,160 --> 00:15:30,900
+افترضي ان ال content اللي حصل الدرب هذا معناه اكبر
+
+134
+00:15:30,900 --> 00:15:43,580
+من واحد طيب نعطي فرض اخر لف ال P ب A positive ولا
+
+135
+00:15:43,580 --> 00:15:44,340
+prime
+
+136
+00:15:46,640 --> 00:15:52,800
+با prime divisor
+
+137
+00:15:52,800 --> 00:15:55,980
+of
+
+138
+00:15:55,980 --> 00:16:10,900
+ال content of f of x في ال main of g of x افترضت
+
+139
+00:16:10,900 --> 00:16:16,820
+ان في عندى رقم و الرقم هذا prime numberوبيقسم ال
+
+140
+00:16:16,820 --> 00:16:20,740
+content تبع ال f of x في g of x اللي هو main له
+
+141
+00:16:20,740 --> 00:16:26,300
+أكبر من main من الواحد يمكن اتنين يمكن تلاتة يمكن
+
+142
+00:16:26,300 --> 00:16:30,420
+اربعة قدمك ان شاء الله يكون عشرة فى عندى prime بدي
+
+143
+00:16:30,420 --> 00:16:37,740
+يقسم هذا main هذا ال content تمام طيب بدنا نشغل
+
+144
+00:16:37,740 --> 00:16:47,880
+كمان شغلة شغلة تانية بدي أقولالـ F bar of X والـ G
+
+145
+00:16:47,880 --> 00:16:58,800
+bar of X and الـ F bar في الـ G bar of X اللي هي
+
+146
+00:16:58,800 --> 00:17:07,320
+بدها تساوي F of X في الـ G of X اللي كل bar بـ
+
+147
+00:17:07,320 --> 00:17:09,540
+Pronomials
+
+148
+00:17:16,830 --> 00:17:33,090
+obtained from اللي هو ال F of X وال G of X and ال
+
+149
+00:17:33,090 --> 00:17:42,530
+F of X في ال G of X by reducing
+
+150
+00:17:46,100 --> 00:17:52,460
+the coefficients coefficients
+
+151
+00:17:52,460 --> 00:17:59,080
+of u لو p فبستنى
+
+152
+00:17:59,080 --> 00:18:04,360
+شوية بدنا نفهم الحكاية هذا كويس مرة تانية بنا
+
+153
+00:18:04,360 --> 00:18:11,260
+نفترض إن ال content لل FG ليه سواء أكبر من مين؟ من
+
+154
+00:18:11,260 --> 00:18:17,130
+الواحدطيب اخد P هو prime divisor لل content
+
+155
+00:18:17,130 --> 00:18:23,470
+المتوقع تبع ال F of X في مين ال D of G of X هاي
+
+156
+00:18:23,470 --> 00:18:29,230
+الفتوى الأولى فتوى الثاني عمل polynomials جديدة من
+
+157
+00:18:29,230 --> 00:18:34,150
+polynomials موجودة من ال polynomials الجديدة F
+
+158
+00:18:34,150 --> 00:18:41,380
+prime of X وG prime of X وحاصل ضربهما primeأو با
+
+159
+00:18:41,380 --> 00:18:43,840
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+160
+00:18:43,840 --> 00:18:45,320
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+161
+00:18:45,320 --> 00:18:49,700
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+162
+00:18:49,700 --> 00:18:49,860
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+163
+00:18:49,860 --> 00:19:01,580
+بي بي بي بي بي بي بي بي
+
+164
+00:19:08,920 --> 00:19:14,260
+by reducing their coefficients modulo p يبقى روحت
+
+165
+00:19:14,260 --> 00:19:19,000
+على معاملة f of x وعلى معاملة g of x وعلى معاملة
+
+166
+00:19:19,000 --> 00:19:24,800
+حصل الضرب وكتبتهم بيه modulo p يبقى في اشي بعضهم
+
+167
+00:19:24,800 --> 00:19:30,340
+حصير ب zero وبعضهم بصيرش ب zero ما علينا مش مشكلة
+
+168
+00:19:30,340 --> 00:19:35,900
+يبقى هذول اصفاتهم كله modulo p السؤال هويبقى بنات
+
+169
+00:19:35,900 --> 00:19:47,240
+F bar وG bar وين موجودة؟ في Z P of X، صح؟ نعم،
+
+170
+00:19:47,240 --> 00:19:48,620
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+171
+00:19:48,620 --> 00:19:49,180
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+172
+00:19:49,180 --> 00:19:50,160
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+173
+00:19:50,160 --> 00:19:52,320
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+174
+00:19:52,320 --> 00:19:53,480
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+175
+00:19:53,480 --> 00:19:58,900
+نعم، نعم، نعم،
+
+176
+00:19:58,900 --> 00:20:03,100
+نعم،
+
+177
+00:20:03,100 --> 00:20:13,850
+نطب ZP of X is an integral domain صح يبقى and ZP
+
+178
+00:20:13,850 --> 00:20:24,250
+of X is an integral domain وده أخدناها قبل ذلك
+
+179
+00:20:24,250 --> 00:20:31,550
+لإنه ZP لإنه ZP is an integral domain
+
+180
+00:20:35,960 --> 00:20:41,780
+مرتين جيت على F وجيه وحصل الضرر حولت المعاملات
+
+181
+00:20:41,780 --> 00:20:47,420
+كلها مديونو P يبقى حصلت على polynomials جديدة اللي
+
+182
+00:20:47,420 --> 00:20:52,460
+حطيت عليها الشرطة فوق وتنطق F bar of X G bar of X
+
+183
+00:20:52,460 --> 00:20:58,040
+F of X في G of X الكل بار ممتاز يبقى كل واحدة منهم
+
+184
+00:20:58,040 --> 00:21:07,230
+موجودة وين بيزدد مش هجدك و بس انيالـ F bar of X
+
+185
+00:21:07,230 --> 00:21:15,350
+مضروبة في الـ G bar of X اللي هي الـ F of X في الـ
+
+186
+00:21:15,350 --> 00:21:20,810
+G of X في الكل bar أنا أزعم أنها الـ zero تبعي الـ
+
+187
+00:21:20,810 --> 00:21:24,750
+ZP معقول؟
+
+188
+00:21:24,750 --> 00:21:30,190
+معقول؟ الله أعلم شو السبب؟ because
+
+189
+00:21:57,520 --> 00:22:07,780
+مفهوم هذا اكيد افوت يعنيمش مفهومة انا عارف 90%
+
+190
+00:22:07,780 --> 00:22:13,520
+منكم على الأقل ان كنت متواضع مش فاهمين هذا هنفهمها
+
+191
+00:22:13,520 --> 00:22:19,820
+لكم في سطرين صغار تمام تعالوا نفهمها احنا بنقول ال
+
+192
+00:22:19,820 --> 00:22:25,340
+content هنا ماله؟ بدأ افترض ال content رقم يبقى
+
+193
+00:22:25,340 --> 00:22:30,340
+بدأ افترض ال content يساوي key تمام؟ فلو جيت في
+
+194
+00:22:30,340 --> 00:22:41,100
+الها مش هيك بذلك ال contentتبع ال F في G S K تمام؟
+
+195
+00:22:41,100 --> 00:22:48,280
+إيش يعني؟ لو أخدت أي element من حاصل المعامل تبع
+
+196
+00:22:48,280 --> 00:22:57,160
+حاصل ضرب لأي واحدة يوم تروح تسميته S مش يساوي ال
+
+197
+00:22:57,160 --> 00:23:02,300
+content اللي هو K في S Prime مثلا
+
+198
+00:23:05,350 --> 00:23:10,030
+مش فيه حصل الضرب F في G جيت على أي عنصر من حصل
+
+199
+00:23:10,030 --> 00:23:14,490
+الضرب Polynomial طويلة أو عريضة أخد عنصر منها
+
+200
+00:23:14,490 --> 00:23:19,230
+Element مضروب في X تربية ولا في X تكيب ولا في X
+
+201
+00:23:19,230 --> 00:23:24,390
+أربعة اللي بدكيا روحت أخدت المعامل تبعه تبع حصل
+
+202
+00:23:24,390 --> 00:23:31,930
+الضرب سميته AS يبقى هذا AS هو ال content مضروب في
+
+203
+00:23:31,930 --> 00:23:38,740
+element تاني مناللي هو من الفيديو اللي عندنا، صحيح
+
+204
+00:23:38,740 --> 00:23:46,100
+ولا لا؟ مش ال content هو ناقص خارج قسمة كل العوامل
+
+205
+00:23:46,100 --> 00:23:50,220
+أو المعاملات اللي عندي تبعتي ال polynomial، مش هذا
+
+206
+00:23:50,220 --> 00:23:55,140
+تعريف ال content فرضته كي يبقى أي واحد فيه عبارة
+
+207
+00:23:55,140 --> 00:24:01,000
+عن K في element A، مظبوط ولا لا؟ طيبإيش أنا جايل
+
+208
+00:24:01,000 --> 00:24:07,920
+هنا خد ال P prime divisor لل content يعني ال P بدي
+
+209
+00:24:07,920 --> 00:24:14,300
+يقسم ال K صح ولا لأ؟ يبقى أنا عندي كمان ال P بدي
+
+210
+00:24:14,300 --> 00:24:23,640
+يقسم ال K هذا يعني إنه K تساوي P في T شيل ال K هذه
+
+211
+00:24:23,640 --> 00:24:32,480
+اللي فوق و بدي أحط بدالهااس يساوي كيله PT في S
+
+212
+00:24:32,480 --> 00:24:40,200
+فراعي يبقى كل معامل داخل ال polynomial قدرت أكتب
+
+213
+00:24:40,200 --> 00:24:45,240
+دلالة ال P يبقى لما نقصدته جداش مدي يكون Zero،
+
+214
+00:24:45,240 --> 00:24:48,000
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+215
+00:24:48,000 --> 00:24:48,660
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+216
+00:24:48,660 --> 00:24:52,500
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+217
+00:24:52,500 --> 00:24:54,700
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+218
+00:24:54,700 --> 00:25:00,090
+Zero،يبقى هاي حاصل الضرب يساوي zero because each
+
+219
+00:25:00,090 --> 00:25:07,150
+coefficient of هذه is a multiple of P طيب تعالوا
+
+220
+00:25:07,150 --> 00:25:13,270
+نستفيد شغل تاني حاصل الضرب يساوي zero واحنا بنشتغل
+
+221
+00:25:13,270 --> 00:25:20,050
+وين؟ في الول انتجرال الماني يبقى هذا الكلام مش
+
+222
+00:25:20,050 --> 00:25:24,770
+صحيح إلا إذا كان يا الأول ب zero يا التاني ب zero
+
+223
+00:25:25,300 --> 00:25:33,040
+يبقى الآن بداية أقوله f bar of x في ال g bar of x
+
+224
+00:25:33,040 --> 00:25:40,820
+بديه سوى zero ان z في a of x اللي هو الانتقال دبي
+
+225
+00:25:40,820 --> 00:25:48,260
+يبقى هذا معناه ان ال f bar of x بديه سوى zero or
+
+226
+00:25:48,260 --> 00:25:56,450
+ال g bar of x بديه سوى zeroطيب تعالى نسألك السؤال
+
+227
+00:25:56,450 --> 00:26:03,310
+التالف لما نقول F bar of X يساوي Zero يعني ال F of
+
+228
+00:26:03,310 --> 00:26:10,370
+X ده كل معاملاتها سقطت بدلالة P يعني معناته P
+
+229
+00:26:10,370 --> 00:26:17,610
+بتقسم كل معامل من معاملات F of X صح ولا لا؟ يبقى
+
+230
+00:26:17,610 --> 00:26:27,020
+this means that this meansthat هذا يعني ان ال P
+
+231
+00:26:27,020 --> 00:26:37,200
+divide each coefficient of
+
+232
+00:26:37,200 --> 00:26:49,040
+ال F of X او ال P divide each coefficient of ال G
+
+233
+00:26:49,040 --> 00:26:49,760
+of X
+
+234
+00:26:53,050 --> 00:27:00,330
+يبقى ال P بتقسم كل معامل ل F of X او ال P بتقسم كل
+
+235
+00:27:00,330 --> 00:27:06,450
+معامل لمين ل G of X هذا يعني ان ال F of X is
+
+236
+00:27:06,450 --> 00:27:15,150
+primitive لأو التانية ماهياش primitive يبقى فال F
+
+237
+00:27:15,150 --> 00:27:19,970
+of X is not primitive
+
+238
+00:27:22,670 --> 00:27:33,250
+أو الـ g of x is not primitive إما
+
+239
+00:27:33,250 --> 00:27:37,510
+هذه ماهياشي primitive أو هذه ماهياشي primitive إيش
+
+240
+00:27:37,510 --> 00:27:42,750
+رايحين؟ تناقض؟ لإن احنا من الرأس المثلجون ناخد
+
+241
+00:27:42,750 --> 00:27:47,670
+هدول ع ال primitive polynomial يبقى وصلنا إلى
+
+242
+00:27:47,670 --> 00:27:48,690
+contraction
+
+243
+00:27:50,910 --> 00:27:58,290
+وصلنا إلى Contradiction يبقى فرضي اللي أنا فرضته
+
+244
+00:27:58,290 --> 00:28:04,150
+هذا غلط و الله صح غلط و عكسه هو الصح يبقى ال
+
+245
+00:28:04,150 --> 00:28:10,670
+content لل F يجيب دي سواء جدال واحد صحيح يبقى
+
+246
+00:28:10,670 --> 00:28:16,230
+Therefore ال
+
+247
+00:28:16,230 --> 00:28:17,430
+content of
+
+248
+00:28:21,130 --> 00:28:30,190
+الـ F of X فى الـ G of X is one هذا يعطيكي ان الـ
+
+249
+00:28:30,190 --> 00:28:41,270
+F of X فى الـ G of X is a primitive البيانات
+
+250
+00:28:41,270 --> 00:28:45,490
+من الآن فصاعدة ال product of two primitive
+
+251
+00:28:45,490 --> 00:28:53,160
+polynomials is a primitiveوهذا الكلام صحيح في z of
+
+252
+00:28:53,160 --> 00:28:59,720
+x اللي المعاملات كلها أعداد صحيح طيب ننتقل إلى
+
+253
+00:28:59,720 --> 00:29:06,120
+النظرية التي تليها theorem
+
+254
+00:29:06,120 --> 00:29:12,120
+little
+
+255
+00:29:12,120 --> 00:29:23,360
+f of xموجودة في كافة z of x if
+
+256
+00:29:23,360 --> 00:29:33,740
+ال f of x is reducible if ال f of x is reducible
+
+257
+00:29:33,740 --> 00:29:46,630
+over ال Q then over ال Q thenالـ F of X is
+
+258
+00:29:46,630 --> 00:29:58,970
+reducible of Z سؤال يقول خد F of X في Z of X شوفوا
+
+259
+00:29:58,970 --> 00:30:02,590
+شو النظرية بتقول يبقى بيقول لو كانت ال F of X
+
+260
+00:30:02,590 --> 00:30:07,690
+reducible على ال Q هذا يتطلب ان تكون reducible على
+
+261
+00:30:07,690 --> 00:30:15,380
+مين؟ على Zوكأن ال reducibility على ال Eq بده ينسحب
+
+262
+00:30:15,380 --> 00:30:20,340
+عالميا لل reducibility على ال Z إيه بالبرهان
+
+263
+00:30:20,340 --> 00:30:26,520
+كالتالي يجب بالدالي أقوله little f of X موجودة في
+
+264
+00:30:26,520 --> 00:30:38,240
+Z of X بعد هيك SU افترض ان ال F of X is reducible
+
+265
+00:30:39,730 --> 00:30:44,110
+بعد ذلك
+
+266
+00:30:44,110 --> 00:30:48,530
+F of X يساوي
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b492febcfefb46ea2b7c3a9cbf911c889e14f4c3
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU.srt
@@ -0,0 +1,1493 @@
+1
+00:00:21,530 --> 00:00:26,610
+بسم الله الرحمن الرحيم. عودنا على البداية، نرجع لنفس الـ
+
+2
+00:00:26,610 --> 00:00:31,270
+chapter اللي معانا، اللي هو الـ integral domain. آخر
+
+3
+00:00:31,270 --> 00:00:35,450
+حاجة عرفناها المرة اللي فاتت، الـ characteristic للـ
+
+4
+00:00:35,450 --> 00:00:40,830
+ring هو أصغر
+
+5
+00:00:40,830 --> 00:00:47,370
+عدد صحيح موجب، بضربه في جميع عناصر الـ ring بيعطيني
+
+6
+00:00:47,370 --> 00:00:54,870
+الـ zero element. طيب، في عندنا نظرية هنا، أو أكثر من
+
+7
+00:00:54,870 --> 00:00:59,430
+نظرية. نأتي إلى النظرية الأولى، بتقول: little rb a
+
+8
+00:00:59,430 --> 00:01:05,210
+ring with unity one. أخدنا الـ unity اللي هو الواحد.
+
+9
+00:01:05,210 --> 00:01:11,070
+if الـ unity has infinite order under addition،
+
+10
+00:01:11,070 --> 00:01:16,430
+يبقى، إن حدث ذلك، يبقى الـ characteristic لهذه الـ
+
+11
+00:01:16,430 --> 00:01:20,840
+ring هو عبارة عن الـ zero. طبعاً احنا في التعريف أخدنا
+
+12
+00:01:20,840 --> 00:01:25,080
+الـمرة اللي فاتت، إذا ما قدرناش نلاقي هذا العدد،
+
+13
+00:01:25,080 --> 00:01:28,680
+اللي لو ضربته في جميع عناصر الـ ring بده يعطينا
+
+14
+00:01:28,680 --> 00:01:33,340
+zero، بنقول يبقى الـ characteristic لـ يساوي مين؟ يساوي
+
+15
+00:01:33,340 --> 00:01:39,900
+zero. إذا كان الواحد has finite order، وليكن N، تحت
+
+16
+00:01:39,900 --> 00:01:43,760
+عملية الجمع، يبقى الـ characteristic للـ ring بده
+
+17
+00:01:43,760 --> 00:01:49,520
+يساوي مين؟ الـ N. خلينا نرجع بالذاكرة قليلاً إلى الورقة
+
+18
+00:01:49,520 --> 00:01:53,880
+قبل ما نبرهن. كيف نرجع بالذاكرة قليلاً إلى الورقة
+
+19
+00:01:53,880 --> 00:01:59,620
+طبعاً، order للـ element في الـ group قلنا هو أصغر
+
+20
+00:01:59,620 --> 00:02:04,580
+عدد صحيح موجب، بحط أس للـ element بيعطينا الـ
+
+21
+00:02:04,580 --> 00:02:08,780
+identity. طبعاً لكن احنا عندنا هنا على ring two
+
+22
+00:02:08,780 --> 00:02:13,600
+operations. كلامنا محدود بالنسبة لعملية الجمع، وليس
+
+23
+00:02:13,600 --> 00:02:19,510
+بعملية الضرب. يبقى الواحد لو كان has infinite order،
+
+24
+00:02:19,510 --> 00:02:24,290
+يبقى الـ characteristic  لـه يساوي zero. وبعد ذلك،
+
+25
+00:02:24,290 --> 00:02:28,890
+لو كان finite، وليكن N، بدي أثبت أن الـ
+
+26
+00:02:28,890 --> 00:02:35,970
+characteristic يساوي مين؟ يساوي الـ N. يبقى هنا الـ 1
+
+27
+00:02:35,970 --> 00:02:44,040
+موجودة في الـ 1، أو الـ unity موجودة في R. and I
+
+28
+00:02:44,040 --> 00:02:54,340
+assume أننا نفترض أن الواحد has infinite order،
+
+29
+00:02:54,340 --> 00:03:01,020
+يعني under addition.
+
+30
+00:03:01,020 --> 00:03:05,320
+مدام
+
+31
+00:03:05,320 --> 00:03:11,900
+infinite، يعني ليس ممكن أن أجد عدد N أضربه فيه و
+
+32
+00:03:11,900 --> 00:03:18,770
+يطلع الناتج zero.  يبقى  لتعريف
+
+33
+00:03:18,770 --> 00:03:28,570
+الـ characteristic مظبوط، يبقى then there is no
+
+34
+00:03:28,570 --> 00:03:39,790
+integer N such that N في واحد بده يساوي zero.
+
+35
+00:03:39,790 --> 00:03:44,020
+مش هقدر ألاقيه. من تعريف المرة اللي فاتت، كتبناها في
+
+36
+00:03:44,020 --> 00:03:47,840
+نهاية المحاضرة. يبقى الـ... الـ ring هذه الـ
+
+37
+00:03:47,840 --> 00:03:53,320
+characteristic تبعها يساوي zero. هذا بده يعطينا
+
+38
+00:03:53,320 --> 00:04:02,120
+أن الـ characteristic للـ R is zero. طيب، هي النقطة
+
+39
+00:04:02,120 --> 00:04:10,980
+الأولى. ننتقل الآن للنقطة الثانية. يبقى assume that
+
+40
+00:04:12,360 --> 00:04:23,440
+الواحد اللي موجود في R has finite order, that is
+
+41
+00:04:23,440 --> 00:04:31,740
+under addition. برضه تحت عملية الجمع under addition.
+
+42
+00:04:31,740 --> 00:04:40,840
+تحت عملية الجمع. يعني هذا إيش معناه؟ معناه إن الـ N
+
+43
+00:04:41,290 --> 00:04:50,010
+في الواحد يساوي zero. بدي أحاول أثبت أن الـ N هذه هي
+
+44
+00:04:50,010 --> 00:04:55,170
+الـ characteristic تبع مين؟ الـ ring R. لذلك هذه N في
+
+45
+00:04:55,170 --> 00:05:01,190
+واحد يساوي zero. ماذا عن بقية عناصر الـ ring اللي
+
+46
+00:05:01,190 --> 00:05:10,290
+عندنا؟ فبدي أقول له: let الـ X be any element
+
+47
+00:05:11,950 --> 00:05:19,150
+يعني A. افترض هذا الـ X هو عبارة عن أي عنصر في A. نجي
+
+48
+00:05:19,150 --> 00:05:26,910
+نشوف هذا الكلام إيش بده يساوي. then نشوف هل الـ N
+
+49
+00:05:26,910 --> 00:05:32,310
+في X بدها تساوي zero ولا لأ؟ طب الـ X أخدته عشوائي،
+
+50
+00:05:32,310 --> 00:05:37,010
+يعني ينطبق على أي عنصر من عناصر الـ ring اللي عندنا.
+
+51
+00:05:37,010 --> 00:05:45,880
+بنجي على الـ NX. كأن الـ X مجموعة مع نفسها N من المرات.
+
+52
+00:05:45,880 --> 00:05:55,080
+يبقى هذه كأنها X + X + ... + X كم مرة؟ N
+
+53
+00:05:55,080 --> 00:06:03,320
+times. يبقى هذه N من المرات. طيب، أليست هذه بالضبط؟
+
+54
+00:06:03,320 --> 00:06:12,980
+هي واحد في X + واحد في X + واحد في X كمان N
+
+55
+00:06:12,980 --> 00:06:19,820
+times. مظبوط؟ طب لو جيت على الـ distributive law،
+
+56
+00:06:19,820 --> 00:06:24,760
+يبقى الـ NX يساوي، حسب الـ distributive اللي هو
+
+57
+00:06:24,760 --> 00:06:34,180
+واحد + واحد + واحد... كله في X. تمام؟ ودول كده N
+
+58
+00:06:34,180 --> 00:06:44,250
+times كذلك. يبقى هذا معناه أن N مضروبة في واحد،
+
+59
+00:06:44,250 --> 00:06:51,270
+كله في X اللي برا. طبعاً عندي هنا N في واحد بقد إيش؟ zero.
+
+60
+00:06:51,270 --> 00:06:58,910
+يبقى هذا الكلام يساوي zero في X يساوي zero. يبقى
+
+61
+00:06:58,910 --> 00:07:04,750
+صار الـ N في X بيساوي zero لكل الـ X اللي موجودة في
+
+62
+00:07:04,750 --> 00:07:10,860
+R. هذا الكلام صحيح لكل الـ X اللي موجود في R. إيش
+
+63
+00:07:10,860 --> 00:07:15,480
+تفسيرنا لهذه العبارة؟ إن الـ N هو الـ characteristic
+
+64
+00:07:15,480 --> 00:07:22,140
+لمين؟ للـ ring R. هذا بده يعطينا إن الـ characteristic
+
+65
+00:07:22,140 --> 00:07:27,500
+للـ R بده يساوي الـ N. وهو المفروض
+
+66
+00:07:30,530 --> 00:07:35,810
+الـ... الـ ring اللي فيها unity، الـ characteristic
+
+67
+00:07:35,810 --> 00:07:43,770
+تبعها يا إما zero يا إما N، رقم. قدر الله أعلى.
+
+68
+00:07:43,770 --> 00:07:51,530
+طيب، في نظرية ثانية مرتبطة بها تماماً، لأن كمان نظرية
+
+69
+00:07:51,530 --> 00:07:59,230
+أخرى، وهي آخر نظرية موجودة في هذا الـ section، بتقول: the
+
+70
+00:07:59,230 --> 00:08:08,710
+characteristic of
+
+71
+00:08:08,710 --> 00:08:23,870
+an integral domain R is zero
+
+72
+00:08:23,870 --> 00:08:25,790
+or prime.
+
+73
+00:08:48,340 --> 00:08:53,320
+النظرية اللي فوق بتقول: لو عندي ring with unity،
+
+74
+00:08:53,320 --> 00:08:57,520
+يبقى أحد أمرين: يا إما الـ characteristic اللي يساوي
+
+75
+00:08:57,520 --> 00:09:01,480
+zero، يا إما الـ characteristic اللي يساوي عدد
+
+76
+00:09:25,700 --> 00:09:32,870
+ماذا يعني؟ معناه الـ unity موجودة في الـ R؟ يبقى
+
+77
+00:09:32,870 --> 00:09:46,410
+implies أن الـ R has a unity، وليكن one. same، و يبقى
+
+78
+00:09:46,410 --> 00:09:50,890
+حكي الـ R فيها الـ unity. يبقى بالنظرية اللي فوق، الـ
+
+79
+00:09:50,890 --> 00:09:59,310
+characteristic إلها يا إما zero يا إما N. by the
+
+80
+00:09:59,310 --> 00:10:00,870
+above.
+
+81
+00:10:06,870 --> 00:10:17,590
+الـ characteristic للـ R is 0 or
+
+82
+00:10:17,590 --> 00:10:23,230
+N. طب
+
+83
+00:10:23,230 --> 00:10:27,910
+نظريتنا إيش بتقول؟ يا إما zero يا إما prime. إذا
+
+84
+00:10:27,910 --> 00:10:32,550
+احنا لو أثبتنا إن الـ N is a prime بتبقى المطلوب
+
+85
+00:10:32,550 --> 00:10:44,850
+صح؟ يبقى if we show that إن الـ N is a prime, then
+
+86
+00:10:44,850 --> 00:10:54,110
+we have the result. يبقى
+
+87
+00:10:54,110 --> 00:10:59,520
+بيكون حصلنا على النتيجة المطلوبة. يبقى ما علينا باقي
+
+88
+00:10:59,520 --> 00:11:06,480
+لنثبت إيش؟ أن الـ N is a prime. تمام؟ إيش N is a
+
+89
+00:11:06,480 --> 00:11:12,220
+prime؟ يعني لا يقسم إلا على نفسه وعلى الواحد
+
+90
+00:11:12,220 --> 00:11:17,980
+الصحيح. أنا بدي أمشي بالعكس، بدي أفترض أن الـ N بقدر
+
+91
+00:11:17,980 --> 00:11:23,900
+أحللها إلى حاصل ضرب رقمين، والرقمين أكبر من الواحد،
+
+92
+00:11:23,900 --> 00:11:31,470
+وأصغر من الـ N، ونشوف وين بتوجه الدنيا. طبعاً الآن احنا
+
+93
+00:11:31,470 --> 00:11:36,650
+بالنظرية الأولانية من فوق، هذه قلنا لها الـ
+
+94
+00:11:36,650 --> 00:11:42,630
+characteristic zero يا إما مين؟ يا إما الـ N. طبعاً
+
+95
+00:11:42,630 --> 00:11:48,630
+طيب، يبقى احنا بنقول هنا: لو طبعاً الـ zero هو اللي
+
+96
+00:11:48,630 --> 00:11:53,000
+مطلوب، إن أنا أقول الـ zero يا إما prime. يبقى zero هو
+
+97
+00:11:53,000 --> 00:11:59,200
+zero. ضل علينا بس الـ N أثبتها يا إني هي prime. يبقى
+
+98
+00:11:59,200 --> 00:12:09,560
+بده أروح أفرض إن الـ N بدها تساوي مثلاً S في T، وكل
+
+99
+00:12:09,560 --> 00:12:16,640
+من الـ S والـ T أكبر من الواحد وأقل من الـ N.
+
+100
+00:12:20,000 --> 00:12:25,700
+يبقى دول كل واحد فيهم أكبر من واحد وأقل من الـ N.
+
+101
+00:12:25,700 --> 00:12:34,140
+تمام؟ طيب، هنا احنا قلنا إن الـ characteristic لها
+
+102
+00:12:34,140 --> 00:12:41,340
+إما zero يا إما N. هذه إيش N؟ الـ characteristic. يبقى
+
+103
+00:12:41,340 --> 00:12:47,660
+الـ N في X بده يساوي zero للكل. صح ولا لأ؟ أو الـ N في
+
+104
+00:12:47,660 --> 00:12:53,640
+واحد بدها تساوي مين؟ بدها تساوي 0 للكل. فجأة باجي
+
+105
+00:12:53,640 --> 00:13:05,820
+بقول: since the characteristic is N, we have أن الـ N
+
+106
+00:13:05,820 --> 00:13:12,020
+في واحد بده يساوي 0. طيب،
+
+107
+00:13:12,020 --> 00:13:20,870
+يعني 0 بده يساوي الـ N في واحد. قد إيش فرضنا الـ N؟ S في T.
+
+108
+00:13:20,870 --> 00:13:31,090
+يبقى هذا S في T في واحد، اللي بقدر أكتبها S في واحد في
+
+109
+00:13:31,090 --> 00:13:39,550
+T في واحد. يبقى قدرت أكتب N في واحد على شكل S في واحد
+
+110
+00:13:39,550 --> 00:13:44,030
+في T في واحد. يبقى هذا عنصر وهذا عنصر ثاني، حاصل ضربهما يساوي قد إيش؟ zero. هل هذا الكلام صحيح إلا إذا... هالكلام
+
+111
+00:13:50,760 --> 00:13:56,720
+هذا مش صحيح إلا إذا كان الأول بـ zero أو الثاني بـ
+
+112
+00:13:56,720 --> 00:14:01,860
+zero. لإيش؟ عندنا integral domain. يبقى هذا بدي
+
+113
+00:14:01,860 --> 00:14:10,960
+يعطينا ماذا؟ أن الـ S في واحد بده يساوي zero or T في
+
+114
+00:14:10,960 --> 00:14:22,370
+واحد بده يساوي zero. لأن الـ R is an integral domain.
+
+115
+00:14:22,370 --> 00:14:27,110
+إيش يعني integral domain؟ يعني he has no zero
+
+116
+00:14:27,110 --> 00:14:32,210
+divisors. ما عندوش zero divisors إلا zero. يبقى يا
+
+117
+00:14:32,210 --> 00:14:36,750
+إما هذا بـ zero يا إما هذا بـ zero. طيب، تعالوا نقف
+
+118
+00:14:36,750 --> 00:14:40,990
+مع كل واحدة من هدول. احنا قلنا الـ
+
+119
+00:14:40,990 --> 00:14:49,140
+characteristic للـ ring N. صح؟ مين هو الـ N؟ هو أصغر عدد
+
+120
+00:14:49,140 --> 00:14:54,020
+بضربه في الواحد بيعطينا الناتج يساوي صفر. لجأنا لأصغر منه، صح؟ يبقى هذا الكلام مش ممكن إلا إذا كان
+
+121
+00:15:01,920 --> 00:15:06,500
+الأول بيساوي الـ N أو الثاني بيساوي الـ N. يبقى هنا
+
+122
+00:15:06,500 --> 00:15:14,540
+بقوله: but ولكن الـ N is the smallest
+
+123
+00:15:18,510 --> 00:15:23,590
+positive integer such
+
+124
+00:15:23,590 --> 00:15:31,870
+that الـ N في الواحد بده يساوي zero. لقيت S في واحد
+
+125
+00:15:31,870 --> 00:15:36,530
+بده يساوي zero أو T في واحد بده يساوي zero، وهو
+
+126
+00:15:36,530 --> 00:15:42,670
+أصغر منه. يبقى هذا الكلام ما يمكن أن يكون صحيحاً إلا
+
+127
+00:15:42,670 --> 00:15:50,630
+إذا كان S في واحد هو مين؟ الـ N. تمام؟ أو الـ T في واحد
+
+128
+00:15:50,630 --> 00:16:04,930
+هو مين؟ هو الـ N. يبقى this is a true only if الـ N
+
+129
+00:16:04,930 --> 00:16:13,230
+بدها تساوي الـ S or الـ N بدها تساوي T. مدام هي
+
+130
+00:16:13,230 --> 00:16:19,940
+كمان N، يعني هل الـ N بقدر أحللها إلى حاصل ضرب رقمين
+
+131
+00:16:19,940 --> 00:16:24,980
+أكبر من الواحد وأصغر من الـ N؟ لأ. يبقى معناته الفرض
+
+132
+00:16:24,980 --> 00:16:32,220
+اللي أنا فرضته في الأول خطأ، وعكسه هو الصح. يبقى so
+
+133
+00:16:32,220 --> 00:16:43,960
+الـ N cannot be factored into
+
+134
+00:16:45,850 --> 00:16:49,890
+a product of
+
+135
+00:16:49,890 --> 00:17:00,330
+smaller integers. ما قدرش أحلله. وده ما قدرش أحلله،
+
+136
+00:17:00,330 --> 00:17:08,690
+و يبقى الـ N إيش معناه؟ الـ prime. يبقى  N
+
+137
+00:17:08,690 --> 00:17:15,080
+is a prime. يبقى بيّنّا بلات من الـ alpha صاعداً، بديك
+
+138
+00:17:15,080 --> 00:17:19,280
+تفهم الحاجة. يقول لك: integral domain يبقى الـ
+
+139
+00:17:19,280 --> 00:17:23,880
+characteristic أحد أمرين: يا إما zero يا إما عدد
+
+140
+00:17:23,880 --> 00:17:30,300
+أولي على طول الخط. يعني ما عنديش عدد أولي زوجي إلا
+
+141
+00:17:30,300 --> 00:17:35,440
+اثنين. وبالتالي لا يمكن الـ characteristic يكون عدد
+
+142
+00:17:35,440 --> 00:17:39,180
+زوجي للـ integral domain غير اثنين. أما تقول لي أربعة،
+
+143
+00:17:39,180 --> 00:17:45,410
+ستة، ثمانية... هذا الكلام مستبعد، ما له وجود لحد
+
+144
+00:17:45,410 --> 00:17:50,130
+هنا. انتهى الجزء النظري تبع الـ section. لكن راح أحط
+
+145
+00:17:50,130 --> 00:17:55,870
+بعض الأشياء النظرية في مسائل التدريب. يبدأ احنا
+
+146
+00:17:55,870 --> 00:17:59,990
+بدنا نروح نحطها في نهاية هذا الـ section، وناخد
+
+147
+00:17:59,990 --> 00:18:06,410
+عليها بعض الأمثلة. وبالتالي بيصير تطبيق لهذا الـ
+
+148
+00:18:06,410 --> 00:18:13,000
+section. للأشياء الملحقة، تعريفين. ودول التعريفين ما
+
+149
+00:18:13,000 --> 00:18:18,380
+شوفناهمش قبل ذلك. التعريف الأول بيقول ما يأتي:
+
+150
+00:18:18,380 --> 00:18:24,200
+little a bearing
+
+151
+00:18:24,200 --> 00:18:32,400
+with unity little
+
+152
+00:18:32,400 --> 00:18:43,110
+a أو little.  الـ A belongs to R if A<sup>N</sup> بده يساوي
+
+153
+00:18:43,110 --> 00:18:51,570
+zero for some positive integer
+
+154
+00:18:51,570 --> 00:18:56,290
+N.
+
+155
+00:18:56,290 --> 00:19:06,530
+for some positive integer N, then الـ A is called an
+
+156
+00:19:06,530 --> 00:19:17,770
+nilpotent element. التعريف
+
+157
+00:19:17,770 --> 00:19:30,090
+الثاني هو: let A belong to ring A.
+
+158
+00:19:35,830 --> 00:19:49,590
+إذا كان A<sup>2</sup> يساوي A، فالـ A يسمى كـ
+
+159
+00:19:49,590 --> 00:19:55,270
+idempotent
+
+160
+00:19:55,270 --> 00:20:04,730
+element. Idempotent
+
+161
+00:20:06,480 --> 00:20:13,940
+مثال واحد، مثال
+
+162
+00:20:13,940 --> 00:20:23,160
+واحد. المسألة 14 من الكتاب بتقول: show that
+
+163
+00:20:23,160 --> 00:20:33,580
+the set of the nilpotent elements are not potent
+
+164
+00:20:34,740 --> 00:20:46,500
+elements of a commutative ring R of a commutative
+
+165
+00:20:46,500 --> 00:20:53,860
+ring R form
+
+166
+00:20:53,860 --> 00:20:56,600
+a subring of R.
+
+167
+00:21:29,360 --> 00:21:34,480
+مرة ثانية، نحاول نفهم التعريفين مشان نبدأ نحل
+
+168
+00:21:34,480 --> 00:21:39,060
+مجموعة من الأمثلة عليهم، والأمثلة بنجيبهم من
+
+169
+00:21:39,060 --> 00:21:44,340
+أسئلة التمرين. التعريف الأول بيقول: يخلق R ring
+
+170
+00:21:44,340 --> 00:21:48,920
+with unit، هو اللي عنصر موجود في R، إذا والله العنصر
+
+171
+00:21:48,920 --> 00:21:55,100
+هذا رفعته لعدد صحيح موجب كأُس، إله يعطاني zero،
+
+172
+00:21:55,100 --> 00:22:01,700
+وشافوا قال لي: for some، مش for all. يعني عدد صحيح،
+
+173
+00:22:01,700 --> 00:22:07,260
+رفعته كأُس، إله أها then الـ A عطاني zero، then الـ A
+
+174
+00:22:07,260 --> 00:22:11,000
+is called a nilpotent element. يبقى nilpotent
+
+175
+00:22:11,000 --> 0
+
+223
+00:27:31,280 --> 00:27:38,800
+sin زائد ألف لكل أسنون، إيش بجينا نسميها هذه النظرية؟
+
+224
+00:27:38,800 --> 00:27:46,120
+ذات الحدين، الـ binomial، ذات الحدين، يبقى بجينا نقول
+
+225
+00:27:46,120 --> 00:27:50,760
+بذكركم، بتذكر بالثانوية، بجينا نقول sin زائد ألف كل
+
+226
+00:27:50,760 --> 00:27:57,560
+أسنون، نسوي سين أسنون زائد نون قاف واحد، يعني توفيق
+
+227
+00:27:57,560 --> 00:28:03,140
+نون للأشياء مقودة واحد واحد، سين أسنون ناقص واحد
+
+228
+00:28:03,140 --> 00:28:09,120
+ألف زائد نون قاف اثنين، سين أسنون ناقص اثنين ألف
+
+229
+00:28:09,120 --> 00:28:14,240
+تربيع، السين أسّها بينقص، والألف أسّها
+
+230
+00:28:14,240 --> 00:28:20,220
+بيزداد لغاية ما نوصل إلى ألف أسنون. يبقى هنا بدنا
+
+231
+00:28:20,220 --> 00:28:24,280
+نمشي بنفس التكتيك تبع الشيء اللي اتعلمناه في
+
+232
+00:28:24,280 --> 00:28:29,800
+الثانوية. حد فيكم أخذ احتمالات؟ أخذنا احتمالات، طب
+
+233
+00:28:29,800 --> 00:28:33,320
+في عندك... في أخذتوها، التوزيع ذات الحدين تبعهم في
+
+234
+00:28:33,320 --> 00:28:37,520
+الاحتمالات، مظبوط؟ يبقى تبع هذه معلومات طازجة أجد
+
+235
+00:28:37,520 --> 00:28:42,780
+منها من الثانوية العامة. يبقى لو جينا بروح بنقول
+
+236
+00:28:42,780 --> 00:28:50,420
+هذه A أس N زائد M. لو الإشارة هذه زائد، كله بيكون
+
+237
+00:28:50,420 --> 00:28:54,580
+زائد، لكن مدام الإشارة هذه ناقص، بصير حد موجب وحد
+
+238
+00:28:54,580 --> 00:29:03,700
+سالب، يبقى بده يصير ناقص واحد أس M،  نون قاف، يعني توفيق N
+
+239
+00:29:03,700 --> 00:29:10,280
+زائد M من الأشياء مقودة واحد واحد. إذا نجي للـ A قص
+
+240
+00:29:10,280 --> 00:29:19,190
+N زائد M، بنطرح منها واحد، في B قص واحد، اللي بعدها
+
+241
+00:29:19,190 --> 00:29:29,950
+بالموجب، زائد نون قاف اثنين، A أس N زائد M
+
+242
+00:29:29,950 --> 00:29:39,730
+ناقص اثنين، ب تربيع، وهكذا نمشي لغاية ما نصل إلى... إلى
+
+243
+00:29:39,730 --> 00:29:48,990
+مين؟ N زائد M، نون قاف M،  M بس
+
+244
+00:29:48,990 --> 00:29:54,050
+ضايل علينا مين؟ ضايل علينا الإشارة يا رجال، يبقى هذه
+
+245
+00:29:54,050 --> 00:30:04,170
+زائد، وهنا ناقص واحد أس M، تمام؟ في A أس N، تبقى الـ M
+
+246
+00:30:04,170 --> 00:30:09,010
+مين خلصت؟ ناقص اثنين، ناقص ثلاثة، ناقص أربعة، خلصت
+
+247
+00:30:09,010 --> 00:30:14,950
+وصلنا إلى A أس N. في هذه الحالة، B زادت حتى وصلت إلى
+
+248
+00:30:14,950 --> 00:30:23,540
+مين؟ إلى M، تمام؟ الآن زائد، زائد
+
+249
+00:30:23,540 --> 00:30:30,880
+مين؟ زائد ناقص واحد to the power M زائد واحد
+
+250
+00:30:30,880 --> 00:30:37,640
+الإشارة الأُسّ تبقى بتزيد واحد، يبقى هنا N زائد M، و
+
+251
+00:30:37,640 --> 00:30:47,520
+هنا M زائد واحد، في الـ A أس N ناقص واحد، B أس M زائد
+
+252
+00:30:47,520 --> 00:30:52,060
+واحد. الـ A الأسّ تبعها بينقص واحد، والـ M الأسّ تبعها
+
+253
+00:30:52,060 --> 00:30:59,980
+بيزيد واحد. هنظل ماشيين لغاية ما نصل إلى آخر حد، آخر
+
+254
+00:30:59,980 --> 00:31:10,460
+حد بيكون ناقص واحد أس N زائد M، في B أس N زائد M
+
+255
+00:31:10,460 --> 00:31:18,220
+وبتبقى صار A أس صفر، اللي هو بواحد. طيب، كذا هذا
+
+256
+00:31:18,220 --> 00:31:23,060
+الكلام، مساوي ق ص
+
+257
+00:31:23,060 --> 00:31:31,660
+نون ق ص، ميم ق ص، نون ق صفر، هذا صفر، وهذا صفر، وهذا
+
+258
+00:31:31,660 --> 00:31:37,840
+صفر، وهذا صفر. need you to learn it better. هذا مش
+
+259
+00:31:37,840 --> 00:31:43,160
+صفر، لكن هذا بي قص ميم، في بي قص واحد، بي قص ميم بصفر
+
+260
+00:31:43,160 --> 00:31:49,550
+يبقى هذا صفر، هذا بيوسم في بيوسم، بيوسم بصفر، يبقى
+
+261
+00:31:49,550 --> 00:31:57,910
+هذا كله بده يساوي صفر، زائد ناقص صفر، زائد صفر، ناقص
+
+262
+00:31:57,910 --> 00:32:06,770
+مش عارف مين، زائد ناقص واحد أسّ، أو ناقص واحد أسّ ام
+
+263
+00:32:06,770 --> 00:32:13,530
+زائد انفينيتي صفر، جد ما يكون، يبقى الناتج كله جد صفر
+
+264
+00:32:13,530 --> 00:32:19,860
+مدام صفر، يبقى بروح بقول الـ sol، E ناقص الـ A ناقص B
+
+265
+00:32:19,860 --> 00:32:32,100
+الـ A nil potent، nil potent element، مدام nil potent
+
+266
+00:32:32,100 --> 00:32:37,720
+element، يعني معناته أن الـ A ناقص الـ B موجود وين؟ في
+
+267
+00:32:37,720 --> 00:32:44,020
+S. إذا احنا هنا أخذنا عنصرين موجودات في S، لجينا
+
+268
+00:32:44,020 --> 00:32:49,580
+الفرق فيما بينهما موجود في S. بقيت علينا النقطة
+
+269
+00:32:49,580 --> 00:32:55,380
+الأخيرة. إيش النقطة الأخيرة؟ بتقول: افترض أن الـ A و
+
+270
+00:32:55,380 --> 00:33:01,620
+الـ B موجودات في S، then الـ A أُسّ M بده يساوي صفر
+
+271
+00:33:01,620 --> 00:33:07,680
+and الـ B أُسّ M بده يساوي صفر. بدي أثبت أن حاصل
+
+272
+00:33:07,680 --> 00:33:14,940
+ضربهما موجود في S يساوي صفر لو رفعته لأسّ معين
+
+273
+00:33:14,940 --> 00:33:21,880
+خذ الرقم اللي بدك إياه، حبيتي N ماشي، حبيتي M ماشي
+
+274
+00:33:21,880 --> 00:33:28,540
+ولا داعي لمجموعهما أو حاصل ضربهما، صح؟ يبقى لو جيت
+
+275
+00:33:28,540 --> 00:33:35,480
+قلت مثلاً أسّ M، وواحدة ثانية أخذت أسّ N، صح؟ مية مية
+
+276
+00:33:35,920 --> 00:33:43,300
+يبقى هذا a أُسّ m في b أُسّ m. هذا الكلام صحيح لأن الـ
+
+277
+00:33:43,300 --> 00:33:47,160
+R is commutative. لكن لو ما كانت commutative، هذا
+
+278
+00:33:47,160 --> 00:33:51,300
+كلام نهار غلط. هو في المثال قال الـ R is commutative.
+
+279
+00:33:51,300 --> 00:33:57,660
+هذا الكلام بده يساوي a أُسّ m في صفر، بده يساوي صفر
+
+280
+00:33:57,660 --> 00:34:01,860
+هذا بده يعطينا أن a في b is
+
+281
+00:34:04,000 --> 00:34:10,260
+fourteen، هذا
+
+282
+00:34:10,260 --> 00:34:17,920
+بيقول أن الـ A في B موجود في S. إذا انتقلت الشروط
+
+283
+00:34:17,920 --> 00:34:25,020
+الثلاثة، يبقى علينا S is a subring، يبقى لص الـ
+
+284
+00:34:25,020 --> 00:34:31,740
+S is a subring of A
+
+285
+00:34:34,430 --> 00:34:39,870
+البتالي الثاني، البتالي
+
+286
+00:34:39,870 --> 00:34:46,990
+الثاني، له سؤال ثمانية عشر، سؤال ستة عشر من الكتاب، سؤال
+
+287
+00:34:46,990 --> 00:34:54,630
+ستة عشر، بيقول prove that، prove that the only
+
+288
+00:34:54,630 --> 00:35:02,090
+idempotent، the only idempotent
+
+289
+00:35:04,090 --> 00:35:13,810
+the only idempotents in an integral domain
+
+290
+00:35:13,810 --> 00:35:22,970
+in integral domain are the zero and الواحد
+
+291
+00:35:33,450 --> 00:35:38,870
+يقول لي: اثبت لي أنه في الـ integral domain ما عنديش
+
+292
+00:35:38,870 --> 00:35:44,970
+idempotents إلا اثنين فقط، اللي هم مين؟ الـ
+
+293
+00:35:44,970 --> 00:35:51,030
+zero والواحد، تمام؟ الآن أنا عندي integral domain
+
+294
+00:35:51,030 --> 00:35:57,230
+يبقى هو commutative ring with unit، صح؟ يبقى الـ
+
+295
+00:35:57,230 --> 00:36:09,470
+أو assume، للـ R is an integral domain، assume الـ
+
+296
+00:36:09,470 --> 00:36:18,610
+R is an integral domain، then الـ R has a unit
+
+297
+00:36:18,610 --> 00:36:28,230
+مثلاً، واحد على سبيل المثال. طيب
+
+298
+00:36:28,230 --> 00:36:38,390
+الآن، لماذا الـ A دي الـ idempotent
+
+299
+00:36:38,390 --> 00:36:47,070
+in A؟  أفترض أن A عنصر موجود في A وهذا idempotent
+
+300
+00:36:47,070 --> 00:36:54,950
+يبقى then الـ A تربيع تساوي الـ A، حسب تعريف الـ
+
+301
+00:36:54,950 --> 00:37:00,430
+idempotent.  قبض فريق رايكم نعملها معادلة صفرية
+
+302
+00:37:00,800 --> 00:37:06,940
+إذا، إيه تربيع ناقص إيه بده يساوي صفر. طيب، من الـ
+
+303
+00:37:06,940 --> 00:37:11,940
+distributive law، إيه في إيه ناقص واحد يساوي صفر
+
+304
+00:37:11,940 --> 00:37:18,860
+الطريقة دي بقدر أعملها لو الـ R فيها unity.  ده
+
+305
+00:37:18,860 --> 00:37:22,580
+بقدرش، لكن هذا علشان الـ integral domain، والـ
+
+306
+00:37:22,580 --> 00:37:26,280
+commutative ring، والـ unity. يعني الـ unity اللي
+
+307
+00:37:26,280 --> 00:37:30,730
+هو الواحد موجود فيها. إذا قدرت أستخدم الـ distributive
+
+308
+00:37:30,730 --> 00:37:38,710
+law. طيب هذا بده يعطيني أن الـ a تساوي صفر، or الـ a
+
+309
+00:37:38,710 --> 00:37:45,450
+ناقص واحد بده يساوي صفر. هل هذا كلام صحيح في أي ring؟
+
+310
+00:37:45,450 --> 00:37:50,490
+لا، مش صحيح، لكن صحيح في مين؟ الـ integral، والـ
+
+311
+00:37:50,490 --> 00:37:53,490
+integral domain، والـ integral domain ما فيش فيه
+
+312
+00:37:53,490 --> 00:38:02,600
+zero divisors. يبقى هنا هذا because الأرض
+
+313
+00:38:02,600 --> 00:38:11,320
+ليس لديها قواسم صفرية. يعني إيش؟ لو وجدت حاصل ضرب
+
+314
+00:38:11,320 --> 00:38:16,580
+كميتين بيكون بصفر، بيكون الأولى بصفر أو الثانية
+
+315
+00:38:16,580 --> 00:38:23,640
+بصفر. هذا بدّه يعطينا إن الـ a تساوي صفر، أو الـ a
+
+316
+00:38:23,640 --> 00:38:30,450
+تساوي واحد، صحيح؟ تمام؟ يبقى الـ Idempotent Element
+
+317
+00:38:30,450 --> 00:38:34,150
+اللي عندنا طلع مين؟ طلع الـ Zero والواحد، في
+
+318
+00:38:34,150 --> 00:38:40,950
+غيرهم؟ ما فيش غيرهم. يبقى في حالة الـ Integral Domain،
+
+319
+00:38:40,950 --> 00:38:47,970
+the only idempotent elements are Zero and the one،
+
+320
+00:38:48,350 --> 00:38:50,750
+غيرهم يبعد الله
+
+321
+00:38:56,210 --> 00:39:06,970
+طيب، هذا كان سؤال ستة عشر. مثال رقم ثلاثة... ثلاثة
+
+322
+00:39:06,970 --> 00:39:16,270
+في سؤال ثمانية عشر من الكتاب، بيقول الـ F الـ R بـ A
+
+323
+00:39:16,270 --> 00:39:25,330
+ring، F الـ A الموجود في R is an
+
+324
+00:39:29,700 --> 00:39:38,740
+idempotent، idempotent، then الـ a n بده يساوي الـ a
+
+325
+00:39:38,740 --> 00:39:49,740
+for all، for all positive integers، اللي موجودة
+
+326
+00:39:49,740 --> 00:39:50,820
+في Z plus
+
+327
+00:40:10,550 --> 00:40:15,270
+أخذ عنصر موجود فيها، والعنصر كان هذا idempotent،
+
+328
+00:40:15,270 --> 00:40:20,870
+إيش يعني؟ A تربيع بده يساوي الـ A.  جاي يبين لي إن الـ
+
+329
+00:40:20,870 --> 00:40:27,310
+A n بده يساوي الـ A لكل الـ N اللي موجودة في Z plus،
+
+330
+00:40:27,310 --> 00:40:32,900
+يعني، الـ n is a positive... أو for all n، والـ n is
+
+331
+00:40:32,900 --> 00:40:38,520
+a positive integer.  بقول له: بسيطة، بالحلقات التالية، احنا
+
+332
+00:40:38,520 --> 00:40:43,640
+عندنا معتقد أن الـ a is idempotent، صح؟ يبقى باللي
+
+333
+00:40:43,640 --> 00:40:52,860
+بقوله، الـ a تربيع بده يساوي الـ a. طيب، بدنا نثبت أن
+
+334
+00:40:52,860 --> 00:40:59,720
+الـ a to the power n تساوي الـ a. يبقى باجي بقوله: want
+
+335
+00:40:59,720 --> 00:41:02,860
+to show
+
+336
+00:41:02,860 --> 00:41:12,320
+أن الـ a n بده يساوي الـ a لكل الـ n اللي موجودة في
+
+337
+00:41:12,320 --> 00:41:17,020
+Z plus.  بنحاول
+
+338
+00:41:17,020 --> 00:41:22,680
+نثبت هذا باستخدام الاستقراء الرياضي، الـ induction، عشان
+
+339
+00:41:22,680 --> 00:41:28,030
+تاخذوا ثلاث طرق، أو ثلاث طرق للبراهين، أحدها الاستقراء الرياضي، الـ induction. طيب، السؤال هو: قداش
+
+340
+00:41:28,030 --> 00:41:33,930
+أقل عدد صحيح موجب بيحقق هذه العلاقة؟ واحد، اثنين
+
+341
+00:41:33,930 --> 00:41:40,950
+اثنين.  مش واحد. it's idempotent، يبقى أقل واحد صحيح هو
+
+342
+00:41:40,950 --> 00:41:46,870
+اثنين. سمي لي هذه الـ statement  stop
+
+343
+00:41:53,580 --> 00:42:04,880
+تبقى باجي بقول له: النقطة الأولى، the statement is
+
+344
+00:42:04,880 --> 00:42:17,200
+true at n يساوي اثنين. السبب because أن الـ a is an
+
+345
+00:42:17,200 --> 00:42:20,300
+idempotent
+
+346
+00:42:20,800 --> 00:42:27,300
+يعني إيش؟ يعني الـ A تربيع، أو بدل هذه لو قلت لي
+
+347
+00:42:27,300 --> 00:42:30,820
+because الـ A تربيع تساوي A، الكلام اللي هو صحيح
+
+348
+00:42:30,820 --> 00:42:39,800
+طيب، يبقى العبارة صحيحة عند أقل قيمة من الـ N بتحقق
+
+349
+00:42:39,800 --> 00:42:46,860
+هذه المعادلة، وهي اثنين. بدي أفترض أنها صحيحة عند رقم، و
+
+350
+00:42:46,860 --> 00:42:55,860
+أثبت صحتها عند الرقم m زائد واحد. يبقى هنا assume that
+
+351
+00:42:55,860 --> 00:42:59,420
+the equation
+
+352
+00:42:59,420 --> 00:43:14,800
+a star is true at n تساوي m، that is، أن الـ a أُسّ
+
+353
+00:43:14,800 --> 00:43:25,980
+m بده يساوي a، وأروح بدي آخذ consider A أُسّ M زائد
+
+354
+00:43:25,980 --> 00:43:32,060
+واحد، أشوف هل هذه العبارة صحيحة عندها ولا لا. يبقى
+
+355
+00:43:32,060 --> 00:43:39,160
+هذا بقدر أقول A أُسّ M في A أُسّ M، ما بيبقى داشر
+
+356
+00:43:39,160 --> 00:43:44,820
+يبقى A. يبقى بده يساوي A في A، و A في A ما بيبقى داشر
+
+357
+00:43:44,820 --> 00:43:50,840
+إيه تربيع وإيه تربيع إيه
+
+358
+00:43:50,840 --> 00:43:51,640
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+359
+00:43:51,640 --> 00:43:52,620
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+360
+00:43:52,620 --> 00:43:54,560
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+361
+00:43:54,560 --> 00:43:54,980
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+362
+00:43:54,980 --> 00:44:02,240
+إيه إيه إيه إيه إيه إيه
+
+363
+00:44:02,240 --> 00:44:05,340
+إيه
+
+364
+00:44:05,530 --> 00:44:13,490
+لكل الـ N اللي موجودة في الأعداد الصحيحة الموجبة
+
+365
+00:44:13,490 --> 00:44:18,710
+يبقى المعلومة يا بنات استفدناها، وسنستخدمها بعد ذلك
+
+366
+00:44:18,710 --> 00:44:23,330
+المعلومة إيش بتقول؟ بتقول: إن لو كان عندي element
+
+367
+00:44:23,330 --> 00:44:28,310
+idempotent، يبقى هذا الـ element لو رفعته لأُسّ صحيح
+
+368
+00:44:28,310 --> 00:44:34,370
+موجب من اثنين فصاعداً، بده يكون الناتج يعطيني الـ A
+
+369
+00:44:34,370 --> 00:44:42,990
+أثبتناها. طيب، أروح للسؤال الراجع، السؤال الراجع اللي هو
+
+370
+00:44:42,990 --> 00:44:49,390
+سؤال تسعة عشر من الكتاب، إيش بيقول؟ بيقول determine
+
+371
+00:44:49,390 --> 00:44:55,830
+ordering elements، determine ordering
+
+372
+00:44:55,830 --> 00:44:58,810
+elements
+
+373
+00:44:59,780 --> 00:45:05,780
+تحدد لي كل العناصر اللي في الـ ring that are both
+
+374
+00:45:05,780 --> 00:45:14,160
+that are both، واللي بتكون that are both
+
+375
+00:45:14,160 --> 00:45:19,800
+nilpotents، nilpotents
+
+376
+00:45:19,800 --> 00:45:24,140
+and idempotents
+
+377
+00:45:33,160 --> 00:45:38,260
+مدمنين، العناصر اللي بتكون في الـ ring اللي بنفع
+
+378
+00:45:38,260 --> 00:45:45,280
+تكون nilpotent و idempotent في نفس الوقت، معقول
+
+379
+00:45:45,280 --> 00:45:51,200
+يا بنات تكون العناصر nilpotent و idempotent في
+
+380
+00:45:51,200 --> 00:45:56,990
+أهل واحد؟ ممكن تجيبوا لي ولا عنصر واحد؟ الـ Zero. Zero
+
+381
+00:45:56,990 --> 00:45:59,810
+to the power of N بصفر، وصفر تربيع بصفر
+
+382
+00:45:59,810 --> 00:46:04,590
+تبقى، يبقى Zero is an idempotent element. يبقى يتعرف
+
+383
+00:46:04,590 --> 00:46:08,710
+عليه، بيشوف في غيره، والله ما فيش من خلال
+
+384
+00:46:08,710 --> 00:46:14,410
+المعلومات اللي عنده. يبقى بيقول: حدد لي كل عناصر الـ
+
+385
+00:46:14,410 --> 00:46:18,770
+ring اللي بيكون nilpotent و idempotent في نفس
+
+386
+00:46:18,770 --> 00:46:28,580
+الوقت. يبقى الحل كالتالي: solution، لأ A belongs في R
+
+387
+00:46:28,580 --> 00:46:40,320
+و R is a ring، تمام؟ such that بحيث أن nilpotent
+
+388
+00:46:40,320 --> 00:46:50,360
+يعني الـ A أُسّ N بده يساوي صفر for some N
+
+389
+00:46:50,360 --> 00:47:02,290
+اللي موجود في Z plus، and الـ A تربيع يساوي الـ A، idempotent
+
+390
+00:47:02,290 --> 00:47:06,330
+
+445
+00:53:13,190 --> 00:53:20,630
+الحالة الثانية: F لجريس الـ common divisor للـ N أو
+
+446
+00:53:20,630 --> 00:53:31,230
+للـ K و الـ N بده يساوي D مثلاً، و الـ D هذه أكبر من
+
+447
+00:53:31,230 --> 00:53:38,330
+الواحد، رقم أكبر من الواحد. طيب، بده أشوف معنى هذا
+
+448
+00:53:38,330 --> 00:53:45,570
+الكلام، أن الـ A مضاعفة الـ D، صح ولا لأ؟ يبقى هذا
+
+449
+00:53:45,570 --> 00:53:52,070
+الكلام بده يعطينا الـ there exists M موجود في Z
+
+450
+00:53:52,070 --> 00:54:03,840
+plus such that بحيث أن الـ A بده يساوي M في D. طبعاً
+
+451
+00:54:03,840 --> 00:54:08,620
+يبقى الكلام ده اللي class is called divisor لديه مع
+
+452
+00:54:08,620 --> 00:54:15,760
+أن يساوي D بدل غضب ورقم مضروب في D. بدي أحاول أثبت
+
+453
+00:54:15,760 --> 00:54:22,820
+أن الكلام ده هو zero divisor. لذلك بقول: لو جربت أضرب
+
+454
+00:54:22,820 --> 00:54:33,960
+K في N على D. سؤال: هل N على D يساوي Zero؟ لأ.
+
+455
+00:54:33,960 --> 00:54:39,300
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+456
+00:54:39,300 --> 00:54:39,640
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+457
+00:54:39,640 --> 00:54:39,760
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+458
+00:54:39,760 --> 00:54:39,800
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+459
+00:54:39,800 --> 00:54:40,740
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+460
+00:54:40,740 --> 00:54:54,960
+لأ
+
+461
+00:54:54,960 --> 00:55:01,060
+لأ. يبقى مضاعفات الـ N بقد إيش؟ بـ Zero. يبقى هذا الناتج
+
+462
+00:55:01,060 --> 00:55:08,240
+يساوي Zero. يبقى صار الـ K is a Zero divisor لأن الـ
+
+463
+00:55:08,240 --> 00:55:14,500
+K لا يساوي Zero و الـ N على D لا يساوي Zero. هذا
+
+464
+00:55:14,500 --> 00:55:23,590
+معناه أن الـ K is a Zero divisor. يبقى كل عنصر في Z
+
+465
+00:55:23,590 --> 00:55:28,630
+in يا إما unit يا إما zero divisor. لكن هذا الكلام
+
+466
+00:55:28,630 --> 00:55:34,450
+على أي ring؟ لأ، مش على Z in لأن طبعاً سألنا سؤال
+
+467
+00:55:34,450 --> 00:55:39,610
+أخذنا Z  لأنها  فيها  toilets ومافيهاش
+
+468
+00:55:39,610 --> 00:55:44,350
+zero divisor. يلا، في الوقت اتمرنوا في الأسئلة
+
+469
+00:55:44,350 --> 00:55:52,690
+التالية. يبقى exercises على شطر 13. ساعة خمسة هيو
+
+470
+00:55:52,690 --> 00:56:00,930
+حلّيناها: خمسة، وثمانية، وعشر، وعشرين، وواحد وعشرين،
+
+471
+00:56:00,930 --> 00:56:11,050
+وأربعة وعشرين، وواحد وثلاثين، واتنين وثلاثين،
+
+472
+00:56:11,050 --> 00:56:19,490
+وأربعين، واتنين وأربعين، وستة وأربعين، واتنين
+
+473
+00:56:19,490 --> 00:56:20,550
+وخمسين،
+
+474
+00:56:25,020 --> 00:56:35,580
+واتنين وخمسين، وثلاثة وخمسين، وستة وخمسين، وثمانية
+
+475
+00:56:35,580 --> 00:56:36,840
+وخمسين
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..33990f152380f7f3bd7a0f40fcb013527aa352c4
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU_raw.srt
@@ -0,0 +1,1924 @@
+1
+00:00:21,530 --> 00:00:26,610
+بسم الله الرحمن الرحيم عودنا على بدء نرجع لنفس ال
+
+2
+00:00:26,610 --> 00:00:31,270
+chapter اللي معانا اللي هو ال integral domain أخر
+
+3
+00:00:31,270 --> 00:00:35,450
+حاجة عرفناها المرة اللي فاتت ال characteristic لل
+
+4
+00:00:35,450 --> 00:00:40,830
+ring هو أصغر
+
+5
+00:00:40,830 --> 00:00:47,370
+عدد صحيح موجب بضربه في جميع عناصر ال ring بيعطيني
+
+6
+00:00:47,370 --> 00:00:54,870
+ال zero elementطيب في عندنا نظرية هنا او اكثر من
+
+7
+00:00:54,870 --> 00:00:59,430
+نظرية نأتي الى النظرية الاولى بتقول little rb a
+
+8
+00:00:59,430 --> 00:01:05,210
+ring with unity one اخدنا ال unity اللي هو الواحد
+
+9
+00:01:05,210 --> 00:01:11,070
+if ال unity has infinite or dot under addition
+
+10
+00:01:11,070 --> 00:01:16,430
+يبقى ان حدث ذلك يبقى ال characteristic لهذه ال
+
+11
+00:01:16,430 --> 00:01:20,840
+ring هو عبارة عن ال zeroطبعا احنا في التعريف أخدنا
+
+12
+00:01:20,840 --> 00:01:25,080
+المرة اللي فاتت إذا ما جدرناش اللي لاجي هذا العدد
+
+13
+00:01:25,080 --> 00:01:28,680
+اللي لو ضربته في جميع عناصر ال ring بده يعطينا
+
+14
+00:01:28,680 --> 00:01:33,340
+zero بنقول يبقى ال characteristic ل يسوى مين يسوى
+
+15
+00:01:33,340 --> 00:01:39,900
+zero إذا كان الواحد has finite order و ليكن N تحت
+
+16
+00:01:39,900 --> 00:01:43,760
+عملية الجامعة يبقى ال characteristic لل ring بده
+
+17
+00:01:43,760 --> 00:01:49,520
+يسوى مين ال Mخلينا نرجع بالذاكره قليلا الى الوراق
+
+18
+00:01:49,520 --> 00:01:53,880
+قبل ما نبرهن كيف نرجع بالذاكره قليلا الى الوراق
+
+19
+00:01:53,880 --> 00:01:59,620
+طبعا order لل element في ال group نقولنا هو أصغر
+
+20
+00:01:59,620 --> 00:02:04,580
+عدد صحيح موجب بحط أس لل element بيعطينا ال
+
+21
+00:02:04,580 --> 00:02:08,780
+identity طبعا لكن احنا عندنا هنا على ring two
+
+22
+00:02:08,780 --> 00:02:13,600
+operations بكلامنا محدود بالنسبة لعملية الجمع وليس
+
+23
+00:02:13,600 --> 00:02:19,510
+بعملية الضغطيبقى الواحد لو كان has infinite order
+
+24
+00:02:19,510 --> 00:02:24,290
+يبقى ال characteristic لغينه ساوى zero و بعد ذلك
+
+25
+00:02:24,290 --> 00:02:28,890
+لو كان finite وليكن N بدي أثبت ان ال
+
+26
+00:02:28,890 --> 00:02:35,970
+characteristic يساوى مين؟ يساوى ال M يبقى هنا ال Y
+
+27
+00:02:35,970 --> 00:02:44,040
+موجود في ال واحد او ال unity موجود في R andI
+
+28
+00:02:44,040 --> 00:02:54,340
+assume أننا نفترض أن الواحد has infinite order
+
+29
+00:02:54,340 --> 00:03:01,020
+يعني under addition
+
+30
+00:03:01,020 --> 00:03:05,320
+مدام
+
+31
+00:03:05,320 --> 00:03:11,900
+infinite يعني ليس ممكن أن أجد عدد M أضربه فيه و
+
+32
+00:03:11,900 --> 00:03:18,770
+يطلع الناتجالعادى مش العادى انت زيرو تبقى لتعريف
+
+33
+00:03:18,770 --> 00:03:28,570
+ال characteristics مظبوط يبقى then there is no
+
+34
+00:03:28,570 --> 00:03:39,790
+integer in such that ال n في واحد بده يساوي زيرو
+
+35
+00:03:39,790 --> 00:03:44,020
+مش هقدر ألاقيمن تعريف المرة اللى فترة كتبناها في
+
+36
+00:03:44,020 --> 00:03:47,840
+نهاية المحاضرة يبقى ال .. ال ring هذه ال
+
+37
+00:03:47,840 --> 00:03:53,320
+characteristic تبعي يساوي جدير zero هذا بده يعطينا
+
+38
+00:03:53,320 --> 00:04:02,120
+انه ال characteristic لل R is zero طيب هي النقطة
+
+39
+00:04:02,120 --> 00:04:10,980
+الأولى بدهاجى الآن للنقطة الثانية يبقى assume that
+
+40
+00:04:12,360 --> 00:04:23,440
+الواحد اللى موجود في R has finite order that is
+
+41
+00:04:23,440 --> 00:04:31,740
+under addition برضه تحت عملية الجمع under addition
+
+42
+00:04:31,740 --> 00:04:40,840
+تحت عملية الجمع يعني هذا إيش معناه؟ معناه إن ال N
+
+43
+00:04:41,290 --> 00:04:50,010
+فى الواحد يساوي زيرو بدا أحاول أثبت أن ال N هذه هي
+
+44
+00:04:50,010 --> 00:04:55,170
+ال characteristic تبع مين ال ring R لذلك هذه N فى
+
+45
+00:04:55,170 --> 00:05:01,190
+واحد يساوي زيرو ماذا عن بقية عناصر ال ring اللى
+
+46
+00:05:01,190 --> 00:05:10,290
+عندنا فبدا فى أقول له let ال X be any element
+
+47
+00:05:11,950 --> 00:05:19,150
+يعني A افترض هذا ال X هو عبارة عن أي عنصر في A نجي
+
+48
+00:05:19,150 --> 00:05:26,910
+نشوف هذا الكلام إيش بده يساوي then زي شوف هل ال N
+
+49
+00:05:26,910 --> 00:05:32,310
+في X بدها تساوي Zero ولا لأ؟ طب ال X أخدته عشوائي
+
+50
+00:05:32,310 --> 00:05:37,010
+يعني انطبق على أي عنصر من عناصر ال ring اللي عندها
+
+51
+00:05:37,010 --> 00:05:45,880
+يتجه ال N Xكأن الـ X مجموعة مع نفسها N من المرات
+
+52
+00:05:45,880 --> 00:05:55,080
+يبقى هذه كأنها X زائد X زائد زائد X كم مرة؟ N
+
+53
+00:05:55,080 --> 00:06:03,320
+times يبقى هذه N من المرات طيب، أليست هذه بالضبط؟
+
+54
+00:06:03,320 --> 00:06:12,980
+هي واحد في X زائد واحد في Xزائد واحد في X كمان in
+
+55
+00:06:12,980 --> 00:06:19,820
+times مظبوط؟ طب لو جيت على ال distributive law
+
+56
+00:06:19,820 --> 00:06:24,760
+يبقى ال in X يساوي حسب ال distributive اللي هو
+
+57
+00:06:24,760 --> 00:06:34,180
+واحد زائد واحد زائد واحد كله في X تمام؟ ودول كدهش؟
+
+58
+00:06:34,180 --> 00:06:44,250
+in times كذلكيبقى هذا معناه ان N مضروبة في واحد
+
+59
+00:06:44,250 --> 00:06:51,270
+كله في X اللي برا طبعا عندي هنا N واحد بقداش Zero
+
+60
+00:06:51,270 --> 00:06:58,910
+يبقى هذا الكلام يساوي Zero في X يساوي Zero يبقى
+
+61
+00:06:58,910 --> 00:07:04,750
+صار ال N في X بيساوي Zero لكل ال X اللي موجودة في
+
+62
+00:07:04,750 --> 00:07:10,860
+R هذا الكلام صحيحلكل ال X اللي موجود في R إيش
+
+63
+00:07:10,860 --> 00:07:15,480
+تفسيرنا لهذه العبارة إن ال N هو ال characteristic
+
+64
+00:07:15,480 --> 00:07:22,140
+لمن؟ لل ring R هذا بده يعطينا إن ال characteristic
+
+65
+00:07:22,140 --> 00:07:27,500
+لل A بده يسوى ال N وهو المفروض
+
+66
+00:07:30,530 --> 00:07:35,810
+ال .. ال ring اللي فيها unity ال characteristic
+
+67
+00:07:35,810 --> 00:07:43,770
+تبعها يا إما zero يا إما in رقم قدر يطلع الله أعلى
+
+68
+00:07:43,770 --> 00:07:51,530
+طيب في نظرية ثانية مرتبطة بها تماما لأن كمان نظرية
+
+69
+00:07:51,530 --> 00:07:59,230
+أخرى وهي أخر نظرية موجودة في هذا section بتقولthe
+
+70
+00:07:59,230 --> 00:08:08,710
+characteristic of
+
+71
+00:08:08,710 --> 00:08:23,870
+an integral domain is an integral domain R is zero
+
+72
+00:08:23,870 --> 00:08:25,790
+or prime
+
+73
+00:08:48,340 --> 00:08:53,320
+النظرية اللى فوق بتقول لو عندى ring with unity
+
+74
+00:08:53,320 --> 00:08:57,520
+يبقى احد امرين يا اما ال characteristic اللى يساوي
+
+75
+00:08:57,520 --> 00:09:01,480
+zero يا اما ال characteristic اللى يساوي عدد
+
+76
+00:09:25,700 --> 00:09:32,870
+ماذا يعني معناه ال unit موجودة في ال R؟يبقى
+
+77
+00:09:32,870 --> 00:09:46,410
+implies ان ال R has a unity وليكن one same ويبقى
+
+78
+00:09:46,410 --> 00:09:50,890
+حصار ال R فيها ال unity يبقى بالنظرية اللي فوق ال
+
+79
+00:09:50,890 --> 00:09:59,310
+characteristic إلها يا إما zero يا إما N by the
+
+80
+00:09:59,310 --> 00:10:00,870
+above
+
+81
+00:10:06,870 --> 00:10:17,590
+الكاركترستيك للـ R is 0 or
+
+82
+00:10:17,590 --> 00:10:23,230
+N طب
+
+83
+00:10:23,230 --> 00:10:27,910
+نظريتنا إيش بتقول؟ يا إما Zero يا إما Prideإذا
+
+84
+00:10:27,910 --> 00:10:32,550
+إحنا لو أثبتنا إن ال in is a prime بتبقى المطلوب
+
+85
+00:10:32,550 --> 00:10:44,850
+صح؟ يبقى if we show that إن ال in is a prime then
+
+86
+00:10:44,850 --> 00:10:54,110
+we have the result يبقى
+
+87
+00:10:54,110 --> 00:10:59,520
+بيكون حصلنا على النتيجة المطلوبةيبقى ما علينا باقي
+
+88
+00:10:59,520 --> 00:11:06,480
+لنثبت إيش ان ال N is a prime تمام؟ إيش N is a
+
+89
+00:11:06,480 --> 00:11:12,220
+prime؟ يعني لا يقسم إلا على نفسه وعلى الواحد
+
+90
+00:11:12,220 --> 00:11:17,980
+الصحيح أنا بدي أمشي بالعكس بدي أفترض أن ال N بقدر
+
+91
+00:11:17,980 --> 00:11:23,900
+أحللها إلى حاصل ضرب رقمين والرقمين أكبر من الواحد
+
+92
+00:11:23,900 --> 00:11:31,470
+وأصغر من ال Nوشوف وين بيتوجه الدنيا طبعا الان احنا
+
+93
+00:11:31,470 --> 00:11:36,650
+بالنظرية الأولانية لفوق هذه قلنا الها ال
+
+94
+00:11:36,650 --> 00:11:42,630
+characteristic zero يا اما مين يا اما ال N طبعا
+
+95
+00:11:42,630 --> 00:11:48,630
+طيب يبقى احنا بنقول هنا لو طبعا ال zero هو اللي
+
+96
+00:11:48,630 --> 00:11:53,000
+مطلوب ان انا اقول ال zero يا اما primeيبقى Zero هو
+
+97
+00:11:53,000 --> 00:11:59,200
+Zero ضلي عليه بس ال N أثبتها ياش انه هي Prime يبقى
+
+98
+00:11:59,200 --> 00:12:09,560
+بده أروح أضله لت ال N بدها تساوي مثلا S في T وكل
+
+99
+00:12:09,560 --> 00:12:16,640
+من ال S و ال T أكبر من الواحد و أقل من ال N
+
+100
+00:12:20,000 --> 00:12:25,700
+يبقى دول كل واحد فيهم اكبر من واحد و اقل من ال N
+
+101
+00:12:25,700 --> 00:12:34,140
+تمام؟ طيب هنا احنا قلنا ان ال characteristic ليها
+
+102
+00:12:34,140 --> 00:12:41,340
+اما Zero يا اما N هذه ايش N ال characteristic يبقى
+
+103
+00:12:41,340 --> 00:12:47,660
+ال N في X بده يساوي Zero للكل صح ولا لأ او ال N في
+
+104
+00:12:47,660 --> 00:12:53,640
+واحدبدها تساوي مين؟ بدها تساوي 0 للكل يفجأة باجي
+
+105
+00:12:53,640 --> 00:13:05,820
+بقول since the characteristic is n we have ان ال n
+
+106
+00:13:05,820 --> 00:13:12,020
+في واحد بده ساوي 0 طيب
+
+107
+00:13:12,020 --> 00:13:20,870
+يعني 0 بده ساوي ال n في واحدقداش فرض ال N S في T
+
+108
+00:13:20,870 --> 00:13:31,090
+يبقى هذا S T في واحد اللي بقدر أكتبها S في واحد في
+
+109
+00:13:31,090 --> 00:13:39,550
+T في واحد يبقى قدرت أكتب N في واحد عليه شكل S واحد
+
+110
+00:13:39,550 --> 00:13:44,030
+T واحد يبقى هذا عنصر و هذا عنصر تاني حاصل ضربه ما
+
+111
+00:13:44,030 --> 00:13:50,760
+يساوي قداش Zeroهل هذا كلام صحيح إلا إذا .. هالكلام
+
+112
+00:13:50,760 --> 00:13:56,720
+هذا مش صحيح إلا إذا كان الأول ب zero أو الثاني ب
+
+113
+00:13:56,720 --> 00:14:01,860
+zero لإيش عندنا integral domain يبقى هذا بدي
+
+114
+00:14:01,860 --> 00:14:10,960
+يعطينا ميادة ان ال S في واحد بدي يسوي zero or T في
+
+115
+00:14:10,960 --> 00:14:22,370
+واحد بدي يسوي zero لأنالـ R is an integral domain
+
+116
+00:14:22,370 --> 00:14:27,110
+ايش يعني integral domain يعني he has no zero
+
+117
+00:14:27,110 --> 00:14:32,210
+divisors ماعندوش zero divisors الا zero يبقى يا
+
+118
+00:14:32,210 --> 00:14:36,750
+اما هذا في zero يا اما هذا في zero طيب تعالوا نقف
+
+119
+00:14:36,750 --> 00:14:40,990
+مع كل واحدة من هدول احنا قداشي قولنا ال
+
+120
+00:14:40,990 --> 00:14:49,140
+characteristic لارين N صح؟مين هو ال N هو أصغر عدد
+
+121
+00:14:49,140 --> 00:14:54,020
+بضربه في الواحد بيعطينا الناتج يساوي صفر لجأتي
+
+122
+00:14:54,020 --> 00:15:01,920
+أصغر منه صح؟ يبقى هذا الكلام مش ممكن إلا إذا كان
+
+123
+00:15:01,920 --> 00:15:06,500
+الأول بيساوي ال N أو التاني بيساوي ال N يبقى هنا
+
+124
+00:15:06,500 --> 00:15:14,540
+بقوله but ولكن ال N is the smallest
+
+125
+00:15:18,510 --> 00:15:23,590
+positive انتجار such
+
+126
+00:15:23,590 --> 00:15:31,870
+that ال N في ال واحد بده يساوي زيرو لقيت S في واحد
+
+127
+00:15:31,870 --> 00:15:36,530
+بده يساوي زيرو او T في واحد بده يساوي زيرو وهو
+
+128
+00:15:36,530 --> 00:15:42,670
+اصغر منه يبقى هذا الكلام مايمكن ان يكون صحيحا الا
+
+129
+00:15:42,670 --> 00:15:50,630
+اذا كان S في واحد هو مينال N تمام أو ال T في واحد
+
+130
+00:15:50,630 --> 00:16:04,930
+هو مين هو ال N يبقى this is a true only if ال N
+
+131
+00:16:04,930 --> 00:16:13,230
+بدها تساوي ال S or ال N بدها تساوي T مدام هي
+
+132
+00:16:13,230 --> 00:16:19,940
+كمانات يعني هل ال Nبقدر أحللها إلى حصر ضرب رقمين
+
+133
+00:16:19,940 --> 00:16:24,980
+أكبر من الواحد وأصغر من ال N لأ يبقى معناته فرض
+
+134
+00:16:24,980 --> 00:16:32,220
+اللي أنا فرضته في الأول خطأ وعكسه هو الصح يبقى so
+
+135
+00:16:32,220 --> 00:16:43,960
+ال N cannot be factored into
+
+136
+00:16:45,850 --> 00:16:49,890
+product of
+
+137
+00:16:49,890 --> 00:17:00,330
+smallest integers ماقدرش أحلله وده ماقدرش أحلله
+
+138
+00:17:00,330 --> 00:17:08,690
+ويبقى ال N إيش معناه ال إفرايه يبقى ضاص وهكذا ال N
+
+139
+00:17:08,690 --> 00:17:15,080
+is a primeيبقى بياد بلات من ال alpha صعدا بديك
+
+140
+00:17:15,080 --> 00:17:19,280
+تفهم الحجم يقولك integral domain يبقى ال
+
+141
+00:17:19,280 --> 00:17:23,880
+characteristic أحد أمرين يا إما zero يا إما عدد
+
+142
+00:17:23,880 --> 00:17:30,300
+أولي على طول الخط يعني ماعنديش عدد أولي زوجي إلا
+
+143
+00:17:30,300 --> 00:17:35,440
+اتنين وبالتالي لا يمكن ال characteristic يكون عدد
+
+144
+00:17:35,440 --> 00:17:39,180
+زوجي لل integral domain غير اتنين اما تقوللي اربع
+
+145
+00:17:39,180 --> 00:17:45,410
+ستة تمانية هذا معنىكل كلام مستبعد مالوش وجود لحد
+
+146
+00:17:45,410 --> 00:17:50,130
+هنا انتهى الجزء النظري تبع ال section لكن راح أحط
+
+147
+00:17:50,130 --> 00:17:55,870
+بعض الأشياء النظرية في مسائل التدريب يبدأ احنا
+
+148
+00:17:55,870 --> 00:17:59,990
+بدنا نروح نحطها في نهاية هذا ال section و ناخد
+
+149
+00:17:59,990 --> 00:18:06,410
+عليها بعض الأمثلة وبالتالي بصير مضحكا لهذا ال
+
+150
+00:18:06,410 --> 00:18:13,000
+sectionللأشياء الملحقة تعريفين ودول التعريفين ما
+
+151
+00:18:13,000 --> 00:18:18,380
+شوفناهم مش قبل ذلك التعريف الأول بيقول ما ياتي
+
+152
+00:18:18,380 --> 00:18:24,200
+little a bearing
+
+153
+00:18:24,200 --> 00:18:32,400
+with unity little
+
+154
+00:18:32,400 --> 00:18:43,110
+a أو littleالـ A belongs to R if ال A N بده ساوي
+
+155
+00:18:43,110 --> 00:18:51,570
+Zero for some positive integer
+
+156
+00:18:51,570 --> 00:18:56,290
+N
+
+157
+00:18:56,290 --> 00:19:06,530
+for some positive integer M then ال Ais called an
+
+158
+00:19:06,530 --> 00:19:17,770
+important and important element التعريف
+
+159
+00:19:17,770 --> 00:19:30,090
+الثاني هو let ال A belong to hearing A
+
+160
+00:19:35,830 --> 00:19:49,590
+إذا كان الـ A تربيع بيساوي الـ A، فالـ A يُسمى كـ
+
+161
+00:19:49,590 --> 00:19:55,270
+Idempotent
+
+162
+00:19:55,270 --> 00:20:04,730
+Element Idempotent
+
+163
+00:20:06,480 --> 00:20:13,940
+مثال واحد مثال
+
+164
+00:20:13,940 --> 00:20:23,160
+واحد المسؤال أربع تاشر من الكتاب بيقول show that
+
+165
+00:20:23,160 --> 00:20:33,580
+the set of the important elements are not potent
+
+166
+00:20:34,740 --> 00:20:46,500
+Elements of a commutative ring R of a commutative
+
+167
+00:20:46,500 --> 00:20:53,860
+ring R form
+
+168
+00:20:53,860 --> 00:20:56,600
+a sub ring of R
+
+169
+00:21:29,360 --> 00:21:34,480
+مرة تانية نحاول نفهم التعريفين مشان نبدأ نحل
+
+170
+00:21:34,480 --> 00:21:39,060
+مجموعة من الأمثلة عليهم والأمثلة بإن نجيبهم من
+
+171
+00:21:39,060 --> 00:21:44,340
+أسئلتي التمرين التعريف الأول بيقول يخلق R ring
+
+172
+00:21:44,340 --> 00:21:48,920
+with unit هو اللي عنصر موجود في Rإذا والله العنصر
+
+173
+00:21:48,920 --> 00:21:55,100
+هذا رفعته لعدد صحيح موجب كأس إله يعطاني zero
+
+174
+00:21:55,100 --> 00:22:01,700
+وشايفه قال لي for some مش for all يعني عدد صحيح
+
+175
+00:22:01,700 --> 00:22:07,260
+رفعته كأس إله اها then ال L عطاني zero then ال A
+
+176
+00:22:07,260 --> 00:22:11,000
+is called any potent element يبقى any potent
+
+177
+00:22:11,000 --> 00:22:16,350
+element هو عنصر من ال ring Rرفعته لأُس اللي هو
+
+178
+00:22:16,350 --> 00:22:22,370
+الأس عدد صحيح موجب أعطاني الـ 0 إن حدث ذلك يبقى في
+
+179
+00:22:22,370 --> 00:22:27,390
+هذه الحالة بسمي هذا ال element Nilpotent element
+
+180
+00:22:27,390 --> 00:22:32,570
+نيجي للتعريف التاني اللي هو ال idempotent element
+
+181
+00:22:32,570 --> 00:22:37,370
+فباجي بقول ال element A اللي موجود في ال ring R
+
+182
+00:22:37,370 --> 00:22:44,280
+بسميه idempotent لو ربعته أو ضربته في نفسهبدي
+
+183
+00:22:44,280 --> 00:22:48,880
+يعطيني مين؟ بدي يعطيني نفس العنصر يبقى الـ
+
+184
+00:22:48,880 --> 00:22:55,480
+idempotent element هو مين؟ اللي كان A تربعي سوية A
+
+185
+00:22:55,480 --> 00:22:59,580
+بقى الـ A بسمي مين؟ idempotent بدي ناخد بعض
+
+186
+00:22:59,580 --> 00:23:05,300
+الأمثلة على هذين التعريفين المثل الأول سؤال 14 من
+
+187
+00:23:05,300 --> 00:23:09,360
+الكتاب بيقول بيبينلي أن الست من ال potent elements
+
+188
+00:23:09,360 --> 00:23:15,200
+of B هي commutative ring Aبيطوللي ال sub ring من
+
+189
+00:23:15,200 --> 00:23:22,600
+ال a يبقى بالده دي افترض انه عندي S و ال S subset
+
+190
+00:23:22,600 --> 00:23:30,560
+من a where هدى اعرف مين هى ال S هدى يبقى ال S هي
+
+191
+00:23:30,560 --> 00:23:38,100
+the sixth of all elements a such that ال a n بدى
+
+192
+00:23:38,100 --> 00:23:49,720
+ساوي zero for somepositive or some positive انتجار
+
+193
+00:23:49,720 --> 00:24:00,880
+N أو الـ N موجودة في Zero طب السؤال إيه N يسوى
+
+194
+00:24:00,880 --> 00:24:07,180
+Zero لو لقيتني ال potent element آخر B بيكون ال B
+
+195
+00:24:07,180 --> 00:24:14,730
+أس N يسوى Zero والله بي أس رقم آخرمش رقم اخر لجالي
+
+196
+00:24:14,730 --> 00:24:20,350
+for some مجاليش for ال يعني مش كلهم لهم نفس الرقم
+
+197
+00:24:20,350 --> 00:24:26,870
+في واحد يوم عنصر A تكحيب يساوي Zero عنصر تاني بيقص
+
+198
+00:24:26,870 --> 00:24:31,910
+سبعة يساوي Zero واحد ال C يساوي عشرين يساوي Zero
+
+199
+00:24:31,910 --> 00:24:38,850
+يبقى كلهم هدول ال potent elements يبقى الأس هذا مش
+
+200
+00:24:38,850 --> 00:24:44,580
+ثابت يا بنات الأسيختلف من عنصرين إلى آخر طب احنا
+
+201
+00:24:44,580 --> 00:24:54,420
+بنثبت هذه ال suffering يبقى one to show that ان ال
+
+202
+00:24:54,420 --> 00:25:03,760
+S is a suffering of R مشان أثبت ال suffering يبقى
+
+203
+00:25:03,760 --> 00:25:12,090
+بدي أثبت ثلاث نقاط النقطة الأولى ان ال Sis non
+
+204
+00:25:12,090 --> 00:25:17,950
+-empty بنقدر نجيب عنصر موجود في S يا بنات يعني
+
+205
+00:25:17,950 --> 00:25:25,030
+عنصر أعفر للـS إن يبقى هناك شخصية لهمين Zero is
+
+206
+00:25:25,030 --> 00:25:31,870
+non-empty since Zero to the power N بده يسوى Zero
+
+207
+00:25:31,870 --> 00:25:40,220
+هذا معناه إن Zero موجود في الـS Why؟يبقى هنا من
+
+208
+00:25:40,220 --> 00:25:45,940
+النقطة الأولى بروح للنقطة الثانية بدي أخد عنصرين A
+
+209
+00:25:45,940 --> 00:25:53,060
+و B موجودات في ال S يبقى بروح بقوله then ال A to
+
+210
+00:25:53,060 --> 00:26:00,340
+the power N يسوى Zero and ال B to the power M يسوى
+
+211
+00:26:00,340 --> 00:26:11,370
+Zero for some N و Mاللي موجودة في Z plus يعني
+
+212
+00:26:11,370 --> 00:26:19,510
+أعداد صحيحة موجبة طبعا طيب الآن على فرض عددين
+
+213
+00:26:19,510 --> 00:26:25,090
+موجودات في S بدي أثبت أن الفرق بينما بينهما موجود
+
+214
+00:26:25,090 --> 00:26:33,910
+في S إذا بدي أخد ال A ناقص ال B و أرفعها لأس ما
+
+215
+00:26:33,910 --> 00:26:41,090
+الله أعلم منهبدى الناتج يساوي Z إضافى إيش تقترحوا
+
+216
+00:26:41,090 --> 00:26:45,210
+هذا الأس يكون؟
+
+217
+00:26:45,210 --> 00:26:57,750
+إيش يكون؟ N في M و الله N زائد M نعم N زائد M لإن
+
+218
+00:26:57,750 --> 00:27:07,000
+لو جيت قلت N زائد Mوالله إذا طلع هذا الكلب بيزيره،
+
+219
+00:27:07,000 --> 00:27:11,460
+بيقول خلاصنا الحمد لله، بص يهدن القوت المحتل.
+
+220
+00:27:11,720 --> 00:27:19,360
+السؤال هو بنقدر نفك القوس هذا؟ كيف؟
+
+221
+00:27:19,360 --> 00:27:26,360
+صحيح؟ ممتاز،
+
+222
+00:27:26,360 --> 00:27:31,280
+يعني إيش بنسمي المفكوك هذا؟لما كنت أقول في ثانوية
+
+223
+00:27:31,280 --> 00:27:38,800
+sin زائد ألف لكل أسنون إيش بجينا نسميها هذه نظرية
+
+224
+00:27:38,800 --> 00:27:46,120
+ذات الحدين ال binomial ذات الحدين يبقى بجينا نقول
+
+225
+00:27:46,120 --> 00:27:50,760
+بذكركوا تذكر بالثانوية بجينا نقول sin زائد ألف كل
+
+226
+00:27:50,760 --> 00:27:57,560
+أسنونيسوي سين أسنون زائد نون قاف واحد يعني توفيق
+
+227
+00:27:57,560 --> 00:28:03,140
+نوم للأشياء مقودة واحد واحد سين أسنون ناقص واحد
+
+228
+00:28:03,140 --> 00:28:09,120
+ألف زائد نون قاف اتنين سين أسنون ناقص اتنين ألف
+
+229
+00:28:09,120 --> 00:28:14,240
+تربيع السين الأستبعها بينقص والألف الأستبعها
+
+230
+00:28:14,240 --> 00:28:20,220
+بيزداد لغاية ما نوصل إلى ألف أسنونيبقى هنا بدنا
+
+231
+00:28:20,220 --> 00:28:24,280
+نمشي بنفس التكتيك تبع الشيء اللي اتعلمناه في
+
+232
+00:28:24,280 --> 00:28:29,800
+الثانوية حد فيكوا أخدت احتمالات؟ أخدنا احتمالات طب
+
+233
+00:28:29,800 --> 00:28:33,320
+في عندك .. في أخدتوها تلت حدين تبعهم في
+
+234
+00:28:33,320 --> 00:28:37,520
+الاحتمالات، مظبوط؟ يبقى تبع هذه معلومات طازة أجد
+
+235
+00:28:37,520 --> 00:28:42,780
+من مين من الثانوية العامة يبقى لو جينا بروح بنقول
+
+236
+00:28:42,780 --> 00:28:50,420
+هذه A أس N زائد Mلو الإشارة هذه زائد كله بيكون
+
+237
+00:28:50,420 --> 00:28:54,580
+زائد لكن مدام الإشارة هذه ناقص وصير حد موجب وحد
+
+238
+00:28:54,580 --> 00:29:03,700
+سالب يبقى بده يصير ناقص N زائد M one يعني توفيق N
+
+239
+00:29:03,700 --> 00:29:10,280
+زائد M من الأشياء مقودة واحد واحد اذا نجي لل A قص
+
+240
+00:29:10,280 --> 00:29:19,190
+N زائد M فنطح منها واحد في B قص واحداللي بعدها
+
+241
+00:29:19,190 --> 00:29:29,950
+بالموجة زائد N زائد M توفيق اتنين A أس N زائد M
+
+242
+00:29:29,950 --> 00:29:39,730
+نقص اتنين ب تربيع وانظر نمشي لغاية ما نصل الى الى
+
+243
+00:29:39,730 --> 00:29:48,990
+مين N زائد M M توفيق N زائد M لشام أخوها M Mبس
+
+244
+00:29:48,990 --> 00:29:54,050
+ضايل علينا مين ضايل علينا الإشارة يا رجال يبقى هذه
+
+245
+00:29:54,050 --> 00:30:04,170
+زادت و هنا ناقص واحد أس M تمام في A أس N تبقى ال M
+
+246
+00:30:04,170 --> 00:30:09,010
+مين خلصت ناقص اتنين ناقص تلاتة ناقص أربع خلصت
+
+247
+00:30:09,010 --> 00:30:14,950
+وصلنا إلى A أس N في هذه الحالة B زادت حتى وصلت إلى
+
+248
+00:30:14,950 --> 00:30:23,540
+مين إلى M تمامالان زائد زائد
+
+249
+00:30:23,540 --> 00:30:30,880
+مين؟ زائد ناقص واحد to the power M زائد واحد
+
+250
+00:30:30,880 --> 00:30:37,640
+الإشارة الأوس تبقى بزيد واحد يبقى هنا N زائد M و
+
+251
+00:30:37,640 --> 00:30:47,520
+هنا M زائد واحد في ال A أس N ناقص واحد B أس M زائد
+
+252
+00:30:47,520 --> 00:30:52,060
+واحدالـ A الأس تبعها بينقص واحد والـ M الأس تبعها
+
+253
+00:30:52,060 --> 00:30:59,980
+بيزيد واحد هنظل ناشين لغاية ما نصل إلى آخر حد آخر
+
+254
+00:30:59,980 --> 00:31:10,460
+حد بيكون ناقص واحد أس N زائد M في B أس N زائد M
+
+255
+00:31:10,460 --> 00:31:18,220
+وبتبقى صار A أس Zero اللي هو بواحد طيبكداش هدا
+
+256
+00:31:18,220 --> 00:31:23,060
+الكلام مساوي اقص
+
+257
+00:31:23,060 --> 00:31:31,660
+n في اقص m اقص n ب zero فهدا zero و هدا zero و هدا
+
+258
+00:31:31,660 --> 00:31:37,840
+zero و هدا zero need you to learn it better هذا مش
+
+259
+00:31:37,840 --> 00:31:43,160
+zero لكن هذا بيقص m في بيقص واحد بيقص m ب zero
+
+260
+00:31:43,160 --> 00:31:49,550
+يبقى هذا zeroهذا بيوسم في بيوسم بيوسم بزيرو يبقى
+
+261
+00:31:49,550 --> 00:31:57,910
+هذا كله بده يساوي زيرو زا ناقص زيرو زائد زيرو ناقص
+
+262
+00:31:57,910 --> 00:32:06,770
+مش عارف مين زائد ناقص واحد أس او ناقص واحد أس ام
+
+263
+00:32:06,770 --> 00:32:13,530
+زائد انف زيرو جد ما يكون يبقى النتج كله جد زيرو
+
+264
+00:32:13,530 --> 00:32:19,860
+مدام زيرويبقى بروح بقول ال sol E ناقص ال A ناقص B
+
+265
+00:32:19,860 --> 00:32:32,100
+ال A نل potent نل potent element مدام نل potent
+
+266
+00:32:32,100 --> 00:32:37,720
+element يعني معناته ان ال A ناقص ال B موجود وين في
+
+267
+00:32:37,720 --> 00:32:44,020
+S إذا احنا هنا أخدنا عنصرين موجودات في Sلجينا
+
+268
+00:32:44,020 --> 00:32:49,580
+الفرق فيما بينهما موجود في S بقيت علينا النقطة
+
+269
+00:32:49,580 --> 00:32:55,380
+الأخيرة ايش النقطة الأخيرة؟ بتقول افترض ان ال A و
+
+270
+00:32:55,380 --> 00:33:01,620
+ال B موجودات في S then ال A أُس M بده يساوي Zero
+
+271
+00:33:01,620 --> 00:33:07,680
+and ال B أُس M بده يساوي Zero بدي أثبت انه حاصل
+
+272
+00:33:07,680 --> 00:33:14,940
+دار بيهماموجود في S يساوي Zero لو رفعته لأس معين
+
+273
+00:33:14,940 --> 00:33:21,880
+خد الرقم اللي بديك أن حبيتي N ماشي حبيتي M ماشي
+
+274
+00:33:21,880 --> 00:33:28,540
+ولا داعي لمجموعهما أو حاصل ضربهما صح؟ يبقى لو جيت
+
+275
+00:33:28,540 --> 00:33:35,480
+قل مثلا أس M ايه واحدة ثانية أخدت أس N صح ميا ميا
+
+276
+00:33:35,920 --> 00:33:43,300
+يبقى هذا a أُس m في b أُس m هذا الكلام صحيح لأن ال
+
+277
+00:33:43,300 --> 00:33:47,160
+R is commutative لكن لو ماكنتش commutative هذا
+
+278
+00:33:47,160 --> 00:33:51,300
+كلام نهار غلط هو في المثلة قال ال R is commutative
+
+279
+00:33:51,300 --> 00:33:57,660
+هذا الكلام بده يسوى a أُس m في zero بده يسوى zero
+
+280
+00:33:57,660 --> 00:34:01,860
+هذا بده يعطينا أن a في b is
+
+281
+00:34:04,000 --> 00:34:10,260
+four ten L هذا
+
+282
+00:34:10,260 --> 00:34:17,920
+بيقول ان ال A في B موجود في S إذا انتقلت الشروط
+
+283
+00:34:17,920 --> 00:34:25,020
+التلاتة يبقى لنا علينا S is a suffering يبقى لص ال
+
+284
+00:34:25,020 --> 00:34:31,740
+S is a suffering of A
+
+285
+00:34:34,430 --> 00:34:39,870
+البتالي الثاني البتالي
+
+286
+00:34:39,870 --> 00:34:46,990
+الثاني له سؤال تمانتاشر سؤال ستاشر من الكتاب سؤال
+
+287
+00:34:46,990 --> 00:34:54,630
+ستاشر بقول prove that prove that the only
+
+288
+00:34:54,630 --> 00:35:02,090
+idempotence the only idempotence
+
+289
+00:35:04,090 --> 00:35:13,810
+the only are the importance in an integral domain
+
+290
+00:35:13,810 --> 00:35:22,970
+in integral domain are the zero and الواحد
+
+291
+00:35:33,450 --> 00:35:38,870
+يقولي اثبتلي انه في ال integral domain ماعنديش
+
+292
+00:35:38,870 --> 00:35:44,970
+idempotency اللي اتنين فقط لغير اللي هم من؟ ال
+
+293
+00:35:44,970 --> 00:35:51,030
+zero و ال واحد تمام؟ الان انا عندي integral domain
+
+294
+00:35:51,030 --> 00:35:57,230
+يبقى هو commutative ring with unit صح؟ يبقى ال ا
+
+295
+00:35:57,230 --> 00:36:09,470
+او assume لالـ R is an integral domain Assume الـ
+
+296
+00:36:09,470 --> 00:36:18,610
+R is an integral domain then الـ R has a unit
+
+297
+00:36:18,610 --> 00:36:28,230
+مثلاً 1 على سبيل المثال طيب
+
+298
+00:36:28,230 --> 00:36:38,390
+الآن لماذاالـ A دي الـ idemportant
+
+299
+00:36:38,390 --> 00:36:47,070
+in A صرت أن A عنصر موجود في A وهذا idemportant
+
+300
+00:36:47,070 --> 00:36:54,950
+يبقى then الـ A ترابيع تساوي الـ A حسب تعريف الـ
+
+301
+00:36:54,950 --> 00:37:00,430
+idemportant قبض لفريق رايكوا نعملها معادلة صفرية
+
+302
+00:37:00,800 --> 00:37:06,940
+إذا إيه تربية ناقص إيه بده يساوي زيه طيب من ال
+
+303
+00:37:06,940 --> 00:37:11,940
+distributive law إيه في إيه ناقص واحد يساوي زيه
+
+304
+00:37:11,940 --> 00:37:18,860
+العملية ده بقدر أعملها لو ال R فيهاش unity ده
+
+305
+00:37:18,860 --> 00:37:22,580
+بقدرش لكن هذا علشان ال integral domain و ال
+
+306
+00:37:22,580 --> 00:37:26,280
+commutative ring و ال unity يعني ال unity اللي
+
+307
+00:37:26,280 --> 00:37:30,730
+واحد موجود فيها إذا جدرتأستخدم الـ distributive
+
+308
+00:37:30,730 --> 00:37:38,710
+law طيب هذا بده يعطيني ان ال a تساوي 0 or ال a
+
+309
+00:37:38,710 --> 00:37:45,450
+ناقص واحد بده ساوي 0 هل هذا كلام صحيح في أي ring؟
+
+310
+00:37:45,450 --> 00:37:50,490
+لا مش صحيح لكن صحيح في من؟ ال integral و ال
+
+311
+00:37:50,490 --> 00:37:53,490
+integral domain و ال integral domain مافيش فيه
+
+312
+00:37:53,490 --> 00:38:02,600
+zero divisor يبقى هنا هذاbecause الارض
+
+313
+00:38:02,600 --> 00:38:11,320
+ليس لديها قطعين لا زرع يعني إيش؟ لو وجدت حاصل ضرب
+
+314
+00:38:11,320 --> 00:38:16,580
+كميتين بيكون بزيرو، بيكون الأولى بزيرو أو الثانية
+
+315
+00:38:16,580 --> 00:38:23,640
+بزيرو هذا بدّي يعطينا إن ال a تساوي zero أو ال a
+
+316
+00:38:23,640 --> 00:38:30,450
+تساوي واحد صحيحتمام؟ يبقى الـIdempotent Element
+
+317
+00:38:30,450 --> 00:38:34,150
+اللي عندنا طلع مين؟ طلع الـ Zero و الواحد، في
+
+318
+00:38:34,150 --> 00:38:40,950
+غيرهم؟ مش غيرهم، يبقى في حالة الـIntegral Domain،
+
+319
+00:38:40,950 --> 00:38:47,970
+the only idempotent element is Zero and the only,
+
+320
+00:38:48,350 --> 00:38:50,750
+غيرهم يبعد الله
+
+321
+00:38:56,210 --> 00:39:06,970
+طيب، هذا كان سؤال ستاشر مثال رقم تلاتة .. تلاتة
+
+322
+00:39:06,970 --> 00:39:16,270
+في سؤال فمانتاشر من الكتاب بيقول الـ F الـ R بـ A
+
+323
+00:39:16,270 --> 00:39:25,330
+ring F الـ A الموجود في R is add
+
+324
+00:39:29,700 --> 00:39:38,740
+idempotent idempotent then ال a n بده يساوي ال a
+
+325
+00:39:38,740 --> 00:39:49,740
+for all for all positive integers ان اللي موجودة
+
+326
+00:39:49,740 --> 00:39:50,820
+في z plus
+
+327
+00:40:10,550 --> 00:40:15,270
+أخد عنصر موجود فيها والعنصر كان هدا I important،
+
+328
+00:40:15,270 --> 00:40:20,870
+إيش يعني؟ A تربيع بده ساوي ال A، جال يبينلي إن ال
+
+329
+00:40:20,870 --> 00:40:27,310
+A N بده ساوي ال A لكل ال N اللي موجودة في Z plus،
+
+330
+00:40:27,310 --> 00:40:32,900
+يعنيو ال n is a positive .. او for all n و ال n is
+
+331
+00:40:32,900 --> 00:40:38,520
+a positive integer بقوله بسيطة الحلقة التالية احنا
+
+332
+00:40:38,520 --> 00:40:43,640
+عندنا معتقد ان ال a is important صح يبقى بالي
+
+333
+00:40:43,640 --> 00:40:52,860
+بقوله ال a ترافية بده يساوي ال a طيب بدنا نثبت ان
+
+334
+00:40:52,860 --> 00:40:59,720
+ال a to the power n تساوي ال aيبقى باجي بقوله want
+
+335
+00:40:59,720 --> 00:41:02,860
+فشاء
+
+336
+00:41:02,860 --> 00:41:12,320
+ان ال a n بده ساوي ال a لكل ال n اللي موجودة في
+
+337
+00:41:12,320 --> 00:41:17,020
+ذات ال plus بتحاول
+
+338
+00:41:17,020 --> 00:41:22,680
+أثبت هذا بواصفة السينتاج الرياضي ال induction عشان
+
+339
+00:41:22,680 --> 00:41:28,030
+تاخدوا ثلاث طرق أو ثلاث طرق للبراهينأحدهم نفس
+
+340
+00:41:28,030 --> 00:41:33,930
+التجارب الرياضية ال induction طيب السؤال هو قداش
+
+341
+00:41:33,930 --> 00:41:40,950
+أقل عدد صحيح موجة بيحقق هذه العلاقات؟ واحد اتنين
+
+342
+00:41:40,950 --> 00:41:46,870
+اتنين مش هانا it's important يبقى أقل واحد صحيح هو
+
+343
+00:41:46,870 --> 00:41:50,930
+اتنين سميلي هذه ال statement stop
+
+344
+00:41:53,580 --> 00:42:04,880
+تبقى باجي بقوله النقطة الأولى the statement is a
+
+345
+00:42:04,880 --> 00:42:17,200
+true at in يساوي اتنين السبب because ان ال a is an
+
+346
+00:42:17,200 --> 00:42:20,300
+idempotent
+
+347
+00:42:20,800 --> 00:42:27,300
+يعني ايش؟ يعني الـ A تربيه أو بدل هذه لو قلتلي
+
+348
+00:42:27,300 --> 00:42:30,820
+because الـ A تربيه سوى A plus الكلام اللي هو صحيح
+
+349
+00:42:30,820 --> 00:42:39,800
+طيب يبقى العبارة صحيحة عند أقل قيمة من ال N بتحقق
+
+350
+00:42:39,800 --> 00:42:46,860
+هذه المعادلة وهي 2 بدي أفترض أنها صحيحة عند رقم و
+
+351
+00:42:46,860 --> 00:42:55,860
+أثبت صحتها عند الرقم زي 1يبقى هنا assume that
+
+352
+00:42:55,860 --> 00:42:59,420
+equation
+
+353
+00:42:59,420 --> 00:43:14,800
+a star is a true at n تساوي m that is ان ال a أُس
+
+354
+00:43:14,800 --> 00:43:25,980
+m بدي ساوي aوروح بدي أخد consider A أُس M ذائد
+
+355
+00:43:25,980 --> 00:43:32,060
+واحد أشوف هل هذه العبارة صحيحة عندها ولا لا يبقى
+
+356
+00:43:32,060 --> 00:43:39,160
+هذا بقدر أقول A أُس M في ال AEOSM مابيبقى داشر
+
+357
+00:43:39,160 --> 00:43:44,820
+يبقى A يبقى بده يساوي A في A و A في A مابيبقى داشر
+
+358
+00:43:44,820 --> 00:43:50,840
+ايه تربية و ايه تربية ايه
+
+359
+00:43:50,840 --> 00:43:51,640
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+360
+00:43:51,640 --> 00:43:52,620
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+361
+00:43:52,620 --> 00:43:54,560
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+362
+00:43:54,560 --> 00:43:54,980
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+363
+00:43:54,980 --> 00:44:02,240
+ايه ايه ايه ايه ايه ايه
+
+364
+00:44:02,240 --> 00:44:05,340
+ايه
+
+365
+00:44:05,530 --> 00:44:13,490
+لكل الـ N اللي موجودة في الأعداد الصحيحة الموجب
+
+366
+00:44:13,490 --> 00:44:18,710
+يبقى المعلومة يا بنات استفدناها وسنستخدمها بعد ذلك
+
+367
+00:44:18,710 --> 00:44:23,330
+المعلومة أيش بتقول؟ بتقول إن لو كان عندي ID
+
+368
+00:44:23,330 --> 00:44:28,310
+important يبقى هذا ال element لو رفعته لأ الصحيح
+
+369
+00:44:28,310 --> 00:44:34,370
+موجبمن اتنين فصاعدا بدي يكون النتج يعطيني الـA
+
+370
+00:44:34,370 --> 00:44:42,990
+أتسن طيب أروح للسؤال الراجع السؤال الراجع اللي هو
+
+371
+00:44:42,990 --> 00:44:49,390
+سؤال تسعتاش من البيتار ايش بيقول بيقول determine
+
+372
+00:44:49,390 --> 00:44:55,830
+ordering elements determine ordering
+
+373
+00:44:55,830 --> 00:44:58,810
+elements
+
+374
+00:44:59,780 --> 00:45:05,780
+تحدد لك كل العناصر اللي في ال ring that are both
+
+375
+00:45:05,780 --> 00:45:14,160
+that are both و اللي بتكون that are both
+
+376
+00:45:14,160 --> 00:45:19,800
+Nilpotents Nilpotents
+
+377
+00:45:19,800 --> 00:45:24,140
+and Idipotents
+
+378
+00:45:33,160 --> 00:45:38,260
+مدمنين العناصر اللي بتكون في ال ring اللي بنفع
+
+379
+00:45:38,260 --> 00:45:45,280
+تكون Neil Potent و Idem Potent في نفس الوقت معقول
+
+380
+00:45:45,280 --> 00:45:51,200
+يا رناتي تكون العناصر Neil Potent و Idem Potent في
+
+381
+00:45:51,200 --> 00:45:56,990
+أهل واحد؟ ممكن تجيبولي ولا عنصر واحدالـ Zero Zero
+
+382
+00:45:56,990 --> 00:45:59,810
+to the power of N بـ Zero و Zero ترميع بـ Zero
+
+383
+00:45:59,810 --> 00:46:04,590
+تبقى يبقى Zero is an idempotent element يبقى يتعرف
+
+384
+00:46:04,590 --> 00:46:08,710
+عليها بيشوف فيه غيره و الله مافيش من خلال
+
+385
+00:46:08,710 --> 00:46:14,410
+المعلومات اللي عنده يبقى بيقول حددني كل عناصر ال
+
+386
+00:46:14,410 --> 00:46:18,770
+ring اللي بيكون nil potent و idempotent في نفس
+
+387
+00:46:18,770 --> 00:46:28,580
+الوقت يبقى الحل كالتالي solution لأA belongs في R
+
+388
+00:46:28,580 --> 00:46:40,320
+و R is a ring تمام such that بحيث ان null potent
+
+389
+00:46:40,320 --> 00:46:50,360
+يعني ال A أُس N بده يساوي Zero for some N
+
+390
+00:46:50,360 --> 00:47:02,290
+اللي موجود في Z plusand الـA ترابيع يساوي الـA I
+
+391
+00:47:02,290 --> 00:47:06,330
+important نيه ال important السؤال اللي بيجيبله إيش
+
+392
+00:47:06,330 --> 00:47:12,030
+بيقول بيقول لو كان ال element I important يبقى ال
+
+393
+00:47:12,030 --> 00:47:19,750
+A to the power M بيساوي ال A صح طيب هذا إيش معناه
+
+394
+00:47:19,750 --> 00:47:27,750
+I importantيبقى هذا معناه ان ال a to the power n
+
+395
+00:47:27,750 --> 00:47:35,410
+بتساوي ال a اللي هو example example
+
+396
+00:47:35,410 --> 00:47:42,790
+three اللي فوق above يبقى مثل ثلاثة اللي فوق
+
+397
+00:47:42,790 --> 00:47:50,660
+وعندنا هنا ال a أُس n بتساوي zeroطب من الاتنين
+
+398
+00:47:50,660 --> 00:47:55,460
+هذول مع بعض ايش بنستنتج بقى الطرف الشمال هو الطرف
+
+399
+00:47:55,460 --> 00:48:00,440
+الشمال إذا الطرف اليمين هو الطرف اليمين هذا بدي
+
+400
+00:48:00,440 --> 00:48:07,120
+أعطيك أنه A تساوي Zero يبقى Zero هو ال only null
+
+401
+00:48:07,120 --> 00:48:13,880
+potent and idempotent element يبقى هنا هذا بدي
+
+402
+00:48:13,880 --> 00:48:18,400
+يعطينا Zero as the only
+
+403
+00:48:33,590 --> 00:48:41,830
+سؤال شفته في الكتاب بيقوله تقدر تجيبولي ring و ال
+
+404
+00:48:41,830 --> 00:48:48,030
+ring هذه فيها element له unit و له zero divisor
+
+405
+00:48:51,120 --> 00:48:56,160
+هنجيب عنصر في ring العنصر هذا لا هو unit ولا هو
+
+406
+00:48:56,160 --> 00:49:05,220
+zero divisor 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
+
+407
+00:49:05,220 --> 00:49:06,400
+6 6 6 6 6 6 6 6 6 6 6
+
+408
+00:49:20,240 --> 00:49:23,820
+كم unit فيها؟ الواحد بيستغل الواحد مية المية اتنين
+
+409
+00:49:23,820 --> 00:49:28,680
+فيها units في الآخر طب فيها zero division؟ لأ لأ
+
+410
+00:49:28,680 --> 00:49:33,500
+يعني بدبر الاقي رقمين فيها حصل ضرهم يساوي zero لأ
+
+411
+00:49:33,500 --> 00:49:38,400
+يبقى ينسى الموضوع مفيش او مثال بسيط التلاتة موجود
+
+412
+00:49:38,400 --> 00:49:44,920
+في z والتلاتة له unit وله zero division صح؟ يبقى
+
+413
+00:49:44,920 --> 00:49:51,990
+hiringوفيها عناصر ليهم units وليهم zero divisors
+
+414
+00:49:51,990 --> 00:50:02,070
+طيب عندك هنا exercises خمسة من أسئلة التوريط بيقول
+
+415
+00:50:02,070 --> 00:50:17,510
+لي every element of ZN is a unit ofA0 Divider
+
+416
+00:50:17,510 --> 00:50:22,170
+Solution
+
+417
+00:50:22,170 --> 00:50:26,970
+كل
+
+418
+00:50:26,970 --> 00:50:32,110
+أنص في هذه ال ring أحد ال ring يا إما unit يا إما
+
+419
+00:50:32,110 --> 00:50:39,970
+every non-zero element every non-zero element of
+
+420
+00:50:39,970 --> 00:50:45,800
+ZIN is A unit or A0 Dividerيبقى بتقول خدلي K
+
+421
+00:50:45,800 --> 00:50:53,160
+موجودة في ZN such that و بحيث ال K above or equal
+
+422
+00:50:53,160 --> 00:50:58,940
+to Z بدي أثبت هذا ال K يا إما unit يا إما zero
+
+423
+00:50:58,940 --> 00:51:06,000
+divisor طب الآن في عندي حالتين احتمال انه ل
+
+424
+00:51:06,000 --> 00:51:12,800
+grasses common divisor لمن لل K و لل N يسوى واحد
+
+425
+00:51:13,730 --> 00:51:22,030
+ممكن زد ستة يبقى الستة و الخمسة مش الخمسة موجودة
+
+426
+00:51:22,030 --> 00:51:27,150
+في زد ستة اتنين are relatively prime صح يعني ال
+
+427
+00:51:27,150 --> 00:51:31,490
+classes common divisor قلهم جدير مثلا سيبقى من
+
+428
+00:51:31,490 --> 00:51:36,090
+الخمسة التلاتة موجودة في زد ستة ال classes common
+
+429
+00:51:36,090 --> 00:51:42,600
+divisor تلاتة مش الحل بطل يصير واحديبقى هنا f
+
+430
+00:51:42,600 --> 00:51:46,980
+لجريس ال common divisor اتنين اتنين f لجريس ال
+
+431
+00:51:46,980 --> 00:51:50,600
+common divisor اتنين اتنين f لجريس ال common
+
+432
+00:51:50,600 --> 00:51:53,460
+divisor اتنين اتنين f لجريس ال common divisor
+
+433
+00:51:53,460 --> 00:51:57,040
+اتنين اتنين f لجريس ال common divisor اتنين f
+
+434
+00:51:57,040 --> 00:51:57,040
+لجريس ال common divisor اتنين f لجريس ال common
+
+435
+00:51:57,040 --> 00:51:57,040
+divisor اتنين f لجريس ال common divisor اتنين f
+
+436
+00:51:57,040 --> 00:51:57,040
+لجريس ال common divisor اتنين f لجريس ال common
+
+437
+00:51:57,040 --> 00:51:57,040
+divisor اتنين f لجريس ال common divisor اتنين f
+
+438
+00:51:57,040 --> 00:51:57,040
+لجريس ال common divisor اتنين f لجريس ال common
+
+439
+00:51:57,040 --> 00:51:59,040
+divisor اتنين f لجريس ال common divisor اتنين f
+
+440
+00:51:59,040 --> 00:52:05,360
+لجريس ال common divisor اتنين f لجريس ال common
+
+441
+00:52:05,360 --> 00:52:06,540
+divis
+
+442
+00:52:11,210 --> 00:52:22,990
+S وT موجودة في Z such that بحيث ان K بS زائد M في
+
+443
+00:52:22,990 --> 00:52:31,850
+T يسوى واحد طب هذه كلها بنى كم مضاعفات M في Z N
+
+444
+00:52:31,850 --> 00:52:38,950
+كم؟ Zero كم؟ Zero خايفين ليش؟ Zero يبقى هذه كلها ب
+
+445
+00:52:38,950 --> 00:52:45,330
+Zeroيبقى بيطلع هنا مين؟ K في S يساوي ال one حاصل
+
+446
+00:52:45,330 --> 00:52:50,050
+ضربته elements يساوي ال unity يبقى كل واحد فيهم is
+
+447
+00:52:50,050 --> 00:52:57,650
+a unit يبقى هذا يبدو يعطينا ان ال A is a unit
+
+448
+00:52:57,650 --> 00:53:06,710
+تمام؟ يبقى العنصر اللي جيبناه في ZN وافترضنا ان K
+
+449
+00:53:06,710 --> 00:53:13,190
+طلع unitقد يكون zero divisor يبقى بده اروح اخد
+
+450
+00:53:13,190 --> 00:53:20,630
+الحالة التانية F لجريس ال common divisor لل N او
+
+451
+00:53:20,630 --> 00:53:31,230
+لل K و ال N بده يساوي D مثلا و ال D هذه اكبر من
+
+452
+00:53:31,230 --> 00:53:38,330
+الواحد رقم اكبر من من الواحدطيب بده اشوف معنى هذا
+
+453
+00:53:38,330 --> 00:53:45,570
+الكلام ان ال A مضاعفة ال D صح ولا لأ يبقى هذا
+
+454
+00:53:45,570 --> 00:53:52,070
+الكلام بده يعطينا ال there exists M موجود في Z
+
+455
+00:53:52,070 --> 00:54:03,840
+plus such that بحيث ان ال A بده يساوي M في Dطبعا
+
+456
+00:54:03,840 --> 00:54:08,620
+يبقى الكهة ده اللي class is called divisor لديه مع
+
+457
+00:54:08,620 --> 00:54:15,760
+ان يساوي D بدل غضب ورقم مضروب في دي بدي احاول اثبت
+
+458
+00:54:15,760 --> 00:54:22,820
+ان الكهة ده هو zero divisor لذلك بقول لو جربت اضرب
+
+459
+00:54:22,820 --> 00:54:33,960
+K في N على D سؤال هوهل N على D يساوي Zero؟ لأ لأ
+
+460
+00:54:33,960 --> 00:54:39,300
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+461
+00:54:39,300 --> 00:54:39,640
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+462
+00:54:39,640 --> 00:54:39,640
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+463
+00:54:39,640 --> 00:54:39,760
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+464
+00:54:39,760 --> 00:54:39,800
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+465
+00:54:39,800 --> 00:54:40,740
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+466
+00:54:40,740 --> 00:54:54,960
+لأ
+
+467
+00:54:54,960 --> 00:55:01,060
+لأ ليبقى مضاعفات ال N بقداش ب Zero يبقى هذا الناتج
+
+468
+00:55:01,060 --> 00:55:08,240
+يساوي Zero يبقى صار ال K is a Zero divisor لإن ال
+
+469
+00:55:08,240 --> 00:55:14,500
+K لا يساوي Zero وال N على D لا يساوي Zero هذا
+
+470
+00:55:14,500 --> 00:55:23,590
+معناه إن ال K is a Zero divisorيبقى كل عنصر في Z
+
+471
+00:55:23,590 --> 00:55:28,630
+in يا إما unit يا إما zero divisor لكن هذا الكلام
+
+472
+00:55:28,630 --> 00:55:34,450
+على أي ring؟ لأ مش على Z in لأن طبعا سألتوا سؤال
+
+473
+00:55:34,450 --> 00:55:39,610
+أخدنا Z لاجئنا فيها فيش إلا toilets ومافيش فيها
+
+474
+00:55:39,610 --> 00:55:44,350
+zero divisor يالا في الوقت اتمرنوا في الأسئلة
+
+475
+00:55:44,350 --> 00:55:52,690
+التالية يبقى exercises على شطر 13ساعة خمسة هيو
+
+476
+00:55:52,690 --> 00:56:00,930
+حلناها خمسة و تمانية و عشر و عشرين و واحد و عشرين
+
+477
+00:56:00,930 --> 00:56:11,050
+و اربعة و عشرين و واحد و ثلاثين و اتنين و تلاتين و
+
+478
+00:56:11,050 --> 00:56:19,490
+اربعين و اتنين و اربعين و ستة و اربعين و اتنين و
+
+479
+00:56:19,490 --> 00:56:20,550
+خمسين
+
+480
+00:56:25,020 --> 00:56:35,580
+نين و خمسين و تلاتة و خمسين و ستة و خمسين و تمانية
+
+481
+00:56:35,580 --> 00:56:36,840
+و خمسين
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..140bb524558059bffc202b5a167b1985c3641d44
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4.srt
@@ -0,0 +1,1374 @@
+1
+00:00:20,920 --> 00:00:26,160
+بسم الله الرحمن الرحيم، نكمل ما ابتدأنا في المحاضرة
+
+2
+00:00:26,160 --> 00:00:34,400
+الماضية، ولا زلنا مع الـ Factor Rings، مثاله رقم خمسة
+
+3
+00:00:34,400 --> 00:00:40,220
+بيقول يستخدم الـ R[X] تمثل Ring of polynomials
+
+4
+00:00:40,220 --> 00:00:46,480
+كثيرات الحدود with real coefficients، يبقى المعاملات
+
+5
+00:00:46,480 --> 00:00:53,700
+أعداد حقيقية.  نأخذ الـ
+
+6
+00:00:53,700 --> 00:00:57,080
+Principle Ideal Generated by X تربيع زائد واحد
+
+7
+00:00:57,080 --> 00:01:01,160
+الذي هو كل العناصر F(X) التي مضروبة في X تربيع
+
+8
+00:01:01,160 --> 00:01:05,960
+زائد واحد، في هذه الـ F(X) الموجودة في R[X]، أذكرك
+
+9
+00:01:05,960 --> 00:01:10,800
+بأننا نقول الـ Principle Ideal Generated by A هو
+
+10
+00:01:10,800 --> 00:01:17,450
+كل العناصر على الشكل R × A، بحيث أن الـ R موجودة في R
+
+11
+00:01:17,450 --> 00:01:21,470
+يبقى نفس التعريف، الـ R التي موجودة في R هي
+
+12
+00:01:21,470 --> 00:01:26,130
+function، والـ A الذي موجود في الـ principle الذي هو
+
+13
+00:01:26,130 --> 00:01:30,110
+X تربيع زائد واحد. يبقى هذا التعريف السابق الذي
+
+14
+00:01:30,110 --> 00:01:34,470
+أخذناه لمين؟ للـ principle ideal generated by A هو
+
+15
+00:01:34,470 --> 00:01:39,730
+الـ principle ideal generated by X تربيع زائد واحد
+
+16
+00:01:40,320 --> 00:01:44,140
+يبقى في هذه الحالة نكوّن الـ Factoring الـ
+
+17
+00:01:44,140 --> 00:01:50,520
+Factoring لـ R[X] modulo X تربيع زائد واحد، من
+
+18
+00:01:50,520 --> 00:01:55,120
+عناصرها عنصر من G + الـ principle ideal
+
+19
+00:01:55,120 --> 00:02:01,100
+generated by X تربيع زائد واحد، عنصر من R[X] هو G
+
+20
+00:02:01,100 --> 00:02:07,910
+[X] + الـ ideal الذي عندنا.  أنا أزعم أن هذا
+
+21
+00:02:07,910 --> 00:02:13,170
+يكون على الشكل ax + b، يعني معادلة من الدرجة
+
+22
+00:02:13,170 --> 00:02:17,410
+الأولى + x تربيع + واحد، وبعدها الـ a والـ
+
+23
+00:02:17,410 --> 00:02:24,750
+b أعداد حقيقية. طيب، تعالوا نتفهم الآن الـ g(x)
+
+24
+00:02:24,750 --> 00:02:32,190
+موجودة أين؟ في R[x]. هي Polynomial من الدرجة
+
+25
+00:02:32,190 --> 00:02:35,810
+الأولى، و الله ممكن الأولى والثانية والثالثة و
+
+26
+00:02:35,810 --> 00:02:41,490
+العاشرة، والنونية وما إلى ذلك. أيوة، يبقى هنا عندي
+
+27
+00:02:41,490 --> 00:02:45,170
+من أي درجة؟ إن شاء الله يكون من الدرجة الخامسة.
+
+28
+00:02:45,170 --> 00:02:51,330
+تمام، لكن أنا أزعم أني أقدر أكتبها على الشكل معادلة
+
+29
+00:02:51,330 --> 00:02:55,510
+من الدرجة الأولى، زي الـ principle ideal generated
+
+30
+00:02:55,510 --> 00:03:02,860
+by X تربيع + الواحد. بقول هذه الصيغة صحيحة، this is
+
+31
+00:03:02,860 --> 00:03:07,760
+true because لو كانت الـ G(X) موجودة في الـ R[X]
+
+32
+00:03:07,760 --> 00:03:15,800
+then، شوف يا سيدي، هذه الكتابة بتاعة الـ G(X) أقدر أكتبها
+
+33
+00:03:15,800 --> 00:03:24,460
+على شكل دالة في X، Q(X) مضروبة في X تربيع زائد
+
+34
+00:03:24,460 --> 00:03:34,860
+واحد + R(X)، والـ R(X) يا إما بتساوي صفر، يا
+
+35
+00:03:34,860 --> 00:03:44,860
+إما الـ degree للـ R(X) أقل من إثنين.  إيش اللغز هذا؟
+
+36
+00:03:44,860 --> 00:03:49,800
+بدنا نفهم، من أين جاء هذا الكلام؟  نجحنا فرضا
+
+37
+00:03:49,800 --> 00:03:55,140
+أنها AX + B؟  انظروا إليها قليلا. الآن، أنا أخذت g(x)
+
+38
+00:03:55,140 --> 00:04:00,680
+موجودة في الـ polynomial الأصلية R[x]، يبقى هذه
+
+39
+00:04:00,680 --> 00:04:04,460
+الدرجة، يمكن الثالثة، يمكن الرابعة، الخامسة، جد ما
+
+40
+00:04:04,460 --> 00:04:11,720
+يكون.  أنا أزعم أني أقدر أحطها على شكل معادلة من الدرجة
+
+41
+00:04:11,720 --> 00:04:18,270
+الأولى. نفترض أنه كانت من الدرجة العاشرة، g(x)، يبقى
+
+42
+00:04:18,270 --> 00:04:24,550
+لماذا أضطرُّ إلى أن أجري عملية قسمة مطولة على من؟ على X
+
+43
+00:04:24,550 --> 00:04:29,650
+تربيع زائد واحد. يبقى الـ g(x) التي من الدرجة
+
+44
+00:04:29,650 --> 00:04:34,530
+العاشرة، بدي أجسمها على الـ polynomial X تربيع زائد
+
+45
+00:04:34,530 --> 00:04:40,950
+واحد الذي من الدرجة الثانية.  أُكمل القسمة لغاية الدرجة
+
+46
+00:04:40,950 --> 00:04:46,320
+الناتجة أقل من الدرجة الثانية، يعني أقل من درجة X
+
+47
+00:04:46,320 --> 00:04:51,900
+تربيع + واحد، مضبوط؟ يبقى يطلع عندنا خارج القسمة
+
+48
+00:04:51,900 --> 00:04:57,400
+ويبقى عندنا الباقي. هذا الباقي قد يكون صفر، زي ما
+
+49
+00:04:57,400 --> 00:05:02,200
+نجد مثلا، أي عدد على عدد، إذا قلت ثمانية على
+
+50
+00:05:02,200 --> 00:05:08,160
+اثنين يبقى أربعة، عدد صحيح، ما بضل عندي باقي، تمام؟ لكن
+
+51
+00:05:08,160 --> 00:05:16,270
+لو قلنا قسمة تسعة على اثنين، يبقى أربعة، ولسة بزيد
+
+52
+00:05:16,270 --> 00:05:21,390
+واحد، بدنا نقسمه على اثنين، مضبوط ولا لا؟ يبقى هذا
+
+53
+00:05:21,390 --> 00:05:27,150
+الذي هو الباقي، الذي يُسمى R(X). يبقى الـ Q(
+
+54
+00:05:27,150 --> 00:05:33,270
+X) يُعتبر عددا صحيحا، يعني بلغتنا في سياق الـ
+
+55
+00:05:33,270 --> 00:05:38,950
+polynomial، مضروبة في المقسوم عليه، X تربيع زائد
+
+56
+00:05:38,950 --> 00:05:43,870
+واحد، زائد الـ remainder، الباقي الذي عندنا هو R(
+
+57
+00:05:43,870 --> 00:05:49,510
+X). إذن الـ G(X) حطيتها على الشكل الذي عندنا هذا
+
+58
+00:05:49,510 --> 00:05:56,310
+والـ R(X) قد تكون صفر، تكون صفر إذا قسمة G(X)
+
+59
+00:05:56,310 --> 00:06:01,330
+على X تربيع زائد واحد بدون باقي. لو قسمة بدون باقي
+
+60
+00:06:01,330 --> 00:06:07,370
+يبقى R(X) بكم؟ بصفر. طيب، إذا قسمة وبقي عندنا
+
+61
+00:06:07,370 --> 00:06:13,430
+الباقي، نسميه R(X). R(X) درجته أقل من اثنين،
+
+62
+00:06:13,430 --> 00:06:19,350
+يعني أقل من درجة X تربيع زائد واحد، لأننا نقول إذا
+
+63
+00:06:19,350 --> 00:06:23,890
+درجة البسط أكبر من درجة المقام، أو درجة البسط جت
+
+64
+00:06:23,890 --> 00:06:29,530
+درجة المقام، نجري عملية قسمة مطولة لها، حتى تصير درجة البسط
+
+65
+00:06:29,530 --> 00:06:34,370
+أقل من درجة المقام، مضبوط؟ مش هكذا في القسمة المطولة
+
+66
+00:06:34,370 --> 00:06:41,030
+العادية؟ تماما هنا، تماما. قسمة الـ G(X) على الـ X
+
+67
+00:06:41,030 --> 00:06:47,890
+تربيع + 1، طلع النتيجة Q(X)، وخرج دالة اسمها R(
+
+68
+00:06:47,890 --> 00:06:53,050
+X). إذا الـ G(X) = Q(X) × X تربيع + 1 + R(
+
+69
+00:06:53,050 --> 00:06:59,130
+X). R(X) لم يبق شيء، يبقى R(X) = 0.  بقت دالة
+
+70
+00:06:59,130 --> 00:07:06,270
+نقول عليها R(X) التي درجتها أقل من درجة المقسوم عليه،
+
+71
+00:07:06,270 --> 00:07:12,990
+أقل من اثنين، يعني كده؟ واحد. مضبوط ولا لأ؟ يعني إيش
+
+72
+00:07:12,990 --> 00:07:20,570
+يصير؟ يصير ax + b، معادلة من الدرجة الأولى،
+
+73
+00:07:20,570 --> 00:07:27,010
+وإذا طلعت f0، يبقى constant b. يبقى in general نقول
+
+74
+00:07:27,010 --> 00:07:32,210
+ax + b، قدر ما تطلع a تطلع، وقدر ما تطلع b تطلع،
+
+75
+00:07:32,210 --> 00:07:37,350
+معناه ما فيش مشكلة. يبقى بناء عليه، من الممكن أن نقول يا
+
+76
+00:07:37,350 --> 00:07:46,090
+بناتي، g(x) + principle ideal generated by x
+
+77
+00:07:46,090 --> 00:07:52,810
+تربيع + واحد، مش بده يساوي؟ بده يساوي هي الـ q(
+
+78
+00:07:52,810 --> 00:08:01,860
+x) × U(X) × X تربيع + واحد + R(X) +
+
+79
+00:08:01,860 --> 00:08:05,720
+reference principle ideal generated by X تربيع
+
+80
+00:08:05,720 --> 00:08:11,540
+زائد واحد. السؤال هو، إيش رأيكم في هذه مع reference
+
+81
+00:08:11,540 --> 00:08:16,960
+principle ideal؟ إيش هذه موجودة هنا؟ إذا حسب الكلام
+
+82
+00:08:16,960 --> 00:08:23,240
+الذي نحن نقوله، هذه R(X) + الـ Principal Ideal
+
+83
+00:08:23,240 --> 00:08:29,060
+Generated By X تربيع زائد واحد. تبقى R(x) أقل من
+
+84
+00:08:29,060 --> 00:08:35,180
+الدرجة الثانية بمقدار واحد أو بمقدار اثنين. يبقى
+
+85
+00:08:35,180 --> 00:08:43,180
+نأخذ الأكبر، وهذه تساوي AX + B + الـ Principal
+
+86
+00:08:43,180 --> 00:08:48,810
+Ideal Generated By X تربيع زائد واحد. يبقى كلامنا
+
+87
+00:08:48,810 --> 00:08:55,510
+الذي قلناه صحيح، ولا لا؟ يبقى أي Polynomial في G، أو
+
+88
+00:08:55,510 --> 00:09:00,750
+أي Polynomial في الـ R[X] الأصلية، أقدر أكتبها على
+
+89
+00:09:00,750 --> 00:09:04,970
+شكل Polynomial من الدرجة الأولى + الـ principle
+
+90
+00:09:04,970 --> 00:09:10,450
+ideal generated by X تربيع + واحد.  ها أوريكم كيف
+
+91
+00:09:10,450 --> 00:09:15,470
+حصلنا عليها. طيب، السؤال الأول. طيب، نحن لو عندنا two
+
+92
+00:09:15,470 --> 00:09:19,700
+elements، كيف نضربهم؟ لأنها ستطلع معادلة من الدرجة
+
+93
+00:09:19,700 --> 00:09:23,060
+الثانية، صحيح ولا لأ؟  يقول معادلة من الدرجة الأولى،
+
+94
+00:09:23,060 --> 00:09:26,400
+وهما من الدرجة الأولى.  ضربناهم، تطلع معادلة من الدرجة
+
+95
+00:09:26,400 --> 00:09:30,580
+الثانية. كيف؟  في هذه الحلقة، نقول لكم القصة بسيطة
+
+96
+00:09:30,580 --> 00:09:37,580
+جدا، كيف؟ بسيطة جدا، تعالوا شوفوا  باختصار الآن، note that
+
+97
+00:09:37,580 --> 00:09:41,140
+لاحظوا
+
+98
+00:09:41,140 --> 00:09:50,120
+باختصار الآن، يا بنات، لو جئت قلت X تربيع + واحد ∈
+
+99
+00:09:50,120 --> 00:09:55,600
+الـ principle ideal generated by X تربيع + واحد،
+
+100
+00:09:55,600 --> 00:10:02,740
+هذا يعطيني الـ principle ideal generated by X
+
+101
+00:10:02,740 --> 00:10:08,080
+تربيع + واحد، لأن هذا عنصر موجود فيه، صحيح ولا لأ؟
+
+102
+00:10:08,080 --> 00:10:14,550
+طيب، ينفع أقول هذا؟ ينفع صفر ∈ الـ principle ideal
+
+103
+00:10:14,550 --> 00:10:20,310
+generated by one، صحيح ولا لا؟ إذا، بناء عليه،
+
+104
+00:10:20,310 --> 00:10:29,410
+يصير عندي X تربيع + واحد = صفر، طبعا؟ طيب،
+
+105
+00:10:29,410 --> 00:10:35,670
+معناه هذا الكلام أن X تربيع = كم؟ =
+
+106
+00:10:35,670 --> 00:10:45,970
+سالب واحد، طبعا؟ إذا، داخل هذه الـ ring، ستجدون
+
+107
+00:10:45,970 --> 00:10:50,930
+مفاجأة. أيوة،  لاحظوا، هم لا يعملون على الـ real line،
+
+108
+00:10:50,930 --> 00:10:57,110
+هم يعملون داخل من؟ داخل الـ ring R[X]. وإلا، لو كان
+
+109
+00:10:57,110 --> 00:11:01,490
+على الـ real line، هذه المعادلة عندي مالهاش حل، صحيح ولا
+
+110
+00:11:01,490 --> 00:11:07,630
+لا؟ لأن لا يمكن لمجموع مربعين كميتين موجبتين أن يكون صفر، فالكلام غير ممكن إلا إذا
+
+111
+00:11:07,630 --> 00:11:13,360
+كانت كل واحدة منهما صفر، لكن إحنا عندنا X تربيع =
+
+112
+00:11:13,360 --> 00:11:18,580
+سالب واحد، على الـ polynomials هؤلاء، وليس على الـ
+
+113
+00:11:18,580 --> 00:11:24,640
+...يعني داخل الـ ring التي عندنا. طيب، أُريكُم كيف
+
+114
+00:11:24,640 --> 00:11:29,340
+الحسابات تصير داخل هذه الـ ring، لو بدي أضرب
+
+115
+00:11:29,340 --> 00:11:34,720
+مثلا، بدي أضرب عنصرين.  ستحصلون على معادلة خطية، يلا، صُمِّموا
+
+116
+00:11:34,720 --> 00:11:41,240
+يعني، يعني زي X من الدرجة الأولى، معادلة عادية، حط
+
+117
+00:11:41,240 --> 00:11:46,080
+الرقم العادي، 3X + 2، 2، ممتاز،
+
+118
+00:11:46,080 --> 00:11:52,000
+جدا. يبقى أنا عندي 3X + 2 + الـ
+
+119
+00:11:52,000 --> 00:11:58,160
+principle ideal generated by one، بدي أضربه، فاهمين؟
+
+120
+00:12:04,910 --> 00:12:13,250
+هاتي Polynomial ثانية غير هذه، 5X
+
+121
+00:12:13,250 --> 00:12:19,830
+- 3، يبقى عندي 5X - 3 + الـ principal ideal
+
+122
+00:12:19,830 --> 00:12:26,390
+generated by one.  هذه polynomials، لما أضربها، ستساوي
+
+123
+00:12:26,390 --> 00:12:36,600
+3X + 2 × 5X - 3، وهنا زائد الـ principal ideal
+
+124
+00:12:36,600 --> 00:12:41,640
+generated by X تربيع - 1. يبقى هذه بدي
+
+125
+00:12:41,640 --> 00:12:47,560
+أضرب الآن. بدي أفك حاصل الضرب: ثلاثة في خمسة بخمسة
+
+126
+00:12:47,560 --> 00:12:55,180
+عشرة X تربيع، تمام؟  وثلاثة X في ناقص ثلاثة، بناقص
+
+127
+00:12:55,180 --> 00:13:04,520
+تسعة X، ناقص تسعة X + عشرة X، زائد عشرة X،
+
+128
+00:13:04,520 --> 00:13:10,780
+وناقص التوزيع لـ Principal Ideal Generated by X
+
+129
+00:13:10,780 --> 00:13:15,620
+تربيع + واحد. الآن يا بنات، الـ X تربيع هنا بكم؟
+
+130
+00:13:15,620 --> 00:13:20,880
+سالب واحد، إذا هشيل X تربيع وحط مكانها سالب
+
+131
+00:13:20,880 --> 00:13:26,840
+واحد. هذا الكلام بده يصير 15 × -1.
+
+132
+00:13:27,200 --> 00:13:34,980
+عندك ناقص تسعة X زائد عشرة X، بضل زائد X، وهنا ناقص
+
+133
+00:13:34,980 --> 00:13:40,140
+ستة، زائد الـ principle ideal generated by X تربيع
+
+134
+00:13:40,140 --> 00:13:47,180
++ واحد. طبعا هنا ناقص خمسة عشر، عشان ناقص ستة ناقص
+
+135
+00:13:47,180 --> 00:13:54,150
+واحدة وعشرين. إذا صارت عندي X ناقص واحد وعشرين، زائد
+
+136
+00:13:54,150 --> 00:13:59,110
+الـ principle ideal generated by one. X تربيع زائد
+
+137
+00:13:59,110 --> 00:14:04,690
+by one، تمام؟ يبقى هذه عملية الضرب. أنا من ضربت
+
+138
+00:14:04,690 --> 00:14:08,810
+عنصرين، هيطلع عندي X تربيع، وين طلعت X تربيع؟
+
+139
+00:14:08,810 --> 00:14:15,190
+بشيلها، بحط بدلها سالب واحد، وبالتالي، بتعود الباقي
+
+140
+00:14:15,190 --> 00:14:19,090
+العنصر إلى معادلة من الدرجة الأولى + الـ
+
+141
+00:14:19,090 --> 00:14:24,610
+principle ideal generated by X تربيع زائد واحد،
+
+142
+00:14:24,610 --> 00:14:30,630
+تمام؟ إذا هذه عملية الضرب داخل من؟ داخل الـ ring
+
+143
+00:14:30,630 --> 00:14:37,090
+الذي عملناه. ننتقل الآن إلى تعريف جديد. يبقى
+
+144
+00:14:37,090 --> 00:14:43,030
+definition.  إحنا من أول الـ section هنا وإحنا عرفنا
+
+145
+00:14:43,030 --> 00:14:49,230
+الـ ideal، وأخذنا منه الـ Trivial Ideal الذي هو الـ
+
+146
+00:14:49,230 --> 00:14:54,450
+Zero، الذي لا يحتوي على الـ Zero، وسميناه الـ Ideal
+
+147
+00:14:54,450 --> 00:14:59,990
+البديهي أو الـ Ideal التافه، لأن أي واحد بيجيبه فيه
+
+148
+00:14:59,990 --> 00:15:05,250
+مشكلة. لكن بدنا نيجي لحالات خاصة من الـ Ideals، حاجة
+
+149
+00:15:05,250 --> 00:15:12,320
+نسميها Prime Ideal و Maximal Ideal. نعطي تعريف لكل
+
+150
+00:15:12,320 --> 00:15:18,260
+منهما، ثم نذهب إلى أمثلة على ذلك. الـ Definition
+
+151
+00:15:18,260 --> 00:15:31,140
+الأول: A prime ideal A of a commutative ring R
+
+152
+00:15:40,480 --> 00:15:51,120
+is a proper ideal. is a proper ideal. is a proper
+
+153
+00:15:51,120 --> 00:16:05,440
+ideal of R such that بحيث أن such that if
+
+154
+00:16:05,440 --> 00:16:18,860
+a × b ∈ A and a ∈ A, then
+
+155
+00:16:18,860 --> 00:16:29,720
+a ∈ A  و b ∈ A.  التعريف الثاني:
+
+156
+00:16:29,720 --> 00:16:43,380
+Maximal ideal. هي Maximal ideal.  A of
+
+157
+00:16:43,380 --> 00:16:50,140
+a commutative ring
+
+158
+00:16:50,140 --> 00:17:04,400
+R is a proper ideal of R. is a proper ideal of R.
+
+159
+00:17:04,400 --> 00:17:14,290
+such that بحيث أن whenever
+
+160
+00:17:14,290 --> 00:17:18,550
+whenever
+
+161
+00:17:18,550 --> 00:17:35,990
+B is an ideal of A and A ⊂ B ⊂ R then B = A
+
+162
+00:17:36,610 --> 00:17:46,930
+or B = R.  then B = A or B = R.
+
+163
+00:17:46,930 --> 00:17:54,750
+B = A or B = R.
+
+164
+00:17:54,750 --> 00:18:02,490
+B = R. example one.
+
+165
+00:18:02,490 --> 00:18:12,660
+لو السؤال تسعة من الكتاب.  هو ليالٍ الآن أكبر من
+
+166
+00:18:12,660 --> 00:18:18,000
+الواحد، integer،
+
+167
+00:18:18,000 --> 00:18:29,160
+عدد صحيح، integer، then in
+
+168
+00:18:29,160 --> 00:18:34,300
+the ring Z,
+
+169
+00:18:35,170 --> 00:18:45,230
+I think that the ... the ideal nZ
+
+170
+00:18:45,230 --> 00:18:52,270
+is prime is
+
+171
+00:18:52,270 -->
+
+223
+00:24:19,290 --> 00:24:28,550
+موجود وين؟ موجود في الـ NZ يبقى بدأت أقول له let الـ
+
+224
+00:24:28,550 --> 00:24:38,090
+A و الـ B موجودة في Z such that بحيث أن الـ A في الـ
+
+225
+00:24:38,090 --> 00:24:41,430
+B موجودة في الـ NZ
+
+226
+00:24:44,850 --> 00:24:50,350
+أخذت عنصرين من الـ ring الأصلية A و B و افترضت أن
+
+227
+00:24:50,350 --> 00:24:55,590
+حاصل ضربهما موجود في الـ ID اللي عندي الـ ID الم
+
+228
+00:24:55,590 --> 00:25:03,490
+اللي عندي مين؟ NZ طبعا فجأة صار حاصل ضربهما موجود
+
+229
+00:25:03,490 --> 00:25:10,130
+في الـ NZ ممتاز جدا، طب مدام حاصل ضربهما موجود في الـ
+
+230
+00:25:10,130 --> 00:25:19,680
+NZ، إذا شكل حاصل الضرب A في B بيساوي الـ N في X for
+
+231
+00:25:19,680 --> 00:25:27,940
+some X اللي موجودة في Z صحيح ولا مناقش؟ حاصل الضرب
+
+232
+00:25:27,940 --> 00:25:34,180
+موجود هنا، شكل العنصر هنا هو N في أي element أو في
+
+233
+00:25:34,180 --> 00:25:40,760
+some element من Z، يبقى الـ A بيساوي الـ N X
+
+234
+00:25:41,230 --> 00:25:46,810
+طلع لي هذه المعادلة الـ X و الـ N و الـ B و الـ A
+
+235
+00:25:46,810 --> 00:25:53,090
+كلهم integers أعداد صحيحة، نرجع بالذاكرة إلى الوراق
+
+236
+00:25:53,090 --> 00:25:58,950
+أليس معنى هذه المعادلة أن الـ N بتقسم الـ A  بـ B؟
+
+237
+00:25:58,950 --> 00:26:06,250
+تمام تمام، يبقى هذا معناه أن الـ N divides الـ A في
+
+238
+00:26:06,250 --> 00:26:14,060
+B، هذا معناه أن الـ N بيقسم الـ A أو الـ N بيقسم الـ B
+
+239
+00:26:14,060 --> 00:26:23,060
+يا إما الـ N بتقسم الـ A يا إما الـ N بتقسم الـ B، مدام
+
+240
+00:26:23,060 --> 00:26:34,100
+بتقسم الـ A يبقى الـ A بدها تساوي N M for some M
+
+241
+00:26:34,100 --> 00:26:44,170
+اللي موجودة في Z، مظبوط يا جبابرة، or الـ B تساوي N
+
+242
+00:26:44,170 --> 00:26:52,650
+كفار صمك اللي موجودة في Z، صحيح؟
+
+243
+00:26:52,650 --> 00:27:01,710
+طيب مدام هيك الـ A يساوي N في M، الـ M هي الـ element
+
+244
+00:27:01,710 --> 00:27:07,040
+الثابت، الـ M موجودة في Z، معناه هذا الكلام أن
+
+245
+00:27:07,040 --> 00:27:14,460
+الـ A موجود وين؟ في الـ NZ، يبقى معناه هذا الكلام أن
+
+246
+00:27:14,460 --> 00:27:27,820
+الـ A موجودة في الـ NZ أو الـ B موجودة في الـ NZ، ليش
+
+247
+00:27:27,820 --> 00:27:34,320
+أن الـ K في Z و M في Z؟ أظن أن هو المطلوب؟ إذا وصلنا
+
+248
+00:27:34,320 --> 00:27:40,880
+و أحنا مش دارين، يبقى هذا معناه إيش؟ معناته إن NZ
+
+249
+00:27:40,880 --> 00:27:48,740
+is a prime ideal طبقا للـ definition اللي عندنا، هذا
+
+250
+00:27:48,740 --> 00:27:53,360
+الاتجاه الأول، بنمشي للاتجاه الثاني، يبقى بضروح
+
+251
+00:27:53,360 --> 00:28:06,570
+أقوله conversely، assume that إن الـ Nz is a prime
+
+252
+00:28:06,570 --> 00:28:16,490
+ideal،  هش اللي بدنا ياه، want to show، بدنا نروح نبين
+
+253
+00:28:16,490 --> 00:28:24,770
+أن الـ N is a prime، because we noticed أن هذا عدد
+
+254
+00:28:24,770 --> 00:28:30,090
+صحيح أولي، طيب، هروح أقول suppose not
+
+255
+00:28:33,640 --> 00:28:40,460
+يعني إيش؟ يعني ما هو عدد أولي، ده ما هو عدد
+
+256
+00:28:40,460 --> 00:28:46,440
+أولي، إذا بقدر أحلله إلى حاصل ضرب عددين، صحيح ولا
+
+257
+00:28:46,440 --> 00:28:53,840
+لا؟ يبقى suppose not، then الـ N هذا بيساوي حاصل
+
+258
+00:28:53,840 --> 00:29:00,370
+ضرب S في T، كونه عدد ما هو عدد أولي، بقدر أقول بحاصل
+
+259
+00:29:00,370 --> 00:29:07,450
+ضرب S في T، وفي المقابل S و T أصغر من N، وأكبر من
+
+260
+00:29:07,450 --> 00:29:15,010
+الواحد الصحيح، مظبوط؟ إيه، الآن أنا أدعي أنه ليس عددًا
+
+261
+00:29:15,010 --> 00:29:20,730
+أولياً، مدام ليس عددًا أوليًا، إذا بقدر أحلله على صيغة
+
+262
+00:29:20,730 --> 00:29:26,390
+حاصل ضرب عددين، الواحد فيهم أكبر من الواحد الصحيح،
+
+263
+00:29:26,390 --> 00:29:36,380
+وكل واحد فيهم أقل من N، طيب الآن يا بناتي الـ N موجود
+
+264
+00:29:36,380 --> 00:29:44,880
+في الـ NZ أكيد، لأن
+
+265
+00:29:44,880 --> 00:29:49,700
+الواحد موجود في الـ Z، إذا الـ N بقدر أقول عليها N
+
+266
+00:29:49,700 --> 00:29:55,520
+في واحد، يبقى صلة الـ N موجود في الـ NZ، جيب جدش بده
+
+267
+00:29:55,520 --> 00:30:05,870
+يعطينا جدش الـ N، الـ S و T موجودة في الـ NZ، يعني معنى
+
+268
+00:30:05,870 --> 00:30:16,450
+هذا الكلام أن الـ S و T هتساوي N في Y مثلاً، for some
+
+269
+00:30:16,450 --> 00:30:24,970
+Y اللي موجودة في Z، طيب، بدنا نجي لتفسير رياضي لهذه
+
+270
+00:30:24,970 --> 00:30:34,600
+المعادلة، أليست N تقسم الـ S و T؟ يبقى هنا ساعة الـ N
+
+271
+00:30:34,600 --> 00:30:43,680
+divides الـ S و T، هذا معناه أن الـ N divides الـ S or
+
+272
+00:30:43,680 --> 00:30:49,840
+الـ N divides الـ T، شو رأيكوا بالكلام؟ آه، صح والله
+
+273
+00:30:51,470 --> 00:30:57,890
+غلط، غلط، ليش؟ لأن هذا أقل من N، كيف الـ N اللي هو
+
+274
+00:30:57,890 --> 00:31:02,090
+الكبير بده يقسم صغير؟ هذا كلام غير منطقي، بس لو
+
+275
+00:31:02,090 --> 00:31:05,970
+كان العدد صغير ممكن أن يقسم عدد كبير، لكن العدد
+
+276
+00:31:05,970 --> 00:31:09,690
+الكبير يقسم العدد اللي أصغر منه؟ هذا كلام غير
+
+277
+00:31:09,690 --> 00:31:16,230
+وارد، إذا هذا كلام ما له؟ Impossible، هذا الكلام
+
+278
+00:31:16,230 --> 00:31:17,810
+Impossible
+
+279
+00:31:20,630 --> 00:31:26,990
+هذا كلام غير ممكن، طيب شوفي بنفسك، تقول الفرض الخطأ
+
+280
+00:31:26,990 --> 00:31:32,630
+ده وين جد؟ قلنا suppose not، يعني افترض أن العدد
+
+281
+00:31:32,630 --> 00:31:39,350
+ما هو prime، قعدنا إلى خطأ، إيش؟ دي فرض، دي صح
+
+282
+00:31:39,350 --> 00:31:47,090
+ولا غلط؟ غلط، وعكسه هو الصحيح، يبقى هنا الـ الـ
+
+283
+00:31:47,090 --> 00:31:49,090
+الـ الـ prime
+
+284
+00:31:53,180 --> 00:32:04,060
+طب ننتقل الآن إلى المثال الثاني، رامبل تيك
+
+285
+00:32:04,060 --> 00:32:08,220
+مقولة
+
+286
+00:32:08,220 --> 00:32:13,320
+FLR is an integral thing، والله قبل المثال الثاني
+
+287
+00:32:13,320 --> 00:32:17,900
+خذ لك هذه الملاحظة، Note that
+
+288
+00:32:25,350 --> 00:32:43,190
+هل يومًا ما الـ zero is a prime ideal in the ...
+
+289
+00:32:43,190 --> 00:32:48,990
+إحنا بندعي هيك، لكن كل ادعاء بده إيش؟ بده إثبات،
+
+290
+00:32:48,990 --> 00:32:52,090
+يبقى بادي بقوله because
+
+291
+00:32:56,780 --> 00:33:06,560
+If الـ A و الـ B موجودة في الـ Z، and حاصل ضربهما
+
+292
+00:33:06,560 --> 00:33:15,780
+الـ A في B موجود في الـ Zero، طلع ماشي مع التعريف
+
+293
+00:33:15,780 --> 00:33:19,480
+بالضبط، و الـ Zero proper لأنه أصغر من الـ ring
+
+294
+00:33:19,480 --> 00:33:21,320
+الأصلي اللي هو الـ Z
+
+295
+00:33:25,270 --> 00:33:30,730
+الـ A و B يبدو بيساوي Zero، لأنه ما فيه إلا عنصر
+
+296
+00:33:30,730 --> 00:33:35,310
+واحد هو العنصر الصفري، طب الـ A و الـ B integers
+
+297
+00:33:35,310 --> 00:33:41,970
+صح؟ هل يُعقل أنه حاصل ضرب 2 integers يساوي Zero؟ ليش
+
+298
+00:33:41,970 --> 00:33:49,330
+معقول إلا إذا كان أحدهم يساوي Zero؟ يبقى هذا معناه
+
+299
+00:33:49,330 --> 00:33:58,440
+أن الـ A بيساوي Zero Or الـ B بيساوي 0، صح؟
+
+300
+00:33:58,440 --> 00:34:05,880
+طب لو كان الـ A يساوي 0، إذا الـ A موجود في الـ 0، Or
+
+301
+00:34:05,880 --> 00:34:16,620
+الـ B موجود في الـ 6 اللي هي 0، انطبق التعريف، يبقى
+
+302
+00:34:16,620 --> 00:34:26,130
+صار الـ 0 عبارة عن الـ prime ideal in Z، الـ zero is
+
+303
+00:34:26,130 --> 00:34:37,670
+prime ideal الـ 0 اللي عندنا هذه، and Z طيب
+
+304
+00:34:37,670 --> 00:34:44,410
+Z هذه ring واحدة ما فيش غيرها، فلو روحنا وقلنا ...
+
+305
+00:34:44,410 --> 00:34:51,930
+قلنا بدنا ناخذ أكثر من ring، يعني ممكن الكلام هذا
+
+306
+00:34:51,930 --> 00:34:56,930
+يحصل لمجموعة من الرمز، والله ما فيش غير هذا الكلام
+
+307
+00:34:56,930 --> 00:35:04,350
+للـ Z، هذا السؤال اللي بدنا نجاوزه بالمثال رقم
+
+308
+00:35:04,350 --> 00:35:14,670
+اتنين، example اتنين، بيقول ما يتلف، الـ R is an
+
+309
+00:35:14,670 --> 00:35:18,570
+integral domain
+
+310
+00:35:20,700 --> 00:35:28,040
+لو كان الـ R integral domain، then الـ zero is a
+
+311
+00:35:28,040 --> 00:35:41,240
+prime ID، is a prime ID of R، solution
+
+312
+00:35:41,240 --> 00:35:46,180
+عندنا
+
+313
+00:35:46,180 --> 00:35:55,450
+R integral domain، يبقى assume، افترض أن الـ R is an
+
+314
+00:35:55,450 --> 00:36:03,310
+integral domain، يعني ما فيش فيها قواسم للصفر إلا
+
+315
+00:36:03,310 --> 00:36:11,570
+الصفر نفسه، مظبوط؟ طيب، بدي أخذ عنصرين في R،
+
+316
+00:36:11,570 --> 00:36:16,990
+وحاصل ضربهما موجود وين؟ في الـ 0، يبقى بدي أقول له
+
+317
+00:36:16,990 --> 00:36:26,220
+let الـ A و الـ B موجودات في R such that الـ A في الـ B
+
+318
+00:36:26,220 --> 00:36:35,860
+موجود في Zero، يبقى then الـ A في الـ B بتساوي Zero
+
+319
+00:36:35,860 --> 00:36:44,120
+بقى وجود هذا يعني أن الـ A تساوي Zero or الـ
+
+320
+00:36:44,120 --> 00:36:49,720
+B تساوي Zero؟ طيب، ليش؟ لأن الـ R Integral Domain
+
+321
+00:36:49,720 --> 00:36:55,240
+لو ما كانش Integral Domain، كلامي هذا غلط، تمام، يبقى
+
+322
+00:36:55,240 --> 00:37:05,940
+هذا هذا because because الـ R is an Integral
+
+323
+00:37:05,940 --> 00:37:13,560
+Domain، هذا الكلام صحيح، لإن هذا integral domain
+
+324
+00:37:13,560 --> 00:37:21,260
+مدام هذا، يعني أن الـ A موجود في الـ ideal اللي
+
+325
+00:37:21,260 --> 00:37:28,340
+هو الـ zero أو الـ B موجود في الـ zero، هذا بدي
+
+326
+00:37:28,340 --> 00:37:39,560
+أعطيكم إياه، أن الـ zero is a prime ideal in R، يبقى أيضًا
+
+327
+00:37:39,560 --> 00:37:46,580
+صحيح أنك شغلت شغلتين، الشغل الأولى أنه الـ ideal zero هو
+
+328
+00:37:46,580 --> 00:37:51,080
+prime ideal في الـ ring of integers، من الملاحظة اللي
+
+329
+00:37:51,080 --> 00:37:56,820
+هناك، وبعد هيك كمان الـ zero is a prime ideal في الـ
+
+330
+00:37:56,820 --> 00:38:03,740
+integral domain، طيب بدنا نروح لمثال آخر، تمام؟
+
+331
+00:38:03,740 --> 00:38:12,060
+و هذا يكون ثالث ثلاثة بنات، اللي هو سؤال خمسة عشر من
+
+332
+00:38:12,060 --> 00:38:27,860
+الكتاب، بيقول لك الـ A، B، A ring with unity 1، if
+
+333
+00:38:27,860 --> 00:38:43,570
+الـ A is an ideal، لو كان الـ A عبارة عن ideal of R، and الـ
+
+334
+00:38:43,570 --> 00:38:53,690
+1، الواحد موجود في الـ A، موجود في الـ A، then الـ A
+
+335
+00:38:53,690 --> 00:39:00,730
+بتساوي R، سؤال
+
+336
+00:39:00,730 --> 00:39:08,220
+سهل، عندنا الـ ring with unity هي الواحد، قال الـ إيه
+
+337
+00:39:08,220 --> 00:39:13,280
+الـ ideal؟ الواحد اللي هو الـ unity موجود في الـ
+
+338
+00:39:13,280 --> 00:39:19,140
+ideal، فلنحدد الآن، يبقى الـ ideal إيش؟ بده يساوي
+
+339
+00:39:19,140 --> 00:39:24,680
+الـ ring كلها، الـ ring كلها؟ آه، الـ ring كلها، طب
+
+340
+00:39:24,680 --> 00:39:29,150
+خليني أسأل سؤال في مبادئ الرياضيات، كيف بنجي الناس
+
+341
+00:39:29,150 --> 00:39:37,630
+تثبت أن two sets are equal، يعني كل واحدة فيهم
+
+342
+00:39:37,630 --> 00:39:41,990
+subset من الثانية، يعني في الاتجاهين، أن حدث ذلك
+
+343
+00:39:41,990 --> 00:39:48,070
+بقول له two sets are equal، طيب، تمام، يبقى solution
+
+344
+00:39:48,070 --> 00:39:55,450
+بدي أكتب أول معادلة، وأشوف إيش رأيكم فيها، صح هذا
+
+345
+00:39:55,450 --> 00:40:05,590
+بنا non-ideal proper، يعني ideal من R، تمام، يبقى هذه
+
+346
+00:40:05,590 --> 00:40:12,330
+المعادلة رقم واحد، إذا قدرت أثبت أنها subset من A
+
+347
+00:40:12,330 --> 00:40:16,350
+بكون جبت الاتجاه الثاني، وبالثاني بصير الـ A تساوي
+
+348
+00:40:16,350 --> 00:40:24,030
+مين؟ تساوي الـ R، طيب الآن بدي أقول، خذ للـ R موجودة
+
+349
+00:40:24,030 --> 00:40:31,110
+في A عشوائية، لتحاول تثبت أن الـ R هذه موجودة في إيه؟
+
+350
+00:40:31,110 --> 00:40:43,110
+موجودة في إيه؟ then الـ R تساوي واحد في R، صح؟ طيب،
+
+351
+00:40:43,110 --> 00:40:53,010
+تساوي R في واحد، مظبوط؟ أنا أدعي أن هذه موجودة في
+
+352
+00:40:53,010 --> 00:40:55,230
+إيه؟ أكيد؟
+
+353
+00:40:56,980 --> 00:41:00,800
+عشان الـ 1 دي، الـ 1 عشان الـ A، الـ 1 في A، والـ A
+
+354
+00:41:00,800 --> 00:41:05,940
+ideal دي، يبقى لو جبت أي element من R ضربته في هذا
+
+355
+00:41:05,940 --> 00:41:10,940
+الواحد، بيكون موجود في A، صح ولا لا؟ ممتاز جداً، يبقى
+
+356
+00:41:10,940 --> 00:41:18,380
+هذا موجود في A، السبب because أن الواحد موجود في A
+
+357
+00:41:18,380 --> 00:41:28,560
+and الـ A is an ideal، طيب، يبقى الآن الـ R اللي موجود
+
+358
+00:41:28,560 --> 00:41:34,940
+في R، لقيته موجود وين؟ إيش تفسيركم لهذا الكلام؟ R
+
+359
+00:41:34,940 --> 00:41:44,680
+subset من A، يبقى هنا R subset من A، وهذه العلاقة رقم 2
+
+360
+00:41:44,680 --> 00:41:54,720
+أروح أقول له هنا، from واحد واثنين we have، يبقى بده
+
+361
+00:41:54,720 --> 00:42:02,900
+يصير الـ A تساوي R، يبقى يا بنات من الآن فصاعدًا لو
+
+362
+00:42:02,900 --> 00:42:08,560
+قدرت أثبت أن الـ unity موجود في الـ ideal، يبقى الـ
+
+363
+00:42:08,560 --> 00:42:13,100
+ideal بده يساوي مين؟ بده يساوي الـ ring الأصلية
+
+364
+00:42:13,100 --> 00:42:21,180
+تمام تمام، طيب هذا كان مثال ثلاثة، بدنا نروح لمثال
+
+365
+00:42:21,180 --> 00:42:21,980
+أربعة
+
+366
+00:42:25,420 --> 00:42:34,000
+مثال أربعة، نعطيكم مثال عادلين، أعتقد أن هذا سهل
+
+367
+00:42:34,000 --> 00:42:43,440
+بالنسبة لكم، لأنه وقته مثل فيه الظروف، طيب
+
+368
+00:42:43,440 --> 00:42:53,060
+المثال بيقول ما يعني، يبقى example أربعة بيقول إيه
+
+369
+00:42:53,060 --> 00:43:03,580
+little A مثل A تساوي Z12، then the only
+
+370
+00:43:03,580 --> 00:43:14,320
+ideals، then the only ideals، ideals
+
+371
+00:43:14,320 --> 00:43:22,840
+of A، قالوا
+
+372
+00:43:22,840 --> 00:43:28,910
+لكم Z12، فيها مجموعة من الـ ideals، بدنا
+
+373
+00:43:28,910 --> 00:43:37,130
+نعرفهم، تقدروا تجيبوا لي أسفل الأتنين الـ zero وين؟
+
+374
+00:43:37,130 --> 00:43:45,050
+والـ R؟ صح، مش هيجي من نفسها، يبقى هدول قدّ بعض حاجة
+
+375
+00:43:45,050 --> 00:43:48,650
+اللي لازم كل واحد حتى لو ما جريش جبر يكون عارفه
+
+376
+00:43:48,650 --> 00:43:55,540
+يبقى هنا الـ zero اللي هو الـ trivial ideal، وزائد اتناشر
+
+377
+00:43:55,540 --> 00:44:02,440
+it's الـ Z12 تمام، ومين كمان؟ الـ principle ideal
+
+378
+00:44:02,440 --> 00:44:09,360
+generated by اتنين، مين عناصرها؟ Zero، اتنين، أربعة،
+
+379
+00:44:09,540 --> 00:44:17,540
+ستة، ثمانية، عشرة، كفي، أليس هذا هو 2Z12؟
+
+380
+00:44:17,540 --> 00:44:25,790
+صح؟ طيب لو قلت الـ principle ideal generated
+
+381
+00:44:25,790 --> 00:44:33,770
+by تلاتة، Zero، تلاتة، ستة، تسعة، أليس هو الـ ideal
+
+382
+00:44:33,770 --> 00:44:42,590
+اللي هو 3Z12؟ طيب، الـ أربعة، الـ principle
+
+383
+00:44:42,590 --> 00:44:50,820
+ideal generated by أربعة، اللي هو 4Z12، الـ
+
+384
+00:44:50,820 --> 00:44:56,040
+principle ideal generated by ستة، Zero وستة، ما فيش
+
+385
+00:44:56,040 --> 00:45:04,760
+غيرهم؟ يبقى هذا 6Z12، ما فيش غيرهم؟ ما نعرفش،
+
+386
+00:45:04,760 --> 00:45:11,540
+يمكن يكون فيه، يمكن يكون فيه، الله أعلم، إيش اسم كنت
+
+387
+00:45:11,540 --> 00:45:25,080
+قاعد؟ ملك، أشطة، رفعت، يبقى ملكة، داعي أنها لا تملك كل
+
+388
+00:45:25,080 --> 00:45:32,980
+هذه الـ ideals على هذه الـ ring، نشوف الموافقين على
+
+389
+00:45:32,980 --> 00:45:36,220
+رأيها، وال
+
+445
+00:52:21,690 --> 00:52:34,640
+بقول not that. Not that أن خمسة عشر وسبعة عشر
+
+446
+00:52:34,640 --> 00:52:49,260
+خمسة عشر  و أحد عشر  are not a prime and not
+
+447
+00:52:49,260 --> 00:52:57,780
+maximal ideals
+
+448
+00:52:59,650 --> 00:53:06,110
+because they
+
+449
+00:53:06,110 --> 00:53:13,330
+are not
+
+450
+00:53:13,330 --> 00:53:22,310
+proper or because they are improper. دعواتك كلها
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..be34642bdc696fc7ad70946b6a744279ee3bad04
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4_raw.srt
@@ -0,0 +1,1800 @@
+1
+00:00:20,920 --> 00:00:26,160
+بسم الله الرحمن الرحيم نكمل ما اتدناه في المحاضرة
+
+2
+00:00:26,160 --> 00:00:34,400
+الماضية ولازلنا مع الـ Factor Rings مثاله رقم خمسة
+
+3
+00:00:34,400 --> 00:00:40,220
+بيقول يستخدم الـ R of X تمثل Ring of polynomials
+
+4
+00:00:40,220 --> 00:00:46,480
+كثيرات الحدود with real coefficientsيبقى المعاملات
+
+5
+00:00:46,480 --> 00:00:53,700
+تبعد كثيرات الحدود هي كلها أعداد حقيقية ناخد الـ
+
+6
+00:00:53,700 --> 00:00:57,080
+Principle Ideal Generated by X تربيه زايد واحد
+
+7
+00:00:57,080 --> 00:01:01,160
+اللي هو كل العناصر F of X اللي مضروبة في X تربيه
+
+8
+00:01:01,160 --> 00:01:05,960
+زايد واحد في هذه الـ F of X موجودة في R of X بذكرك
+
+9
+00:01:05,960 --> 00:01:10,800
+بجينا نقول الـ Principle Ideal Generated by A هو
+
+10
+00:01:10,800 --> 00:01:17,450
+كل العناصر على الشكل R في Aبحيث الـ R موجودة في R
+
+11
+00:01:17,450 --> 00:01:21,470
+يبقى نفس التعريف الـ R اللي موجودة في R هي
+
+12
+00:01:21,470 --> 00:01:26,130
+function والـ A اللي موجود في ال principle اللي هو
+
+13
+00:01:26,130 --> 00:01:30,110
+X تربية زائد واحد يبقى هذا التعريف السابق اللي
+
+14
+00:01:30,110 --> 00:01:34,470
+أخدناه لمين لل principle ideal generated by A هو
+
+15
+00:01:34,470 --> 00:01:39,730
+ال principle ideal generated by X تربية زائد واحد
+
+16
+00:01:40,320 --> 00:01:44,140
+يبقى في هذه الحالة نكوّل الـ Factoring الـ
+
+17
+00:01:44,140 --> 00:01:50,520
+Factoring لـ R of X modulo X تربية زائد واحد من
+
+18
+00:01:50,520 --> 00:01:55,120
+عناصرها عنصر من G زائد الـ principle ideal
+
+19
+00:01:55,120 --> 00:02:01,100
+generated by X تربية زائد واحد عنصر من R of X هو G
+
+20
+00:02:01,100 --> 00:02:07,910
+of X زائد الـ ideal اللي عندنا هذا أنا أزعمإن هذا
+
+21
+00:02:07,910 --> 00:02:13,170
+بيكون على الشكل ax زائد b يعني معادلة من الدرجة
+
+22
+00:02:13,170 --> 00:02:17,410
+الأولى زائد ال x تربيه زائد واحد وبعدها ال a و ال
+
+23
+00:02:17,410 --> 00:02:24,750
+b أعدادا حقيقي طب تعالوا نتفهم الآن ال g of x
+
+24
+00:02:24,750 --> 00:02:32,190
+موجودة وين؟ ال R of xاروبكس هي pronomial من الدرجة
+
+25
+00:02:32,190 --> 00:02:35,810
+الأولى و الله ممكن الأولى و التانية و التالتة و
+
+26
+00:02:35,810 --> 00:02:41,490
+العشرة و النونية و ما إلى ذلك أيوة يبقى هنا عندي
+
+27
+00:02:41,490 --> 00:02:45,170
+من أي درجة ان شاء الله يكون من الدرجة الخمسمية
+
+28
+00:02:45,170 --> 00:02:51,330
+تمام لكن انا ازعم اني بقدر اكتبها على الشكل معادلة
+
+29
+00:02:51,330 --> 00:02:55,510
+من الدرجة الأولى زي ال principle ideal generated
+
+30
+00:02:55,510 --> 00:03:02,860
+by X تربية زي الواحدةبقول هذه الصيغة صحيحة this is
+
+31
+00:03:02,860 --> 00:03:07,760
+true because لو كانت الـG of X موجودة في الـR of X
+
+32
+00:03:07,760 --> 00:03:15,800
+then شوف يا الكتابة هذه تبعت الـG of X بقدر أكتبها
+
+33
+00:03:15,800 --> 00:03:24,460
+على شكل دالة في X EQ of X مضروبة في X تربية زائد
+
+34
+00:03:24,460 --> 00:03:34,860
+واحد زائد R of Xو ال R of X يا إما بتتساوي Zero يا
+
+35
+00:03:34,860 --> 00:03:44,860
+إما ال degree لل R of X أقل من إثنين إيش اللاتيني
+
+36
+00:03:44,860 --> 00:03:49,800
+هذا؟ بدنا نفهم، من أين جاي بهذا الكلام؟ نجحنا فرضا
+
+37
+00:03:49,800 --> 00:03:55,140
+أنها AX؟ بصوا برا عليها شويةالان انا ماخد g of x
+
+38
+00:03:55,140 --> 00:04:00,680
+موجودة في ال polynomial الاصلية r of x يبقى هذه
+
+39
+00:04:00,680 --> 00:04:04,460
+الدرجة يمكن التالتة يمكن الرابعة الخامسة جد ما
+
+40
+00:04:04,460 --> 00:04:11,720
+يكون انا ازعم ان بقدر احطها على شكل معدن من الدرجة
+
+41
+00:04:11,720 --> 00:04:18,270
+الأولى نفترض انه كانت من الدرجة العشرة g of xيبقى
+
+42
+00:04:18,270 --> 00:04:24,550
+ليش بضروح أعمل بضروح أجسم جسمة مطولة على مين على X
+
+43
+00:04:24,550 --> 00:04:29,650
+تربية زائد واحد يبقى ال Ge of X اللي من الدرجة
+
+44
+00:04:29,650 --> 00:04:34,530
+العاشرة بدي أجسمها على ال polynomial X تربية زائد
+
+45
+00:04:34,530 --> 00:04:40,950
+واحد اللي من الدرجة الثانية بضل أجسم لغاية الدرجة
+
+46
+00:04:40,950 --> 00:04:46,320
+الصينية أقل من الدرجة الثانيةيعني أقل من درجة X
+
+47
+00:04:46,320 --> 00:04:51,900
+تربية وزايد واحد مظبوط يبقى بطل عندنا خارج القسمة
+
+48
+00:04:51,900 --> 00:04:57,400
+و بضل عندنا تحت باقي الباقي هذا قد يكون صفر زي ما
+
+49
+00:04:57,400 --> 00:05:02,200
+تجسمي مثلا اي عدد على عدد اذا ما تقولي تمانية على
+
+50
+00:05:02,200 --> 00:05:08,160
+اتنين يبقى اربع عدد صحيح ماضلش عندي باقي تمام لكن
+
+51
+00:05:08,160 --> 00:05:16,270
+لو قلنا جسمنا تسعة على اتنينبظل أربع و لسه بزيد
+
+52
+00:05:16,270 --> 00:05:21,390
+واحد بدنا نقسمه على اتنين مظبوط ولا لا يبقى هذا
+
+53
+00:05:21,390 --> 00:05:27,150
+اللي هو الباقي اللي بده يسميه R of X يبقى ال Q of
+
+54
+00:05:27,150 --> 00:05:33,270
+X تعتبر عددا صحيحا يعني بلغتنا في السوء ال
+
+55
+00:05:33,270 --> 00:05:38,950
+polynomialمضروبة في المقسوم عليه له X تربية زائد
+
+56
+00:05:38,950 --> 00:05:43,870
+واحد زائد الـ remainder الباقي اللي عندنا هو R of
+
+57
+00:05:43,870 --> 00:05:49,510
+X إذاً الـG of X حطيتها على الشكل اللي عندنا هذا
+
+58
+00:05:49,510 --> 00:05:56,310
+والـR of X قد تكون Zero بتكون Zero إذا تقسم G of X
+
+59
+00:05:56,310 --> 00:06:01,330
+على X تربية زائد واحد بدون باقي لو قسمت بدون باقي
+
+60
+00:06:01,330 --> 00:06:07,370
+يبقى R of X بقداش ب Zeroطيب إذا جسمته بقي عندنا
+
+61
+00:06:07,370 --> 00:06:13,430
+الباقي بظلمين R of X R of X درجته أقل من اتنين
+
+62
+00:06:13,430 --> 00:06:19,350
+يعني أقل من درجة X تربيه زي واحد لإن بنقول إذا
+
+63
+00:06:19,350 --> 00:06:23,890
+درجة البصر أكبر من درجة المقام أو درجة البصر جت
+
+64
+00:06:23,890 --> 00:06:29,530
+درجة المقام بنجسم جسمة متولة لها يتمصير درجة البصر
+
+65
+00:06:29,530 --> 00:06:34,370
+أقل من درجة المقام مظبوطمش هيك في القسمة المطولة
+
+66
+00:06:34,370 --> 00:06:41,030
+العادية تماما هنا تماما جسمنا الـG of X على الـX
+
+67
+00:06:41,030 --> 00:06:47,890
+تربية زي 1 طلع النتيجة Q of X وزال دلة اسمها R of
+
+68
+00:06:47,890 --> 00:06:53,050
+X إذا الـG of X يسبق Q of X في الـX تربية زي 1 زي
+
+69
+00:06:53,050 --> 00:06:59,130
+R of X R of X كان مضلش شيء يبقى R of X بـ0 ضلت دلة
+
+70
+00:06:59,130 --> 00:07:06,270
+بنقولها R of Xاللي درجتها أقل من درجة المقسوم عليه
+
+71
+00:07:06,270 --> 00:07:12,990
+أقل من اتنين يعني كده؟ واحد، مظبوط ولا لأ يعني ايش
+
+72
+00:07:12,990 --> 00:07:20,570
+بيصير؟ بيصير ax زائد b معادلة من الدرجة الأولى
+
+73
+00:07:20,570 --> 00:07:27,010
+وإذا طلعت F0 بيظل constant Bيبقى in general نقول
+
+74
+00:07:27,010 --> 00:07:32,210
+ax زايد بقدر ما تطلع ايه تطلع وقدر ما تطلع بيه
+
+75
+00:07:32,210 --> 00:07:37,350
+تطلع ماعناه مشكلة يبقى بناء عليه لمن قد يقول يا
+
+76
+00:07:37,350 --> 00:07:46,090
+بناتي g of x زايد principle ideal generated by x
+
+77
+00:07:46,090 --> 00:07:52,810
+تربيه زايد واحد مش بده يساوي بده يساوي هي ال q of
+
+78
+00:07:52,810 --> 00:08:01,860
+xU of X في X تربيع زائد واحد زائد R of X زائد
+
+79
+00:08:01,860 --> 00:08:05,720
+reference principle ideal generated by X تربيع
+
+80
+00:08:05,720 --> 00:08:11,540
+زائد واحد السؤال هو إيش رايك هذه مع reference
+
+81
+00:08:11,540 --> 00:08:16,960
+principle ideal إيش هذه موجودة هنا إذا حسب الكلام
+
+82
+00:08:16,960 --> 00:08:23,240
+اللي إحنا بنقوله هذه R of Xزائد لـPrincipal Ideal
+
+83
+00:08:23,240 --> 00:08:29,060
+Generated By X تربية زائد واحد تبقى Renovix أقل من
+
+84
+00:08:29,060 --> 00:08:35,180
+الدرجة الثانية بمقدار واحد أو مقدار اتنين يبقى
+
+85
+00:08:35,180 --> 00:08:43,180
+بناخد الأكبر وهذه تساوي AX زائد B زائد لPrincipal
+
+86
+00:08:43,180 --> 00:08:48,810
+Ideal Generated By X تربية زائد واحديبقى كلامنا
+
+87
+00:08:48,810 --> 00:08:55,510
+اللي قلناه صحيح ولا لا يبقى اي polynomial في جي او
+
+88
+00:08:55,510 --> 00:09:00,750
+اي polynomial في ال R of X الأصلية بقدر اكتبها على
+
+89
+00:09:00,750 --> 00:09:04,970
+سيط polynomial من الدرجة الأولى زاد ال principle
+
+90
+00:09:04,970 --> 00:09:10,450
+ideal generated by X تربيع زاد وعدها يورناك كيف
+
+91
+00:09:10,450 --> 00:09:15,470
+حصلنا عليها طب السؤال الأول طب احنا لو عندنا two
+
+92
+00:09:15,470 --> 00:09:19,700
+elements كيف بتضرمهم؟لأنها هتطلع معادل من الدرجة
+
+93
+00:09:19,700 --> 00:09:23,060
+التانية صحيح ولا لأ؟ يقول معادل من الدرجة الأولى
+
+94
+00:09:23,060 --> 00:09:26,400
+وهم الدرجة اللى ضربناهم تطلع معادل من الدرجة
+
+95
+00:09:26,400 --> 00:09:30,580
+التانية كيف سوى في هذه الحلقة نقولك القصة فسيطة
+
+96
+00:09:30,580 --> 00:09:37,580
+جدا كيف فسيطة جدا تعالى شوفى باياتك الان note that
+
+97
+00:09:37,580 --> 00:09:41,140
+لاحظي
+
+98
+00:09:41,140 --> 00:09:50,120
+باياتك الان يا بنات لو جيت قلتx تربيع زائد واحد زي
+
+99
+00:09:50,120 --> 00:09:55,600
+ال principle ideal generated by x تربيع زائد واحد
+
+100
+00:09:55,600 --> 00:10:02,740
+هداش بيعطيني ال principle ideal generated by x
+
+101
+00:10:02,740 --> 00:10:08,080
+تربيع زائد واحد لأن هذا عنصر موجود فيه صحيح ولا لأ
+
+102
+00:10:08,080 --> 00:10:14,550
+طب بنفع اقول هذا بنفع zeroزاد ال principle ideal
+
+103
+00:10:14,550 --> 00:10:20,310
+generated by one صحيح ولا لا؟ إذا البناء النعلي
+
+104
+00:10:20,310 --> 00:10:29,410
+بصير عند X تربية زائد واحد بده ساوي zero طبعا؟ طيب
+
+105
+00:10:29,410 --> 00:10:35,670
+معناه هذا الكلام إن ال X تربية بده ساوي كده؟ بده
+
+106
+00:10:35,670 --> 00:10:45,970
+ساوي سالف واحد طبعا؟إذا داخل هذه ال ring ها تشوف
+
+107
+00:10:45,970 --> 00:10:50,930
+تعد لمخك أيوة داري بارك هم مشغولش على ال real line
+
+108
+00:10:50,930 --> 00:10:57,110
+هم نشغل داخل مين؟ داخل ال ring R of X وإلا لو كان
+
+109
+00:10:57,110 --> 00:11:01,490
+على ال real line هذه المعادلة عندى ملهاش حل صح ولا
+
+110
+00:11:01,490 --> 00:11:07,630
+لا؟ لأنه لا يمكن لمجموع كميتين كميتين مربعات أو
+
+111
+00:11:07,630 --> 00:11:13,360
+كميتين موجبتينإن يكون صفر فالكلام مش ممكن إلا إذا
+
+112
+00:11:13,360 --> 00:11:18,580
+كانت كل واحدة فيهم صفر لكن إحنا عنا X تربية بدأت
+
+113
+00:11:18,580 --> 00:11:24,640
+ساوي سالب واحد على ال pronomials هدول وليس على ال
+
+114
+00:11:24,640 --> 00:11:29,340
+.. يعني داخل ال ring اللي عندنا طيب ان وريكي لهم
+
+115
+00:11:29,340 --> 00:11:34,720
+كيف الحسابات بصير داخل هذه ال ring لو بدي أضرب
+
+116
+00:11:34,720 --> 00:11:41,240
+مثلًا بدي أضرب عنصرين هتيليمعادلة خطية يالا صمي
+
+117
+00:11:41,240 --> 00:11:46,080
+يعني يعني زي اكس من طريقة الأولى معادلة عادية حط
+
+118
+00:11:46,080 --> 00:11:52,000
+الرقم الي عادي ثلاثة اكس زائد اتنين اتنين ممتاز
+
+119
+00:11:52,000 --> 00:11:58,160
+جدا يبقى انا عندي تلاتة اكس زائد اتنين زائد ال
+
+120
+00:11:58,160 --> 00:12:04,360
+principle ideal generated by one بدي اضربه فاهمين
+
+121
+00:12:04,910 --> 00:12:13,250
+هاتي لـ polynomial تانية غير هذه 5x
+
+122
+00:12:13,250 --> 00:12:19,830
+-3 يبقى عندى 5x-3 زائد لـ principal ideal
+
+123
+00:12:19,830 --> 00:12:26,390
+generated by one هذه المناطق لما أضربها بدأت تسوى
+
+124
+00:12:26,390 --> 00:12:36,600
+3x زائد 2 في 5x-3وهنا زائد لـ principal ideal
+
+125
+00:12:36,600 --> 00:12:41,640
+generated by x تربيع minus ال one يبقى هذه بدي
+
+126
+00:12:41,640 --> 00:12:47,560
+أضرب الآن بدي أفك حاصل ضربي فتلاتة في خمسة بخمس
+
+127
+00:12:47,560 --> 00:12:55,180
+طعشر x تربيع تمام و تلاتة x في ناقص تلاتة بناقص
+
+128
+00:12:55,180 --> 00:13:04,520
+تسعة x ناقص تسعة x وزائد عشرة xوزائد عشر عليه
+
+129
+00:13:04,520 --> 00:13:10,780
+وناقص التوزيع لـPrincipal Ideal Generated by X
+
+130
+00:13:10,780 --> 00:13:15,620
+تربية plus one.الحين يا بنات ال X تربية هنا مقداش؟
+
+131
+00:13:15,620 --> 00:13:20,880
+سالب واحد، إذا هشيل ال X تربية وحط مكانها سالب
+
+132
+00:13:20,880 --> 00:13:26,840
+واحد. هذا الكلام بدي يصير خمستاشر في سالب واحد.
+
+133
+00:13:27,200 --> 00:13:34,980
+عندك ناقص تسعة X وزائد عشرة X بظل زائد X وهنا ناقص
+
+134
+00:13:34,980 --> 00:13:40,140
+ستة زائد ال principle ideal generated by X ترمية
+
+135
+00:13:40,140 --> 00:13:47,180
+plus one طبعا هنا ناقص خمس عشان ناقص ستة ناقص
+
+136
+00:13:47,180 --> 00:13:54,150
+واحدة وعشرين إذا صارت عندي X ناقص واحدة وعشرينزايد
+
+137
+00:13:54,150 --> 00:13:59,110
+ال principle ideal generated by one X تربيع زايد
+
+138
+00:13:59,110 --> 00:14:04,690
+by one تمام؟ يبقى هذه عملية الضرفياني من حد مضرب
+
+139
+00:14:04,690 --> 00:14:08,810
+عنصرين هيطلع عند X تربيع وين طلعت ال X تربيع؟
+
+140
+00:14:08,810 --> 00:14:15,190
+بشيلها بحفظ بدلها سالب واحد وبالتالي بتعود البعود
+
+141
+00:14:15,190 --> 00:14:19,090
+العنصر إلى معادلة من الدرجة الأولى زايد ال
+
+142
+00:14:19,090 --> 00:14:24,610
+principle ideal generatedby x تربيع زائد واحد
+
+143
+00:14:24,610 --> 00:14:30,630
+تمام؟ إذا هذه عملية الضرب داخل من؟ داخل ال ring
+
+144
+00:14:30,630 --> 00:14:37,090
+اللي عملناه ننتقل الآن إلى تعريف جديد يبقى
+
+145
+00:14:37,090 --> 00:14:43,030
+definition احنا من أول ال section هنا و احنا عرفنا
+
+146
+00:14:43,030 --> 00:14:49,230
+ال idealواخدنا منه الـ Trivial Ideal اللي هو الـ
+
+147
+00:14:49,230 --> 00:14:54,450
+Zero اللي لا يحتوي على الـ Zero وسمناه الـ Ideal
+
+148
+00:14:54,450 --> 00:14:59,990
+البديهي أو الـ Ideal التغفر لأن أي واحد بيجيبه فيه
+
+149
+00:14:59,990 --> 00:15:05,250
+مشكلة لكن بدنا نيجي لحالات خاصة من ال Ideals حاجة
+
+150
+00:15:05,250 --> 00:15:12,320
+بنسميها Prime Ideal و Maximal Idealبنعطي تعريف لكل
+
+151
+00:15:12,320 --> 00:15:18,260
+منهما ثم نذهب الى أمثلة على ذلك الـ Definition
+
+152
+00:15:18,260 --> 00:15:31,140
+الأول A prime ID A of a commutative ring R
+
+153
+00:15:40,480 --> 00:15:51,120
+is a proper ideal is a proper ideal is a proper
+
+154
+00:15:51,120 --> 00:16:05,440
+ideal of R such that بحيث أن such that if
+
+155
+00:16:05,440 --> 00:16:18,860
+ال A و ال Bموجودة في a and ال a بي موجود في a then
+
+156
+00:16:18,860 --> 00:16:29,720
+ال a موجود في a هو ال b موجود فيه تعريف التاني
+
+157
+00:16:29,720 --> 00:16:43,380
+maximal id هي maximal id ايه ايه maximumأيديل A of
+
+158
+00:16:43,380 --> 00:16:50,140
+a commutative in
+
+159
+00:16:50,140 --> 00:17:04,400
+R is a proper ideal of R is a proper ideal of R
+
+160
+00:17:04,400 --> 00:17:14,290
+such thatبحيث ان الله دي ما صادش ده whenever
+
+161
+00:17:14,290 --> 00:17:18,550
+whenever
+
+162
+00:17:18,550 --> 00:17:35,990
+B is an id of A and ال A صاب ستة أو تسعة و ال B
+
+163
+00:17:36,610 --> 00:17:46,930
+subset أو تساوي الـR then الـB بديو يساوي الـA
+
+164
+00:17:46,930 --> 00:17:54,750
+الـB بديو يساوي الـAR الـD بديو يساوي الـD بديو
+
+165
+00:17:54,750 --> 00:18:02,490
+يساوي الـR example one
+
+166
+00:18:02,490 --> 00:18:12,660
+لو السؤال تسعةمن الكتاب هو ليلات الان اكبر من
+
+167
+00:18:12,660 --> 00:18:18,000
+الواحد بانتجر
+
+168
+00:18:18,000 --> 00:18:29,160
+عدد صحيح بانتجر then in
+
+169
+00:18:29,160 --> 00:18:34,300
+the rain زاد
+
+170
+00:18:35,170 --> 00:18:45,230
+I think that ال .. the ideal in
+
+171
+00:18:45,230 --> 00:18:52,270
+the is prime is
+
+172
+00:18:52,270 --> 00:19:02,410
+a prime if and only if if and only if ال N is a
+
+173
+00:19:02,410 --> 00:19:02,850
+prime
+
+174
+00:19:09,090 --> 00:19:15,050
+بنرجع للتعريفين اللي احنا كتبينه الـPrime Ideal ثم
+
+175
+00:19:15,050 --> 00:19:19,870
+الـMaximal Ideal يقول الـPrime Ideal ايه؟ Of a
+
+176
+00:19:19,870 --> 00:19:25,050
+commutative ring A is a proper ideal. يبقى الشرط
+
+177
+00:19:25,050 --> 00:19:29,110
+الأول الذي يجب ان يتحقق في الـIdeal حتى يكون
+
+178
+00:19:29,110 --> 00:19:31,870
+الـPrime هو؟ ماذا يعني proper?
+
+179
+00:19:35,240 --> 00:19:41,220
+ماشي معناه proper ideal يعني؟ يعني مايسويش ال ring
+
+180
+00:19:41,220 --> 00:19:49,180
+الأصلية أقل منها، subset منها، تمام؟ يبقى هذا الـ
+
+181
+00:19:49,180 --> 00:19:55,440
+improper بده يساويها، تمام؟ يبقى proper ideal
+
+182
+00:19:55,440 --> 00:20:02,330
+الشرق الأول، وبحيث ان لو كانت عنصرينموجودات في ال
+
+183
+00:20:02,330 --> 00:20:08,210
+ring R وحاصل ضاربهما موجود في ال ideal A يبقى يا
+
+184
+00:20:08,210 --> 00:20:14,310
+إما ال A بيكون في A يا إما ال B بيكون في A إن حدث
+
+185
+00:20:14,310 --> 00:20:20,170
+ذلك بقول ال A هو prime ideal يبقى إذا قال لي أثبت
+
+186
+00:20:20,170 --> 00:20:26,630
+أن هذا ال ideal هو prime بفترض أن عندي عنصرين في
+
+187
+00:20:26,630 --> 00:20:34,180
+ال ring R وحاصل ضاربهما وين موجودفي الـ ID ان حدث
+
+188
+00:20:34,180 --> 00:20:40,560
+ذلك يبقى بتروح اثبت ان احد العنصرين موجود وين؟ في
+
+189
+00:20:40,560 --> 00:20:46,340
+ال ID يبقى يا اما ايه موجود في ايه او ال ايه موجود
+
+190
+00:20:46,340 --> 00:20:52,440
+فيه تعالى نشوف معنى ال maximum ال ID maximum جاي
+
+191
+00:20:52,440 --> 00:20:57,870
+من maximum ايش يعني maximum اكبر ما يمكنوهذا
+
+192
+00:20:57,870 --> 00:21:04,050
+المقصود يبقى أكبر ما يمكن كيف؟ تعالوا نشوف يبقى ال
+
+193
+00:21:04,050 --> 00:21:08,910
+maximum ideal من الكميوتر ت bring هو يبقى ال
+
+194
+00:21:08,910 --> 00:21:13,810
+proper ideal of our يبقى زي مين؟ زي ال prime يبقى
+
+195
+00:21:13,810 --> 00:21:18,830
+ال prime و .. و ال maximum الأتنين are ال proper
+
+196
+00:21:18,830 --> 00:21:26,520
+ideal و بحيث أن لو كان عنديB هو ideal آخر من ال
+
+197
+00:21:26,520 --> 00:21:32,080
+ring R وكان ال ideal اللي أنا بتدعي انه maximal
+
+198
+00:21:32,080 --> 00:21:37,660
+subset من B و ال B subset من R يبقى هناك أحد
+
+199
+00:21:37,660 --> 00:21:44,060
+احتمالين يا إما ال A و ال B يتساووا يا إما ال B و
+
+200
+00:21:44,060 --> 00:21:50,140
+ال R يتساووا يبقى هذه هي الطريقة المثلاء لإثبات أن
+
+201
+00:21:50,140 --> 00:21:54,830
+ال A هو maximal ideal من Rيبقى في حالة الـ Prime
+
+202
+00:21:54,830 --> 00:21:59,850
+بتروح للعناصر، في حالة الـ Maximal بتروح أجيب
+
+203
+00:21:59,850 --> 00:22:05,190
+Ideal تاني، بحيث الـ Ideal اللي عندي ال subset منه
+
+204
+00:22:05,190 --> 00:22:10,430
+و ال Ideal هذا subset من ال ring R، بدي أثير، يا
+
+205
+00:22:10,430 --> 00:22:14,610
+إما A تساوي بيه، يا إما B تساوي منه، تساوية.
+
+206
+00:22:15,170 --> 00:22:19,090
+تعالوا ناخد أمثلة مختلفة على الـ Prime Ideals والـ
+
+207
+00:22:19,090 --> 00:22:24,040
+Maximal Ideals.كون الـ prime ideal هو التعريف
+
+208
+00:22:24,040 --> 00:22:29,180
+الأول إذا هناخد السؤال الأول أو المثال الأول على
+
+209
+00:22:29,180 --> 00:22:34,020
+الـ prime ideal قال خذ ال N أكبر من واحد نين تلاتة
+
+210
+00:22:34,020 --> 00:22:39,180
+أربعة خمسة زي ما بدك P an integer then in the ring
+
+211
+00:22:39,180 --> 00:22:46,440
+Z ال NZ هو عبارة عن ideal هأثبتنا طبعا سابقا Z
+
+212
+00:22:46,440 --> 00:22:51,910
+ideal و كذلك sub ringيبقى الانزد هذا بيكون a prime
+
+213
+00:22:51,910 --> 00:22:58,630
+if and only if الان is a prime تمام؟ يبقى القرآن
+
+214
+00:22:58,630 --> 00:23:04,870
+ده صير وين؟ اتجاه الان يبقى بدي اخد الاتجاه الأول
+
+215
+00:23:04,870 --> 00:23:09,230
+assume that
+
+216
+00:23:09,230 --> 00:23:13,870
+ان الان is a prime
+
+217
+00:23:18,720 --> 00:23:26,740
+want to show that
+
+218
+00:23:26,740 --> 00:23:41,440
+ان ال NZ is a prime ID طيب
+
+219
+00:23:41,440 --> 00:23:55,260
+we know thatWe know that احنا بنعرف ان الـNZ is a
+
+220
+00:23:55,260 --> 00:24:05,520
+proper ideal of مجموعة الأعداد الصحيحة اللي هي Z
+
+221
+00:24:05,520 --> 00:24:12,760
+أثبتناها سابقاً طيب الان بدي امشي حسب التحريك بدي
+
+222
+00:24:12,760 --> 00:24:19,290
+افترضإن في عندي عنصرين من ال ring Z حاصل ضربيهم
+
+223
+00:24:19,290 --> 00:24:28,550
+موجود وين؟ موجود في ال NZ يبقى بدأت أقول له let ال
+
+224
+00:24:28,550 --> 00:24:38,090
+A و ال B موجودة في Z such that بحيث أن ال A في ال
+
+225
+00:24:38,090 --> 00:24:41,430
+B موجودة في ال NZ
+
+226
+00:24:44,850 --> 00:24:50,350
+اخدت عنصرين من ال ring الأصلية A وB وافترضت ان
+
+227
+00:24:50,350 --> 00:24:55,590
+حاصل ضربهما موجود في ال ID اللي عندي ال ID المي
+
+228
+00:24:55,590 --> 00:25:03,490
+اللي عندي مين؟ NZ طبعا يفجأة صار حاصل ضربهما موجود
+
+229
+00:25:03,490 --> 00:25:10,130
+في ال NZ ممتاز جدا طب مدام حاصل ضربهما موجود في ال
+
+230
+00:25:10,130 --> 00:25:19,680
+NZإذا شكل حاصل الضرب A في B بديساو ال N في X for
+
+231
+00:25:19,680 --> 00:25:27,940
+some X اللي موجودة في Z صحيح ولا مناقش؟ حاصل الضرب
+
+232
+00:25:27,940 --> 00:25:34,180
+موجود هنا شكل العنصر هنا هو N في أي element أو في
+
+233
+00:25:34,180 --> 00:25:40,760
+some element من Z يبقى ال A بيه بديساو ال N X
+
+234
+00:25:41,230 --> 00:25:46,810
+طلعيلي هذه المعادلة الـ X و الـ N و الـ B و الـ A
+
+235
+00:25:46,810 --> 00:25:53,090
+كلهم integers أعداد صحيحة نرجع بالذاكرة إلى الوراق
+
+236
+00:25:53,090 --> 00:25:58,950
+أليس معنى هذه المعادلة أن الـ N بتقسم الـ A بـ B
+
+237
+00:25:58,950 --> 00:26:06,250
+تمام تمام يبقى هذا معناه أن الـ N divides الـ A في
+
+238
+00:26:06,250 --> 00:26:14,060
+Bهذا معناه ان ال N بيقسم ال A أو ال N بيقسم ال B
+
+239
+00:26:14,060 --> 00:26:23,060
+يا إما ال N بتقسم ال A يا إما ال N بتقسم ال B مدام
+
+240
+00:26:23,060 --> 00:26:34,100
+بتقسم ال A يبقى ال A بدها تساوي N M for some M
+
+241
+00:26:34,100 --> 00:26:44,170
+اللي موجودة في Zمظبوط يا جابانان or ال B تساوي N
+
+242
+00:26:44,170 --> 00:26:52,650
+كفار صمك اللي موجودة في ذلك صحيح؟
+
+243
+00:26:52,650 --> 00:27:01,710
+طيب مدان هيك ال A يساوي N في M ال M هي ال element
+
+244
+00:27:01,710 --> 00:27:07,040
+هذا الثابتو ال M موجودة في Z معناه هذا الكلام ان
+
+245
+00:27:07,040 --> 00:27:14,460
+ال A موجود وين؟ في ال N Z يبقى معناه هذا الكلام ان
+
+246
+00:27:14,460 --> 00:27:27,820
+ال A موجودة في ال N Z او ال B موجودة في ال N Z ليش
+
+247
+00:27:27,820 --> 00:27:34,320
+ان ال K في Z و M في Z؟ اظن ان هو المطلوب؟إذا وصلنا
+
+248
+00:27:34,320 --> 00:27:40,880
+و أحنا مش دارين يبقى هذا معناه إيش؟ معناته إن NZ
+
+249
+00:27:40,880 --> 00:27:48,740
+is a prime ideal طبقا لل definition اللي عندنا هذا
+
+250
+00:27:48,740 --> 00:27:53,360
+الاتجاه الأول بنا نمشي لاتجاه الثاني يبقى بضروح
+
+251
+00:27:53,360 --> 00:28:06,570
+أقوله conversely assume that إن ال Nz is a prime
+
+252
+00:28:06,570 --> 00:28:16,490
+ideal هش اللي بدنا ياه want to show بدنا نروح نبين
+
+253
+00:28:16,490 --> 00:28:24,770
+ان ال N is a prime because we noticed ان هذا عدد
+
+254
+00:28:24,770 --> 00:28:30,090
+صحيح أولي طيب هروح أقول suppose not
+
+255
+00:28:33,640 --> 00:28:40,460
+يعني إيش؟ يعني ما هواش عدد أول، ده ما هواش عدد
+
+256
+00:28:40,460 --> 00:28:46,440
+أول، إذا بقدر أحلله إلى حاصل ضرب عددين، صحيح ولا
+
+257
+00:28:46,440 --> 00:28:53,840
+لا؟ يبقى suppose not then الـN هذا بده يساوي حاصل
+
+258
+00:28:53,840 --> 00:29:00,370
+ضرب SVT، كونه عدد ما هواش عدد أوليبقدر أقول بحاصل
+
+259
+00:29:00,370 --> 00:29:07,450
+ضرب S في T وفي المقابل S وT أصغر من أنه أكبر من
+
+260
+00:29:07,450 --> 00:29:15,010
+الواحد الصحيح مظبوط إيه الان أنا أدعي أنه ليس عددا
+
+261
+00:29:15,010 --> 00:29:20,730
+أولية مدام ليس عددا أولية إذا بقدر أحلله على صيغة
+
+262
+00:29:20,730 --> 00:29:26,390
+حاصل ضرب عددين الواحد فيهم أكبر من الواحد الصحيح
+
+263
+00:29:26,390 --> 00:29:36,380
+كل واحد فيهموأقل من N طيب الان يا بناتي ال N موجود
+
+264
+00:29:36,380 --> 00:29:44,880
+في ال NZ أكيد لأن
+
+265
+00:29:44,880 --> 00:29:49,700
+ال واحد موجود في ال Z إذا ال N بقدر أقول عليها N
+
+266
+00:29:49,700 --> 00:29:55,520
+وافي واحد يبقى صلة ال N موجود في ال NZ جيب جدش بده
+
+267
+00:29:55,520 --> 00:30:05,870
+يعطينا جدش ال Nالـ S T موجودة في الـ N Z يعني معنى
+
+268
+00:30:05,870 --> 00:30:16,450
+هذا الكلام ان الـ S T هتساوي N في Y مثلا for some
+
+269
+00:30:16,450 --> 00:30:24,970
+Y اللي موجودة في Z طيب، بدنا نجي تفسير رياضي لهذه
+
+270
+00:30:24,970 --> 00:30:34,600
+المعادلةأليست N تقسم ال S T؟ يبقى هنا ساعة ال N
+
+271
+00:30:34,600 --> 00:30:43,680
+divides ال S T هذا معناه ان ال N divides ال S or
+
+272
+00:30:43,680 --> 00:30:49,840
+ال N divides ال T شو رأيكوا الكلام؟ اه صح والله
+
+273
+00:30:51,470 --> 00:30:57,890
+غلط، غلط ليش؟ لإن هذا أقل من N كيف ال N اللي هو
+
+274
+00:30:57,890 --> 00:31:02,090
+الكبير بدي يقسم لصغير؟ هذا كلام غير مضطر، بس لو
+
+275
+00:31:02,090 --> 00:31:05,970
+كان العدد صغير ممكن أن يقسم عدد كبير، لكن العدد
+
+276
+00:31:05,970 --> 00:31:09,690
+الكبير يقسم العدد اللي أصغر منه؟ هذا كلام غير
+
+277
+00:31:09,690 --> 00:31:16,230
+وارد، إذا هذا كلام ما له؟ Impossible، هذا الكلام
+
+278
+00:31:16,230 --> 00:31:17,810
+Impossible
+
+279
+00:31:20,630 --> 00:31:26,990
+هذا كلام غير ممكن طيب شوفي بنفسك تقول الفرض الخطأ
+
+280
+00:31:26,990 --> 00:31:32,630
+ده وين جد؟ قولنا suppose not يعني افترض ان العدد
+
+281
+00:31:32,630 --> 00:31:39,350
+ان ما هوش prime قعدنا الى خطأ أيه؟ دي فرض دي صح
+
+282
+00:31:39,350 --> 00:31:47,090
+ولا غلط؟ غلط وعكسه هو الصحيح يبقى هنا ال .. ال ..
+
+283
+00:31:47,090 --> 00:31:49,090
+ال .. ال prime
+
+284
+00:31:53,180 --> 00:32:04,060
+طب ننتقل الان الى المثال الثاني رامبل تيك
+
+285
+00:32:04,060 --> 00:32:08,220
+مقول
+
+286
+00:32:08,220 --> 00:32:13,320
+FLR is an integral thing و الله قبل المثال الثاني
+
+287
+00:32:13,320 --> 00:32:17,900
+خديلك هالملاحظة Note that
+
+288
+00:32:25,350 --> 00:32:43,190
+هل يومنات الـ zero is a prime ideal in the ..
+
+289
+00:32:43,190 --> 00:32:48,990
+احنا بندعي هيك لكن كل ادعاء بده إيه؟ بده إثبات
+
+290
+00:32:48,990 --> 00:32:52,090
+يبقى بادي بقوله because
+
+291
+00:32:56,780 --> 00:33:06,560
+If الـ A و الـ B موجودة في الـ Z and حاصل ضربهما
+
+292
+00:33:06,560 --> 00:33:15,780
+الـ A في B موجود في الـ Zero طلع ماشي مع التعريف
+
+293
+00:33:15,780 --> 00:33:19,480
+بالضبط و الـ Zero proper لأنه أصغر من الـ ring
+
+294
+00:33:19,480 --> 00:33:21,320
+الأصلي اللي هو الـ Z
+
+295
+00:33:25,270 --> 00:33:30,730
+الـ A و B يبدو يساوي Zero لأنه مافيش فيه إلا عنصر
+
+296
+00:33:30,730 --> 00:33:35,310
+واحد هو العنصري الصفري طب الـ A و الـ B انتجارز
+
+297
+00:33:35,310 --> 00:33:41,970
+صح؟ هل يُعقل إنه حصل ضرب 2 انتجار يساوي Zero؟ ليه
+
+298
+00:33:41,970 --> 00:33:49,330
+معقول إلا إذا كان أحدهم يساوي Zero؟ يبقى هذا معناه
+
+299
+00:33:49,330 --> 00:33:58,440
+إن الـ A يبدو يساوي ZeroOr الـ B يبدو يساوي 0 صح ؟
+
+300
+00:33:58,440 --> 00:34:05,880
+طب لو كان ال A يساوي 0 إذا ال A موجود في ال 0 Or
+
+301
+00:34:05,880 --> 00:34:16,620
+ال B موجود في ال 6 اللي هي 0 انطبخ التعريف يبقى
+
+302
+00:34:16,620 --> 00:34:26,130
+صار ال 0 عبارة عن ال prime ideal in Zالـ zero is
+
+303
+00:34:26,130 --> 00:34:37,670
+prime ideal الست اللي عندنا هذه and Z طيب
+
+304
+00:34:37,670 --> 00:34:44,410
+Z هذه ring واحدة مافيش غيرها فلو روحنا و قولنا ..
+
+305
+00:34:44,410 --> 00:34:51,930
+قولنا بدنا ناخد أكثر من ring يعني ممكنالكلام هذا
+
+306
+00:34:51,930 --> 00:34:56,930
+يحصل لمجموعة من الرمز والله مافيش غير هذا الكلام
+
+307
+00:34:56,930 --> 00:35:04,350
+للـ Z هذا السؤال اللي بدنا نجاوز عليه بالمثال رقم
+
+308
+00:35:04,350 --> 00:35:14,670
+اتنين example اتنين يقول ما يتلف ال R is an
+
+309
+00:35:14,670 --> 00:35:18,570
+integral domain
+
+310
+00:35:20,700 --> 00:35:28,040
+لو كان الـR integral domain then الـ zero is a
+
+311
+00:35:28,040 --> 00:35:41,240
+prime ID is a prime ID of R solution
+
+312
+00:35:41,240 --> 00:35:46,180
+عندنا
+
+313
+00:35:46,180 --> 00:35:55,450
+R integral domain يبقى assumeأفترضه أن الـR is an
+
+314
+00:35:55,450 --> 00:36:03,310
+integral domain يعني مافيش فيها قواسم لصفر إلا
+
+315
+00:36:03,310 --> 00:36:11,570
+الصفر نفسه، مظبوط؟ طيب، بدي أخد عنصرين في R،
+
+316
+00:36:11,570 --> 00:36:16,990
+فهتحاصل ضربه موجود وين؟ في الـ0، يبقى بدالي أقوله
+
+317
+00:36:16,990 --> 00:36:26,220
+let الـA و الـBموجودات في R such that ال A في ال B
+
+318
+00:36:26,220 --> 00:36:35,860
+موجود في Zero يبقى then ال A في ال B بتساوي Zero
+
+319
+00:36:35,860 --> 00:36:44,120
+بقى وجود اغاناط هذا يعني ان ال A تساوي ZeroAll الـ
+
+320
+00:36:44,120 --> 00:36:49,720
+P تساوي Zero؟ طيب ليه؟ لأن الـ R Integral Domain
+
+321
+00:36:49,720 --> 00:36:55,240
+لو ماكنش Integral Domain كلامي هذا غلط تمام يبقى
+
+322
+00:36:55,240 --> 00:37:05,940
+هذا .. هذا because because الـ R is an Integral
+
+323
+00:37:05,940 --> 00:37:13,560
+Domain هذا الكلام صحيحلشان هذا integral الدولي
+
+324
+00:37:13,560 --> 00:37:21,260
+مدام هات هذا يعني ان ال a موجود في ال ideal اللي
+
+325
+00:37:21,260 --> 00:37:28,340
+هو ال zero او ال b موجود في ال zero هذا بدي
+
+326
+00:37:28,340 --> 00:37:39,560
+اعطيكوا ان ال zero is a prime ideal in R يبقى ايضا
+
+327
+00:37:39,560 --> 00:37:46,580
+صحيح انك شغلتينالشغل الأولى انه ال ideal zero هو
+
+328
+00:37:46,580 --> 00:37:51,080
+prime ideal في ال six of integers من الملاحظة اللي
+
+329
+00:37:51,080 --> 00:37:56,820
+هناك و بعد هيك كمان ال zero is a prime ideal في ال
+
+330
+00:37:56,820 --> 00:38:03,740
+integrant domain طيب بدنا نروح لك لمثال آخر تمام؟
+
+331
+00:38:03,740 --> 00:38:12,060
+و هذا يكون ثالثثلاثة بنات اللي هو سؤال خمس تاشر من
+
+332
+00:38:12,060 --> 00:38:27,860
+الكتاب بيقولت الـ A B A ring with unity in one if
+
+333
+00:38:27,860 --> 00:38:43,570
+ال A is an ideaلو كان ال A عبارة عن ID of R and ال
+
+334
+00:38:43,570 --> 00:38:53,690
+F الواحد موجود في ال A موجود في ال A then ال A
+
+335
+00:38:53,690 --> 00:39:00,730
+تساوي R سؤال
+
+336
+00:39:00,730 --> 00:39:08,220
+مرتينعندنا الـ ring of unity هي الواحد قال ال إيه
+
+337
+00:39:08,220 --> 00:39:13,280
+ال ideal؟ الواحد اللي هو ال unity موجود في ال
+
+338
+00:39:13,280 --> 00:39:19,140
+ideal فلإن حد دلوقتي يبقى ال ideal إيه؟ بده يسوي
+
+339
+00:39:19,140 --> 00:39:24,680
+ال ring كلها ال ring كلها؟ أه ال ring كلها طب
+
+340
+00:39:24,680 --> 00:39:29,150
+خليني أسأل سؤال في مبادئ الرياضياتكيف بجينا الناس
+
+341
+00:39:29,150 --> 00:39:37,630
+تثبت ان two sets are equal يعني كل واحدة فيهم
+
+342
+00:39:37,630 --> 00:39:41,990
+subset من التانية يعني في الاتجاهين ان حدث ذلك
+
+343
+00:39:41,990 --> 00:39:48,070
+بقول له two sets are equal طيب تمام يبقى solution
+
+344
+00:39:48,070 --> 00:39:55,450
+بدي اكتب اول معادلة و اشوف ايش رأيكوا فيها صح هذا
+
+345
+00:39:55,450 --> 00:40:05,590
+بناnon-ideally proper يعني أجال من R تمام يبقى هذه
+
+346
+00:40:05,590 --> 00:40:12,330
+المعادلة رقم واحد إذا كنت أثبت أنها subset من A
+
+347
+00:40:12,330 --> 00:40:16,350
+بكون جبت الاتجاه الثاني وبالثاني بصير ال A تساوي
+
+348
+00:40:16,350 --> 00:40:24,030
+مين؟ تساوي ال R طيب الآن بدي أقول خد لل R موجودة
+
+349
+00:40:24,030 --> 00:40:31,110
+في A عشوائيةلتحاول اثبت ان ال R هذه موجودة في ايه؟
+
+350
+00:40:31,110 --> 00:40:43,110
+موجودة في ايه؟ then ال R تساوم واحد في R، صح؟ طيب،
+
+351
+00:40:43,110 --> 00:40:53,010
+تساوم R في واحد، مظبوط؟ انا ادعي ان هذه موجودة في
+
+352
+00:40:53,010 --> 00:40:55,230
+ايه؟ اكيد؟
+
+353
+00:40:56,980 --> 00:41:00,800
+عشان ال I دي ال واحد عشان ال A ال واحد في A وال A
+
+354
+00:41:00,800 --> 00:41:05,940
+I دي يبقى لو جبت اي element من الأرض ضربته في هذا
+
+355
+00:41:05,940 --> 00:41:10,940
+الواحد بيكون موجود في A صح ولا لا؟ ممتاز جدا يبقى
+
+356
+00:41:10,940 --> 00:41:18,380
+هذا موجود في السبب because ان الواحد موجود في A
+
+357
+00:41:18,380 --> 00:41:28,560
+and ال A is an I Dطيب يبقى العلم الـ R اللي موجود
+
+358
+00:41:28,560 --> 00:41:34,940
+في R لقيته موجود وين؟ ايش تفسيركم لهذا الكلام؟ R
+
+359
+00:41:34,940 --> 00:41:44,680
+صبست من A يبقى هنا R صبست من A و هذه العناقة رقم 2
+
+360
+00:41:44,680 --> 00:41:54,720
+اروح بقوله هنا from واحد و اتنين we haveيبقى بده
+
+361
+00:41:54,720 --> 00:42:02,900
+يصير الـA تساوي A يبقى يا بنات من الآن فصاعدا لو
+
+362
+00:42:02,900 --> 00:42:08,560
+قدرت أثبت ان ال unity موجود في ال ideal يبقى ال
+
+363
+00:42:08,560 --> 00:42:13,100
+ideal بده يساوي مين؟ بده يساوي ال ring الأصلية
+
+364
+00:42:13,100 --> 00:42:21,180
+تمام تمام طيب هذا كان مثال ثلاثة بدنا نروح لمثال
+
+365
+00:42:21,180 --> 00:42:21,980
+أربع
+
+366
+00:42:25,420 --> 00:42:34,000
+مثال أربع نعطيكم مثال عادلين أعتقد أن هذا سهل
+
+367
+00:42:34,000 --> 00:42:43,440
+بالنسبة لكم لأن وقته مثل فيه الظروف طيب
+
+368
+00:42:43,440 --> 00:42:53,060
+المثال بيقول ما يعني يبقى example أربع بيقول ايه
+
+369
+00:42:53,060 --> 00:43:03,580
+little aمثل A تساوي Z ده اتناشى then the only
+
+370
+00:43:03,580 --> 00:43:14,320
+ideals then the only ideals ideals
+
+371
+00:43:14,320 --> 00:43:22,840
+of AA قالوا
+
+372
+00:43:22,840 --> 00:43:28,910
+لكم Z ده اتناشىفيها مجموعة من ال ideals بدنا
+
+373
+00:43:28,910 --> 00:43:37,130
+نعرفهم تقدروا تجيبولي أسفل الأتنين ال zero وين؟
+
+374
+00:43:37,130 --> 00:43:45,050
+و الأرض؟ صح مش هيجيل من نفسها يبقى هدول قدفة حاجة
+
+375
+00:43:45,050 --> 00:43:48,650
+اللي لازم كل واحد حتى لو ماجريش جبر يكون عارفه
+
+376
+00:43:48,650 --> 00:43:55,540
+يبقى هنا ال zero اللي هو ال trivial idealوزد اتناش
+
+377
+00:43:55,540 --> 00:44:02,440
+it's ال تمام ومين كمان ال principle ideal
+
+378
+00:44:02,440 --> 00:44:09,360
+generated by اتنين مين عناسره؟ Zero, اتنين, اربع,
+
+379
+00:44:09,540 --> 00:44:17,540
+ستة, تمانية, اهاشران كفي أليس هذا هو اتنين زد
+
+380
+00:44:17,540 --> 00:44:25,790
+اتناش؟ صح؟ طيبلو قلت ال principle ideal generated
+
+381
+00:44:25,790 --> 00:44:33,770
+by تلاتة، Zero، تلاتة، ستة، تسعة، أليس هو ال ideal
+
+382
+00:44:33,770 --> 00:44:42,590
+اللي هو تلاتة زي اتناش؟ طيب، الأربع ال principle
+
+383
+00:44:42,590 --> 00:44:50,820
+ideal generated by أربع اللي هو أربع زي اتناشالـ
+
+384
+00:44:50,820 --> 00:44:56,040
+principle ideal generated by ستة، Zero وستة، فيش
+
+385
+00:44:56,040 --> 00:45:04,760
+غيرهم؟ يبقى هذا ستة زد اتناش.في غيرهم؟ مش عارفين،
+
+386
+00:45:04,760 --> 00:45:11,540
+يمكن يكون فيه. يمكن يكون فيه الله أعلم.ش اسم كنت
+
+387
+00:45:11,540 --> 00:45:25,080
+قاعد؟ ملك اشطة رفعيبقى ملكتات داعي أنها لا تملك كل
+
+388
+00:45:25,080 --> 00:45:32,980
+هذه الـ Ideal على هذه الرنجة نشوف الموافقين على
+
+389
+00:45:32,980 --> 00:45:36,220
+رأيها، والله مش الموافقين تعالوا نشوف.
+
+390
+00:45:39,140 --> 00:45:43,780
+الآن أنا عند اتنين، تلاتة، اربعة، خمسة، مش اتنين،
+
+391
+00:45:43,780 --> 00:45:48,860
+تلاتة، اربعة، ستة، الخمسة مش موجودة.والسبعة مش
+
+392
+00:45:48,860 --> 00:45:53,460
+موجودة والتمانية والتسعة والعشرة كلهم مش موجودات
+
+393
+00:45:53,460 --> 00:45:57,540
+والاحداشة كمان مع ال principle ideal generated by
+
+394
+00:45:57,540 --> 00:46:04,420
+احداشة طبعا طيب يبقى اللي مش موجودات هدول بدهم
+
+395
+00:46:04,420 --> 00:46:10,880
+يساووا كل واحد اسئلة واحد من هاللي موجودة ولا لا
+
+396
+00:46:10,880 --> 00:46:17,100
+بس مش كل واحد هو البعض ليس بالضرورة الكل شوفوا كده
+
+397
+00:46:17,670 --> 00:46:27,510
+مثلا لو جيتك وقلت بدأ أخد عشرة زد اتناش عشرة زد
+
+398
+00:46:27,510 --> 00:46:32,350
+اتناش اللي مش موجودة هنا هذه بدها تساوي عشرة في
+
+399
+00:46:32,350 --> 00:46:38,950
+zero في zero عشرة في واحد يبقى عشرة عشرة في اتنين
+
+400
+00:46:38,950 --> 00:46:47,100
+تمامية ممتاز عشرة في تلاتةتلاتين، شيلي أربعة
+
+401
+00:46:47,100 --> 00:46:53,320
+وعشرين، بيظل ستة، عشرة في أربعة، بيظل اربعين،
+
+402
+00:46:53,320 --> 00:46:57,280
+تلاتة في اتناشر، بيظل ستة وتلاتين، بيظل اربعة،
+
+403
+00:46:57,280 --> 00:47:02,300
+عشرة في خمسة، بيظل خمسين، شيلي أربعة في اتناشر،
+
+404
+00:47:02,300 --> 00:47:13,020
+بيظل اتنين، عشرة في ستة، ستين، ستين، فلسنا، يبقى
+
+405
+00:47:13,020 --> 00:47:22,830
+رجالفيش غيرهم أليس هذا هو هذا حرفيا يبقى هذا بده
+
+406
+00:47:22,830 --> 00:47:32,290
+يساوي اتنين زي اتناش بنفس الطريقة هنا في عندنا من؟
+
+407
+00:47:32,290 --> 00:47:39,630
+في عندنا بالعشرة زي اتناش التمانية والتسعة زي
+
+408
+00:47:39,630 --> 00:47:47,570
+اتناش التسعة زي اتناشبدي ساوي تلاتة زد اتناش
+
+409
+00:47:47,570 --> 00:47:56,270
+وزيادة على ذلك and التمانية زد اتناش بدي ساوي
+
+410
+00:47:56,270 --> 00:48:05,070
+الأربعة زد اتناش يبقى هدول التسعة والتمانية مظهروش
+
+411
+00:48:05,070 --> 00:48:10,890
+إلي هنا لأنهم موجوداتهم مش داري هذا ال principle
+
+412
+00:48:10,890 --> 00:48:15,060
+ideal generated by أربعةوهذا ال principle ideal
+
+413
+00:48:15,060 --> 00:48:18,940
+generated by تلاتة وهذا ال principle ideal
+
+414
+00:48:18,940 --> 00:48:25,460
+generated by اتنين وحداشر
+
+415
+00:48:25,460 --> 00:48:37,280
+ماشي انا ادعي الان انا ادعي مياتي ان خمسة زي اتناش
+
+416
+00:48:37,280 --> 00:48:45,830
+تساوي سبعة زي اتناشتساوي 11 زد 12 تساوي زد 12
+
+417
+00:48:45,830 --> 00:48:50,830
+itself جاربعة ده الكل هم ال prize الخمسة و السبعة
+
+418
+00:48:50,830 --> 00:48:54,910
+و الأحداشر عدد أوليها اضرب في كل أنصر هيطلع عندك
+
+419
+00:48:54,910 --> 00:49:03,010
+مين؟ زد 12 itself تمام؟ إذا بدنا نروح نعمل شبكية
+
+420
+00:49:03,010 --> 00:49:11,550
+لبين لل ideals هدول اه يبقى هنا بروح بقولهThe
+
+421
+00:49:11,550 --> 00:49:26,010
+lattice of ideals in Z12 is ببدأ من ات اللي هو Z12
+
+422
+00:49:26,010 --> 00:49:34,450
+الول امام بدي اتفرع منها two ideals ال ideal الأول
+
+423
+00:49:34,450 --> 00:49:44,040
+اتنين Z12الأيديل التاني ثلاثة زد اتناش في بينهم
+
+424
+00:49:44,040 --> 00:49:53,020
+تقاطع و لا عنصر تمام؟ هذه بدي يجي منها مين؟ أربعة
+
+425
+00:49:53,020 --> 00:50:00,520
+زد اتناش لإن الأربعة زد اتناش صاب ست والأربعة زد
+
+426
+00:50:00,520 --> 00:50:08,220
+اتناش هي صاب ست من الاتنين تمام؟ هذه ستة زد اتناشو
+
+427
+00:50:08,220 --> 00:50:16,340
+هذه صبست من مين؟ ستة زد اتنين صبست من تلاتة هذه
+
+428
+00:50:16,340 --> 00:50:24,300
+الستة وهذه التلاتة مش عاجزاكم بس و ستة هذه صبست من
+
+429
+00:50:24,300 --> 00:50:33,520
+اتنين ولا لا؟ طيب هنا ال zero صبست من هذه و صبست
+
+430
+00:50:33,520 --> 00:50:39,540
+من هذه ولا لا؟يبقى هيه مننا شبكية لل sub-ideals
+
+431
+00:50:39,540 --> 00:50:43,720
+اللي عندنا تمام؟ كله يبقى هذي بيسميها اللي هي
+
+432
+00:50:43,720 --> 00:50:49,900
+lattice لل ideals ليزد اتناش السؤال هو وين ال
+
+433
+00:50:49,900 --> 00:50:59,000
+maximum ideal هنا؟ proper ولا يوجد اكبر منها اتنين
+
+434
+00:50:59,000 --> 00:51:05,110
+زد اتناش و تلاتة زد اتناشيبقى هنا بروح بقوله from
+
+435
+00:51:05,110 --> 00:51:17,330
+this lattice the maximum ideals
+
+436
+00:51:17,330 --> 00:51:30,410
+are اتنين زد اتناش and تلاتة زد اتناش ولا يوجد
+
+437
+00:51:30,410 --> 00:51:39,720
+غيرهم maximumطبعا؟ طيب سؤال الأخير وبيسألوني هذه
+
+438
+00:51:39,720 --> 00:51:47,720
+المحاضرة في واحد فيهم من ال ideals هدود اللي
+
+439
+00:51:47,720 --> 00:51:52,340
+تركناهم اللي هو الخمسة والسبعة والإحدى عشر بيكون
+
+440
+00:51:52,340 --> 00:51:58,680
+maximum ideal أو ال prime ideal السبعة
+
+441
+00:51:58,680 --> 00:52:03,450
+من الستة أنا بتكلم عن السبعةوالخمسة والإحدى عشر
+
+442
+00:52:03,450 --> 00:52:09,410
+زدها اتنين. هذا طبعا كله يستوي من ال ring الأصلي؟
+
+443
+00:52:09,410 --> 00:52:15,870
+إذا بنفع يكون ideal او maximal ideal؟ ليش ان الشرط
+
+444
+00:52:15,870 --> 00:52:21,690
+الأول لا يتحقق و هو انه proper ideal. لذا بروح
+
+445
+00:52:21,690 --> 00:52:34,640
+بقول not that. Not that ان خمسةزد اتناش وسبع زد
+
+446
+00:52:34,640 --> 00:52:49,260
+اتناش and احداشر زد اتناش are not a prime and not
+
+447
+00:52:49,260 --> 00:52:57,780
+maximal ideals
+
+448
+00:52:59,650 --> 00:53:06,110
+because they
+
+449
+00:53:06,110 --> 00:53:13,330
+are not
+
+450
+00:53:13,330 --> 00:53:22,310
+proper or because they are improper دعواتك كلها
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..65cfcf6858171496c040188d56d87f181b661974
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4703, "start": 21.13, "end": 47.03, "text": "بالله الرحمن الرحيم انتهينا الآن من ال three chapters و الان نمشي لل chapter الرابع اللي بتحدث عن ال ring homomorphism لنعطي تعريف لل ring homomorphism و نشوف وجه الاختلاف بينه و بين ال group homomorphism بقول لو عندى two rings R و S", "tokens": [3555, 6027, 43761, 34892, 5016, 27842, 34892, 5016, 32640, 16472, 47395, 1829, 8315, 6024, 48506, 9154, 2423, 1045, 20013, 4032, 2423, 7649, 8717, 2304, 8592, 1829, 24976, 7187, 34892, 16758, 3615, 13672, 1829, 39894, 24401, 12984, 18871, 2423, 4875, 3655, 32702, 1434, 5296, 1863, 3615, 9566, 1829, 37279, 16572, 5172, 24976, 4875, 3655, 32702, 1434, 4032, 8717, 8592, 38688, 49610, 3224, 2423, 47283, 2655, 15040, 5172, 49374, 3224, 4032, 49374, 2423, 1594, 3655, 32702, 1434, 4724, 39648, 45164, 43242, 7578, 732, 11136, 497, 4032, 318], "avg_logprob": -0.20585028671248015, "compression_ratio": 1.72, "no_speech_prob": 0.0, "words": [{"start": 21.13, "end": 21.49, "word": "بالله", "probability": 0.6963704427083334}, {"start": 21.49, "end": 21.89, "word": " الرحمن", "probability": 0.9189453125}, {"start": 21.89, "end": 22.51, "word": " الرحيم", "probability": 0.9866536458333334}, {"start": 22.51, "end": 24.81, "word": " انتهينا", "probability": 0.8206787109375}, {"start": 24.81, "end": 25.29, "word": " الآن", "probability": 0.772216796875}, {"start": 25.29, "end": 25.59, "word": " من", "probability": 0.9853515625}, {"start": 25.59, "end": 25.71, "word": " ال", "probability": 0.85986328125}, {"start": 25.71, "end": 25.95, "word": " three", "probability": 0.65966796875}, {"start": 25.95, "end": 26.67, "word": " chapters", "probability": 0.93115234375}, {"start": 26.67, "end": 27.27, "word": " و", "probability": 0.72607421875}, {"start": 27.27, "end": 27.51, "word": " الان", "probability": 0.523345947265625}, {"start": 27.51, "end": 27.79, "word": " نمشي", "probability": 0.58770751953125}, {"start": 27.79, "end": 27.99, "word": " لل", "probability": 0.7939453125}, {"start": 27.99, "end": 28.41, "word": " chapter", "probability": 0.9482421875}, {"start": 28.41, "end": 29.07, "word": " الرابع", "probability": 0.8367513020833334}, {"start": 29.07, "end": 29.57, "word": " اللي", "probability": 0.769287109375}, {"start": 29.57, "end": 30.25, "word": " بتحدث", "probability": 0.8902994791666666}, {"start": 30.25, "end": 30.57, "word": " عن", "probability": 0.9775390625}, {"start": 30.57, "end": 30.79, "word": " ال", "probability": 0.8486328125}, {"start": 30.79, "end": 31.17, "word": " ring", "probability": 0.8828125}, {"start": 31.17, "end": 32.95, "word": " homomorphism", "probability": 0.91845703125}, {"start": 32.95, "end": 34.95, "word": " لنعطي", "probability": 0.76708984375}, {"start": 34.95, "end": 35.41, "word": " تعريف", "probability": 0.9095052083333334}, {"start": 35.41, "end": 35.61, "word": " لل", "probability": 0.73193359375}, {"start": 35.61, "end": 35.85, "word": " ring", "probability": 0.92529296875}, {"start": 35.85, "end": 36.79, "word": " homomorphism", "probability": 0.9563802083333334}, {"start": 36.79, "end": 37.29, "word": " و", "probability": 0.91650390625}, {"start": 37.29, "end": 37.55, "word": " نشوف", "probability": 0.9765625}, {"start": 37.55, "end": 37.99, "word": " وجه", "probability": 0.967529296875}, {"start": 37.99, "end": 39.07, "word": " الاختلاف", "probability": 0.91162109375}, {"start": 39.07, "end": 39.73, "word": " بينه", "probability": 0.98828125}, {"start": 39.73, "end": 39.97, "word": " و", "probability": 0.80419921875}, {"start": 39.97, "end": 40.37, "word": " بين", "probability": 0.98388671875}, {"start": 40.37, "end": 40.77, "word": " ال", "probability": 0.66796875}, {"start": 40.77, "end": 41.15, "word": " group", "probability": 0.990234375}, {"start": 41.15, "end": 42.59, "word": " homomorphism", "probability": 0.9615885416666666}, {"start": 42.59, "end": 44.37, "word": " بقول", "probability": 0.947998046875}, {"start": 44.37, "end": 44.55, "word": " لو", 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"word": " من", "probability": 0.9765625}, {"start": 50.41, "end": 50.91, "word": " R", "probability": 0.87841796875}, {"start": 50.91, "end": 51.35, "word": " إلى", "probability": 0.93798828125}, {"start": 51.35, "end": 51.89, "word": " S", "probability": 0.98291015625}, {"start": 51.89, "end": 52.85, "word": " يبقى", "probability": 0.9600830078125}, {"start": 52.85, "end": 53.13, "word": " الـ", "probability": 0.858642578125}, {"start": 53.13, "end": 53.27, "word": " Phi", "probability": 0.7470703125}, {"start": 53.27, "end": 53.67, "word": " بقول", "probability": 0.614501953125}, {"start": 53.67, "end": 54.13, "word": " عنها", "probability": 0.994873046875}, {"start": 54.13, "end": 54.59, "word": " Ring", "probability": 0.533203125}, {"start": 54.59, "end": 55.77, "word": " Homomorphism", "probability": 0.9239908854166666}, {"start": 55.77, "end": 56.35, "word": " كلمة", "probability": 0.9278971354166666}, {"start": 56.35, "end": 57.41, "word": " Homomorphism", "probability": 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"end": 65.71, "word": " لجميع", "probability": 0.986572265625}, {"start": 65.71, "end": 66.59, "word": " عناصر", "probability": 0.9586588541666666}, {"start": 66.59, "end": 66.87, "word": " A", "probability": 0.89453125}, {"start": 66.87, "end": 67.29, "word": " وB", "probability": 0.816650390625}, {"start": 67.29, "end": 67.53, "word": " اللي", "probability": 0.883056640625}, {"start": 67.53, "end": 68.09, "word": " موجودة", "probability": 0.989501953125}, {"start": 68.09, "end": 68.33, "word": " في", "probability": 0.97265625}, {"start": 68.33, "end": 68.73, "word": " R", "probability": 0.93603515625}, {"start": 68.73, "end": 69.07, "word": " We", "probability": 0.339599609375}, {"start": 69.07, "end": 69.59, "word": " have", "probability": 0.94873046875}, {"start": 69.59, "end": 70.51, "word": " condition", "probability": 0.5341796875}, {"start": 70.51, "end": 71.11, "word": " الأول", "probability": 0.9638671875}, {"start": 71.11, "end": 71.47, "word": " Phi", "probability": 0.9267578125}, {"start": 71.47, "end": 71.81, "word": " of", "probability": 0.88671875}, {"start": 71.81, "end": 72.15, "word": " A", "probability": 0.9755859375}, {"start": 72.15, "end": 72.61, "word": " زائد", "probability": 0.8357747395833334}, {"start": 72.61, "end": 72.89, "word": " B", "probability": 0.3994140625}, {"start": 72.89, "end": 73.35, "word": " بساوي", "probability": 0.59478759765625}, {"start": 73.35, "end": 73.69, "word": " Phi", "probability": 0.8935546875}, {"start": 73.69, "end": 74.01, "word": " of", "probability": 0.958984375}, {"start": 74.01, "end": 74.27, "word": " A", "probability": 0.98876953125}, {"start": 74.27, "end": 74.63, "word": " زائد", "probability": 0.93408203125}, {"start": 74.63, "end": 74.97, "word": " Phi", "probability": 0.9482421875}, {"start": 74.97, "end": 75.27, "word": " of", "probability": 0.9677734375}, {"start": 75.27, "end": 75.51, "word": " B", "probability": 0.998046875}], "temperature": 1.0}, {"id": 3, "seek": 10470, "start": 75.9, "end": 104.7, "text": "والـ Condition التاني Phi of A في B بيكون Phi of A مضروب في Phi of B لجميع قيم A وB الموجودة في R يبدأ إذا Phi حققت هذين الشرتين بقول عن Phi Homomorphism إذا حصل زيادة على ذلك ما هي هذه الزيادة؟ كانت الـ Function Phi هي one to one and unto", "tokens": [2407, 6027, 39184, 21793, 849, 16712, 7649, 1829, 41435, 295, 316, 8978, 363, 4724, 1829, 30544, 41435, 295, 316, 3714, 11242, 32887, 3555, 8978, 41435, 295, 363, 5296, 7435, 2304, 40228, 12174, 32640, 316, 4032, 33, 9673, 29245, 23328, 3660, 8978, 497, 7251, 44510, 10721, 11933, 15730, 41435, 11331, 4587, 38149, 8032, 8848, 9957, 25124, 43500, 9957, 4724, 39648, 18871, 41435, 20903, 32702, 1434, 11933, 15730, 11331, 36520, 30767, 1829, 18513, 3660, 15844, 29910, 23275, 19446, 39896, 29538, 6024, 110, 1829, 18513, 3660, 22807, 25961, 2655, 2423, 39184, 11166, 882, 41435, 39896, 472, 281, 472, 293, 16521], "avg_logprob": -0.24202806274501645, "compression_ratio": 1.5260869565217392, "no_speech_prob": 0.0, 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97.54, "end": 98.12, "word": " ذلك", "probability": 0.99169921875}, {"start": 98.12, "end": 98.38, "word": " ما", "probability": 0.70654296875}, {"start": 98.38, "end": 98.66, "word": " هي", "probability": 0.935546875}, {"start": 98.66, "end": 99.1, "word": " هذه", "probability": 0.97998046875}, {"start": 99.1, "end": 100.3, "word": " الزيادة؟", "probability": 0.9080403645833334}, {"start": 100.3, "end": 100.78, "word": " كانت", "probability": 0.94140625}, {"start": 100.78, "end": 101.04, "word": " الـ", "probability": 0.769775390625}, {"start": 101.04, "end": 101.56, "word": " Function", "probability": 0.72998046875}, {"start": 101.56, "end": 102.02, "word": " Phi", "probability": 0.90869140625}, {"start": 102.02, "end": 102.36, "word": " هي", "probability": 0.8447265625}, {"start": 102.36, "end": 102.68, "word": " one", "probability": 0.363525390625}, {"start": 102.68, "end": 103.02, "word": " to", "probability": 0.8681640625}, {"start": 103.02, "end": 103.44, "word": " one", "probability": 0.9462890625}, {"start": 103.44, "end": 104.1, "word": " and", "probability": 0.8955078125}, {"start": 104.1, "end": 104.7, "word": " unto", "probability": 0.471435546875}], "temperature": 1.0}, {"id": 4, "seek": 13269, "start": 105.1, "end": 132.7, "text": "نبقى الخيب ده سميها isomorphism كلمة homomorphism أخدتوها في ال groups وكان معناها التشاكل لكن isomorphism التشاكل النماطي إيش يعني التشاكل النماطي هي ترجمة عربية، عربية أنا بدي المعنى الرياضي لها ف homomorphism في علاقة ما بين ring و ring أخرى", "tokens": [1863, 3555, 4587, 7578, 33962, 1829, 3555, 11778, 3224, 8608, 2304, 1829, 11296, 307, 32702, 1434, 9122, 19528, 3660, 3655, 32702, 1434, 5551, 9778, 3215, 2655, 2407, 11296, 8978, 2423, 3935, 4032, 41361, 20449, 8315, 11296, 16712, 8592, 995, 28820, 44381, 307, 32702, 1434, 16712, 8592, 995, 28820, 28239, 2304, 41193, 1829, 11933, 1829, 8592, 37495, 22653, 16712, 8592, 995, 28820, 28239, 2304, 41193, 1829, 39896, 6055, 47341, 46007, 6225, 25513, 10632, 12399, 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order اللي يساوي خمسة يبقى هذه فيها أربعة عناصر ال order فيها اللي يساوي خمسة إذا فيها هذه unity يبقى ال ring التانية فيها unity وباختصار", "tokens": [3555, 2655, 5016, 4587, 4587, 25124, 2288, 9566, 9957, 8032, 8848, 12610, 5551, 4117, 2655, 2288, 9154, 39896, 4117, 19446, 3615, 1863, 16254, 8592, 44381, 11933, 15730, 307, 32702, 1434, 7251, 3555, 4587, 7578, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 8978, 2423, 4875, 16247, 12610, 7578, 10874, 3215, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 8978, 2423, 4875, 6024, 104, 7649, 10632, 34105, 11933, 15730, 8978, 11296, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 5551, 25513, 27884, 18871, 33546, 2288, 2423, 1668, 13672, 1829, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 7251, 3555, 4587, 7578, 29538, 8978, 11296, 5551, 25513, 27884, 18871, 33546, 2288, 2423, 1668, 8978, 11296, 13672, 1829, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 11933, 15730, 8978, 11296, 29538, 18205, 7251, 3555, 4587, 7578, 2423, 4875, 16712, 7649, 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{"start": 377.09, "end": 377.47, "word": " one", "probability": 0.9453125}, {"start": 377.47, "end": 378.41, "word": " operation", "probability": 0.91845703125}, {"start": 378.41, "end": 378.69, "word": " أو", "probability": 0.5419921875}, {"start": 378.69, "end": 378.91, "word": " one", "probability": 0.94482421875}, {"start": 378.91, "end": 379.53, "word": " binary", "probability": 0.82568359375}, {"start": 379.53, "end": 380.65, "word": " operation", "probability": 0.94189453125}, {"start": 380.65, "end": 381.45, "word": " طيب", "probability": 0.8003743489583334}, {"start": 381.45, "end": 381.73, "word": " ال", "probability": 0.95458984375}, {"start": 381.73, "end": 382.35, "word": " conditioning", "probability": 0.52001953125}, {"start": 382.35, "end": 383.35, "word": " التاني", "probability": 0.86865234375}], "temperature": 1.0}, {"id": 14, "seek": 41138, "start": 384.14, "end": 411.38, "text": "فاي of K في M حسب التعريف يبقى K في M موديولو N من ال number three يبقى ده K موديولو N مضروب في M موديولو N ال K موديولو N هي ديمين فاي of K", "tokens": [5172, 47302, 295, 591, 8978, 376, 11331, 35457, 16712, 3615, 16572, 5172, 7251, 3555, 4587, 7578, 591, 8978, 376, 3714, 2407, 16254, 12610, 2407, 426, 9154, 2423, 1230, 1045, 7251, 3555, 4587, 7578, 11778, 3224, 591, 3714, 2407, 16254, 12610, 2407, 426, 3714, 11242, 32887, 3555, 8978, 376, 3714, 2407, 16254, 12610, 2407, 426, 2423, 591, 3714, 2407, 16254, 12610, 2407, 426, 39896, 11778, 32640, 9957, 6156, 47302, 295, 591], "avg_logprob": -0.261003530361283, "compression_ratio": 1.703125, "no_speech_prob": 0.0, "words": [{"start": 384.14, "end": 385.04, "word": "فاي", "probability": 0.314697265625}, {"start": 385.04, "end": 385.52, "word": " of", "probability": 0.25830078125}, {"start": 385.52, "end": 386.02, "word": " K", "probability": 0.426025390625}, {"start": 386.02, "end": 386.8, "word": " في", "probability": 0.82666015625}, {"start": 386.8, "end": 387.04, "word": " M", "probability": 0.923828125}, {"start": 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434.65, "word": " يعتبر", "probability": 0.9534505208333334}, {"start": 434.65, "end": 435.17, "word": " مثال", "probability": 0.867431640625}, {"start": 435.17, "end": 435.91, "word": " بصير", "probability": 0.8365885416666666}, {"start": 435.91, "end": 436.99, "word": " ومباشر", "probability": 0.928125}, {"start": 436.99, "end": 437.97, "word": " ومافيش", "probability": 0.966552734375}, {"start": 437.97, "end": 438.61, "word": " فيه", "probability": 0.98046875}, {"start": 438.61, "end": 439.37, "word": " تفكير", "probability": 0.99609375}], "temperature": 1.0}, {"id": 16, "seek": 46889, "start": 439.93, "end": 468.89, "text": "ننتقل إلى مثال آخر example two بيقول define a function define a function Phi من ال set of complex numbers إلى ال set of complex numbers نفسها by Phi of ال a زائد ال b في ال I يساوي ال a", "tokens": [1863, 29399, 4587, 1211, 30731, 50113, 6027, 19753, 34740, 1365, 732, 4724, 1829, 39648, 6964, 257, 2445, 6964, 257, 2445, 41435, 9154, 2423, 992, 295, 3997, 3547, 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{"start": 456.59, "end": 456.93, "word": " ال", "probability": 0.76953125}, {"start": 456.93, "end": 457.31, "word": " set", "probability": 0.9736328125}, {"start": 457.31, "end": 457.75, "word": " of", "probability": 0.96728515625}, {"start": 457.75, "end": 458.49, "word": " complex", "probability": 0.88134765625}, {"start": 458.49, "end": 459.39, "word": " numbers", "probability": 0.91455078125}, {"start": 459.39, "end": 460.49, "word": " نفسها", "probability": 0.9928385416666666}, {"start": 460.49, "end": 460.91, "word": " by", "probability": 0.1925048828125}, {"start": 460.91, "end": 463.25, "word": " Phi", "probability": 0.72998046875}, {"start": 463.25, "end": 463.99, "word": " of", "probability": 0.923828125}, {"start": 463.99, "end": 464.65, "word": " ال", "probability": 0.491455078125}, {"start": 464.65, "end": 465.01, "word": " a", "probability": 0.5966796875}, {"start": 465.01, "end": 465.73, "word": " زائد", "probability": 0.7430826822916666}, {"start": 465.73, "end": 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478.51, "end": 481.13, "word": " isomorphism", "probability": 0.9064127604166666}, {"start": 481.13, "end": 485.75, "word": " كلمة", "probability": 0.9103190104166666}, {"start": 485.75, "end": 486.91, "word": " isomorphism", "probability": 0.912109375}, {"start": 486.91, "end": 487.83, "word": " هختصرها", "probability": 0.8861328125}, {"start": 487.83, "end": 488.73, "word": " ISO", "probability": 0.732421875}, {"start": 488.73, "end": 489.79, "word": " ISO", "probability": 0.31103515625}, {"start": 489.79, "end": 490.37, "word": " هحط", "probability": 0.7996419270833334}, {"start": 490.37, "end": 490.81, "word": " نقطة", "probability": 0.9112955729166666}, {"start": 490.81, "end": 491.05, "word": " يبقى", "probability": 0.7435302734375}, {"start": 491.05, "end": 492.17, "word": " تفهميني", "probability": 0.708984375}, {"start": 492.17, "end": 492.67, "word": " ان", "probability": 0.52685546875}, {"start": 492.67, "end": 493.11, "word": " هذا", "probability": 0.5810546875}, {"start": 493.11, "end": 494.37, "word": " isomorphism", "probability": 0.8160807291666666}, {"start": 494.37, "end": 495.03, "word": " يبقى", "probability": 0.8997802734375}, {"start": 495.03, "end": 495.43, "word": " عجلة", "probability": 0.69189453125}, {"start": 495.43, "end": 495.85, "word": " عن", "probability": 0.98828125}, {"start": 495.85, "end": 497.01, "word": " homomorphism", "probability": 0.9085286458333334}], "temperature": 1.0}, {"id": 18, "seek": 52602, "start": 497.34, "end": 526.02, "text": "حقق ال two conditions وزيادة على ذلك وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وان", "tokens": [5016, 4587, 4587, 2423, 732, 4487, 4032, 11622, 1829, 18513, 3660, 15844, 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2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649, 2655, 14407, 4032, 7649], "avg_logprob": -0.04027777618832058, "compression_ratio": 9.558441558441558, "no_speech_prob": 0.0, "words": [{"start": 497.34, "end": 497.88, "word": "حقق", "probability": 0.7194010416666666}, {"start": 497.88, "end": 498.1, "word": " ال", "probability": 0.95361328125}, {"start": 498.1, "end": 498.24, "word": " two", "probability": 0.55419921875}, {"start": 498.24, "end": 499.12, "word": " conditions", "probability": 0.859375}, {"start": 499.12, "end": 500.22, "word": " وزيادة", "probability": 0.9546875}, {"start": 500.22, "end": 500.42, "word": " على", "probability": 0.77099609375}, {"start": 500.42, "end": 500.98, "word": " ذلك", "probability": 0.99169921875}, {"start": 500.98, "end": 502.7, "word": " وانتوا", "probability": 0.53314208984375}, {"start": 502.7, "end": 503.44, "word": " وانتوا", "probability": 0.803466796875}, {"start": 503.44, "end": 503.82, "word": " وانتوا", "probability": 0.9251708984375}, {"start": 503.82, "end": 503.82, "word": " وانتوا", "probability": 0.884033203125}, {"start": 503.82, "end": 504.12, "word": " وانتوا", "probability": 0.967041015625}, {"start": 504.12, "end": 504.12, "word": " وانتوا", "probability": 0.9752197265625}, {"start": 504.12, "end": 504.14, "word": " وانتوا", "probability": 0.9788818359375}, {"start": 504.14, "end": 504.22, "word": " وانتوا", "probability": 0.976318359375}, {"start": 504.22, "end": 506.14, "word": " وانتوا", "probability": 0.969970703125}, {"start": 506.14, "end": 506.88, "word": " وانتوا", "probability": 0.9661865234375}, {"start": 506.88, "end": 507.62, "word": " وانتوا", "probability": 0.97216796875}, {"start": 507.62, "end": 507.66, "word": " وانتوا", "probability": 0.979736328125}, {"start": 507.66, "end": 507.76, "word": " وانتوا", "probability": 0.985107421875}, {"start": 507.76, "end": 507.76, "word": " وانتوا", "probability": 0.98876953125}, {"start": 507.76, "end": 507.76, "word": " وانتوا", "probability": 0.9910888671875}, {"start": 507.76, "end": 507.76, "word": " وانتوا", "probability": 0.992431640625}, {"start": 507.76, "end": 507.76, "word": " وانتوا", "probability": 0.9931640625}, {"start": 507.76, "end": 507.76, "word": " وانتوا", "probability": 0.993896484375}, {"start": 507.76, "end": 507.78, "word": " وانتوا", "probability": 0.9940185546875}, {"start": 507.78, "end": 507.98, "word": " وانتوا", "probability": 0.9945068359375}, {"start": 507.98, "end": 507.98, "word": " وانتوا", "probability": 0.99462890625}, {"start": 507.98, "end": 508.0, "word": " وانتوا", "probability": 0.99462890625}, {"start": 508.0, "end": 508.76, "word": " وانتوا", "probability": 0.9947509765625}, {"start": 508.76, "end": 508.76, "word": " وانتوا", "probability": 0.9947509765625}, {"start": 508.76, "end": 509.0, "word": " وانتوا", "probability": 0.9951171875}, {"start": 509.0, "end": 509.5, "word": " وانتوا", "probability": 0.9949951171875}, {"start": 509.5, "end": 509.5, "word": " وانتوا", "probability": 0.9949951171875}, {"start": 509.5, "end": 509.5, "word": " وانتوا", "probability": 0.9949951171875}, {"start": 509.5, "end": 509.5, "word": " وانتوا", "probability": 0.9949951171875}, {"start": 509.5, "end": 509.54, "word": " وانتوا", "probability": 0.9949951171875}, {"start": 509.54, "end": 510.46, "word": " وانتوا", "probability": 0.994873046875}, {"start": 510.46, "end": 511.22, "word": " وانتوا", "probability": 0.9949951171875}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.9947509765625}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.9947509765625}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.9945068359375}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.9945068359375}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.994384765625}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.994140625}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.994384765625}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.993896484375}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.993896484375}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.9935302734375}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.9931640625}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.992919921875}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.9925537109375}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.99267578125}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.992431640625}, {"start": 511.22, "end": 511.22, "word": " وانتوا", "probability": 0.991943359375}, {"start": 511.22, "end": 511.74, "word": " وانتوا", "probability": 0.9912109375}, {"start": 511.74, "end": 512.34, "word": " وانتوا", "probability": 0.9913330078125}, {"start": 512.34, "end": 516.88, "word": " وانتوا", "probability": 0.9906005859375}, {"start": 516.88, "end": 525.88, "word": " وانتوا", "probability": 0.98974609375}, {"start": 525.88, "end": 526.02, "word": " وان", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 19, "seek": 55001, "start": 526.11, "end": 550.01, "text": "يبقى بقوله let الـA زائد الـBI والـC زائد الـDI موجودة في set of complex numbers then بتاجر أخد فايل مجموعهما A زائد BI زائد C زائد DI", "tokens": [1829, 3555, 4587, 7578, 4724, 39648, 3224, 718, 2423, 39184, 32, 30767, 16373, 3215, 2423, 39184, 33, 40, 16070, 39184, 34, 30767, 16373, 3215, 2423, 39184, 3085, 3714, 29245, 23328, 3660, 8978, 992, 295, 3997, 3547, 550, 4724, 2655, 26108, 2288, 5551, 9778, 3215, 6156, 995, 26895, 3714, 7435, 2304, 45367, 3224, 15042, 316, 30767, 16373, 3215, 23524, 30767, 16373, 3215, 383, 30767, 16373, 3215, 11953], "avg_logprob": -0.2735541151530707, "compression_ratio": 1.4068965517241379, "no_speech_prob": 0.0, "words": [{"start": 526.11, "end": 526.93, "word": "يبقى", "probability": 0.89404296875}, {"start": 526.93, "end": 527.61, "word": " بقوله", "probability": 0.78271484375}, {"start": 527.61, "end": 528.09, "word": " let", "probability": 0.438232421875}, {"start": 528.09, "end": 529.03, "word": " الـA", "probability": 0.418701171875}, {"start": 529.03, "end": 529.81, "word": " زائد", "probability": 0.6285807291666666}, {"start": 529.81, "end": 530.89, "word": " الـBI", "probability": 0.843505859375}, {"start": 530.89, "end": 531.71, "word": " والـC", "probability": 0.7975260416666666}, {"start": 531.71, "end": 532.87, "word": " زائد", "probability": 0.9591471354166666}, {"start": 532.87, "end": 533.85, "word": " الـDI", "probability": 0.9052734375}, {"start": 533.85, "end": 534.83, "word": " موجودة", "probability": 0.9862060546875}, {"start": 534.83, "end": 534.97, "word": " في", "probability": 0.89599609375}, {"start": 534.97, "end": 535.51, "word": " set", "probability": 0.1800537109375}, {"start": 535.51, "end": 535.87, "word": " of", "probability": 0.90869140625}, {"start": 535.87, "end": 536.69, "word": " complex", "probability": 0.896484375}, {"start": 536.69, "end": 537.35, "word": " numbers", "probability": 0.78955078125}, {"start": 537.35, "end": 538.31, "word": " then", "probability": 0.2255859375}, {"start": 538.31, "end": 540.31, "word": " بتاجر", "probability": 0.47491455078125}, {"start": 540.31, "end": 540.81, "word": " أخد", "probability": 0.8072916666666666}, {"start": 540.81, "end": 541.87, "word": " فايل", "probability": 0.7169596354166666}, {"start": 541.87, "end": 543.81, "word": " مجموعهما", "probability": 0.94384765625}, {"start": 543.81, "end": 544.69, "word": " A", "probability": 0.939453125}, {"start": 544.69, "end": 545.33, "word": " زائد", "probability": 0.8904622395833334}, {"start": 545.33, "end": 546.27, "word": " BI", "probability": 0.70751953125}, {"start": 546.27, "end": 547.33, "word": " زائد", "probability": 0.96533203125}, {"start": 547.33, "end": 547.91, "word": " C", "probability": 0.97802734375}, {"start": 547.91, "end": 549.09, "word": " زائد", "probability": 0.9700520833333334}, {"start": 549.09, "end": 550.01, "word": " DI", "probability": 0.943359375}], "temperature": 1.0}, {"id": 20, "seek": 58157, "start": 552.27, "end": 581.57, "text": "هذا الكلام يُسبب حسب ال complex number إذا جمعنا جزء الحقيقي مع الحقيقي والتخيّلي مع التخيّلي يبقى هذا A زائد C الحقيقي زائد B زائد D في I يبقى هذا صار كله element واحد في set of complex number جمعنا two complex number", "tokens": [3224, 15730, 2423, 28820, 10943, 7251, 10859, 35457, 3555, 11331, 35457, 2423, 3997, 1230, 11933, 15730, 10874, 2304, 3615, 8315, 10874, 11622, 38207, 21542, 38436, 38436, 20449, 21542, 38436, 38436, 16070, 2655, 9778, 1829, 11703, 20292, 20449, 16712, 9778, 1829, 11703, 20292, 7251, 3555, 4587, 7578, 23758, 316, 30767, 16373, 3215, 383, 21542, 38436, 38436, 30767, 16373, 3215, 363, 30767, 16373, 3215, 413, 8978, 286, 7251, 3555, 4587, 7578, 23758, 20328, 9640, 28242, 3224, 4478, 36764, 24401, 8978, 992, 295, 3997, 1230, 10874, 2304, 3615, 8315, 732, 3997, 1230], "avg_logprob": -0.2196180510852072, "compression_ratio": 1.8820224719101124, "no_speech_prob": 0.0, "words": [{"start": 552.27, "end": 552.73, "word": "هذا", "probability": 0.94384765625}, {"start": 552.73, "end": 553.37, "word": " الكلام", "probability": 0.9508463541666666}, {"start": 553.37, "end": 554.23, "word": " يُسبب", "probability": 0.581298828125}, {"start": 554.23, "end": 554.75, "word": " حسب", "probability": 0.903076171875}, {"start": 554.75, "end": 554.97, "word": " ال", "probability": 0.86279296875}, {"start": 554.97, "end": 555.43, "word": " complex", "probability": 0.29052734375}, {"start": 555.43, "end": 556.05, "word": " number", "probability": 0.962890625}, {"start": 556.05, "end": 556.73, "word": " إذا", "probability": 0.6304931640625}, {"start": 556.73, "end": 557.21, "word": " جمعنا", "probability": 0.846923828125}, {"start": 557.21, "end": 557.55, "word": " جزء", "probability": 0.8575846354166666}, {"start": 557.55, "end": 558.37, "word": " الحقيقي", "probability": 0.9391276041666666}, {"start": 558.37, "end": 558.63, "word": " مع", "probability": 0.955078125}, {"start": 558.63, "end": 559.45, "word": " الحقيقي", "probability": 0.9607747395833334}, {"start": 559.45, "end": 560.57, "word": " والتخيّلي", "probability": 0.7899576822916666}, {"start": 560.57, "end": 561.31, "word": " مع", "probability": 0.970703125}, {"start": 561.31, "end": 562.41, "word": " التخيّلي", "probability": 0.95966796875}, {"start": 562.41, "end": 563.29, "word": " يبقى", "probability": 0.8739013671875}, {"start": 563.29, "end": 563.75, "word": " هذا", "probability": 0.82568359375}, {"start": 563.75, "end": 564.41, "word": " A", "probability": 0.259765625}, {"start": 564.41, "end": 565.45, "word": " زائد", "probability": 0.6322835286458334}, {"start": 565.45, "end": 566.25, "word": " C", "probability": 0.6884765625}, {"start": 566.25, "end": 567.95, "word": " الحقيقي", "probability": 0.9049479166666666}, {"start": 567.95, "end": 569.01, "word": " زائد", "probability": 0.9239908854166666}, {"start": 569.01, "end": 569.67, "word": " B", "probability": 0.65869140625}, {"start": 569.67, "end": 570.79, "word": " زائد", "probability": 0.95361328125}, {"start": 570.79, "end": 571.49, "word": " D", "probability": 0.9677734375}, {"start": 571.49, "end": 571.83, "word": " في", "probability": 0.65576171875}, {"start": 571.83, "end": 572.47, "word": " I", "probability": 0.61669921875}, {"start": 572.47, "end": 574.77, "word": " يبقى", "probability": 0.92822265625}, {"start": 574.77, "end": 575.09, "word": " هذا", "probability": 0.8740234375}, {"start": 575.09, "end": 575.47, "word": " صار", "probability": 0.55633544921875}, {"start": 575.47, "end": 576.07, "word": " كله", "probability": 0.838134765625}, {"start": 576.07, "end": 576.65, "word": " element", "probability": 0.8896484375}, {"start": 576.65, "end": 577.41, "word": " واحد", "probability": 0.988037109375}, {"start": 577.41, "end": 577.61, "word": " في", "probability": 0.95703125}, {"start": 577.61, "end": 578.05, "word": " set", "probability": 0.43017578125}, {"start": 578.05, "end": 578.29, "word": " of", "probability": 0.884765625}, {"start": 578.29, "end": 578.89, "word": " complex", "probability": 0.87646484375}, {"start": 578.89, "end": 579.49, "word": " number", "probability": 0.71875}, {"start": 579.49, "end": 580.39, "word": " جمعنا", "probability": 0.8548583984375}, {"start": 580.39, "end": 580.61, "word": " two", "probability": 0.82275390625}, {"start": 580.61, "end": 581.15, "word": " complex", "probability": 0.9150390625}, {"start": 581.15, "end": 581.57, "word": " number", "probability": 0.71337890625}], "temperature": 1.0}, {"id": 21, "seek": 61051, "start": 581.93, "end": 610.51, "text": "طالع عندي one complex number بتطلع عليه تعريف تعريف بيقول ايه؟ five of a زي ال bi يسوى ال a ناقص bi اللي بدأ أسأله، في حق واحدة ضارس complex number؟ كلكم؟ و الله شغالين الحين؟ ممتاز، اللي خدتها و اللي شغالها الحين ممتاز يبقى خليني أسأل السؤال التالي، مدام أنتم ماخدينها", "tokens": [9566, 6027, 3615, 18871, 16254, 472, 3997, 1230, 39894, 9566, 1211, 3615, 47356, 37279, 16572, 5172, 37279, 16572, 5172, 4724, 1829, 39648, 1975, 1829, 3224, 22807, 1732, 295, 257, 30767, 1829, 2423, 3228, 7251, 3794, 2407, 7578, 2423, 257, 8717, 995, 4587, 9381, 3228, 13672, 1829, 47525, 10721, 5551, 3794, 10721, 43761, 12399, 8978, 11331, 4587, 36764, 24401, 3660, 48812, 9640, 3794, 3997, 1230, 22807, 28242, 24793, 22807, 4032, 21984, 13412, 17082, 6027, 9957, 21542, 9957, 22807, 3714, 2304, 2655, 31377, 12399, 13672, 1829, 16490, 3215, 2655, 11296, 4032, 13672, 1829, 13412, 17082, 6027, 11296, 21542, 9957, 3714, 2304, 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{"start": 905.07, "end": 905.79, "word": " as", "probability": 0.32080078125}, {"start": 905.79, "end": 906.01, "word": " if", "probability": 0.9755859375}, {"start": 906.01, "end": 906.31, "word": " Phi", "probability": 0.80908203125}, {"start": 906.31, "end": 906.79, "word": " is", "probability": 0.95947265625}, {"start": 906.79, "end": 907.51, "word": " one", "probability": 0.89453125}, {"start": 907.51, "end": 908.01, "word": " to", "probability": 0.9375}, {"start": 908.01, "end": 908.55, "word": " one", "probability": 0.94873046875}, {"start": 908.55, "end": 909.77, "word": " one", "probability": 0.279052734375}, {"start": 909.77, "end": 910.31, "word": " to", "probability": 0.9775390625}, {"start": 910.31, "end": 911.45, "word": " one", "probability": 0.94775390625}, {"start": 911.45, "end": 913.01, "word": " بدنا", "probability": 0.3878173828125}, {"start": 913.01, "end": 913.45, "word": " نثبت", "probability": 0.991455078125}, {"start": 913.45, "end": 913.91, "word": " صحة", 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العكسية بدي اخد صورتين متساويتين و اثبت ان اصلهم متساويتين ان حدث ذلك يبقى مصير الفاي is one point يبقى باجي بقوله SU افترض ان الفاي of A زائد ال BI بدي ساوي الفاي of C زائد ال DF", "tokens": [2304, 46456, 46538, 3660, 16472, 3224, 1975, 12984, 3555, 2655, 16472, 20328, 13063, 16095, 3714, 46456, 46538, 3660, 1975, 2407, 18863, 42213, 10632, 18863, 4117, 3794, 10632, 4724, 16254, 1975, 9778, 3215, 20328, 13063, 2655, 9957, 44650, 3794, 995, 45865, 2655, 9957, 4032, 1975, 12984, 3555, 2655, 16472, 1975, 36520, 16095, 44650, 3794, 995, 45865, 2655, 9957, 16472, 11331, 3215, 12984, 29910, 23275, 7251, 3555, 4587, 7578, 3714, 9381, 13546, 27188, 47302, 307, 472, 935, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 9872, 1975, 5172, 2655, 43042, 16472, 27188, 47302, 295, 316, 30767, 16373, 3215, 2423, 23524, 4724, 16254, 8608, 995, 45865, 27188, 47302, 295, 383, 30767, 16373, 3215, 2423, 48336], "avg_logprob": -0.2574728188307389, "compression_ratio": 1.9086294416243654, 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"probability": 0.4005126953125}, {"start": 934.01, "end": 934.77, "word": " is", "probability": 0.63623046875}, {"start": 934.77, "end": 935.15, "word": " one", "probability": 0.845703125}, {"start": 935.15, "end": 935.69, "word": " point", "probability": 0.83984375}, {"start": 935.69, "end": 936.57, "word": " يبقى", "probability": 0.9549560546875}, {"start": 936.57, "end": 936.97, "word": " باجي", "probability": 0.714599609375}, {"start": 936.97, "end": 937.77, "word": " بقوله", "probability": 0.83056640625}, {"start": 937.77, "end": 938.79, "word": " SU", "probability": 0.2236328125}, {"start": 938.79, "end": 940.37, "word": " افترض", "probability": 0.960693359375}, {"start": 940.37, "end": 941.25, "word": " ان", "probability": 0.96728515625}, {"start": 941.25, "end": 942.13, "word": " الفاي", "probability": 0.7255859375}, {"start": 942.13, "end": 942.59, "word": " of", "probability": 0.88427734375}, {"start": 942.59, "end": 943.11, "word": " A", "probability": 0.58447265625}, {"start": 943.11, "end": 943.77, "word": " زائد", "probability": 0.7989095052083334}, {"start": 943.77, "end": 944.13, "word": " ال", "probability": 0.69140625}, {"start": 944.13, "end": 944.85, "word": " BI", "probability": 0.1700439453125}, {"start": 944.85, "end": 945.91, "word": " بدي", "probability": 0.726318359375}, {"start": 945.91, "end": 946.51, "word": " ساوي", "probability": 0.7486979166666666}, {"start": 946.51, "end": 947.09, "word": " الفاي", "probability": 0.783447265625}, {"start": 947.09, "end": 947.55, "word": " of", "probability": 0.9716796875}, {"start": 947.55, "end": 947.95, "word": " C", "probability": 0.9736328125}, {"start": 947.95, "end": 948.55, "word": " زائد", "probability": 0.9207356770833334}, {"start": 948.55, "end": 948.77, "word": " ال", "probability": 0.83544921875}, {"start": 948.77, "end": 949.09, "word": " DF", "probability": 0.29248046875}], "temperature": 1.0}, {"id": 34, "seek": 97946, "start": 949.96, "end": 979.46, "text": "يبقى حتة صورتين 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زيدي", "probability": 0.5909830729166666}, {"start": 957.26, "end": 957.36, "word": " ال", "probability": 0.9326171875}, {"start": 957.36, "end": 957.54, "word": " B", "probability": 0.43310546875}, {"start": 957.54, "end": 957.92, "word": " I", "probability": 0.59912109375}, {"start": 957.92, "end": 958.44, "word": " يسوي", "probability": 0.653076171875}, {"start": 958.44, "end": 958.8, "word": " C", "probability": 0.66552734375}, {"start": 958.8, "end": 959.36, "word": " زيدي", "probability": 0.9542643229166666}, {"start": 959.36, "end": 959.46, "word": " ال", "probability": 0.8291015625}, {"start": 959.46, "end": 959.6, "word": " D", "probability": 0.9296875}, {"start": 959.6, "end": 960.0, "word": " I", "probability": 0.974609375}, {"start": 960.0, "end": 960.76, "word": " مصير", "probability": 0.8733723958333334}, {"start": 960.76, "end": 961.46, "word": " الفاي", "probability": 0.364501953125}, {"start": 961.46, "end": 961.82, "word": " is", "probability": 0.689453125}, {"start": 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"word": " اللي", "probability": 0.8974609375}, {"start": 967.72, "end": 968.3, "word": " أخدته", "probability": 0.904052734375}, {"start": 968.3, "end": 969.0, "word": " الصورة", "probability": 0.9915364583333334}, {"start": 969.0, "end": 969.76, "word": " مش", "probability": 0.97998046875}, {"start": 969.76, "end": 970.48, "word": " عبارة", "probability": 0.9942626953125}, {"start": 970.48, "end": 970.64, "word": " عن", "probability": 0.98779296875}, {"start": 970.64, "end": 971.24, "word": " نتيجتها", "probability": 0.89052734375}, {"start": 971.24, "end": 971.5, "word": " هو", "probability": 0.93017578125}, {"start": 971.5, "end": 971.72, "word": " ال", "probability": 0.9619140625}, {"start": 971.72, "end": 972.26, "word": " conjugate", "probability": 0.90673828125}, {"start": 972.26, "end": 973.04, "word": " element", "probability": 0.28173828125}, {"start": 973.04, "end": 973.88, "word": " أه", "probability": 0.57891845703125}, {"start": 973.88, "end": 974.3, "word": " يبقى", "probability": 0.9339599609375}, {"start": 974.3, "end": 974.74, "word": " هذا", "probability": 0.87939453125}, {"start": 974.74, "end": 975.42, "word": " معناه", "probability": 0.86328125}, {"start": 975.42, "end": 975.78, "word": " أن", "probability": 0.76708984375}, {"start": 975.78, "end": 976.14, "word": " ال", "probability": 0.95263671875}, {"start": 976.14, "end": 976.68, "word": " A", "probability": 0.92138671875}, {"start": 976.68, "end": 977.58, "word": " ناقص", "probability": 0.933837890625}, {"start": 977.58, "end": 977.94, "word": " B", "probability": 0.451171875}, {"start": 977.94, "end": 978.56, "word": " I", "probability": 0.90869140625}, {"start": 978.56, "end": 979.46, "word": " بالزاوية", "probability": 0.6947265625}], "temperature": 1.0}, {"id": 35, "seek": 100853, "start": 979.73, "end": 1008.53, "text": "والـ Conjugate لهذه اللي هو C ذات الـ D I خيار A ناقص D I A C ناقص D I كمان درسنا في ال complex لما يكون complex number بيسوي complex number يبقى الجزء الحقيقي 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زائد ال V عارف ممكن أكتبه بطريقة أخرى و هي ال A سالب سالب V عارف سالب في سالب الوجه دي احنا ماسويناش اشي طيب لو رجعت لset of complex number", "tokens": [28814, 1863, 2423, 39184, 316, 30767, 16373, 3215, 2423, 691, 6225, 9640, 5172, 3714, 43020, 5551, 4117, 2655, 3555, 3224, 4724, 9566, 16572, 28671, 5551, 34740, 7578, 4032, 39896, 2423, 316, 8608, 6027, 3555, 8608, 6027, 3555, 691, 6225, 9640, 5172, 8608, 6027, 3555, 8978, 8608, 6027, 3555, 2423, 29245, 3224, 11778, 1829, 1975, 5016, 8315, 19446, 3794, 2407, 9957, 33599, 1975, 8592, 1829, 23032, 1829, 3555, 45164, 12602, 7435, 34268, 5296, 3854, 295, 3997, 1230], "avg_logprob": -0.3336038883630331, "compression_ratio": 1.4695121951219512, "no_speech_prob": 0.0, "words": [{"start": 1149.56, "end": 1149.98, "word": "إن", "probability": 0.738037109375}, {"start": 1149.98, "end": 1150.36, "word": " الـ", "probability": 0.4849853515625}, {"start": 1150.36, "end": 1150.68, "word": " A", "probability": 0.421142578125}, {"start": 1150.68, 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1185.78, "end": 1186.62, "word": " element", "probability": 0.92626953125}, {"start": 1186.62, "end": 1187.68, "word": " سلب", "probability": 0.66552734375}, {"start": 1187.68, "end": 1188.02, "word": " هذا", "probability": 0.95654296875}, {"start": 1188.02, "end": 1188.5, "word": " يبقى", "probability": 0.970947265625}, {"start": 1188.5, "end": 1188.9, "word": " هذا", "probability": 0.900390625}, {"start": 1188.9, "end": 1190.68, "word": " conjugateت", "probability": 0.58544921875}, {"start": 1190.68, "end": 1191.56, "word": " لمن", "probability": 0.7119140625}, {"start": 1191.56, "end": 1192.1, "word": " ل", "probability": 0.472412109375}, {"start": 1192.1, "end": 1192.62, "word": " element", "probability": 0.76904296875}, {"start": 1192.62, "end": 1193.42, "word": " تاني", "probability": 0.8958333333333334}, {"start": 1193.42, "end": 1193.76, "word": " صح", "probability": 0.973876953125}, {"start": 1193.76, "end": 1193.96, "word": " ولا", "probability": 0.98291015625}, {"start": 1193.96, "end": 1194.3, "word": " لأ", "probability": 0.974853515625}, {"start": 1194.3, "end": 1195.1, "word": " يعني", "probability": 0.916748046875}, {"start": 1195.1, "end": 1195.68, "word": " هذا", "probability": 0.84130859375}, {"start": 1195.68, "end": 1196.72, "word": " ههه", "probability": 0.5579427083333334}, {"start": 1196.72, "end": 1197.12, "word": " هو", "probability": 0.75537109375}, {"start": 1197.12, "end": 1198.0, "word": " عبارة", "probability": 0.9931640625}, {"start": 1198.0, "end": 1198.62, "word": " عن", "probability": 0.99853515625}, {"start": 1198.62, "end": 1199.46, "word": " صورة", "probability": 0.9518229166666666}, {"start": 1199.46, "end": 1199.88, "word": " من", "probability": 0.9189453125}, {"start": 1199.88, "end": 1201.14, "word": " صورة", "probability": 0.98046875}, {"start": 1201.14, "end": 1201.98, "word": " الـA", "probability": 0.9392903645833334}, {"start": 1201.98, "end": 1202.84, "word": " الذات", "probability": 0.927001953125}, {"start": 1202.84, "end": 1204.06, "word": " الناقص", "probability": 0.8172607421875}, {"start": 1204.06, "end": 1204.88, "word": " بيه", "probability": 0.8466796875}, {"start": 1204.88, "end": 1205.02, "word": " في", "probability": 0.939453125}, {"start": 1205.02, "end": 1205.52, "word": " الأرض", "probability": 0.983642578125}], "temperature": 1.0}, {"id": 43, "seek": 123544, "start": 1206.66, "end": 1235.44, "text": "أه حسب ال definition اللي احنا كاتبينه Phi of ال element يسوى ال conjugate طيب انا بد ال conjugate لهذا ال conjugate لهذا ان الإشارة اللي يبقى number كلها لها بالزائد يبقى هذا الكلام اللي هو Phi of ال a ناقص بيه في ال R يبقى اي element موجود في set of complex numbers", "tokens": [10721, 3224, 11331, 35457, 2423, 7123, 13672, 1829, 1975, 5016, 8315, 9122, 9307, 3555, 9957, 3224, 41435, 295, 2423, 4478, 7251, 3794, 2407, 7578, 2423, 45064, 23032, 1829, 3555, 1975, 8315, 47525, 2423, 45064, 46740, 15730, 2423, 45064, 46740, 15730, 16472, 33688, 8592, 9640, 3660, 13672, 1829, 7251, 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"probability": 0.848291015625}, {"start": 1210.94, "end": 1211.5, "word": " Phi", "probability": 0.0548095703125}, {"start": 1211.5, "end": 1211.84, "word": " of", "probability": 0.9365234375}, {"start": 1211.84, "end": 1212.04, "word": " ال", "probability": 0.281982421875}, {"start": 1212.04, "end": 1212.42, "word": " element", "probability": 0.85498046875}, {"start": 1212.42, "end": 1213.0, "word": " يسوى", "probability": 0.7969970703125}, {"start": 1213.0, "end": 1213.14, "word": " ال", "probability": 0.95849609375}, {"start": 1213.14, "end": 1213.68, "word": " conjugate", "probability": 0.8994140625}, {"start": 1213.68, "end": 1214.58, "word": " طيب", "probability": 0.9231770833333334}, {"start": 1214.58, "end": 1215.0, "word": " انا", "probability": 0.7376708984375}, {"start": 1215.0, "end": 1215.24, "word": " بد", "probability": 0.55615234375}, {"start": 1215.24, "end": 1215.42, "word": " ال", "probability": 0.80859375}, {"start": 1215.42, "end": 1215.9, "word": " conjugate", "probability": 0.947265625}, {"start": 1215.9, "end": 1216.68, "word": " لهذا", "probability": 0.8544921875}, {"start": 1216.68, "end": 1216.98, "word": " ال", "probability": 0.90771484375}, {"start": 1216.98, "end": 1217.42, "word": " conjugate", "probability": 0.91748046875}, {"start": 1217.42, "end": 1218.06, "word": " لهذا", "probability": 0.982421875}, {"start": 1218.06, "end": 1218.26, "word": " ان", "probability": 0.57470703125}, {"start": 1218.26, "end": 1219.0, "word": " الإشارة", "probability": 0.8778076171875}, {"start": 1219.0, "end": 1219.16, "word": " اللي", "probability": 0.942138671875}, {"start": 1219.16, "end": 1219.34, "word": " يبقى", "probability": 0.6925048828125}, {"start": 1219.34, "end": 1219.56, "word": " number", "probability": 0.129150390625}, {"start": 1219.56, "end": 1220.2, "word": " كلها", "probability": 0.73291015625}, {"start": 1220.2, "end": 1220.64, "word": " لها", "probability": 0.4161376953125}, {"start": 1220.64, "end": 1222.06, "word": " بالزائد", "probability": 0.8753662109375}, {"start": 1222.06, "end": 1222.8, "word": " يبقى", "probability": 0.9464111328125}, {"start": 1222.8, "end": 1223.16, "word": " هذا", "probability": 0.95361328125}, {"start": 1223.16, "end": 1223.8, "word": " الكلام", "probability": 0.9710286458333334}, {"start": 1223.8, "end": 1224.02, "word": " اللي", "probability": 0.75439453125}, {"start": 1224.02, "end": 1224.32, "word": " هو", "probability": 0.9560546875}, {"start": 1224.32, "end": 1225.08, "word": " Phi", "probability": 0.841796875}, {"start": 1225.08, "end": 1225.82, "word": " of", "probability": 0.91552734375}, {"start": 1225.82, "end": 1226.22, "word": " ال", "probability": 0.70654296875}, {"start": 1226.22, "end": 1226.76, "word": " a", "probability": 0.495361328125}, {"start": 1226.76, "end": 1228.12, "word": " ناقص", "probability": 0.9058837890625}, {"start": 1228.12, "end": 1229.04, "word": " بيه", "probability": 0.69775390625}, {"start": 1229.04, "end": 1229.18, "word": " في", "probability": 0.7265625}, {"start": 1229.18, "end": 1229.34, "word": " ال", "probability": 0.8525390625}, {"start": 1229.34, "end": 1229.62, "word": " R", "probability": 0.256103515625}, {"start": 1229.62, "end": 1230.88, "word": " يبقى", "probability": 0.9493408203125}, {"start": 1230.88, "end": 1231.4, "word": " اي", "probability": 0.6829833984375}, {"start": 1231.4, "end": 1232.22, "word": " element", "probability": 0.966796875}, {"start": 1232.22, "end": 1232.9, "word": " موجود", "probability": 0.9860026041666666}, {"start": 1232.9, "end": 1233.14, "word": " في", "probability": 0.759765625}, {"start": 1233.14, "end": 1233.62, "word": " set", "probability": 0.7412109375}, {"start": 1233.62, "end": 1233.9, "word": " of", "probability": 0.96630859375}, {"start": 1233.9, "end": 1234.68, "word": " complex", "probability": 0.8984375}, {"start": 1234.68, "end": 1235.44, "word": " numbers", "probability": 0.6943359375}], "temperature": 1.0}, {"id": 44, "seek": 126125, "start": 1235.81, "end": 1261.25, "text": "اللي جاتله أصل في ال set of complex numbers هو a ناقص bi طيب لو أخدت ال a ناقص bi هيطلع a زائد bi اللي هو ال phi of a زائد bi يبقى احنا بي كانت موجب والله سالبي بالتمنيش element موجب سالب سفر كله صحيح عندي تمام", "tokens": [6027, 20292, 10874, 9307, 43761, 5551, 36520, 8978, 2423, 992, 295, 3997, 3547, 31439, 257, 8717, 995, 4587, 9381, 3228, 23032, 1829, 3555, 45164, 5551, 9778, 3215, 2655, 2423, 257, 8717, 995, 4587, 9381, 3228, 39896, 9566, 1211, 3615, 257, 30767, 16373, 3215, 3228, 13672, 1829, 31439, 2423, 13107, 295, 257, 30767, 16373, 3215, 3228, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 4724, 1829, 25961, 2655, 3714, 29245, 3555, 16070, 43761, 8608, 6027, 3555, 1829, 20666, 39237, 22653, 8592, 4478, 3714, 29245, 3555, 8608, 6027, 3555, 8608, 5172, 2288, 28242, 3224, 20328, 5016, 1829, 5016, 18871, 16254, 46811, 10943], "avg_logprob": -0.2424999949336052, "compression_ratio": 1.6417910447761195, "no_speech_prob": 0.0, "words": [{"start": 1235.81, "end": 1236.23, "word": "اللي", "probability": 0.4976806640625}, {"start": 1236.23, "end": 1237.01, "word": " جاتله", "probability": 0.6229654947916666}, {"start": 1237.01, "end": 1237.77, "word": " أصل", "probability": 0.828857421875}, {"start": 1237.77, "end": 1238.07, "word": " في", "probability": 0.88134765625}, {"start": 1238.07, "end": 1238.27, "word": " ال", "probability": 0.6083984375}, {"start": 1238.27, "end": 1238.59, "word": " set", "probability": 0.53759765625}, {"start": 1238.59, "end": 1238.87, "word": " of", "probability": 0.95458984375}, {"start": 1238.87, "end": 1239.45, "word": " complex", "probability": 0.9189453125}, {"start": 1239.45, "end": 1240.05, "word": " numbers", "probability": 0.6962890625}, {"start": 1240.05, "end": 1240.57, "word": " هو", "probability": 0.9169921875}, {"start": 1240.57, "end": 1241.07, "word": " a", "probability": 0.556640625}, {"start": 1241.07, "end": 1241.93, "word": " ناقص", "probability": 0.740447998046875}, {"start": 1241.93, "end": 1242.61, "word": " bi", "probability": 0.6201171875}, {"start": 1242.61, "end": 1243.57, "word": " طيب", "probability": 0.8821614583333334}, {"start": 1243.57, "end": 1243.79, "word": " لو", "probability": 0.92724609375}, {"start": 1243.79, "end": 1244.49, "word": " أخدت", "probability": 0.9351806640625}, {"start": 1244.49, "end": 1244.69, "word": " ال", "probability": 0.90869140625}, {"start": 1244.69, "end": 1245.05, "word": " a", "probability": 0.95458984375}, {"start": 1245.05, "end": 1245.79, "word": " ناقص", "probability": 0.98095703125}, {"start": 1245.79, "end": 1247.15, "word": " bi", "probability": 0.9599609375}, {"start": 1247.15, "end": 1248.57, "word": " هيطلع", "probability": 0.80389404296875}, {"start": 1248.57, "end": 1248.95, "word": " a", "probability": 0.51416015625}, {"start": 1248.95, "end": 1249.59, "word": " زائد", "probability": 0.6344401041666666}, {"start": 1249.59, "end": 1250.01, "word": " bi", "probability": 0.88330078125}, {"start": 1250.01, "end": 1250.39, "word": " اللي", "probability": 0.7568359375}, {"start": 1250.39, "end": 1250.57, "word": " هو", "probability": 0.95947265625}, {"start": 1250.57, "end": 1250.77, "word": " ال", "probability": 0.6591796875}, {"start": 1250.77, "end": 1251.09, "word": " phi", "probability": 0.2305908203125}, {"start": 1251.09, "end": 1251.45, "word": " of", "probability": 0.91064453125}, {"start": 1251.45, "end": 1251.79, "word": " a", "probability": 0.94140625}, {"start": 1251.79, "end": 1252.41, "word": " زائد", "probability": 0.97216796875}, {"start": 1252.41, "end": 1252.99, "word": " bi", "probability": 0.9267578125}, {"start": 1252.99, "end": 1253.29, "word": " يبقى", "probability": 0.8865966796875}, {"start": 1253.29, "end": 1254.15, "word": " احنا", "probability": 0.8738606770833334}, {"start": 1254.15, "end": 1254.49, "word": " بي", "probability": 0.718017578125}, {"start": 1254.49, "end": 1254.95, "word": " كانت", "probability": 0.768310546875}, {"start": 1254.95, "end": 1255.31, 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1.0}, {"id": 45, "seek": 128871, "start": 1261.49, "end": 1288.71, "text": "إذا بناء عليه صارت الـ Phi is onto لإن ال element اللي موجود في ال set of complex number لاجت له أصل في ال set of complex number يبقى أي element في ال set of complex number له أصل في ال set of complex number يبقى Phi is onto يبقى Phi حققت ال two conditions تبع ال homomorphism حققت ال one to one", "tokens": [28814, 15730, 44945, 16606, 47356, 20328, 9640, 2655, 2423, 39184, 41435, 307, 3911, 5296, 28814, 1863, 2423, 4478, 13672, 1829, 3714, 29245, 23328, 8978, 2423, 992, 295, 3997, 1230, 5296, 26108, 2655, 46740, 5551, 36520, 8978, 2423, 992, 295, 3997, 1230, 7251, 3555, 4587, 7578, 36632, 4478, 8978, 2423, 992, 295, 3997, 1230, 46740, 5551, 36520, 8978, 2423, 992, 295, 3997, 1230, 7251, 3555, 4587, 7578, 41435, 307, 3911, 7251, 3555, 4587, 7578, 41435, 11331, 4587, 38149, 2423, 732, 4487, 6055, 3555, 3615, 2423, 3655, 32702, 1434, 11331, 4587, 38149, 2423, 472, 281, 472], "avg_logprob": -0.19769737249926517, 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"word": " is", "probability": 0.92626953125}, {"start": 1282.17, "end": 1282.45, "word": " onto", "probability": 0.89453125}, {"start": 1282.45, "end": 1282.87, "word": " يبقى", "probability": 0.8924560546875}, {"start": 1282.87, "end": 1283.25, "word": " Phi", "probability": 0.91796875}, {"start": 1283.25, "end": 1284.21, "word": " حققت", "probability": 0.9518229166666666}, {"start": 1284.21, "end": 1284.41, "word": " ال", "probability": 0.9521484375}, {"start": 1284.41, "end": 1284.53, "word": " two", "probability": 0.8916015625}, {"start": 1284.53, "end": 1285.13, "word": " conditions", "probability": 0.90283203125}, {"start": 1285.13, "end": 1285.49, "word": " تبع", "probability": 0.90380859375}, {"start": 1285.49, "end": 1285.71, "word": " ال", "probability": 0.71533203125}, {"start": 1285.71, "end": 1286.73, "word": " homomorphism", "probability": 0.9552408854166666}, {"start": 1286.73, "end": 1287.81, "word": " حققت", "probability": 0.9601236979166666}, {"start": 1287.81, "end": 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F of X بالدي ساوي ال F of 1 show that ان الفاي is", "tokens": [27842, 2423, 39184, 992, 295, 439, 22560, 12356, 365, 957, 31994, 32767, 9957, 24976, 10721, 25513, 27884, 538, 6156, 47302, 295, 2423, 479, 295, 1783, 20666, 16254, 8608, 995, 45865, 2423, 479, 295, 502, 855, 300, 16472, 27188, 47302, 307], "avg_logprob": -0.5201981707317073, "compression_ratio": 1.210144927536232, "no_speech_prob": 0.0, "words": [{"start": 1319.18, "end": 1319.86, "word": "من", "probability": 0.92529296875}, {"start": 1319.86, "end": 1322.38, "word": " الـ", "probability": 0.3017578125}, {"start": 1322.38, "end": 1322.64, "word": " set", "probability": 0.64990234375}, {"start": 1322.64, "end": 1323.04, "word": " of", "probability": 0.9638671875}, {"start": 1323.04, "end": 1323.66, "word": " all", "probability": 0.89990234375}, {"start": 1323.66, "end": 1324.58, "word": " polynomials", "probability": 0.6776123046875}, {"start": 1324.58, "end": 1324.94, "word": " with", "probability": 0.9326171875}, 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isomorphism يبقى يكفيني إيش؟ أني أثبت أنها homomorphism", "tokens": [41185, 3655, 32702, 1434, 41435, 307, 3655, 32702, 1434, 457, 406, 307, 32702, 1434, 5296, 1863, 12984, 3555, 2655, 14739, 29538, 3655, 32702, 1434, 44381, 11296, 32239, 14851, 8978, 21542, 38436, 28671, 307, 32702, 1434, 7251, 3555, 4587, 7578, 7251, 4117, 5172, 9957, 1829, 11933, 1829, 8592, 22807, 14739, 1829, 5551, 12984, 3555, 2655, 14739, 11296, 3655, 32702, 1434], "avg_logprob": -0.2537760347127914, "compression_ratio": 1.6090225563909775, "no_speech_prob": 0.0, "words": [{"start": 1348.75, "end": 1349.07, "word": "في", "probability": 0.08013916015625}, {"start": 1349.07, "end": 1352.21, "word": " homomorphism", "probability": 0.8406575520833334}, {"start": 1352.21, "end": 1353.39, "word": " Phi", "probability": 0.1785888671875}, {"start": 1353.39, "end": 1353.77, "word": " is", "probability": 0.44677734375}, {"start": 1353.77, "end": 1354.97, "word": " homomorphism", "probability": 0.95556640625}, {"start": 1354.97, "end": 1355.97, "word": " but", "probability": 0.49755859375}, {"start": 1355.97, "end": 1357.65, "word": " not", "probability": 0.86328125}, {"start": 1357.65, "end": 1360.07, "word": " isomorphism", "probability": 0.9407552083333334}, {"start": 1360.07, "end": 1362.79, "word": " لنثبت", "probability": 0.9115234375}, {"start": 1362.79, "end": 1363.61, "word": " أن", "probability": 0.40087890625}, {"start": 1363.61, "end": 1364.11, "word": " هذه", "probability": 0.732421875}, {"start": 1364.11, "end": 1365.31, "word": " homomorphism", "probability": 0.92236328125}, {"start": 1365.31, "end": 1366.75, "word": " لكنها", "probability": 0.93798828125}, {"start": 1366.75, "end": 1367.83, "word": " ليست", "probability": 0.979248046875}, {"start": 1367.83, "end": 1368.11, "word": " في", "probability": 0.7685546875}, {"start": 1368.11, "end": 1369.03, "word": " الحقيقة", "probability": 0.9934895833333334}, {"start": 1369.03, "end": 1371.63, "word": " isomorphism", "probability": 0.9108072916666666}, {"start": 1371.63, "end": 1372.49, "word": " يبقى", "probability": 0.9588623046875}, {"start": 1372.49, "end": 1373.31, "word": " يكفيني", "probability": 0.86162109375}, {"start": 1373.31, "end": 1374.13, "word": " إيش؟", "probability": 0.73687744140625}, {"start": 1374.13, "end": 1374.43, "word": " أني", "probability": 0.643798828125}, {"start": 1374.43, "end": 1375.13, "word": " أثبت", "probability": 0.991943359375}, {"start": 1375.13, "end": 1376.11, "word": " أنها", "probability": 0.42474365234375}, {"start": 1376.11, "end": 1377.17, "word": " homomorphism", "probability": 0.9791666666666666}], "temperature": 1.0}, {"id": 49, "seek": 140417, "start": 1377.69, "end": 1404.17, "text": "not one to one او not one to one او واحد من اتنين ليس بالضرورة لكي تكون مهياش ايزو مورفزن لا تريد السبع دي تلو conditions يكشيني ميه ايه اللي تقدر عليه اثبت انه ماهياش one to one خلاص كفى الله المؤمنين القتال اثبت ماهياش one to one يبقى خلاص أي واحدة فيهم طيب الحلقة التالية 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2245.85, "word": " Phi", "probability": 0.91455078125}, {"start": 2245.85, "end": 2246.13, "word": " of", "probability": 0.94384765625}, {"start": 2246.13, "end": 2246.45, "word": " X", "probability": 0.99365234375}, {"start": 2246.45, "end": 2247.11, "word": " زائد", "probability": 0.9474283854166666}, {"start": 2247.11, "end": 2247.73, "word": " Phi", "probability": 0.89501953125}, {"start": 2247.73, "end": 2248.41, "word": " of", "probability": 0.90283203125}, {"start": 2248.41, "end": 2248.67, "word": " Y", "probability": 0.978515625}, {"start": 2248.67, "end": 2249.31, "word": " إذا", "probability": 0.53173828125}, {"start": 2249.31, "end": 2249.65, "word": " روحنا", "probability": 0.80010986328125}, {"start": 2249.65, "end": 2250.07, "word": " مين", "probability": 0.83740234375}, {"start": 2250.07, "end": 2251.13, "word": " للشرط", "probability": 0.8419596354166666}, {"start": 2251.13, "end": 2252.37, "word": " الثاني", "probability": 0.884033203125}, {"start": 2252.37, "end": 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Modulo عشرة. طبعا؟ يعني هذا خمسة X Modulo عشرة في Y Modulo عشرة. يبقى not homomorphism ولا لا؟ أكيد؟ قولوا غيره يا بنات", "tokens": [1829, 3794, 995, 45865, 16490, 2304, 3794, 3660, 1783, 6583, 13455, 6225, 8592, 25720, 13, 6583, 13455, 6225, 8592, 25720, 13, 23032, 3555, 3615, 995, 22807, 37495, 22653, 23758, 16490, 2304, 3794, 3660, 1783, 6583, 13455, 6225, 8592, 25720, 8978, 398, 6583, 13455, 6225, 8592, 25720, 13, 7251, 3555, 4587, 7578, 406, 3655, 32702, 1434, 49429, 20193, 22807, 5551, 4117, 25708, 22807, 12174, 12610, 14407, 32771, 13546, 3224, 35186, 4724, 8315, 2655], "avg_logprob": -0.260916092624403, "compression_ratio": 1.5034482758620689, "no_speech_prob": 0.0, "words": [{"start": 2263.73, "end": 2264.79, "word": "يساوي", "probability": 0.5947265625}, {"start": 2264.79, "end": 2266.35, "word": " خمسة", "probability": 0.8941650390625}, {"start": 2266.35, "end": 2267.05, "word": " X", "probability": 0.64111328125}, {"start": 2267.05, "end": 2268.79, "word": " Modulo", 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Y", "probability": 0.96484375}, {"start": 2281.15, "end": 2281.65, "word": " Modulo", "probability": 0.9541015625}, {"start": 2281.65, "end": 2282.31, "word": " عشرة.", "probability": 0.9817708333333334}, {"start": 2283.15, "end": 2283.83, "word": " يبقى", "probability": 0.9117431640625}, {"start": 2283.83, "end": 2284.27, "word": " not", "probability": 0.5498046875}, {"start": 2284.27, "end": 2285.23, "word": " homomorphism", "probability": 0.81689453125}, {"start": 2285.23, "end": 2285.43, "word": " ولا", "probability": 0.482177734375}, {"start": 2285.43, "end": 2286.63, "word": " لا؟", "probability": 0.80029296875}, {"start": 2286.63, "end": 2290.07, "word": " أكيد؟", "probability": 0.9351806640625}, {"start": 2290.07, "end": 2290.49, "word": " قولوا", "probability": 0.8323567708333334}, {"start": 2290.49, "end": 2290.91, "word": " غيره", "probability": 0.90966796875}, {"start": 2290.91, "end": 2291.03, "word": " يا", "probability": 0.990234375}, {"start": 2291.03, "end": 2291.53, 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قاللي أثبتلي إنه هذه عبارة عن homomorphism يبقى رصد من أنا وعنك بدأتكون homomorphism لإنه قاللي أثبتها يعني بقوله لا أثبتها بقولش إن أنا أثبتها", "tokens": [40228, 22653, 29538, 41435, 295, 1783, 8978, 41435, 295, 398, 29538, 4724, 3794, 28239, 47432, 3660, 13672, 1829, 25961, 2655, 5296, 17082, 11622, 8978, 21136, 33604, 6027, 16070, 3555, 995, 38436, 25124, 17082, 1211, 3714, 3555, 33599, 25720, 37495, 22653, 29538, 13672, 1829, 8978, 11296, 6055, 5172, 4117, 13546, 4724, 3794, 1829, 9566, 9122, 33911, 5551, 9566, 1211, 3615, 9154, 9673, 9566, 16758, 4587, 13672, 1829, 41850, 4032, 4587, 6027, 31371, 3224, 5296, 28814, 1863, 3224, 50239, 20292, 5551, 12984, 3555, 2655, 20292, 36145, 3224, 29538, 6225, 3555, 9640, 3660, 18871, 3655, 32702, 1434, 7251, 3555, 4587, 7578, 12602, 9381, 3215, 9154, 41850, 4032, 3615, 1863, 4117, 47525, 10721, 2655, 30544, 3655, 32702, 1434, 5296, 28814, 1863, 3224, 50239, 20292, 5551, 12984, 3555, 2655, 11296, 37495, 22653, 4724, 39648, 3224, 20193, 5551, 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انت في السؤال اللي فات اثبت انه five is not one to one و سيبت الانت بتقدر تثبت الناس", "tokens": [20292, 3224, 1975, 2655, 1863, 9957, 39894, 3794, 45865, 8592, 30767, 13546, 2407, 1975, 2407, 30767, 13546, 2407, 39894, 3794, 45865, 8592, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 1732, 307, 406, 472, 281, 472, 7251, 3555, 4587, 7578, 1732, 307, 406, 322, 307, 32702, 1434, 23032, 3555, 45164, 36764, 24401, 3660, 11331, 16758, 3660, 6055, 12984, 3555, 2655, 16472, 3224, 1732, 307, 406, 322, 37495, 22653, 16472, 2655, 8978, 21136, 33604, 6027, 13672, 1829, 6156, 9307, 1975, 12984, 3555, 2655, 16472, 3224, 1732, 307, 406, 472, 281, 472, 4032, 8608, 1829, 3555, 2655, 2423, 7649, 2655, 39894, 28543, 2288, 6055, 12984, 3555, 2655, 2423, 8315, 3794], "avg_logprob": -0.24025229248431845, "compression_ratio": 1.9606741573033708, "no_speech_prob": 0.0, "words": [{"start": 2461.32, "end": 2461.94, "word": "ليه", "probability": 0.5322265625}, {"start": 2461.94, "end": 2462.58, "word": " 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تربيع حسب ال definition هي Phi of A والتانية حسب ال definition Phi of B", "tokens": [6027, 1863, 31371, 7435, 3660, 6055, 3794, 995, 45865, 316, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 363, 6055, 2288, 21292, 3615, 2423, 316, 6055, 2288, 21292, 3615, 11331, 35457, 2423, 7123, 39896, 41435, 295, 316, 16070, 2655, 7649, 10632, 11331, 35457, 2423, 7123, 41435, 295, 363], "avg_logprob": -0.2698567733168602, "compression_ratio": 1.5185185185185186, "no_speech_prob": 0.0, "words": [{"start": 2819.07, "end": 2820.31, "word": "النتيجة", "probability": 0.65107421875}, {"start": 2820.31, "end": 2821.13, "word": " تساوي", "probability": 0.7144775390625}, {"start": 2821.13, "end": 2821.63, "word": " A", "probability": 0.281982421875}, {"start": 2821.63, "end": 2822.63, "word": " تربيع", "probability": 0.8204345703125}, {"start": 2822.63, "end": 2823.29, "word": " زائد", "probability": 0.7490234375}, {"start": 2823.29, "end": 2823.61, "word": " B", "probability": 0.8876953125}, {"start": 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homomorphism اثبتنا قال لي بس not isomorphism بقوله ال phi is not isomorphism ليش؟ because اي عدد مستلبته بيديه نفسه لو أخدت منه phi of a قداشه ساوي؟ a تربيه", "tokens": [271, 257, 3655, 32702, 1434, 50239, 32239, 1975, 12984, 3555, 2655, 20292, 16472, 31439, 3655, 32702, 1434, 1975, 12984, 3555, 2655, 8315, 50239, 32239, 4724, 3794, 406, 307, 32702, 1434, 4724, 39648, 3224, 2423, 13107, 307, 406, 307, 32702, 1434, 32239, 8592, 22807, 570, 1975, 1829, 6225, 3215, 3215, 3714, 14851, 46152, 47395, 4724, 1829, 16254, 3224, 8717, 36178, 3224, 45164, 5551, 9778, 3215, 2655, 9154, 3224, 13107, 295, 257, 12174, 3215, 33599, 3224, 8608, 995, 45865, 22807, 257, 6055, 2288, 21292, 3224], "avg_logprob": -0.35398066469601225, "compression_ratio": 1.6127167630057804, "no_speech_prob": 0.0, "words": [{"start": 2891.43, "end": 2892.15, "word": "is", "probability": 0.455810546875}, {"start": 2892.15, "end": 2893.03, "word": " a", "probability": 0.75390625}, {"start": 2893.03, "end": 2895.01, "word": " 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1.0}, {"id": 103, "seek": 294847, "start": 2919.39, "end": 2948.47, "text": "وخد فاى of ناقص اى الناقص اى الكل ترجعله في قدر اى تربيع من الاتنين هدول بدره يقول فاى of اى بده يساوي فاى of سالب اى يبقى صورة تانى متساويه تانى but ولكن ال a لا تساوي سالب اى", "tokens": [2407, 9778, 3215, 6156, 995, 7578, 295, 8717, 995, 4587, 9381, 1975, 7578, 2423, 8315, 4587, 9381, 1975, 7578, 2423, 28820, 6055, 47341, 3615, 43761, 8978, 12174, 3215, 2288, 1975, 7578, 6055, 2288, 21292, 3615, 9154, 2423, 9307, 1863, 9957, 8032, 3215, 12610, 47525, 2288, 3224, 7251, 39648, 6156, 995, 7578, 295, 1975, 7578, 47525, 3224, 7251, 3794, 995, 45865, 6156, 995, 7578, 295, 8608, 6027, 3555, 1975, 7578, 7251, 3555, 4587, 7578, 20328, 13063, 3660, 6055, 7649, 7578, 44650, 3794, 995, 45865, 3224, 6055, 7649, 7578, 457, 35525, 19452, 2423, 257, 20193, 6055, 3794, 995, 45865, 8608, 6027, 3555, 1975, 7578], "avg_logprob": -0.27214806693271526, "compression_ratio": 1.8703703703703705, "no_speech_prob": 0.0, "words": 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{"start": 2927.23, "end": 2927.81, "word": " تربيع", "probability": 0.703125}, {"start": 2927.81, "end": 2928.37, "word": " من", "probability": 0.86083984375}, {"start": 2928.37, "end": 2929.19, "word": " الاتنين", "probability": 0.843994140625}, {"start": 2929.19, "end": 2929.87, "word": " هدول", "probability": 0.8836263020833334}, {"start": 2929.87, "end": 2930.89, "word": " بدره", "probability": 0.462890625}, {"start": 2930.89, "end": 2931.11, "word": " يقول", "probability": 0.73193359375}, {"start": 2931.11, "end": 2931.83, "word": " فاى", "probability": 0.8909505208333334}, {"start": 2931.83, "end": 2932.21, "word": " of", "probability": 0.97216796875}, {"start": 2932.21, "end": 2932.77, "word": " اى", "probability": 0.947998046875}, {"start": 2932.77, "end": 2933.45, "word": " بده", "probability": 0.7724609375}, {"start": 2933.45, "end": 2934.05, "word": " يساوي", "probability": 0.887939453125}, {"start": 2934.05, "end": 2935.15, "word": " فاى", "probability": 0.9373372395833334}, {"start": 2935.15, "end": 2935.43, "word": " of", "probability": 0.9560546875}, {"start": 2935.43, "end": 2936.01, "word": " سالب", "probability": 0.7353515625}, {"start": 2936.01, "end": 2936.47, "word": " اى", "probability": 0.936767578125}, {"start": 2936.47, "end": 2937.23, "word": " يبقى", "probability": 0.91552734375}, {"start": 2937.23, "end": 2937.79, "word": " صورة", "probability": 0.96484375}, {"start": 2937.79, "end": 2938.33, "word": " تانى", "probability": 0.7464192708333334}, {"start": 2938.33, "end": 2940.15, "word": " متساويه", "probability": 0.880078125}, {"start": 2940.15, "end": 2940.79, "word": " تانى", "probability": 0.9427083333333334}, {"start": 2940.79, "end": 2941.31, "word": " but", "probability": 0.28955078125}, {"start": 2941.31, "end": 2943.09, "word": " ولكن", "probability": 0.76806640625}, {"start": 2943.09, "end": 2945.45, "word": " ال", "probability": 0.82373046875}, {"start": 2945.45, "end": 2945.83, "word": " a", "probability": 0.2578125}, {"start": 2945.83, "end": 2946.37, "word": " لا", "probability": 0.5849609375}, {"start": 2946.37, "end": 2947.25, "word": " تساوي", "probability": 0.974609375}, {"start": 2947.25, "end": 2948.03, "word": " سالب", "probability": 0.9833984375}, {"start": 2948.03, "end": 2948.47, "word": " اى", "probability": 0.877197265625}], "temperature": 1.0}, {"id": 104, "seek": 297601, "start": 2949.17, "end": 2976.01, "text": "ماقالليش ماعنديش condition يقوللي انه ايه بده تساوي سالب ايه يبقى بناء عليه الارابي علمه is not one two يبقى هنا five is not and times of not لا يزال هناك المزيد من الأمثلة", "tokens": [15042, 4587, 6027, 20292, 8592, 19446, 3615, 1863, 16254, 8592, 4188, 7251, 39648, 20292, 16472, 3224, 1975, 1829, 3224, 47525, 3224, 6055, 3794, 995, 45865, 8608, 6027, 3555, 1975, 1829, 3224, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 2423, 9640, 16758, 1829, 6225, 19528, 3224, 307, 406, 472, 732, 7251, 3555, 4587, 7578, 34105, 1732, 307, 406, 293, 1413, 295, 406, 20193, 7251, 11622, 6027, 34105, 4117, 9673, 11622, 25708, 9154, 16247, 2304, 12984, 37977], "avg_logprob": -0.3127056026929303, "compression_ratio": 1.563953488372093, "no_speech_prob": 0.0, "words": [{"start": 2949.17, "end": 2949.89, "word": "ماقالليش", "probability": 0.592626953125}, {"start": 2949.89, "end": 2950.43, "word": " ماعنديش", "probability": 0.9119140625}, {"start": 2950.43, "end": 2951.21, "word": " condition", "probability": 0.94970703125}, {"start": 2951.21, "end": 2952.37, "word": " يقوللي", "probability": 0.8640950520833334}, {"start": 2952.37, "end": 2952.91, "word": " انه", "probability": 0.7216796875}, {"start": 2952.91, "end": 2953.69, "word": " ايه", "probability": 0.8995768229166666}, {"start": 2953.69, "end": 2954.63, "word": " بده", "probability": 0.6453857421875}, {"start": 2954.63, "end": 2955.29, "word": " تساوي", "probability": 0.87890625}, {"start": 2955.29, "end": 2955.95, "word": " سالب", "probability": 0.78662109375}, {"start": 2955.95, "end": 2956.43, "word": " ايه", "probability": 0.9514973958333334}, {"start": 2956.43, "end": 2956.93, "word": " يبقى", "probability": 0.8846435546875}, {"start": 2956.93, "end": 2957.31, "word": " بناء", "probability": 0.90087890625}, {"start": 2957.31, "end": 2957.95, "word": " عليه", "probability": 0.71240234375}, {"start": 2957.95, "end": 2959.13, "word": " الارابي", "probability": 0.600830078125}, {"start": 2959.13, "end": 2959.83, "word": " علمه", "probability": 0.5513509114583334}, {"start": 2959.83, "end": 2960.15, "word": " is", "probability": 0.89501953125}, {"start": 2960.15, "end": 2960.83, "word": " not", "probability": 0.94775390625}, {"start": 2960.83, "end": 2961.47, "word": " one", "probability": 0.87255859375}, {"start": 2961.47, "end": 2962.13, "word": " two", "probability": 0.28662109375}, {"start": 2962.13, "end": 2963.13, "word": " يبقى", "probability": 0.9576416015625}, {"start": 2963.13, "end": 2963.49, "word": " هنا", "probability": 0.98779296875}, {"start": 2963.49, "end": 2965.21, "word": " five", "probability": 0.29833984375}, {"start": 2965.21, "end": 2966.99, "word": " is", "probability": 0.830078125}, {"start": 2966.99, "end": 2968.43, "word": " not", "probability": 0.88671875}, {"start": 2968.43, "end": 2969.97, "word": " and", "probability": 0.46044921875}, {"start": 2969.97, "end": 2971.09, "word": " times", "probability": 0.2802734375}, {"start": 2971.09, "end": 2971.41, "word": " of", "probability": 0.68505859375}, {"start": 2971.41, "end": 2971.75, "word": " not", "probability": 0.046783447265625}, {"start": 2971.75, "end": 2972.91, "word": " لا", "probability": 0.49169921875}, {"start": 2972.91, "end": 2973.41, "word": " يزال", "probability": 0.9549153645833334}, {"start": 2973.41, "end": 2973.91, "word": " هناك", "probability": 0.98876953125}, {"start": 2973.91, "end": 2974.77, "word": " المزيد", "probability": 0.99462890625}, {"start": 2974.77, "end": 2975.15, "word": " من", "probability": 0.9921875}, {"start": 2975.15, "end": 2976.01, "word": " الأمثلة", "probability": 0.836181640625}], "temperature": 1.0}, {"id": 105, "seek": 299937, "start": 2976.43, "end": 2999.37, "text": "ومن ضمن الأمثلة القادمة ان شاء الله بدنا نحسب أكم homomorphism عندما ال ring إلى ring أخرى وهذا طبعا عملته في جبر حديث واحد وبدنا نروح نعمل كذلك في جبر حديث اثنين", "tokens": [20498, 1863, 48812, 27842, 16247, 2304, 12984, 37977, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 47525, 8315, 8717, 5016, 35457, 5551, 24793, 3655, 32702, 1434, 43242, 15042, 2423, 4875, 30731, 4875, 5551, 34740, 7578, 37037, 15730, 23032, 3555, 3615, 995, 6225, 42213, 47395, 8978, 10874, 26890, 11331, 16254, 12984, 36764, 24401, 4032, 44510, 8315, 8717, 32887, 5016, 8717, 25957, 1211, 9122, 8848, 23275, 8978, 10874, 26890, 11331, 16254, 12984, 1975, 12984, 1863, 9957], "avg_logprob": -0.16891892133532344, "compression_ratio": 1.6058823529411765, "no_speech_prob": 0.0, "words": [{"start": 2976.43, "end": 2976.91, "word": "ومن", "probability": 0.773193359375}, {"start": 2976.91, "end": 2977.21, "word": " ضمن", "probability": 0.979248046875}, {"start": 2977.21, "end": 2978.13, "word": " الأمثلة", "probability": 0.9852294921875}, {"start": 2978.13, "end": 2979.41, "word": " القادمة", "probability": 0.9938151041666666}, {"start": 2979.41, "end": 2979.81, "word": " ان", "probability": 0.35400390625}, {"start": 2979.81, "end": 2980.25, "word": " شاء", "probability": 0.982177734375}, {"start": 2980.25, "end": 2980.79, "word": " الله", "probability": 0.96044921875}, {"start": 2980.79, "end": 2981.69, "word": " بدنا", "probability": 0.55108642578125}, {"start": 2981.69, "end": 2982.23, "word": " نحسب", "probability": 0.99462890625}, {"start": 2982.23, "end": 2982.97, "word": " أكم", "probability": 0.858154296875}, {"start": 2982.97, "end": 2984.45, "word": " homomorphism", "probability": 0.8304036458333334}, {"start": 2984.45, "end": 2985.53, "word": " عندما", "probability": 0.6429443359375}, {"start": 2985.53, "end": 2985.77, "word": " ال", "probability": 0.7646484375}, {"start": 2985.77, "end": 2986.13, "word": " ring", "probability": 0.8251953125}, {"start": 2986.13, "end": 2986.59, "word": " إلى", "probability": 0.81103515625}, {"start": 2986.59, "end": 2987.71, "word": " ring", "probability": 0.912109375}, {"start": 2987.71, "end": 2988.85, "word": " أخرى", "probability": 0.9620768229166666}, {"start": 2988.85, "end": 2989.67, "word": " وهذا", "probability": 0.665771484375}, {"start": 2989.67, "end": 2990.45, "word": " طبعا", "probability": 0.94775390625}, {"start": 2990.45, "end": 2991.59, "word": " عملته", "probability": 0.9459635416666666}, {"start": 2991.59, "end": 2992.35, "word": " في", "probability": 0.9619140625}, {"start": 2992.35, "end": 2992.83, "word": " جبر", "probability": 0.8779296875}, {"start": 2992.83, "end": 2993.39, "word": " حديث", "probability": 0.8243815104166666}, {"start": 2993.39, "end": 2993.93, "word": " واحد", "probability": 0.958251953125}, {"start": 2993.93, "end": 2994.75, "word": " وبدنا", "probability": 0.7413736979166666}, {"start": 2994.75, "end": 2995.17, "word": " نروح", "probability": 0.9879557291666666}, {"start": 2995.17, "end": 2995.85, "word": " نعمل", "probability": 0.9090169270833334}, {"start": 2995.85, "end": 2996.89, "word": " كذلك", "probability": 0.8248697916666666}, {"start": 2996.89, "end": 2997.33, "word": " في", "probability": 0.9091796875}, {"start": 2997.33, "end": 2997.73, "word": " جبر", "probability": 0.994140625}, {"start": 2997.73, "end": 2998.69, "word": " حديث", "probability": 0.9869791666666666}, {"start": 2998.69, "end": 2999.37, "word": " اثنين", "probability": 0.7806396484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2999.4840625, "duration_after_vad": 2944.685624999987}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5fb7dfd7a25eb3dc074b85b5ee48054a87206e22
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_raw.srt
@@ -0,0 +1,1772 @@
+1
+00:00:21,130 --> 00:00:25,950
+بالله الرحمن الرحيم انتهينا الآن من ال three
+
+2
+00:00:25,950 --> 00:00:30,250
+chapters و الان نمشي لل chapter الرابع اللي بتحدث
+
+3
+00:00:30,250 --> 00:00:35,850
+عن ال ring homomorphism لنعطي تعريف لل ring
+
+4
+00:00:35,850 --> 00:00:40,770
+homomorphism و نشوف وجه الاختلاف بينه و بين ال
+
+5
+00:00:40,770 --> 00:00:47,030
+group homomorphism بقول لو عندى two rings R و S
+
+6
+00:00:47,350 --> 00:00:53,670
+وعندي Phi هي mapping من R إلى S يبقى الـ Phi بقول
+
+7
+00:00:53,670 --> 00:00:58,690
+عنها Ring Homomorphism كلمة Homomorphism هختصرها
+
+8
+00:00:58,690 --> 00:01:02,650
+خلال الكتابة إلى Homo يبقى الـ Phi بسميها
+
+9
+00:01:02,650 --> 00:01:08,090
+Homomorphism إذا كان لجميع عناصر A وB اللي موجودة
+
+10
+00:01:08,090 --> 00:01:13,350
+في R We have condition الأول Phi of A زائد B بساوي
+
+11
+00:01:13,350 --> 00:01:18,060
+Phi of A زائد Phi of Bوالـ Condition التاني Phi of
+
+12
+00:01:18,060 --> 00:01:25,120
+A في B بيكون Phi of A مضروب في Phi of B لجميع قيم
+
+13
+00:01:25,120 --> 00:01:32,320
+A وB الموجودة في R يبدأ إذا Phi حققت هذين الشرتين
+
+14
+00:01:32,320 --> 00:01:38,380
+بقول عن Phi Homomorphism إذا حصل زيادة على ذلك ما
+
+15
+00:01:38,380 --> 00:01:43,020
+هي هذه الزيادة؟ كانت الـ Function Phi هي one to
+
+16
+00:01:43,020 --> 00:01:50,340
+one and untoنبقى الخيب ده سميها isomorphism كلمة
+
+17
+00:01:50,340 --> 00:01:54,720
+homomorphism أخدتوها في ال groups وكان معناها
+
+18
+00:01:54,720 --> 00:02:01,920
+التشاكل لكن isomorphism التشاكل النماطي إيش يعني
+
+19
+00:02:01,920 --> 00:02:05,460
+التشاكل النماطي هي ترجمة عربية، عربية أنا بدي
+
+20
+00:02:05,460 --> 00:02:10,680
+المعنى الرياضي لها ف homomorphism في علاقة ما بين
+
+21
+00:02:10,680 --> 00:02:15,580
+ring و ring أخرىبتحقق الشرطين هذول أكتر من هيك
+
+22
+00:02:15,580 --> 00:02:20,360
+ماعنديش لكن إذا isomorphism يبقى عدد العناصر في ال
+
+23
+00:02:20,360 --> 00:02:24,640
+ring الأولى جد عدد العناصر في ال ring الثانية هنا
+
+24
+00:02:24,640 --> 00:02:32,060
+إذا فيها على سبيل المثال أربعة عناصر ال order اللي
+
+25
+00:02:32,060 --> 00:02:35,720
+يساوي خمسة يبقى هذه فيها أربعة عناصر ال order فيها
+
+26
+00:02:35,720 --> 00:02:39,620
+اللي يساوي خمسة إذا فيها هذه unity يبقى ال ring
+
+27
+00:02:39,620 --> 00:02:45,810
+التانية فيها unity وباختصارجميع الخواص على ال ring
+
+28
+00:02:45,810 --> 00:02:51,330
+الأولى لها مناظر جميع نفس الخواص على ال ring
+
+29
+00:02:51,330 --> 00:02:55,930
+الثاني هذا معنى ال isomorphism لكن رياضيا مشان
+
+30
+00:02:55,930 --> 00:03:00,110
+أثبت ذلك بدي أثبت ال two conditions اللي عندنا و
+
+31
+00:03:00,110 --> 00:03:05,230
+بدي أثبت ان five is one to one and unto بدي ناخد
+
+32
+00:03:05,230 --> 00:03:10,540
+مجموعة من الأمثلة على ذلكالمثال الأول قال اعرف لـ
+
+33
+00:03:10,540 --> 00:03:17,200
+Phi من Z إلى ZL By Phi of K يسوى K Modulo M الـ K
+
+34
+00:03:17,200 --> 00:03:22,840
+هذه موجودة وين؟ في الـ Z و K Modulo N موجودة في ZM
+
+35
+00:03:22,840 --> 00:03:27,400
+قال يبقى Phi في هذه الحالة is a homomorphism
+
+36
+00:03:27,400 --> 00:03:32,300
+because بدالي ال two conditions اللي عندنا هذول
+
+37
+00:03:32,300 --> 00:03:41,600
+أروح أشوفهم تفعل يبقى Phi ofبدأ ياخد K زائد ال M
+
+38
+00:03:41,600 --> 00:03:47,020
+مثلا حسب ال definition اللي احنا حاطينه يبقى K
+
+39
+00:03:47,020 --> 00:03:55,660
+زائد ال M موديولو مين؟ موديولو N هذا الكلام بده
+
+40
+00:03:55,660 --> 00:04:08,790
+ساوي K موديولو N زائد M M موديولو Nهذا هنا هو
+
+41
+00:04:08,790 --> 00:04:15,630
+عمارة من مين؟ Phi of K يبقى هذا بيطيني Phi of K و
+
+42
+00:04:15,630 --> 00:04:24,610
+هذا Phi of M الكلام هذا صحيح لكل K و M اللي موجودة
+
+43
+00:04:24,610 --> 00:04:29,750
+في set of integers اللي هي مين اللي هي Z اللي
+
+44
+00:04:29,750 --> 00:04:34,570
+عندنا لخطر أسأل سؤال قبل ما أروح أجيب ال condition
+
+45
+00:04:34,570 --> 00:04:40,480
+الثانيالزائد اللي عندنا يا بنات هي نفس الزائد هذه
+
+46
+00:04:40,480 --> 00:04:48,800
+نفسها تماما، نفس ال operation لأ بتخلف، بتخلف ليش؟
+
+47
+00:04:48,800 --> 00:04:55,320
+لإن الزائد هذه معرفة على مين؟ على ring Z يبقى هذا
+
+48
+00:04:55,320 --> 00:05:00,880
+جمع الأعداد الصحيحة العادية يعني جمعة the usual
+
+49
+00:05:00,880 --> 00:05:08,430
+additionلكن في Z إن الجمع هذا جمع modulo N يبقى ال
+
+50
+00:05:08,430 --> 00:05:13,270
+condition هذا بنات الجمع هذا غير الجمع هذا هذا
+
+51
+00:05:13,270 --> 00:05:19,370
+العملية المعرفة على Z أو على ال ring R وهذه
+
+52
+00:05:19,370 --> 00:05:23,250
+العملية الزائدة الجمع المعرفة على ال ring بين S
+
+53
+00:05:23,250 --> 00:05:28,990
+يبقى two are different operationsتنتهي المختلفات
+
+54
+00:05:28,990 --> 00:05:34,110
+تماما لكن ممكن يكون اتنين نفس الشيء إذا كان من ال
+
+55
+00:05:34,110 --> 00:05:38,890
+ring إلى نفسها إذا من ال ring إلى نفسها يبقى بيصير
+
+56
+00:05:38,890 --> 00:05:42,510
+نفس العملية مش نفس ال ring تاني يبقى الجامعه على
+
+57
+00:05:42,510 --> 00:05:45,550
+ال ring التاني بيختلف عن الجامعه عالميا على ال
+
+58
+00:05:45,550 --> 00:05:48,790
+ring الأولى و لا كده و نفس الكلام اللي قلته
+
+59
+00:05:48,790 --> 00:05:53,270
+بالنسبة لعملية الضرب يبقى لو راجعنا لل group كان
+
+60
+00:05:53,270 --> 00:05:57,490
+عندي ال condition واحد مافيش غير هذاإذا العملية
+
+61
+00:05:57,490 --> 00:06:02,510
+عملية ضرب أو إذا العملية عملية جمع لكن في ال ring
+
+62
+00:06:02,510 --> 00:06:08,290
+بديت two conditions في آن واحد ومن هنا زدنا شرط عن
+
+63
+00:06:08,290 --> 00:06:12,810
+ما كان في حالة نين في حالة ال groups زي ما ال ring
+
+64
+00:06:12,810 --> 00:06:17,470
+أعرفنا عليها two operations بس ال group كانت one
+
+65
+00:06:17,470 --> 00:06:21,730
+operation أو one binary operation طيب ال
+
+66
+00:06:21,730 --> 00:06:30,240
+conditioning التانيفاي of K في M حسب التعريف يبقى
+
+67
+00:06:30,240 --> 00:06:38,080
+K في M موديولو N من ال number three يبقى ده K
+
+68
+00:06:38,080 --> 00:06:48,300
+موديولو N مضروب في M موديولو N ال K موديولو N هي
+
+69
+00:06:48,300 --> 00:06:57,290
+ديمين فاي of Kوالتانية Phi of M صحيح هذا الكلام
+
+70
+00:06:57,290 --> 00:07:04,130
+لكل ال K و M اللي موجودة وين اللي موجودة في Z يبقى
+
+71
+00:07:04,130 --> 00:07:12,570
+NSA Phi is a homomorphism كما طلب مني واحد في
+
+72
+00:07:12,570 --> 00:07:19,370
+المثل هذا يعتبر مثال بصير ومباشر ومافيش فيه تفكير
+
+73
+00:07:19,930 --> 00:07:27,510
+ننتقل إلى مثال آخر example two بيقول define a
+
+74
+00:07:27,510 --> 00:07:34,190
+function define a function Phi من ال set of
+
+75
+00:07:34,190 --> 00:07:39,390
+complex numbers إلى ال set of complex numbers
+
+76
+00:07:39,390 --> 00:07:48,890
+نفسها by Phi of ال a زائد ال b في ال I يساوي ال a
+
+77
+00:07:49,210 --> 00:08:01,130
+نقص الـP في الـI then I is hearing isomorphism
+
+78
+00:08:01,130 --> 00:08:05,750
+كلمة
+
+79
+00:08:05,750 --> 00:08:12,170
+isomorphism هختصرها ISO ISO هحط نقطة يبقى تفهميني
+
+80
+00:08:12,170 --> 00:08:18,100
+ان هذا isomorphism يبقى عجلة عن homomorphismحقق ال
+
+81
+00:08:18,100 --> 00:08:23,820
+two conditions وزيادة على ذلك وانتوا وانتوا وانتوا
+
+82
+00:08:23,820 --> 00:08:26,880
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+83
+00:08:26,880 --> 00:08:27,760
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+84
+00:08:27,760 --> 00:08:28,760
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+85
+00:08:28,760 --> 00:08:30,460
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+86
+00:08:30,460 --> 00:08:31,220
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+87
+00:08:31,220 --> 00:08:31,220
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+88
+00:08:31,220 --> 00:08:36,880
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+89
+00:08:36,880 --> 00:08:45,880
+وانتوا
+
+90
+00:08:45,880 --> 00:08:53,850
+وانيبقى بقوله let الـA زائد الـBI والـC زائد الـDI
+
+91
+00:08:53,850 --> 00:09:00,810
+موجودة في set of complex numbers then بتاجر أخد
+
+92
+00:09:00,810 --> 00:09:10,010
+فايل مجموعهما A زائد BI زائد C زائد DI
+
+93
+00:09:12,270 --> 00:09:17,210
+هذا الكلام يُسبب حسب ال complex number إذا جمعنا
+
+94
+00:09:17,210 --> 00:09:23,290
+جزء الحقيقي مع الحقيقي والتخيّلي مع التخيّلي يبقى
+
+95
+00:09:23,290 --> 00:09:35,090
+هذا A زائد C الحقيقي زائد B زائد D في I يبقى هذا
+
+96
+00:09:35,090 --> 00:09:39,490
+صار كله element واحد في set of complex number
+
+97
+00:09:39,490 --> 00:09:43,870
+جمعنا two complex numberطالع عندي one complex
+
+98
+00:09:43,870 --> 00:09:50,750
+number بتطلع عليه تعريف تعريف بيقول ايه؟ five of a
+
+99
+00:09:50,750 --> 00:09:56,390
+زي ال bi يسوى ال a ناقص bi اللي بدأ أسأله، في حق
+
+100
+00:09:56,390 --> 00:10:01,790
+واحدة ضارس complex number؟ كلكم؟ و الله شغالين
+
+101
+00:10:01,790 --> 00:10:06,610
+الحين؟ ممتاز، اللي خدتها و اللي شغالها الحين ممتاز
+
+102
+00:10:06,610 --> 00:10:10,510
+يبقى خليني أسأل السؤال التالي، مدام أنتم ماخدينها
+
+103
+00:10:10,820 --> 00:10:16,040
+هذا العنصر ايش بسميه بالنسبة للعنصر هذا المرافق ال
+
+104
+00:10:16,040 --> 00:10:21,500
+conjugate المرافق تبع هذا العنصر يبقى if I لو أثرت
+
+105
+00:10:21,500 --> 00:10:27,280
+على عنصر بتعطيني مرافق هذا العنصر اللي هو كمان
+
+106
+00:10:27,280 --> 00:10:32,620
+element موجود في set of complex number طيب يبقى
+
+107
+00:10:32,620 --> 00:10:38,820
+الأن بتجه طبقا لهذا التعريف يبقى بقول الجزء
+
+108
+00:10:38,820 --> 00:10:50,370
+الحقيقيناقص الجزء التخيلي B زائد D كله في I هذا
+
+109
+00:10:50,370 --> 00:10:56,310
+بقدر اكتبه كمجموع two elements يبقى بقدر اقول هذا
+
+110
+00:10:56,310 --> 00:11:06,250
+A ناقص B I العنصر الأول زائد C ناقص D في I اللي هو
+
+111
+00:11:06,250 --> 00:11:11,590
+العنصر التالفيبقى هذا العنصر استطعت كتابته على
+
+112
+00:11:11,590 --> 00:11:16,110
+مجموع عنصرين بمعنى لو جمعنا هذول اتنين بتطلع مين؟
+
+113
+00:11:16,110 --> 00:11:23,770
+بتطلع الأول طيب هذا الكلام يساوي يساوي
+
+114
+00:11:23,770 --> 00:11:28,230
+يبقى هذا العنصر طيب العنصر الأول هذا من هو؟ Phi of
+
+115
+00:11:28,230 --> 00:11:36,930
+A زي بي I يبقى هذا أصبح Phi of A زي بي I والتاني
+
+116
+00:11:37,430 --> 00:11:45,130
+فاي او C زائد D I يتحقق ال condition الأول من ال
+
+117
+00:11:45,130 --> 00:11:49,550
+two conditions تبعات ال homomorphism نذهب لل
+
+118
+00:11:49,550 --> 00:11:58,810
+condition التاني N فاي او A زائد بي I مضروب في C
+
+119
+00:11:58,810 --> 00:12:06,840
+زائد D Iبدي أخليه عنصر واحد حتى أقدر أدخل الـ Phi
+
+120
+00:12:06,840 --> 00:12:11,100
+عليه لذلك بدي أروح أضرب ال two elements في بعض
+
+121
+00:12:11,100 --> 00:12:19,380
+يبقى هذا الكلام بدي أساوي Phi of A في C الآن تعالى
+
+122
+00:12:19,380 --> 00:12:26,140
+B في DU و I في I و I ترميله بسالب واحد يبقى سالب
+
+123
+00:12:26,140 --> 00:12:34,900
+BD هذا الجزء الحقيقيبنا نيجي للجزء التشيولى زائد
+
+124
+00:12:34,900 --> 00:12:44,260
+الامين A D زائد B C كله في الامين في ال I وهي
+
+125
+00:12:44,260 --> 00:12:52,660
+الفرق صار هذا كله اللى هو الجزء الحقيقي وهذا هو
+
+126
+00:12:52,660 --> 00:12:57,580
+الجزء التشيولى يبقى صورة هذا العصر هو الكنجج
+
+127
+00:12:57,580 --> 00:13:04,520
+التابعيجى ال conjugate التابع هو عبارة عن a c ناقص
+
+128
+00:13:04,520 --> 00:13:14,940
+b d كله ال conjugate ناقص ال a d زائد ال b c كله
+
+129
+00:13:14,940 --> 00:13:23,900
+في ال I تمام هذا الكلام يساوي هل بقدر اكتب العصر
+
+130
+00:13:23,900 --> 00:13:29,890
+هذاعلى صيغة حاصل ضرب two elements إن جدرنا بيكون
+
+131
+00:13:29,890 --> 00:13:35,210
+حلت مشكلتنا ما جدرنا بيكون المشكلة قاعدة طيب
+
+132
+00:13:35,210 --> 00:13:44,210
+اتطلعوا لهك هل هذا هو ايه ناقص ال D I مضروب في C
+
+133
+00:13:44,210 --> 00:13:52,570
+ناقص ال D I تعالوا نضرب هذول ما هم هذول هاي لا بس
+
+134
+00:13:52,570 --> 00:13:58,310
+هم السابقفالله هنا a c بالموجة بغيرها الآن سالف في
+
+135
+00:13:58,310 --> 00:14:04,030
+سالف الموجة بي في دي اي في اي بناقص واحد تبقى سالف
+
+136
+00:14:04,030 --> 00:14:10,270
+بي في دي اي تقرينا من هنا هذا الان اللي هو بي سي
+
+137
+00:14:10,270 --> 00:14:15,810
+بالسالف في اي وهذه اي دي بالسالف في اي يبقى كلام
+
+138
+00:14:15,810 --> 00:14:21,950
+مظبوط إذا ال element هذا حطيته على صيغة حاصل ضرب
+
+139
+00:14:21,950 --> 00:14:28,180
+two elementsالـ Element الأول هذا ال conjugate شو
+
+140
+00:14:28,180 --> 00:14:38,060
+أصله؟ Phi of A زائد B I يبقى Phi of A زائد B I
+
+141
+00:14:38,060 --> 00:14:46,140
+والتاني Phi of C زائد D I يبقى اتحقق ال condition
+
+142
+00:14:46,140 --> 00:14:54,050
+التاني صح؟ يبقى Phi is homomorphicيبقى there فوق
+
+143
+00:14:54,050 --> 00:15:03,710
+ولهذا الـ Phi is a homomorphism الآن بدالي الـ Phi
+
+144
+00:15:03,710 --> 00:15:13,450
+is on as if Phi is one to one one to one بدنا نثبت
+
+145
+00:15:13,450 --> 00:15:18,090
+صحة هذا الكلام مشان نثبت صحة هذا الكلام بدنا ناخد
+
+146
+00:15:18,090 --> 00:15:23,930
+عنصرينمختلفة انه اثبت ان صورهم مختلفة او العملية
+
+147
+00:15:23,930 --> 00:15:29,490
+العكسية بدي اخد صورتين متساويتين و اثبت ان اصلهم
+
+148
+00:15:29,490 --> 00:15:35,690
+متساويتين ان حدث ذلك يبقى مصير الفاي is one point
+
+149
+00:15:35,690 --> 00:15:44,850
+يبقى باجي بقوله SU افترض ان الفاي of A زائد ال BI
+
+150
+00:15:44,850 --> 00:15:52,340
+بدي ساوي الفاي of C زائد ال DFيبقى حتة صورتين
+
+151
+00:15:52,340 --> 00:15:58,800
+متساويتين إذا جدلت أثبت أن ال A زيدي ال B I يسوي C
+
+152
+00:15:58,800 --> 00:16:03,340
+زيدي ال D I مصير الفاي is one to one وخلصنا من
+
+153
+00:16:03,340 --> 00:16:08,300
+الموضوع بقول كويس طيب هذا ال element اللي أخدته
+
+154
+00:16:08,300 --> 00:16:13,040
+الصورة مش عبارة عن نتيجتها هو ال conjugate element
+
+155
+00:16:13,040 --> 00:16:20,130
+أه يبقى هذا معناه أن ال A ناقص B I بالزاويةوالـ
+
+156
+00:16:20,130 --> 00:16:27,610
+Conjugate لهذه اللي هو C ذات الـ D I خيار A ناقص D
+
+157
+00:16:27,610 --> 00:16:34,350
+I A C ناقص D I كمان درسنا في ال complex لما يكون
+
+158
+00:16:34,350 --> 00:16:38,290
+complex number بيسوي complex number يبقى الجزء
+
+159
+00:16:38,290 --> 00:16:43,310
+الحقيقي بيسوي الجزء الحقيقي والتخيلي بيسوي التخيلي
+
+160
+00:16:43,310 --> 00:16:49,840
+إذا بناء عليه بقدر أقول ال A بيسوي ال Cوفي نفس
+
+161
+00:16:49,840 --> 00:16:58,260
+الوقت السالب B بدر يساوي سالب D يبقى هذا معناه ان
+
+162
+00:16:58,260 --> 00:17:05,740
+ال A بدر يساوي CL لو ضربت هنا في سالب 1 بصير ال B
+
+163
+00:17:05,740 --> 00:17:12,800
+بدر يساوي من ال D هذا معناه ان ال A زائد ال B I
+
+164
+00:17:12,800 --> 00:17:21,500
+يساوي ال A من هنا Cيبقى C والـ B من هنا D I وهو
+
+165
+00:17:21,500 --> 00:17:27,180
+المطلوب يبقى خات صوتين متساويتين طلع ان الاصل
+
+166
+00:17:27,180 --> 00:17:33,180
+تبعهم هي متساوي مش هانهيك الـ Phi is one to one.
+
+167
+00:17:33,880 --> 00:17:39,180
+هذا مباشر Direct Pro.يعني لا فيه لا لف ولا دوران
+
+168
+00:17:39,180 --> 00:17:44,020
+ولا فكرة. الآن بدنا نيجي لمين؟ لـ Phi is one to
+
+169
+00:17:44,020 --> 00:17:53,210
+one.يبقى في is on to ليش يعني معناه في is on to
+
+170
+00:17:53,210 --> 00:17:59,510
+بعلم الرياضية التابعنا بالبلد هيك الدول العربية
+
+171
+00:17:59,510 --> 00:18:06,430
+بقول في is on to يعني في دالة فوقية او اقتران فوقي
+
+172
+00:18:06,430 --> 00:18:12,330
+ايش يعني اقتران فوقي يعني غطى جميع أنصر ال code
+
+173
+00:18:12,330 --> 00:18:18,560
+domainيعني الـ Range هو الـ Codomain بالضبط تماماً
+
+174
+00:18:18,560 --> 00:18:23,480
+طب مشان أثبت أن الـ Phi is on to بتروح أخد Element
+
+175
+00:18:23,480 --> 00:18:30,140
+من الـ Codomain عشوائي و أثبت أنه أصل في ال domain
+
+176
+00:18:30,140 --> 00:18:35,860
+إن حدث ذلك يبقى Phi بصير on to يبقى إحنا عندنا Phi
+
+177
+00:18:35,860 --> 00:18:42,490
+من C إلى C بتاخد أي Element في ال Codomainو حاول
+
+178
+00:18:42,490 --> 00:18:48,210
+أثبت إنه إله أصل في ال domain إن جدرنا خلاص بصير
+
+179
+00:18:48,210 --> 00:18:53,870
+ال five as one و بالتالي ال five بصير isomorphism
+
+180
+00:18:53,870 --> 00:19:03,290
+طيب بداجي أقوله الآن ال a زائد ال bi موجود في ال
+
+181
+00:19:03,290 --> 00:19:08,830
+code من الوست of complex numbers هذا بده يعطينا
+
+182
+00:19:08,830 --> 00:19:19,140
+مين؟إن الـ A زائد ال V عارف ممكن أكتبه بطريقة أخرى
+
+183
+00:19:19,140 --> 00:19:27,680
+و هي ال A سالب سالب V عارف سالب في سالب الوجه دي
+
+184
+00:19:27,680 --> 00:19:34,140
+احنا ماسويناش اشي طيب لو رجعت لset of complex
+
+185
+00:19:34,140 --> 00:19:40,760
+numberالـA والـB الـreal number صح ولا لأ يبقى
+
+186
+00:19:40,760 --> 00:19:45,780
+السلب موجود والموجب موجود ماعنده مشكلة إذا هذا
+
+187
+00:19:45,780 --> 00:19:52,620
+element سلب هذا يبقى هذا conjugateت لمن ل element
+
+188
+00:19:52,620 --> 00:19:59,880
+تاني صح ولا لأ يعني هذا ههه هو عبارة عن صورة من
+
+189
+00:19:59,880 --> 00:20:09,160
+صورة الـA الذات الناقص بيه في الأرضأه حسب ال
+
+190
+00:20:09,160 --> 00:20:12,420
+definition اللي احنا كاتبينه Phi of ال element
+
+191
+00:20:12,420 --> 00:20:16,980
+يسوى ال conjugate طيب انا بد ال conjugate لهذا ال
+
+192
+00:20:16,980 --> 00:20:20,200
+conjugate لهذا ان الإشارة اللي يبقى number كلها
+
+193
+00:20:20,200 --> 00:20:26,760
+لها بالزائد يبقى هذا الكلام اللي هو Phi of ال a
+
+194
+00:20:26,760 --> 00:20:33,900
+ناقص بيه في ال R يبقى اي element موجود في set of
+
+195
+00:20:33,900 --> 00:20:39,450
+complex numbersاللي جاتله أصل في ال set of complex
+
+196
+00:20:39,450 --> 00:20:47,150
+numbers هو a ناقص bi طيب لو أخدت ال a ناقص bi
+
+197
+00:20:47,150 --> 00:20:53,290
+هيطلع a زائد bi اللي هو ال phi of a زائد bi يبقى
+
+198
+00:20:53,290 --> 00:20:57,390
+احنا بي كانت موجب والله سالبي بالتمنيش element
+
+199
+00:20:57,390 --> 00:21:03,630
+موجب سالب سفر كله صحيح عندي تمامإذا بناء عليه صارت
+
+200
+00:21:03,630 --> 00:21:07,690
+الـ Phi is onto لإن ال element اللي موجود في ال
+
+201
+00:21:07,690 --> 00:21:12,490
+set of complex number لاجت له أصل في ال set of
+
+202
+00:21:12,490 --> 00:21:17,070
+complex number يبقى أي element في ال set of
+
+203
+00:21:17,070 --> 00:21:21,050
+complex number له أصل في ال set of complex number
+
+204
+00:21:21,050 --> 00:21:25,130
+يبقى Phi is onto يبقى Phi حققت ال two conditions
+
+205
+00:21:25,130 --> 00:21:29,850
+تبع ال homomorphism حققت ال one to oneحققت اللي
+
+206
+00:21:29,850 --> 00:21:39,230
+انتوا يبقى فاي isomorphism يبقى هنا فاي is an
+
+207
+00:21:39,230 --> 00:21:46,430
+isomorphism هذا هو المثال الثاني نروح للمثال
+
+208
+00:21:46,430 --> 00:21:53,390
+الثالث مثل رقم تلاتة بيقول define a map او a
+
+209
+00:21:53,390 --> 00:22:03,660
+function define a functionمن الـ set of all
+
+210
+00:22:03,660 --> 00:22:11,900
+polynomials with real coefficients لمين للأربعة by
+
+211
+00:22:11,900 --> 00:22:22,280
+فاي of ال F of X بالدي ساوي ال F of 1 show
+
+212
+00:22:22,280 --> 00:22:32,210
+that ان الفاي isفي homomorphism
+
+213
+00:22:32,210 --> 00:22:43,610
+Phi is homomorphism but not isomorphism لنثبت أن
+
+214
+00:22:43,610 --> 00:22:51,630
+هذه homomorphism لكنها ليست في الحقيقة isomorphism
+
+215
+00:22:51,630 --> 00:22:58,730
+يبقى يكفيني إيش؟ أني أثبت أنها homomorphismnot one
+
+216
+00:22:58,730 --> 00:23:02,890
+to one او not one to one او واحد من اتنين ليس
+
+217
+00:23:02,890 --> 00:23:07,550
+بالضرورة لكي تكون مهياش ايزو مورفزن لا تريد السبع
+
+218
+00:23:07,550 --> 00:23:11,610
+دي تلو conditions يكشيني ميه ايه اللي تقدر عليه
+
+219
+00:23:11,610 --> 00:23:15,190
+اثبت انه ماهياش one to one خلاص كفى الله المؤمنين
+
+220
+00:23:15,190 --> 00:23:19,430
+القتال اثبت ماهياش one to one يبقى خلاص أي واحدة
+
+221
+00:23:19,430 --> 00:23:27,090
+فيهم طيب الحلقة التالية solutionخلّينا نشوف
+
+222
+00:23:27,090 --> 00:23:33,170
+تعريفنا هذا معقول ولا لأ؟ هنا الـ functions كلها
+
+223
+00:23:33,170 --> 00:23:37,510
+polynomial with real coefficients يبقى ال F of X
+
+224
+00:23:37,510 --> 00:23:44,330
+أي polynomial كودية صورتها مين؟ F of 1 فعطيني رقم،
+
+225
+00:23:44,330 --> 00:23:49,050
+real number، صح؟ موجود وين؟ موجود في أرض التعريف
+
+226
+00:23:49,050 --> 00:23:53,670
+هذا مافي مشكلة، تعريفنا سليم، أخدت ال من ال domain
+
+227
+00:23:53,990 --> 00:23:59,730
+لقيت له صورة في ال code من يبقى function تمام طيب
+
+228
+00:23:59,730 --> 00:24:03,930
+الان هو قال لي function يعني انا مش لازم اللي اروح
+
+229
+00:24:03,930 --> 00:24:07,910
+ابحث هل هي function ولا ما هي function يبقى هو
+
+230
+00:24:07,910 --> 00:24:11,870
+اعطاني وقال لي slim هاي ها دي function عندك بس شوف
+
+231
+00:24:11,870 --> 00:24:17,990
+حالي homomorphism او isomorphism ام لا يبقى
+
+232
+00:24:17,990 --> 00:24:25,990
+بالدقاق ياخد الان file او fالـ F في الـ F of X
+
+233
+00:24:25,990 --> 00:24:29,030
+والـ
+
+234
+00:24:29,030 --> 00:24:38,670
+G of X موجودات في الـ R of X Then بتاخد تأثير الـ
+
+235
+00:24:38,670 --> 00:24:47,590
+Phi على مجموعهما F of X زائد الـ G of X نرجع للـ
+
+236
+00:24:47,590 --> 00:24:55,650
+Calculus أليس هذا يا بنات Phif زائد g كله تأثير
+
+237
+00:24:55,650 --> 00:25:01,210
+على x وهو هذا تعريف مجموعة functions في ال
+
+238
+00:25:01,210 --> 00:25:08,070
+calculus هذا الكلام يساوي يبقى احنا هنا صار ان
+
+239
+00:25:08,070 --> 00:25:14,130
+مجموعة functions هي function جديدة وكأن هذه كلها
+
+240
+00:25:14,130 --> 00:25:20,590
+function جديدة يبقى صورة تميل بدأت تكون f زائد g
+
+241
+00:25:20,660 --> 00:25:27,360
+الـ g كله as a function of one برجه نرجع لل
+
+242
+00:25:27,360 --> 00:25:34,240
+calculus يبقى هذه f of one زائد ال g of one ال f
+
+243
+00:25:34,240 --> 00:25:43,980
+of one يبقى هي فاي لل f of x زائد الفاي لل g of x
+
+244
+00:25:43,980 --> 00:25:49,060
+إذا انت حقق من ال condition الأول بده أروح لل
+
+245
+00:25:49,060 --> 00:25:58,950
+condition التانيفاية الـ F of X مضروبة في الـ G of
+
+246
+00:25:58,950 --> 00:26:04,330
+X نرجع للكلكله ثانية تعرف حاصل ضرب to function
+
+247
+00:26:04,330 --> 00:26:11,630
+يبقى فاية للـ F مضروبة في G as a function of X
+
+248
+00:26:11,630 --> 00:26:19,010
+يبقى حاصل الضرب نتج عند اقتران جديد او دالة جديدة
+
+249
+00:26:19,410 --> 00:26:26,110
+كلها دالة واحدة فاي للدالة هذه تأثيرها على X يساوي
+
+250
+00:26:26,110 --> 00:26:32,570
+بهذه الدالة تأثيرها على الواحد يبقى بده يساوي FG
+
+251
+00:26:32,570 --> 00:26:38,310
+of one حسب ال definition اللي فوق يبقى هذا الكلام
+
+252
+00:26:38,310 --> 00:26:44,790
+بده يساوي ال F of one في ال G of one ال F of one
+
+253
+00:26:45,230 --> 00:26:55,390
+هذه فاي لل F of X وهذه فاي لل G of X إذا انتحقق
+
+254
+00:26:55,390 --> 00:27:06,810
+الشرطان يبقى هنا So فاي is a homomorphism قال اثبت
+
+255
+00:27:06,810 --> 00:27:13,890
+انها homomorphism لكنها ليستإذا أثبتنا إن فاي is
+
+256
+00:27:13,890 --> 00:27:20,590
+not one to one تكون خلصنا من الموضوع إذا بيدروح
+
+257
+00:27:20,590 --> 00:27:28,690
+أخد عمصرين مختلفين و أثبت إن صورهم مختلفة يا إما
+
+258
+00:27:28,690 --> 00:27:34,950
+أو صورهم مختلفة مشان أثبتينها one to one إذا أنا
+
+259
+00:27:34,950 --> 00:27:42,510
+بقول not one to oneبتاخد عمصرين مختلفين بدي أثبت
+
+260
+00:27:42,510 --> 00:27:50,130
+أن صورهم متساوية أو بتاخد صورتين متساويتين و أثبت
+
+261
+00:27:50,130 --> 00:27:58,010
+أن أصلهم غير متساوي، مظبوط؟ طيب، يبقى الأن أنا
+
+262
+00:27:58,010 --> 00:28:03,050
+أزعم أن الـ5 is not one to one بتاخد عمصرين
+
+263
+00:28:03,050 --> 00:28:10,780
+مختلفين في من؟ في R of Xيبقى ماجي بقوله يعني كأنه
+
+264
+00:28:10,780 --> 00:28:16,500
+بدي أخد counter example يبقى لو روحته قولله خد لل
+
+265
+00:28:16,500 --> 00:28:28,940
+F of X مثلا يساوي ال X تكييب زائد مثلا واحد and ال
+
+266
+00:28:28,940 --> 00:28:36,620
+G of X يساوي ال X زائد واحد هل هدون اتنين متساوية؟
+
+267
+00:28:36,620 --> 00:28:41,660
+لأthen ال
+
+268
+00:28:41,660 --> 00:28:53,620
+F of X لا يساوي ال G of X بياخد عنصرين مختلفين but
+
+269
+00:28:53,620 --> 00:29:01,660
+ولكن ال F of واحد كده شو بتساوي يا ابنها؟ F of
+
+270
+00:29:01,660 --> 00:29:09,560
+واحد نهت و G of واحديعني طلع صورتين متساويتين، صح؟
+
+271
+00:29:09,560 --> 00:29:17,600
+يبقى F of واحد تساوي G of واحد يساوي اتنين، يبقى
+
+272
+00:29:17,600 --> 00:29:27,260
+عنصران مختلفان صورتان متساويتين، بنت هيكون one to
+
+273
+00:29:27,260 --> 00:29:34,800
+one؟ لأ، يبقى هذا بده يعطينا ان five is not one to
+
+274
+00:29:34,800 --> 00:29:45,140
+oneمشان هيك So Phi is not an isomorphism كنت عاش
+
+275
+00:29:45,140 --> 00:29:50,980
+أكون Phi isomorphism أروح للشرط الراجل؟ مش داعي
+
+276
+00:29:50,980 --> 00:29:55,820
+خمسين فالمية من الشروط ماظبطتش يبقى خلاص مش داعي
+
+277
+00:29:55,820 --> 00:30:02,080
+أروح لمين للباقي يبقى هذا كده مثال رقم تلاتة مثال
+
+278
+00:30:02,080 --> 00:30:13,330
+رقم أربعاربعة بيقولش show that show that بيقوللي
+
+279
+00:30:13,330 --> 00:30:27,910
+انه قال من من z أربعة الى z عشرة defined by
+
+280
+00:30:27,910 --> 00:30:39,970
+defined by والمعرفة ديfive of x يساوي خمسة x
+
+281
+00:30:39,970 --> 00:30:50,890
+موديولو عشرة is a ring homomorphism is a ring
+
+282
+00:30:50,890 --> 00:30:58,030
+homomorphism
+
+283
+00:30:58,030 --> 00:31:10,920
+but ولكنها not an isomorphismبقى منها isomorphism
+
+284
+00:31:10,920 --> 00:31:21,100
+ولكنها ليست isomorphism solution الجسال
+
+285
+00:31:21,100 --> 00:31:25,440
+اللي جامله أتفتنى homomorphism لكنها ليست
+
+286
+00:31:25,440 --> 00:31:30,120
+isomorphism هذا بنفس الطريقة بدي أثبت أن نفس ال
+
+287
+00:31:30,120 --> 00:31:35,530
+file معرفة هذه عبارة عن homomorphismلكنها ليست
+
+288
+00:31:35,530 --> 00:31:41,030
+isomorphism سؤال انت درست وجبار حديث واحد مع
+
+289
+00:31:41,030 --> 00:31:47,010
+الدكتور محمد صح؟ صح لما كنت بعرف ال co-function من
+
+290
+00:31:47,010 --> 00:31:53,870
+ال group مثلا Zn إلى Zmمش الخطوة الأولى بتثبتلكوا
+
+291
+00:31:53,870 --> 00:31:58,430
+أنه Phi is well defined و بعدين بروح يثبت هذا
+
+292
+00:31:58,430 --> 00:32:03,430
+الكلام مظبط إذا إحنا هنا بنفس الطريقة بدنا نثبت
+
+293
+00:32:03,430 --> 00:32:08,050
+أنه Phi is well defined إيش يعني well defined من
+
+294
+00:32:08,050 --> 00:32:14,590
+الناحية الرياضية يعني بدي أخد عنصرين متساوين من ال
+
+295
+00:32:14,590 --> 00:32:20,590
+ring الأولى أثبت أنه الصورتين متساويتين في ال ring
+
+296
+00:32:20,590 --> 00:32:24,850
+الثانيةيعني عكس مين؟ عكس ال one to one ال one to
+
+297
+00:32:24,850 --> 00:32:28,970
+one باخد صورتين متساويتين بثبت أنه أصل متساوي، لأ
+
+298
+00:32:28,970 --> 00:32:34,250
+هذي بدي أخد عنصرين في الأصل متساويتين لأثبت أن
+
+299
+00:32:34,250 --> 00:32:40,970
+صورتهم متساوية، إن حدث ذلك يبقى بقوله five is well
+
+300
+00:32:40,970 --> 00:32:45,950
+defined يبقى وين ما تشوفي two rings بهذا الشكل
+
+301
+00:32:45,950 --> 00:32:50,820
+الخطوة الأولى تثبت أنه five is well definedيبقى
+
+302
+00:32:50,820 --> 00:32:59,980
+باجب أقولهم Phi is well defined يعني Phi معظفة
+
+303
+00:32:59,980 --> 00:33:06,220
+تعريفها مصحية لذلك بدي أجيب و أقولك افترضي ان عندي
+
+304
+00:33:06,220 --> 00:33:17,540
+عنصرين ال X modulo 4 بدي ساوي ال Y modulo 4 تمام؟
+
+305
+00:33:17,540 --> 00:33:25,820
+طيب هذا معناه مين؟معناته ان ال X ناقص ال Y كل
+
+306
+00:33:25,820 --> 00:33:31,600
+موديوله أربعة بده يساوي ال Zero موديوله أربعة
+
+307
+00:33:31,600 --> 00:33:44,040
+مظبوط هيك؟ طيب هذا معناه ان ال X ناقص ال Y يساوي
+
+308
+00:33:44,040 --> 00:33:53,790
+مضاعفات الأربعةيبقى هذا أربعة K و ال K هذه موجودة
+
+309
+00:33:53,790 --> 00:34:03,790
+في Z طب أنا بدي أوصل للصور شو الصور F of X يسوى
+
+310
+00:34:03,790 --> 00:34:12,750
+خمسة X تمام؟ إذا لو روحت ضربت في خمسة بنفع؟ بنفع
+
+311
+00:34:12,750 --> 00:34:17,680
+ليش ماينفع؟ عشان عندك معادلة رياضية بضرب في خمسةلو
+
+312
+00:34:17,680 --> 00:34:25,100
+ضربنا فيه خمسة بيصير خمسة K X ناقص Y يسوى خمسة في
+
+313
+00:34:25,100 --> 00:34:33,160
+أربعة K طيب بدي أشتغل في Z عشرة فبقول له يبقى هذه
+
+314
+00:34:33,160 --> 00:34:43,400
+خمسة X ناقص خمسة Y موديولو عشرة تسوى عشرين K
+
+315
+00:34:43,400 --> 00:34:51,550
+موديولو عشرةكداش الـ 20K في mod في Z عشرة Zero
+
+316
+00:34:51,550 --> 00:35:02,330
+يبقى هذا الكلام بده ساوي Zero mod 10 يبقى هذه بصير
+
+317
+00:35:02,330 --> 00:35:13,990
+خمسة X mod 10 ناقص خمسة Y mod 10 بده ساوي Zero mod
+
+318
+00:35:13,990 --> 00:35:25,760
+10يبقى هذه كإن الخمسة X Modulo عشرة متساوي خمسة Y
+
+319
+00:35:25,760 --> 00:35:32,540
+Modulo عشرة يعني إيش ال Phi of X متساوي Phi of Y
+
+320
+00:35:32,540 --> 00:35:41,560
+يبقى هذا معناه إن ال Phi of X متساوي Phi of Y لذلك
+
+321
+00:35:41,560 --> 00:35:50,620
+أخدت عنصرين متساويينإثبت إن صورتهم متساوية صورة
+
+322
+00:35:50,620 --> 00:35:55,860
+الأول هي نفس صورة التاني لذلك الدالة معرفة تعريفا
+
+323
+00:35:55,860 --> 00:36:01,820
+سليما ماحدش إله أي ممسك عليها الآن بدي أخش في
+
+324
+00:36:01,820 --> 00:36:09,700
+الموضوع التبعنا بقول لهم Phi is a homomorphism بدي
+
+325
+00:36:09,700 --> 00:36:17,510
+أخد عنصرين موجودين وين في Z أربعإن لو جيت قلت له
+
+326
+00:36:17,510 --> 00:36:29,090
+لأ X وY موجودة في Z أربع then الـ Phi of X زائد ال
+
+327
+00:36:29,090 --> 00:36:36,230
+Y حسب ال definition اللي احنا كاتبينه هذا بده يسوى
+
+328
+00:36:36,230 --> 00:36:44,990
+خمسة في X زائد ال Y موديول و عشر هذا بده يسوى يا
+
+329
+00:36:44,990 --> 00:36:53,770
+بناتالو خمسة X زائد خمسة Y موديولو عشرة هذا بده
+
+330
+00:36:53,770 --> 00:37:04,170
+يسوى خمسة X موديولو عشرة زائد خمسة Y موديولو عشرة
+
+331
+00:37:04,170 --> 00:37:10,330
+هذا بده يسوى من أوله لمن؟ Phi of X والتاني يبقى
+
+332
+00:37:10,330 --> 00:37:19,170
+هذا Phi of Xزائد Phi of Y إذا انتحقق الشرط الأول
+
+333
+00:37:19,170 --> 00:37:25,530
+من شروط ال homomorphism وهو Phi of X زائد Y بسوية
+
+334
+00:37:25,530 --> 00:37:32,370
+Phi of X زائد Phi of Y إذا روحنا مين للشرط الثاني
+
+335
+00:37:32,370 --> 00:37:39,310
+Phi of
+
+336
+00:37:39,310 --> 00:37:49,130
+X Y حسب ال definitionيساوي خمسة X Modulo عشرة.
+
+337
+00:37:49,630 --> 00:37:50,890
+Modulo عشرة.
+
+338
+00:37:53,730 --> 00:38:01,650
+طبعا؟ يعني هذا خمسة X Modulo عشرة في Y Modulo
+
+339
+00:38:01,650 --> 00:38:10,070
+عشرة. يبقى not homomorphism ولا لا؟ أكيد؟
+
+340
+00:38:10,070 --> 00:38:11,530
+قولوا غيره يا بنات
+
+341
+00:38:16,140 --> 00:38:21,740
+ولو كده كمان خمسة يعني لو بدل الخمسة كانت خمسة
+
+342
+00:38:21,740 --> 00:38:26,720
+وعشرين كان ماشي بتقوم ورا. مظبوط؟ بقدروا خمسة X في
+
+343
+00:38:26,720 --> 00:38:31,980
+خمسة Y. صح؟ طب هو الخمسة وعشرين في زيد عشرة في
+
+344
+00:38:31,980 --> 00:38:39,940
+كتير. خمسة يعني هذه بيضبط هي نفسهااللي هو خمسة
+
+345
+00:38:39,940 --> 00:38:47,580
+وعشرين XY موديولو عشر لإن الخمسة وعشرين في زد عشرة
+
+346
+00:38:47,580 --> 00:38:52,880
+هي خمسة اللي هي هذه لأن هذه هي هذه بالضبط تماما
+
+347
+00:38:52,880 --> 00:39:02,060
+إذا بقدر أقول هذه هي خمسة X موديولو عشرة مضروبة في
+
+348
+00:39:02,060 --> 00:39:10,720
+خمسة Y موديولو عشر مظبوط إيه؟يعني هذه Phi of X في
+
+349
+00:39:10,720 --> 00:39:16,520
+Phi of Y هذه بس النقطة اللي كانت لغز في السؤال
+
+350
+00:39:16,520 --> 00:39:21,280
+والباقي الشغل مباشرة يعني هذه اللي فيها تفكير بسيط
+
+351
+00:39:21,280 --> 00:39:25,180
+كيف أطلع من المطابق اللي أنا وقالتيه لإنه قاللي
+
+352
+00:39:25,180 --> 00:39:29,280
+أثبتلي إنه هذه عبارة عن homomorphism يبقى رصد من
+
+353
+00:39:29,280 --> 00:39:33,020
+أنا وعنك بدأتكون homomorphism لإنه قاللي أثبتها
+
+354
+00:39:33,020 --> 00:39:37,310
+يعني بقوله لا أثبتها بقولش إن أنا أثبتهايبقى هنا
+
+355
+00:39:37,310 --> 00:39:45,130
+اثبت انها homomorphic يبقى هنا فاي از هي
+
+356
+00:39:45,130 --> 00:39:55,350
+homomorphic طيب قالتلي انها ماهي ايزو مارفيزيك
+
+357
+00:39:55,350 --> 00:40:02,450
+قلتلتلي طيب اثبتوا ان فاي ماهي اش وان دور يبقى
+
+358
+00:40:02,450 --> 00:40:10,840
+بقوله فاي ازنقص one to one بكفي نجيب
+
+359
+00:40:10,840 --> 00:40:16,660
+counterexample كيف؟ الهي لو سألتك قداش five of
+
+360
+00:40:16,660 --> 00:40:24,680
+zero zero مضيوله عشرة zero مضيوله عشرة و لو سألتك
+
+361
+00:40:24,680 --> 00:40:35,140
+قداش five of اتنين اتنين في خمسة عشرة في زد عشرة
+
+362
+00:40:35,620 --> 00:40:44,880
+zero يبقى هذه بدها تساوي عشرة modulo عشرة يعني
+
+363
+00:40:44,880 --> 00:40:51,920
+zero modulo عشرة يبقى معنى هذا الكلام ان ال five
+
+364
+00:40:51,920 --> 00:40:59,700
+or zero يساوي ال five of اتنين هاي صوتين متساويتين
+
+365
+00:40:59,700 --> 00:41:07,620
+butليه اتنين بتسويش زيرو او زيرو بتسويش اتنين يبقى
+
+366
+00:41:07,620 --> 00:41:15,100
+five is not one to one يبقى five is not on
+
+367
+00:41:15,100 --> 00:41:20,100
+isomorphism طب لو واحدة حابة تثبت انه five is not
+
+368
+00:41:20,100 --> 00:41:25,300
+on يعني انت في السؤال اللي فات اثبت انه five is
+
+369
+00:41:25,300 --> 00:41:31,160
+not one to one و سيبت الانت بتقدر تثبت الناس
+
+370
+00:41:35,340 --> 00:41:39,240
+العنصر من زد عشرة ليس صورة العنصر من زد عشرة ليس
+
+371
+00:41:39,240 --> 00:41:41,340
+صورة العنصر من زد عشرة ليس صورة العنصر من زد عشرة
+
+372
+00:41:41,340 --> 00:41:42,680
+ليس صورة العنصر من زد عشرة ليس صورة العنصر من زد
+
+373
+00:41:42,680 --> 00:41:43,740
+عشرة ليس صورة العنصر من زد عشرة ليس صورة العنصر من
+
+374
+00:41:43,740 --> 00:41:45,520
+زد عشرة ليس صورة العنصر من زد عشرة ليس صورة العنصر
+
+375
+00:41:45,520 --> 00:41:49,160
+من زد عشرة ليس صورة العنصر من زد عشرة ليس صورة
+
+376
+00:41:49,160 --> 00:41:52,160
+العنصر من زد عشرة ليس صورة العنصر من زد عشرة ليس
+
+377
+00:41:52,160 --> 00:41:55,980
+صورة العنصر من زد عشرة ليس صورة العنصر من زد عشرة
+
+378
+00:41:55,980 --> 00:42:02,780
+ليس صتسعة ثلاثة مثلًا؟ سبعة ايوة و واحدة كلهم عشرة
+
+379
+00:42:02,780 --> 00:42:17,140
+طيب بقدر اقوله هنا also five is not only لو
+
+380
+00:42:17,140 --> 00:42:25,280
+جدرس أثبت ان ال range لو جدرس أثبت ان ال range لا
+
+381
+00:42:25,280 --> 00:42:30,500
+يسوى جد عشرةمش بقول خلصنا؟ طب بدنا ندور على ال
+
+382
+00:42:30,500 --> 00:42:39,140
+range نشوف وقدرش ال range فبعيه الفائع يساوي؟ أيه
+
+383
+00:42:39,140 --> 00:42:45,920
+الفائع؟ X موجودة في Z أربع يعني بدي أخد five of
+
+384
+00:42:45,920 --> 00:42:49,520
+zero, five of واحد, five of اتنين, five of تلاتة
+
+385
+00:42:49,520 --> 00:42:53,680
+وشوهش بيعطينا؟ بيعطينا ال range صح ولا لا؟ احنا
+
+386
+00:42:53,680 --> 00:42:58,660
+بدي يعطينا أربع قيم وليس عشريبقى فاي ما هيش،
+
+387
+00:42:58,660 --> 00:43:03,140
+كنتوا، لكن أنا بالدبلي اللي هي رياضية ال ring تبع
+
+388
+00:43:03,140 --> 00:43:09,460
+الفاي، five of zero يسوي zero صح؟ و five of واحد
+
+389
+00:43:09,460 --> 00:43:17,260
+خمسة في واحد هي فامسة طب و five of اتنين هي five
+
+390
+00:43:17,260 --> 00:43:24,490
+of تلاتة خمسة هي five أربعة ماعندكفاي of اتنين
+
+391
+00:43:24,490 --> 00:43:28,590
+اللي هو zero فاي of تلاتة هو خمسة واربع ماعنديش
+
+392
+00:43:28,590 --> 00:43:35,230
+خلاص يبقى غير بس خمسة وزيره لا يسوى ال code من
+
+393
+00:43:35,230 --> 00:43:42,370
+اللي هو زت عشر يبقى فاي is not unto because قوليلي
+
+394
+00:43:42,370 --> 00:43:48,390
+هنا because ما هو معنى أنتوا أني بدي أغطي جميع
+
+395
+00:43:48,390 --> 00:43:54,080
+أنصر الزت عشرة بالاستثناء إن حد تداركبقول هذه five
+
+396
+00:43:54,080 --> 00:44:01,960
+is only هذا كان المثال رقم أربعة ونفس المثال رقم
+
+397
+00:44:01,960 --> 00:44:13,160
+خمسة مثال خمسة بيقول little r d a commutative ring
+
+398
+00:44:13,160 --> 00:44:16,280
+commutative
+
+399
+00:44:16,280 --> 00:44:19,840
+ring of characteristic two
+
+400
+00:44:22,460 --> 00:44:32,240
+characteristic two define a mapping define a
+
+401
+00:44:32,240 --> 00:44:38,480
+mapping بدنا
+
+402
+00:44:38,480 --> 00:44:47,220
+نعرف function والله ده ده five من ال R إلى نفسي من
+
+403
+00:44:47,220 --> 00:44:58,330
+ال ring لنفسها byفاي of A بده ساول A ترابيع لكل ال
+
+404
+00:44:58,330 --> 00:45:10,210
+A اللي موجودة في R show that show that فاي بيقوله
+
+405
+00:45:10,210 --> 00:45:18,750
+ان فاي is a homomorphism but not
+
+406
+00:45:21,270 --> 00:45:36,270
+Isomorphism لكنها ليست Isomorphism سؤال
+
+407
+00:45:36,270 --> 00:45:40,570
+مرة تانية في عندكم mutated brain ال characteristic
+
+408
+00:45:40,570 --> 00:45:45,750
+هي يساوي اتنين يعني لو ضربت اتنين في اي عنصر من
+
+409
+00:45:45,750 --> 00:45:52,330
+عناصرها بيطلع عنصر الصيفريجالي أعرف في من ال ring
+
+410
+00:45:52,330 --> 00:45:56,970
+إلى نفسها ب في of a و 7 a تربيع لكل ال a الموجودة
+
+411
+00:45:56,970 --> 00:46:02,650
+في R بيظهر أن في عبارة عن homomorphism لكنها ليست
+
+412
+00:46:02,650 --> 00:46:10,870
+isomorphism إذا بدي أخد ال a و ال b موجودة في R
+
+413
+00:46:10,870 --> 00:46:20,450
+عشوائية then بدي أخد تأثير ال في على مجموعهمايبقى
+
+414
+00:46:20,450 --> 00:46:28,470
+هذا الكلام بيصير a زائد b لكل ال R is commutative
+
+415
+00:46:28,470 --> 00:46:34,350
+يبقى لو commutative بدي أفك هذه بصير a تربية زائد
+
+416
+00:46:34,350 --> 00:46:41,110
+2ab زائد b تربية لكن لو ماكنتش commutative بدي
+
+417
+00:46:41,110 --> 00:46:47,250
+أقول لك a b زائد ba لكن لما كانت commutative يبقى
+
+418
+00:46:47,250 --> 00:46:48,530
+2ab
+
+419
+00:46:59,070 --> 00:47:06,190
+النتيجة تساوي A تربيع زائد B تربيع ال A تربيع حسب
+
+420
+00:47:06,190 --> 00:47:12,230
+ال definition هي Phi of A والتانية حسب ال
+
+421
+00:47:12,230 --> 00:47:19,840
+definition Phi of B5 of A زي 5 of B تحقق ال
+
+422
+00:47:19,840 --> 00:47:29,000
+condition الأول بدالي لل condition الثاني and 5 of
+
+423
+00:47:29,000 --> 00:47:38,740
+A في B بده يساوي ال A بيه كل تربية و يساوي هل هذا
+
+424
+00:47:38,740 --> 00:47:45,670
+الكلام يساوي A تربية B تربيةلا يسويه إلا إذا كان
+
+425
+00:47:45,670 --> 00:47:52,210
+ترمى commutative ماكانش commutative يبقى a, b, a,
+
+426
+00:47:52,330 --> 00:47:56,530
+b لكن نظرا إلى ان ال commutative ببدل زي ما بده
+
+427
+00:47:56,530 --> 00:48:02,450
+يبقى a تربية, b تربية ال a تربية هي Phi of a و ال
+
+428
+00:48:02,450 --> 00:48:08,490
+b تربية Phi of b يبقى تحقق ال two conditions يبقى
+
+429
+00:48:08,490 --> 00:48:17,150
+باجر بقوله so Phiis a homomorphism قال لي اثبتلي
+
+430
+00:48:17,150 --> 00:48:20,110
+ان هو homomorphism اثبتنا قال لي بس not
+
+431
+00:48:20,110 --> 00:48:29,510
+isomorphism بقوله ال phi is not isomorphism ليش؟
+
+432
+00:48:29,510 --> 00:48:34,610
+because اي عدد مستلبته بيديه نفسه لو أخدت منه phi
+
+433
+00:48:34,610 --> 00:48:43,930
+of a قداشه ساوي؟ a تربيهوخد فاى of ناقص اى الناقص
+
+434
+00:48:43,930 --> 00:48:49,870
+اى الكل ترجعله في قدر اى تربيع من الاتنين هدول
+
+435
+00:48:49,870 --> 00:48:57,230
+بدره يقول فاى of اى بده يساوي فاى of سالب اى يبقى
+
+436
+00:48:57,230 --> 00:49:08,030
+صورة تانى متساويه تانى but ولكن ال a لا تساوي سالب
+
+437
+00:49:08,030 --> 00:49:14,630
+اىماقالليش ماعنديش condition يقوللي انه ايه بده
+
+438
+00:49:14,630 --> 00:49:20,830
+تساوي سالب ايه يبقى بناء عليه الارابي علمه is not
+
+439
+00:49:20,830 --> 00:49:32,910
+one two يبقى هنا five is not and times of not لا
+
+440
+00:49:32,910 --> 00:49:39,410
+يزال هناك المزيد من الأمثلةومن ضمن الأمثلة القادمة
+
+441
+00:49:39,410 --> 00:49:45,770
+ان شاء الله بدنا نحسب أكم homomorphism عندما ال
+
+442
+00:49:45,770 --> 00:49:53,390
+ring إلى ring أخرى وهذا طبعا عملته في جبر حديث
+
+443
+00:49:53,390 --> 00:49:59,370
+واحد وبدنا نروح نعمل كذلك في جبر حديث اثنين
+
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{"start": 1795.98, "end": 1796.9, "word": " polynomial", "probability": 0.38671875}, {"start": 1796.9, "end": 1797.88, "word": " طب", "probability": 0.567626953125}, {"start": 1797.88, "end": 1798.8, "word": " والمعامل", "probability": 0.9072265625}, {"start": 1798.8, "end": 1799.56, "word": " تبعها", "probability": 0.95263671875}, {"start": 1799.56, "end": 1800.06, "word": " AN", "probability": 0.203857421875}, {"start": 1800.06, "end": 1800.74, "word": " هذا", "probability": 0.6640625}, {"start": 1800.74, "end": 1800.94, "word": " اللي", "probability": 0.915771484375}, {"start": 1800.94, "end": 1801.62, "word": " بسويش", "probability": 0.7310791015625}, {"start": 1801.62, "end": 1801.8, "word": " ال", "probability": 0.91259765625}, {"start": 1801.8, "end": 1802.16, "word": " zero", "probability": 0.66845703125}, {"start": 1802.16, "end": 1803.2, "word": " بسميه", "probability": 0.943359375}, {"start": 1803.2, "end": 1803.72, "word": " leading", "probability": 0.6123046875}, {"start": 1803.72, "end": 1804.84, "word": " coefficients", "probability": 0.464599609375}, {"start": 1804.84, "end": 1805.28, "word": " يعني", "probability": 0.927001953125}, {"start": 1805.28, "end": 1806.26, "word": " المعامل", "probability": 0.99267578125}, {"start": 1806.26, "end": 1807.54, "word": " القائد", "probability": 0.9544270833333334}, {"start": 1807.54, "end": 1808.14, "word": " او", "probability": 0.7091064453125}, {"start": 1808.14, "end": 1809.04, "word": " المعامل", "probability": 0.990234375}, {"start": 1809.04, "end": 1810.88, "word": " الرئيسي", "probability": 0.99228515625}, {"start": 1810.88, "end": 1811.4, "word": " تمام", "probability": 0.86279296875}, {"start": 1811.4, "end": 1812.18, "word": " يبقى", "probability": 0.64605712890625}, {"start": 1812.18, "end": 1812.38, "word": " ال", "probability": 0.966796875}, {"start": 1812.38, "end": 1812.88, "word": " AN", "probability": 0.79296875}, {"start": 1812.88, "end": 1813.6, "word": " بسميه", "probability": 0.98193359375}, {"start": 1813.6, "end": 1814.14, "word": " leading", "probability": 0.69970703125}, {"start": 1814.14, "end": 1815.24, "word": " coefficient", "probability": 0.68017578125}, {"start": 1815.24, "end": 1816.12, "word": " المعامل", "probability": 0.9822998046875}, {"start": 1816.12, "end": 1816.92, "word": " الرئيسي", "probability": 0.99619140625}, {"start": 1816.92, "end": 1817.52, "word": " او", "probability": 0.9365234375}, {"start": 1817.52, "end": 1818.12, "word": " المعامل", "probability": 0.992431640625}, {"start": 1818.12, "end": 1818.74, "word": " القائد", "probability": 0.9915364583333334}, {"start": 1818.74, "end": 1819.18, "word": " لل", "probability": 0.90771484375}, {"start": 1819.18, "end": 1820.0, "word": " polynomial", "probability": 0.92138671875}, {"start": 1820.0, "end": 1820.72, "word": " ليش؟", "probability": 0.740966796875}], "temperature": 1.0}, {"id": 58, "seek": 184819, "start": 1820.95, "end": 1848.19, "text": "لأن هذا إن كان لا يسوى Zero يبقى ال X أُس N موجودة لكن لو كان يسوى Zero بطيل ال X أُس وبالتالي تنقص درجة مين ال Polynome اللي هو بالتالي وجوده يترتب عليه أن ال N بتكون موجودة وبتبدأ تنزل الأسس تبع تمين تبع ال X لغاية ما تنعدم تماما", "tokens": [1211, 33456, 23758, 36145, 25961, 20193, 7251, 3794, 2407, 7578, 17182, 7251, 3555, 4587, 7578, 2423, 1783, 5551, 10859, 3794, 426, 3714, 29245, 23328, 3660, 44381, 45164, 25961, 7251, 3794, 2407, 7578, 17182, 4724, 9566, 26895, 2423, 1783, 5551, 10859, 3794, 46599, 6027, 2655, 6027, 1829, 6055, 1863, 4587, 9381, 11778, 47341, 3660, 3714, 9957, 2423, 3635, 2534, 423, 13672, 1829, 31439, 4724, 6027, 2655, 6027, 1829, 49610, 23328, 3224, 7251, 2655, 43500, 3555, 47356, 14739, 2423, 426, 39894, 30544, 3714, 29245, 23328, 3660, 46599, 2655, 44510, 10721, 6055, 1863, 11622, 1211, 16247, 3794, 3794, 6055, 3555, 3615, 6055, 2304, 9957, 6055, 3555, 3615, 2423, 1783, 5296, 17082, 995, 10632, 19446, 6055, 1863, 22488, 2304, 46811, 10943, 995], "avg_logprob": -0.24080882077457524, "compression_ratio": 1.8186046511627907, "no_speech_prob": 0.0, "words": [{"start": 1820.95, "end": 1821.27, "word": "لأن", "probability": 0.723876953125}, {"start": 1821.27, "end": 1821.59, "word": " هذا", "probability": 0.27978515625}, {"start": 1821.59, "end": 1822.03, "word": " إن", "probability": 0.591796875}, {"start": 1822.03, "end": 1822.43, "word": " كان", "probability": 0.91357421875}, {"start": 1822.43, "end": 1822.61, "word": " لا", "probability": 0.408447265625}, {"start": 1822.61, "end": 1823.25, "word": " يسوى", "probability": 0.753662109375}, {"start": 1823.25, "end": 1823.73, "word": " Zero", "probability": 0.328125}, {"start": 1823.73, "end": 1825.29, "word": " يبقى", "probability": 0.933837890625}, {"start": 1825.29, "end": 1825.55, "word": " ال", "probability": 0.77587890625}, {"start": 1825.55, "end": 1826.05, "word": " X", "probability": 0.7705078125}, {"start": 1826.05, "end": 1826.67, "word": " أُس", "probability": 0.7268880208333334}, {"start": 1826.67, "end": 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"end": 1839.33, "word": " ال", "probability": 0.90869140625}, {"start": 1839.33, "end": 1839.59, "word": " N", "probability": 0.92626953125}, {"start": 1839.59, "end": 1840.07, "word": " بتكون", "probability": 0.781494140625}, {"start": 1840.07, "end": 1840.77, "word": " موجودة", "probability": 0.991455078125}, {"start": 1840.77, "end": 1841.75, "word": " وبتبدأ", "probability": 0.80303955078125}, {"start": 1841.75, "end": 1842.51, "word": " تنزل", "probability": 0.9942626953125}, {"start": 1842.51, "end": 1843.51, "word": " الأسس", "probability": 0.8048502604166666}, {"start": 1843.51, "end": 1843.87, "word": " تبع", "probability": 0.9441731770833334}, {"start": 1843.87, "end": 1844.45, "word": " تمين", "probability": 0.7158203125}, {"start": 1844.45, "end": 1845.03, "word": " تبع", "probability": 0.9720052083333334}, {"start": 1845.03, "end": 1845.25, "word": " ال", "probability": 0.85791015625}, {"start": 1845.25, "end": 1845.55, "word": " X", "probability": 0.994140625}, {"start": 1845.55, "end": 1846.27, "word": " لغاية", "probability": 0.9901123046875}, {"start": 1846.27, "end": 1846.53, "word": " ما", "probability": 0.481689453125}, {"start": 1846.53, "end": 1847.35, "word": " تنعدم", "probability": 0.9691162109375}, {"start": 1847.35, "end": 1848.19, "word": " تماما", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 59, "seek": 187536, "start": 1848.84, "end": 1875.36, "text": "يبقى فيه انا شغلة مهمة جدا النقطة الأولى ال N هو درجة ال polynomial وال A N بسميه leading coefficients تعريف التاني بيقول ال leading coefficients ال A N لو كان هو ال unity تبع ال R مين ما يكون ال unity يكون هذا then ال F of X is called a monic polynomial", "tokens": [1829, 3555, 4587, 7578, 8978, 3224, 1975, 8315, 13412, 17082, 37977, 3714, 16095, 3660, 10874, 28259, 28239, 47432, 3660, 16247, 12610, 7578, 2423, 426, 31439, 11778, 47341, 3660, 2423, 26110, 16070, 316, 426, 4724, 38251, 1829, 3224, 5775, 31994, 37279, 16572, 5172, 16712, 7649, 1829, 4724, 1829, 39648, 2423, 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1987.21, "end": 1990.73, "word": " Integral", "probability": 0.619110107421875}, {"start": 1990.73, "end": 1993.77, "word": " domain", "probability": 0.59130859375}], "temperature": 1.0}, {"id": 65, "seek": 203963, "start": 2012.33, "end": 2039.63, "text": "يقولوا لو كان دي Integral domain ماذا نقصد بال Integral domain؟ community bring with unity مافيش فيها Zero divisors إلا الصفر تمام؟ حط المعلومة هذه في دماغنا و بدنا نبدأ نشتغل عليها إذا الخطوة الأولى بدي أقوله let دي be an Integral domain", "tokens": [1829, 39648, 14407, 45164, 25961, 11778, 1829, 23894, 304, 9274, 3714, 45636, 995, 8717, 4587, 9381, 3215, 20666, 23894, 304, 9274, 22807, 1768, 1565, 365, 18205, 19446, 41185, 8592, 8978, 11296, 17182, 25974, 830, 11933, 15040, 31767, 5172, 2288, 46811, 10943, 22807, 11331, 9566, 9673, 30241, 20498, 3660, 29538, 8978, 11778, 2304, 5718, 118, 8315, 4032, 47525, 8315, 8717, 44510, 10721, 8717, 8592, 2655, 17082, 1211, 25894, 11296, 11933, 15730, 33962, 9566, 2407, 3660, 16247, 12610, 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Integral", "probability": 0.851806640625}, {"start": 2016.49, "end": 2017.43, "word": " domain؟", "probability": 0.618896484375}, {"start": 2017.43, "end": 2019.35, "word": " community", "probability": 0.146728515625}, {"start": 2019.35, "end": 2020.11, "word": " bring", "probability": 0.390380859375}, {"start": 2020.11, "end": 2020.85, "word": " with", "probability": 0.701171875}, {"start": 2020.85, "end": 2021.45, "word": " unity", "probability": 0.93798828125}, {"start": 2021.45, "end": 2022.49, "word": " مافيش", "probability": 0.50537109375}, {"start": 2022.49, "end": 2022.77, "word": " فيها", "probability": 0.797119140625}, {"start": 2022.77, "end": 2023.07, "word": " Zero", "probability": 0.546875}, {"start": 2023.07, "end": 2023.99, "word": " divisors", "probability": 0.921875}, {"start": 2023.99, "end": 2024.33, "word": " إلا", "probability": 0.8251953125}, {"start": 2024.33, "end": 2024.95, "word": " الصفر", "probability": 0.9562174479166666}, {"start": 2024.95, "end": 2026.21, "word": " تمام؟", "probability": 0.671142578125}, {"start": 2026.21, "end": 2026.55, "word": " حط", "probability": 0.753173828125}, {"start": 2026.55, "end": 2027.15, "word": " المعلومة", "probability": 0.975830078125}, {"start": 2027.15, "end": 2027.35, "word": " هذه", "probability": 0.64111328125}, {"start": 2027.35, "end": 2027.53, "word": " في", "probability": 0.59375}, {"start": 2027.53, "end": 2027.97, "word": " دماغنا", "probability": 0.8427734375}, {"start": 2027.97, "end": 2028.09, "word": " و", "probability": 0.87158203125}, {"start": 2028.09, "end": 2028.29, "word": " بدنا", "probability": 0.55291748046875}, {"start": 2028.29, "end": 2028.63, "word": " نبدأ", "probability": 0.9747721354166666}, {"start": 2028.63, "end": 2029.31, "word": " نشتغل", "probability": 0.9935546875}, {"start": 2029.31, "end": 2030.11, "word": " عليها", "probability": 0.96533203125}, {"start": 2030.11, "end": 2030.43, "word": " إذا", "probability": 0.617431640625}, {"start": 2030.43, "end": 2031.03, "word": " الخطوة", "probability": 0.77862548828125}, {"start": 2031.03, "end": 2031.53, "word": " الأولى", "probability": 0.9767252604166666}, {"start": 2031.53, "end": 2031.81, "word": " بدي", "probability": 0.41387939453125}, {"start": 2031.81, "end": 2032.51, "word": " أقوله", "probability": 0.7470703125}, {"start": 2032.51, "end": 2033.21, "word": " let", "probability": 0.435302734375}, {"start": 2033.21, "end": 2034.85, "word": " دي", "probability": 0.573974609375}, {"start": 2034.85, "end": 2035.43, "word": " be", "probability": 0.763671875}, {"start": 2035.43, "end": 2036.47, "word": " an", "probability": 0.7197265625}, {"start": 2036.47, "end": 2038.83, "word": " Integral", "probability": 0.785400390625}, {"start": 2038.83, "end": 2039.63, "word": " domain", "probability": 0.95703125}], "temperature": 1.0}, {"id": 66, "seek": 207246, "start": 2042.99, "end": 2072.47, "text": "تمام then ال D is a commutative ring with unity مثلا one say على سبيل المثال بواحد طيب احنا بنثبت", "tokens": [2655, 15042, 2304, 550, 2423, 413, 307, 257, 800, 325, 1166, 4875, 365, 18205, 50113, 15040, 472, 584, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 4724, 14407, 24401, 23032, 1829, 3555, 1975, 5016, 8315, 44945, 12984, 3555, 2655], "avg_logprob": -0.26402244506738126, "compression_ratio": 1.1322314049586777, "no_speech_prob": 0.0, "words": [{"start": 2042.99, "end": 2043.67, "word": "تمام", "probability": 0.6176656087239584}, {"start": 2043.67, "end": 2044.69, "word": " then", "probability": 0.292236328125}, {"start": 2044.69, "end": 2047.93, "word": " ال", "probability": 0.60693359375}, {"start": 2047.93, "end": 2048.29, "word": " D", "probability": 0.67236328125}, {"start": 2048.29, "end": 2049.55, "word": " is", "probability": 0.8515625}, {"start": 2049.55, "end": 2050.59, "word": " a", "probability": 0.9765625}, {"start": 2050.59, "end": 2052.77, "word": " commutative", "probability": 0.96630859375}, {"start": 2052.77, "end": 2055.81, "word": " ring", "probability": 0.428955078125}, {"start": 2055.81, "end": 2059.41, "word": " with", "probability": 0.88525390625}, {"start": 2059.41, "end": 2061.79, "word": " unity", "probability": 0.63427734375}, {"start": 2061.79, "end": 2063.77, "word": " مثلا", "probability": 0.92236328125}, {"start": 2063.77, "end": 2064.31, "word": " one", "probability": 0.64892578125}, {"start": 2064.31, "end": 2065.13, "word": " say", "probability": 0.69677734375}, {"start": 2065.13, "end": 2065.89, "word": " على", "probability": 0.84619140625}, {"start": 2065.89, "end": 2066.47, "word": " سبيل", "probability": 0.9881184895833334}, {"start": 2066.47, "end": 2067.21, "word": " المثال", "probability": 0.9876302083333334}, {"start": 2067.21, "end": 2067.97, "word": " بواحد", "probability": 0.84423828125}, {"start": 2067.97, "end": 2070.95, "word": " طيب", "probability": 0.8917643229166666}, {"start": 2070.95, "end": 2071.55, "word": " احنا", "probability": 0.9378255208333334}, {"start": 2071.55, "end": 2072.47, 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"probability": 0.9345703125}, {"start": 2080.73, "end": 2081.01, "word": " with", "probability": 0.9111328125}, {"start": 2081.01, "end": 2081.55, "word": " unity", "probability": 0.9609375}, {"start": 2081.55, "end": 2082.55, "word": " تمام", "probability": 0.82470703125}, {"start": 2082.55, "end": 2083.55, "word": " يبقى", "probability": 0.8988037109375}, {"start": 2083.55, "end": 2083.91, "word": " باجي", "probability": 0.7421875}, {"start": 2083.91, "end": 2084.65, "word": " بقوله", "probability": 0.8204752604166666}, {"start": 2084.65, "end": 2085.39, "word": " ال", "probability": 0.72900390625}, {"start": 2085.39, "end": 2085.99, "word": " D", "probability": 0.98046875}, {"start": 2085.99, "end": 2086.61, "word": " of", "probability": 0.9482421875}, {"start": 2086.61, "end": 2087.09, "word": " X", "probability": 0.99365234375}, {"start": 2087.09, "end": 2088.29, "word": " is", "probability": 0.83447265625}, {"start": 2088.29, "end": 2091.23, "word": " commutative", "probability": 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then the leading then the leading factors ممكن يساوي زيرو ؟ مش إمكانية يبقى لا يمكن", "tokens": [1211, 2407, 10874, 36081, 2423, 5775, 6771, 550, 264, 5775, 550, 264, 5775, 6771, 3714, 43020, 7251, 3794, 995, 45865, 30767, 1829, 32887, 45520, 37893, 11933, 2304, 41361, 10632, 7251, 3555, 4587, 7578, 20193, 7251, 43020], "avg_logprob": -0.3707770334707724, "compression_ratio": 1.3423423423423424, "no_speech_prob": 0.0, "words": [{"start": 2324.97, "end": 2325.35, "word": "لو", "probability": 0.963623046875}, {"start": 2325.35, "end": 2325.65, "word": " جيت", "probability": 0.82568359375}, {"start": 2325.65, "end": 2325.81, "word": " ال", "probability": 0.81298828125}, {"start": 2325.81, "end": 2326.25, "word": " leading", "probability": 0.56640625}, {"start": 2326.25, "end": 2327.49, "word": " factors", "probability": 0.703125}, {"start": 2327.49, "end": 2329.35, "word": " then", "probability": 0.53515625}, {"start": 2329.35, "end": 2330.37, "word": " the", "probability": 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أعطيكم العافية المرجعة ان شاء الله", "tokens": [9566, 1829, 3555, 12399, 5551, 3615, 9566, 1829, 24793, 18863, 31845, 10632, 9673, 47341, 27884, 16472, 13412, 16606, 21984], "avg_logprob": -0.32402343302965164, "compression_ratio": 1.0588235294117647, "no_speech_prob": 0.0, "words": [{"start": 2472.56, "end": 2472.86, "word": "طيب،", "probability": 0.75189208984375}, {"start": 2472.86, "end": 2473.24, "word": " أعطيكم", "probability": 0.7498046875}, {"start": 2473.24, "end": 2473.74, "word": " العافية", "probability": 0.9099934895833334}, {"start": 2473.74, "end": 2474.52, "word": " المرجعة", "probability": 0.72412109375}, {"start": 2474.52, "end": 2474.64, "word": " ان", "probability": 0.352294921875}, {"start": 2474.64, "end": 2474.92, "word": " شاء", "probability": 0.97119140625}, {"start": 2474.92, "end": 2475.18, "word": " الله", "probability": 0.97265625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2480.309125, "duration_after_vad": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..427ba8e1d0f4f23cbb529369317418597f6279c6
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM.srt
@@ -0,0 +1,1518 @@
+1
+00:00:21,080 --> 00:00:25,780
+بسم الله الرحمن الرحيم. عدنا إلى بدأ المرة التي
+
+2
+00:00:25,780 --> 00:00:30,000
+فاتت، جئنا نتكلم على الـ prime ideals والـ maximal
+
+3
+00:00:30,000 --> 00:00:36,600
+ideals. تمام، وأعطينا على ذلك بعض الأمثلة مع الـ
+
+4
+00:00:36,600 --> 00:00:41,260
+factoring. كذلك، المثال رقم 5 بيقول: show that the
+
+5
+00:00:41,260 --> 00:00:45,260
+ideal، الـ principle ideal generated by X تربيع
+
+6
+00:00:45,260 --> 00:00:51,080
++ 1 is maximal in R[X]. إذا بدنا نثبت أن هذا الـ
+
+7
+00:00:51,080 --> 00:00:55,800
+ideal هو maximal.  way in our operation. لو راجعنا
+
+8
+00:00:55,800 --> 00:01:01,200
+بالذاكرة إلى الوراء قليلاً، مشان نثبت الـ maximality
+
+9
+00:01:01,200 --> 00:01:07,120
+لهذا الـ ideal. بفترض أن في عندي ideal آخر، وهذا الـ
+
+10
+00:01:07,120 --> 00:01:13,420
+ideal subset منه، وهذا الـ ideal subset من R. يا إما
+
+11
+00:01:13,420 --> 00:01:17,440
+الـ ideal اللي عندنا بده يساوي الـ ideal المقترح، يا
+
+12
+00:01:17,440 --> 00:01:22,480
+إما الـ ideal المقترح بده يساوي R. تمام؟
+
+13
+00:01:22,480 --> 00:01:34,120
+إذا، احنا بدنا نفرض هنا: assume that A is an
+
+14
+00:01:34,120 --> 00:01:40,300
+ideal such that... ideal of
+
+15
+00:01:42,090 --> 00:01:49,750
+R[X] such that بحيث أن الـ principle ideal
+
+16
+00:01:49,750 --> 00:01:56,570
+generated by X تربيع + 1 subset من A ولا
+
+17
+00:01:56,570 --> 00:02:06,870
+يساويه. والـ A معروف هو subset من الـ ring R[X]. إذا
+
+18
+00:02:06,870 --> 00:02:13,410
+كان الآن يساوي A، يبقى مطلوب إثبات أن A بده
+
+19
+00:02:13,410 --> 00:02:23,010
+يساوي R[X]. يبقى value بيقول: if we show that إذا
+
+20
+00:02:23,010 --> 00:02:32,090
+قدرنا نثبت أن A بده يساوي R[X] itself، then A
+
+21
+00:02:32,090 --> 00:02:39,350
+is maximal. طيب، also
+
+22
+00:02:41,510 --> 00:02:50,590
+وكذلك، if we show that إذا قدرنا نبين أن الواحد أو
+
+23
+00:02:50,590 --> 00:03:00,490
+الـ unity موجود في A، then A is maximal. مش هذا
+
+24
+00:03:00,490 --> 00:03:06,230
+مثال سابق أخذناه المحاضرة الماضية، أنه لو أخذت أي
+
+25
+00:03:06,230 --> 00:03:09,610
+من الـ ring R[X] اللي بتكون commutative ring with unity
+
+26
+00:03:09,990 --> 00:03:13,950
+ولقيت الـ unity موجود في الـ ideal I، يبقى الـ ideal I
+
+27
+00:03:13,950 --> 00:03:18,330
+اللي بده يساوي R[X]. وأثبتناها عملياً معاكم طبعاً. هو
+
+28
+00:03:18,330 --> 00:03:22,350
+سؤال في التمرين، احنا أعطينا مثال وبدنا نعتمد عليه
+
+29
+00:03:22,350 --> 00:03:32,730
+هنا في إثبات هذا. لسّة مين هي A؟ A فرض
+
+30
+00:03:32,730 --> 00:03:38,380
+من عندي. أهم شيء احنا... احنا الموجود عندنا مين؟ X
+
+31
+00:03:38,380 --> 00:03:42,860
+التربيع + 1. صح؟ هذا الـ ideal مُعطى. هذا اللي
+
+32
+00:03:42,860 --> 00:03:47,900
+بدي أثبت أنه maximal. من تعريف الـ maximal اللي عندك
+
+33
+00:03:47,900 --> 00:03:54,480
+بنقول: هذا maximal إذا وجدنا ideal ثاني بحيث
+
+34
+00:03:54,480 --> 00:03:59,640
+هذا subset منه، والـ ideal الثاني طبعاً subset من R[X]
+
+35
+00:03:59,640 --> 00:04:05,600
+فهو طبيعي أن حدث ذلك، يا إما هذا بيساوي A، يا
+
+36
+00:04:05,600 --> 00:04:09,320
+إما A بيساوي R[X]. مش هيك التعريف اللي مكتوب
+
+37
+00:04:09,320 --> 00:04:12,320
+عندك المرة دي؟ التعريف المكتوب للـ ideal، أيوة،
+
+38
+00:04:12,320 --> 00:04:16,200
+احنا
+
+39
+00:04:16,200 --> 00:04:20,260
+ما بنقول ideal، بنتكلم عن set. set لسه بدنا نثبت من
+
+40
+00:04:20,260 --> 00:04:26,180
+الأول، وهذا ideal. وفرضنا A، ideal ثاني. إذا
+
+41
+00:04:26,180 --> 00:04:32,720
+هذا الـ ideal هو subset من A ولا يساويه، يبقى إجباري
+
+42
+00:04:32,720 --> 00:04:36,700
+مشان يكون maximal، لازم أثبت أن A بده يساوي مين؟
+
+43
+00:04:36,700 --> 00:04:42,360
+بده يساوي R[X] طبعاً. يبقى هنا قلنا: إذا قدرنا نبين
+
+44
+00:04:42,360 --> 00:04:46,120
+أن A بده يساوي R[X]، يبقى A بيصير maximal. طبق
+
+45
+00:04:46,120 --> 00:04:51,120
+التعريف. طبق المثال اللي فات. إذا قدرت أثبت أن
+
+46
+00:04:51,120 --> 00:04:55,500
+الواحد موجود في A، يبقى A بده يساوي R[X]، يبقى
+
+47
+00:04:55,500 --> 00:05:02,780
+A maximal. عادي، مظبوط، أيه؟ بقول: كويس. طيب، بدنا
+
+48
+00:05:02,780 --> 00:05:07,460
+نحاول نثبت أن هذا A maximal، أو أن الواحد موجود
+
+49
+00:05:07,460 --> 00:05:15,560
+وين؟ موجود في A. لذلك بروح آخذ element موجود في
+
+50
+00:05:15,560 --> 00:05:20,720
+الـ ring R[X]، أو آخذه موجود في A ومش موجود في الـ
+
+51
+00:05:20,720 --> 00:05:25,260
+principle ideal generated by X تربيع + 1. يبقى باجي بقول:
+
+52
+00:05:25,260 --> 00:05:32,210
+افترض أن عندي الـ element f(x) موجود في الـ Ideal
+
+53
+00:05:32,210 --> 00:05:39,570
+A، والـ f(x) مش موجود في الـ Principle Ideal
+
+54
+00:05:39,570 --> 00:05:44,710
+generated by X تربيع + 1. ازاي الواحد؟ إذا أخذت element
+
+55
+00:05:44,710 --> 00:05:49,870
+موجود هنا ومش موجود هنا. هذا subset قد يساوي وقد لا
+
+56
+00:05:49,870 --> 00:05:55,250
+يساوي. على فرض لا يساوي، إذا ممكن ألاقي عناصر هنا مش
+
+57
+00:05:55,250 --> 00:06:00,150
+موجودة هنا. تمام؟ لكن كل العناصر اللي هنا موجودة وين؟
+
+58
+00:06:00,150 --> 00:06:05,590
+موجودة هنا. هذا إجباري. يبقى آخذ f(x) موجودة في
+
+59
+00:06:05,590 --> 00:06:10,450
+A، وأن f(x) مش موجودة في الـ principle ideal
+
+60
+00:06:10,450 --> 00:06:18,370
+generated by X تربيع + 1. السؤال هو: الـ f(x)
+
+61
+00:06:18,370 --> 00:06:24,870
+بقدر أكتبها بصورة أخرى أو بطريقة أخرى؟ السؤال هو: ما
+
+62
+00:06:24,870 --> 00:06:35,740
+هي هذه الصورة؟ بنقول له: then f(x) بدها تساوي...
+
+63
+00:06:35,740 --> 00:06:42,340
+أنا ماخذها وين؟ ماخذها في A. يبقى مش موجودة هنا.
+
+64
+00:06:42,340 --> 00:06:47,820
+يبقى الدرجة تبعتها هتكون أعلى من الدرجة الثانية؛
+
+65
+00:06:47,820 --> 00:06:51,060
+الثالثة، الرابعة، العاشرة، الخ... ما عندنا مشكلة. إذا
+
+66
+00:06:51,060 --> 00:06:58,200
+لو رحنا قسمة مطولة. f(x)
+
+67
+00:06:58,200 --> 00:07:03,160
+قسمناها على الـ polynomial X تربيع + 1، ايش
+
+68
+00:07:03,160 --> 00:07:10,460
+بدي يطلع؟ بدي يطلع q(x)، polynomial في X، X
+
+69
+00:07:10,460 --> 00:07:17,880
+تربيع + 1، زائد الباقي اللي هو r(x).
+
+70
+00:07:17,880 --> 00:07:22,540
+تمام؟ اه. استرسلنا شوية، بدي أنا أفهمها هذه،
+
+71
+00:07:22,540 --> 00:07:27,580
+أفهمها بطريقة بسيطة جداً، ولا حاجة. كيف أفهمها بسيط؟ بقول: ما
+
+72
+00:07:27,580 --> 00:07:33,020
+ياتي لما نقسم كثيرة حدود على كثيرة حدود، يمكن ننتهي
+
+73
+00:07:33,020 --> 00:07:38,440
+بأصفار. يبقى قسمة بدون باقي. يبقى بيكون الـ r(x)
+
+74
+00:07:38,440 --> 00:07:46,480
+يساوي صفر. تمام؟ وممكن يزيد شيء، لكن لما يزيد
+
+75
+00:07:46,480 --> 00:07:50,820
+شيء، درجته بتكون أقل من X تربيع + 1.
+
+76
+00:07:50,820 --> 00:07:55,160
+مظبوط. تمام؟ لأن لو كان أكثر من X تربيع + 1،
+
+77
+00:07:55,160 --> 00:08:00,400
+الـ term اللي عندنا هذا... طيب كويس. هنا بنقول:
+
+78
+00:08:00,400 --> 00:08:07,620
+where r(x) does not equal to zero، ومش
+
+79
+00:08:07,620 --> 00:08:18,040
+صفر، والـ degree لمن؟ للـ r(x) أقل من 2. لأن
+
+80
+00:08:18,040 --> 00:08:22,400
+لو صارت 2، بدها تصير مع الـ q(x) اللي مضروبة في
+
+81
+00:08:22,400 --> 00:08:26,300
+X تربيع + 1. لأن بقول: في الـ polynomial، بنقسم
+
+82
+00:08:26,300 --> 00:08:31,320
+polynomial، درجة البسط قد درجة المقام أو أكبر منه،
+
+83
+00:08:31,320 --> 00:08:36,140
+بنقسم قسمة مطولة. لكن لو كانت درجة البسط أقل من درجة
+
+84
+00:08:36,140 --> 00:08:41,420
+المقام، بقدر أقسم قسمة مطولة؟ لا، بقدرش. تمام؟ إذن
+
+85
+00:08:41,420 --> 00:08:46,780
+صار عندنا r(x) بتاخدها، بتساوي صفر. يبقى معنى هذا: لازم
+
+86
+00:08:47,220 --> 00:08:52,320
+ألاقي function في الـ r(x)، درجتها أقل من 2.
+
+87
+00:08:52,320 --> 00:08:57,460
+يعني من الدرجة الأولى. صح ولا لا؟ يبقى من
+
+88
+00:08:57,460 --> 00:09:03,340
+الدرجة الأولى. طيب، ممتاز. إذا بدي أكتب الـ r(x)
+
+89
+00:09:03,340 --> 00:09:11,460
+على الصيغة التالية: f(x) - q(x)(X تربيع + 1). تمام؟
+
+90
+00:09:11,460 --> 00:09:15,380
+طيب.
+
+91
+00:09:16,060 --> 00:09:20,160
+طيب، أنا هدفنا، f(x) وين موجودة؟ موجودة في A. في
+
+92
+00:09:20,160 --> 00:09:28,900
+A، في A. طيب، وهذه؟ برضه في A. برضه في A.
+
+93
+00:09:28,900 --> 00:09:35,100
+لماذا؟ لأنها في A. generated، وهذه constant. هذه
+
+94
+00:09:35,100 --> 00:09:45,400
+موجودة في A. عشانها... أي element
+
+95
+00:09:45,400 --> 00:09:50,280
+هنا موجود هنا، وأي element هنا على الصيغة اللي
+
+96
+00:09:50,280 --> 00:09:55,780
+قلناها. تعريف الـ principle ideal هو generated by A
+
+97
+00:09:55,780 --> 00:10:02,000
+هو A مضروبة في R[X] بحيث R في R[X]، وA يبقى
+
+98
+00:10:02,000 --> 00:10:11,440
+هنا. ليش هذه؟ because أن الـ principle ideal gene... أو
+
+99
+00:10:11,440 --> 00:10:18,940
+because X تربيع + 1 موجودة فيه. تمام؟ يبقى
+
+100
+00:10:18,940 --> 00:10:23,700
+ضربتها في أي function من R[X] موجودة فيه. إذا
+
+101
+00:10:23,700 --> 00:10:31,860
+صار r(x) موجودة فيه. طب مين هي r(x)؟ الـ r(x)
+
+102
+00:10:31,860 --> 00:10:39,120
+بدها تكون درجة أقل من 2. يبقى number of x...  بالصيغة... على الصيغة ax + b. صح؟ وهذه كلها
+
+103
+00:10:39,120 --> 00:10:49,200
+موجودة في A. وهذه موجودة في A. يبقى الـ term كل
+
+104
+00:10:49,200 --> 00:10:54,000
+هذا موجود هنا. واضح أكثر. يبقى هذا... بدي أعطيك ما
+
+105
+00:11:02,810 --> 00:11:11,810
+ياتي: r(x) تساوي f(x) - q(x)(X تربيع + 1). كلها موجودة في A. طيب، r(x)
+
+106
+00:11:11,810 --> 00:11:19,850
+درجتها أقل من الدرجة الثانية. يبقى درجة أولى. يبقى
+
+107
+00:11:19,850 --> 00:11:26,230
+بيصير عندنا ax + b، أو r(x) تساوي ax + b.
+
+108
+00:11:26,230 --> 00:11:37,790
+اللي هي هذه، اللي هي موجودة وين؟ موجودة في A. طيب،
+
+109
+00:11:37,790 --> 00:11:46,190
+بدي أسألكم السؤال التالي: Now لو أخذت ax + b
+
+110
+00:11:46,190 --> 00:11:54,710
+وضربتها في ax - b، هل هذه موجودة في A؟ في
+
+111
+00:11:54,710 --> 00:12:04,420
+A؟ اه، موجودة في A؟ اه، موجودة. ليش؟ لأن هذا الـ
+
+112
+00:12:04,420 --> 00:12:12,400
+element موجود في A، وA ideal، وضربيه في أي function
+
+113
+00:12:12,400 --> 00:12:18,720
+من R[X] بده يكون موجود في A. صحيح ولا لأ؟ إذا
+
+114
+00:12:18,720 --> 00:12:23,560
+هذه كذلك موجودة في A، because A is an ideal.
+
+115
+00:12:23,560 --> 00:12:33,210
+اللي بيحصل: ضربه... هذا موجود في A. طيب، الآن لو جيت
+
+116
+00:12:33,210 --> 00:12:39,250
+ضربت هذول في بعض، الفرق بين المربعين. يبقى a تربيع x
+
+117
+00:12:39,250 --> 00:12:44,430
+تربيع - b تربيع موجود وين؟ موجود في A.
+
+118
+00:12:58,850 --> 00:13:07,110
+الآن بدي أجيب كمان شغلة ثانية ونشوف هاذه موجودة
+
+119
+00:13:07,110 --> 00:13:17,410
+في A ولا لا. لو جيت قلت لك:  a تربيع x
+
+120
+00:13:17,410 --> 00:13:25,720
+تربيع + 1، هل هذه موجودة في A؟ x تربيع + 1
+
+121
+00:13:25,720 --> 00:13:28,460
+موجودة في الـ principle، والـ principle
+
+122
+00:13:28,460 --> 00:13:33,300
+subset من A. إذا هذا الـ element موجود في A هو ومضاعفاته. يبقى a تربيع x تربيع + a تربيع
+
+123
+00:13:33,300 --> 00:13:39,160
+لو بدنا نسوي a تربيع x تربيع + a تربيع، موجود في
+
+124
+00:13:39,160 --> 00:13:46,060
+A كذلك. طب لو جمعناهم بيكون موجود في A. طب لو
+
+125
+00:13:46,060 --> 00:13:53,090
+طرحناهم، طب لو طرحناهم، يبقى a تربيع x تربيع
+
+126
+00:13:53,090 --> 00:14:00,790
+- a تربيع x تربيع - b تربيع. كل هذا بيكون موجود في A. لو طرحناهم...
+
+127
+00:14:00,790 --> 00:14:09,450
+- a تربيع - b تربيع. كل هذا بيكون موجود في A. لو طرحناهم، بيطلع
+
+128
+00:14:09,450 --> 00:14:16,110
+a تربيع + b تربيع موجودة في A. يبقى طالع عندي
+
+129
+00:14:16,110 --> 00:14:22,950
+دالة ثابتة، اللي هي مين؟ a تربيع + b تربيع
+
+130
+00:14:22,950 --> 00:14:28,550
+موجودة وين؟ موجودة في A. طيب، مقلوبها موجودة في
+
+131
+00:14:28,550 --> 00:14:33,770
+A ولا لا؟ دالة مقلوبها. r(x)، كل الـ functions
+
+132
+00:14:33,770 --> 00:14:40,970
+تبعتها ثوابت، تمام؟ يبقى هذا بيبدأ يعطينا أنه واحد على
+
+133
+00:14:40,970 --> 00:14:48,200
+a تربيع + b تربيع موجودة في A كذلك. طب لو ضربناهم
+
+134
+00:14:48,200 --> 00:14:55,160
+في بعض... لو أخدت a تربيع + b تربيع ضرب واحد
+
+135
+00:14:55,160 --> 00:15:01,960
+على a تربيع + b تربيع، فهو موجود في A. يبقى هذا
+
+136
+00:15:01,960 --> 00:15:10,620
+بده يعطينا أن الواحد موجود في A. يبقى بناء عليه A كم
+
+137
+00:15:10,620 --> 00:15:16,920
+بده يساوي R[X]. It says يبقى هذا معناته A بده
+
+138
+00:15:16,920 --> 00:15:31,800
+يساوي R[X]. وهذا previous example، مثال سابق من
+
+139
+00:15:31,800 --> 00:15:36,960
+المحاضرة الماضية. مدام طلع A بده يساوي R[X]
+
+140
+00:15:36,960 --> 00:15:46,890
+يبقى A is maximal، وخلصنا من هذا المثال. تمام؟
+
+141
+00:15:46,890 --> 00:15:53,750
+كذا نبلغ من الآن فصاعداً، كل كثير... كل الـ
+
+142
+00:15:53,750 --> 00:15:59,070
+دوال  polynomial  معاملاتها أعداد حقيقية، وهي
+
+143
+00:15:59,070 --> 00:16:04,210
+polynomial، الـ X تربيع + 1، الـ principle ideal
+
+144
+00:16:04,210 --> 00:16:08,750
+generated by X تربيع + 1 يمثل maximal ideal
+
+145
+00:16:08,750 --> 00:16:15,400
+في مين؟ في R[X]. طيب، نعطي كمان مثال صغير، مش زي
+
+146
+00:16:15,400 --> 00:16:27,080
+هذا طويل. يبقى مثال 6، اجمع كذا 6... مين اللي
+
+147
+00:16:27,080 --> 00:16:32,720
+بيحكي؟ كيف؟
+
+148
+00:16:32,720 --> 00:16:36,520
+أنتَ
+
+149
+00:16:36,520 --> 00:16:42,330
+كتبت: so it is maximal. هذا آخر... آخر صورة، اللي هي الـ X
+
+150
+00:16:42,330 --> 00:16:49,310
+تربيع + 1، بالشكل هذا هي maximal. صحيح لأن
+
+151
+00:16:49,310 --> 00:16:55,890
+هذا اللي احنا بنثبته. بنجيب الـ ideal الثاني تبعتك. كده منع
+
+152
+00:16:55,890 --> 00:17:01,610
+واحد. بتثبت أن A... A is maximal. فاضح، فاضح، فاضح،
+
+153
+00:17:01,610 --> 00:17:11,100
+فاضح، فاضح، فاضح، فاضح، فاضح، فاضح. هنا؟ أول
+
+154
+00:17:11,100 --> 00:17:16,740
+السؤال. تالت وربع سطر. تالت وربع سطر. تالت وربع سطر.
+
+155
+00:17:16,740 --> 00:17:18,900
+تالت وربع سطر. تالت وربع سطر. تالت وربع سطر. تالت
+
+156
+00:17:18,900 --> 00:17:19,060
+وربع سطر. تالت وربع سطر. تالت وربع سطر. تالت وربع سطر.
+
+157
+00:17:19,060 --> 00:17:19,640
+تالت وربع سطر. تالت وربع سطر. تالت وربع سطر. تالت
+
+158
+00:17:19,640 --> 00:17:23,320
+وربع سطر. تالت وربع سطر. تالت وربع سطر. تالت
+
+159
+00:17:23,320 --> 00:17:32,640
+وربع سطر. تالت وربع سطر. تالت وربع سطر. تالت وربع سطر
+
+160
+00:17:39,930 --> 00:17:45,070
+إذا أثبتنا أن A يساوي R[X]، يساوي A، يصبح
+
+161
+00:17:45,070 --> 00:17:50,030
+A ماكسيمال حسب التعريف اللي عن الماكسيمالية.
+
+162
+00:17:50,030 --> 00:17:57,060
+مظبوط؟ طيب، أنا عشان أثبت هذا، A يساوي R[X]، بقول: لو
+
+163
+00:17:57,060 --> 00:18:02,080
+قدرت أثبت أن الواحد موجود في A، بيصير A يساوي
+
+164
+00:18:02,080 --> 00:18:05,420
+R[X].  بالثالث كيف؟ A، ولا الـ principle ideal
+
+165
+00:18:05,420 --> 00:18:06,640
+A، ولا الـ principle ideal... A، ولا الـ
+
+166
+00:18:06,640 --> 00:18:07,960
+principle ideal... A، ولا الـ principle ideal... A
+
+167
+00:18:07,960 --> 00:18:08,480
+ولا ال
+
+223
+00:23:17,810 --> 00:23:24,690
+A be an ideal
+
+224
+00:23:26,600 --> 00:23:39,120
+أو R، أفضل من R، ثم الـ R موديولو A هو مجموعة
+
+225
+00:23:39,120 --> 00:23:45,100
+انتقالية
+
+226
+00:23:45,100 --> 00:23:53,880
+F اندولي F، F اندولي F، الـ A صحيح
+
+227
+00:23:55,030 --> 00:24:03,930
+لو كان الـ A  Prime
+
+228
+00:24:03,930 --> 00:24:10,870
+ف
+
+229
+00:24:10,870 --> 00:24:14,330
+نعرف بقى الكمية، احنا عالنا R، كمية  to bring with
+
+230
+00:24:14,330 --> 00:24:19,810
+unity والـ A  ideal في R، يبقى بيقول الـ R modulo A
+
+231
+00:24:19,810 --> 00:24:23,990
+بتبقى integral domain إذا كان الـ A prime ideal
+
+232
+00:24:24,550 --> 00:24:29,710
+وكلمة F انتقالية تعنيني أن البرهان سيصير في
+
+233
+00:24:29,710 --> 00:24:36,690
+الاتجاهين، لذلك الاتجاه الأول بدي أفترض أن الـ R
+
+234
+00:24:36,690 --> 00:24:47,790
+modulo A is an integral domain، تمام؟
+
+235
+00:24:47,790 --> 00:24:53,920
+مشان أثبت أن الـ A is a prime، بدي آخد عنصرين من الـ
+
+236
+00:24:53,920 --> 00:24:59,560
+ring A، وأفترض أن حاصل ضربهما موجود وين في الـ
+
+237
+00:24:59,560 --> 00:25:04,600
+ideal A، إذا قدرت أثبت أن واحد منهم موجود في الـ A،
+
+238
+00:25:04,600 --> 00:25:10,580
+يكون الـ A is a prime ideal، مقتضى الـ definition
+
+239
+00:25:10,580 --> 00:25:18,760
+يبقى بدي أقوله: افترض أن الـ A والـ B موجودات في A،
+
+240
+00:25:18,760 --> 00:25:29,450
+such that بحيث أن الـ A في الـ B موجود في الـ A، طبعاً؟
+
+241
+00:25:29,450 --> 00:25:34,750
+مدام الـ A B موجود في الـ A، يبقى الـ A B زائد الـ A
+
+242
+00:25:34,750 --> 00:25:43,450
+جدا شبيهة بأنها الـ A itself، طبعاً؟ طيب مدام هذا
+
+243
+00:25:43,450 --> 00:25:51,470
+هيك، يبقى معناته: مرة ثانية، أخدت عنصرين موجودات
+
+244
+00:25:51,470 --> 00:26:00,770
+في R، بحيث أن حاصل ضربهما موجود في A، بدي أحاول أوصل
+
+245
+00:26:00,770 --> 00:26:06,530
+لشغلة أنه يا إما الـ A موجود في الـ A، يا إما الـ B
+
+246
+00:26:06,530 --> 00:26:14,650
+موجود في الـ A، هذا معناه أنه
+
+247
+00:26:14,650 --> 00:26:24,470
+الـ A زائد الـ A مضروب في الـ B زائد الـ A بدي أساوي
+
+248
+00:26:24,470 --> 00:26:32,670
+الـ A، السؤال هو: الـ A في حد ذاته إيش يمثل بالنسبة
+
+249
+00:26:32,670 --> 00:26:40,230
+للـ factor group R modulo A؟ شو اسم العنصر هذا؟ A
+
+250
+00:26:40,230 --> 00:26:47,650
+في factor group R modulo A؟ Zero element، ممتاز! يبقى
+
+251
+00:26:47,650 --> 00:26:50,950
+الـ zero element في الـ R مديول A، إيش اللي بده
+
+252
+00:26:50,950 --> 00:26:56,490
+يساوي إيش الخصائص؟ أن الـ R إيه؟ Integral Domain
+
+253
+00:26:56,490 --> 00:27:03,350
+مدام Integral Domain، بيطلع عندي حاصل ضرب عنصرين من
+
+254
+00:27:03,350 --> 00:27:08,090
+الـ ring اللي عندنا هذا أعطاني الـ zero، يبقى واحد
+
+255
+00:27:08,090 --> 00:27:13,270
+فيهم بده يكون بـ zero، صح ولا لأ؟ يبقى هذا بده
+
+256
+00:27:13,270 --> 00:27:19,750
+يعطينا يا إما الـ A زائد الـ A بده يساوي الـ A، يا إما
+
+257
+00:27:19,750 --> 00:27:26,430
+الـ B زائد الـ A بده يساوي الـ A itself،  يفهم هذا إيش
+
+258
+00:27:26,430 --> 00:27:31,250
+معناه؟ لما أقول A زائد A يساوي A، معناته الـ A
+
+259
+00:27:31,250 --> 00:27:37,830
+وين موجود؟ في الـ A، هذا معناه إن الـ A موجود في الـ A،
+
+260
+00:27:37,830 --> 00:27:46,970
+or الـ B موجود في الـ A، يبقى هذا معناه مين؟ حاصل ضرب
+
+261
+00:27:46,970 --> 00:27:52,250
+عنصرين موجود في A، أثبت له أن الأول في A، أو الـ B
+
+262
+00:27:52,250 --> 00:27:58,810
+في A، يبقى هذا معناه أن الـ A is a prime ideal، يبقى هذا
+
+263
+00:27:58,810 --> 00:28:07,410
+معناه أن الـ A is a prime ideal، يبقى
+
+264
+00:28:07,410 --> 00:28:10,410
+أثبتنا الاتجاه الأول، نجي للاتجاه الثاني
+
+265
+00:28:10,410 --> 00:28:11,850
+Conversely
+
+266
+00:28:15,260 --> 00:28:23,600
+Assume that إن الـ A is a prime ideal.
+
+267
+00:28:25,900 --> 00:28:35,840
+We want to show, we want to show that
+
+268
+00:28:35,840 --> 00:28:44,240
+بدنا نحاول نثبت أن الـ R modulo A is an integral
+
+269
+00:28:44,240 --> 00:28:50,040
+domain، طيب
+
+270
+00:28:50,040 --> 00:28:54,760
+واكتشف، أقدر أحكم على الـ ring إنها integral domain
+
+271
+00:28:54,760 --> 00:29:02,760
+إذا تحقق شرطان، الشرط الأول: إذا تبقى الـ ring هذه
+
+272
+00:29:02,760 --> 00:29:07,800
+commutative ring with unity، اثنين، مش فيها zero
+
+273
+00:29:07,800 --> 00:29:13,160
+divisors، أو لو وجدت حاصل ضرب عنصرين منها بده يساوي
+
+274
+00:29:13,160 --> 00:29:18,420
+الـ zero، بدي أثبت إن على الأقل واحد فيهم بده
+
+275
+00:29:18,420 --> 00:29:24,520
+يساوي الـ zero، ممتاز جداً! يبقى أنا أزعم أن الـ R
+
+276
+00:29:24,520 --> 00:29:36,200
+modulo A is a commutative ring with unity
+
+277
+00:29:38,710 --> 00:29:47,650
+قد إيش الـ unity؟ الـ A، قلنا zero element، يبقى واحد
+
+278
+00:29:47,650 --> 00:29:57,610
+زائد A، طب ليش هذا الكلام؟ because من
+
+279
+00:29:57,610 --> 00:30:02,330
+نص النظرية، قال الـ R commutative ring with unity
+
+280
+00:30:02,330 --> 00:30:06,370
+يبقى الـ R مديول A commutative ring with unity
+
+281
+00:30:06,890 --> 00:30:23,650
+because الـ R is a commutative ring with unity، تمام؟
+
+282
+00:30:23,650 --> 00:30:30,010
+طيب الآن أنا بدي أثبت إن الـ R عبارة عن integral
+
+283
+00:30:30,010 --> 00:30:36,190
+domain، integral domain يعني لو أخدت عنصرين، وضربتهم
+
+284
+00:30:36,190 --> 00:30:42,730
+في بعض، بدي أثبت أنه على الأقل واحد فيهم معناته بده
+
+285
+00:30:42,730 --> 00:30:48,510
+يساوي zero، يبقى أخدنا A prime ideal، بدنا نثبت هذا
+
+286
+00:30:48,510 --> 00:30:53,950
+integral domain، أثبتنا الشرط الأول، وهو أن الـ R
+
+287
+00:30:53,950 --> 00:31:00,370
+modulo A is a commutative ring with unity، تمام؟
+
+288
+00:31:00,370 --> 00:31:08,880
+الآن بدي أجي آخذ حاصل ضرب عنصرين فيهم، وأفترض أن هذا
+
+289
+00:31:08,880 --> 00:31:14,140
+الكلام بده يساوي مين؟ بده يساوي zero، بالضبط تماماً
+
+290
+00:31:14,140 --> 00:31:25,380
+يبقى بده أفترض أن عندي عنصرين: الـ A زائد الـ A، و
+
+291
+00:31:25,380 --> 00:31:35,870
+الـ B زائد الـ B زائد الـ A موجودة في الـ R مديول A
+
+292
+00:31:35,870 --> 00:31:45,910
+such that بحيث أن الـ A زائد الـ A مضروب في الـ B
+
+293
+00:31:45,910 --> 00:31:55,310
+زائد الـ A بده يساوي الـ zero element، تمام؟
+
+294
+00:31:55,310 --> 00:31:59,670
+يبقى then اللي
+
+295
+00:31:59,670 --> 00:32:07,460
+هو من الـ A B زائد الـ A بده يساوي مين؟ الـ A itself
+
+296
+00:32:07,460 --> 00:32:10,840
+مظبوط؟
+
+297
+00:32:10,840 --> 00:32:20,020
+طيب، هذا إيش معناه؟ هذا معناه إن الـ A B موجودة في
+
+298
+00:32:20,020 --> 00:32:24,700
+الـ A، كويس؟
+
+299
+00:32:24,700 --> 00:32:31,620
+يبقى الـ A B موجودة في الـ A، مدام الـ A B موجودة في
+
+300
+00:32:31,620 --> 00:32:36,880
+الـ A، تعالى نشوف في شغلة إحنا ما استفدناش منها، وهي إن
+
+301
+00:32:36,880 --> 00:32:41,900
+هذا prime ideal، مدام الـ prime ideal، يبقى هذا
+
+302
+00:32:41,900 --> 00:32:48,360
+معناته أن الـ A موجودة في الـ A، or الـ B موجودة في الـ
+
+303
+00:32:48,360 --> 00:32:59,940
+A، السبب because إن الـ A is a prime ideal، يبقى نظراً
+
+304
+00:32:59,940 --> 00:33:04,880
+لأن الـ prime، قاعدين هذا الكلام صحيح، طيب مدام الـ A
+
+305
+00:33:04,880 --> 00:33:10,040
+موجودة في A، يبقى الـ A زائد الـ A قد إيش بده يساوي يا
+
+306
+00:33:10,040 --> 00:33:20,860
+بنات؟ الـ A، or الـ B زائد الـ A بده يساوي الـ A، يبقى
+
+307
+00:33:20,860 --> 00:33:26,780
+أثبت إنه هذا بده يساوي الـ zero element، أو هذا بده
+
+308
+00:33:26,780 --> 00:33:31,920
+يساوي الـ zero element، يبقى هذا إيش معناه؟ إن الـ R
+
+309
+00:33:31,920 --> 00:33:37,640
+modulo A is an integral domain، لأن أخدت حاصل ضرب
+
+310
+00:33:37,640 --> 00:33:43,640
+عنصرين يساوي الصفر، لاقيت واحد فيهم بساوي الصفر،
+
+311
+00:33:43,640 --> 00:33:50,660
+يبقى هذا بده يعطينا إن الـ R modulo A is an
+
+312
+00:33:50,660 --> 00:33:53,700
+integral domain.
+
+313
+00:33:59,660 --> 00:34:06,520
+طيب، فيش حد أحسن من حد؟ الناس كلهم سواء، عشان
+
+314
+00:34:06,520 --> 00:34:12,340
+ماحدش يزعل من التاني. النظرية اتكلمت عن الـ Prime
+
+315
+00:34:12,340 --> 00:34:17,840
+ideals، ولم تتكلم عن؟ عن الـ Maximal ideals،
+
+316
+00:34:17,840 --> 00:34:21,980
+وموضوعنا موضوع الـ Prime والـ Maximal. إذن هناك
+
+317
+00:34:21,980 --> 00:34:29,200
+نظرية مناظرة لها، تتحدث عن مين؟ عن مين؟ الـ maximal
+
+318
+00:34:29,200 --> 00:34:34,980
+علاقته مع الـ factor ring، إذا بروح للنظرية الثانية
+
+319
+00:34:34,980 --> 00:34:43,780
+يبقى الـ theorem، النظرية الثانية بتقول:  Let
+
+320
+00:34:43,780 --> 00:34:56,020
+R be a commutative ring with unity
+
+321
+00:34:58,240 --> 00:35:07,140
+commutative ring with unity and
+
+322
+00:35:07,140 --> 00:35:16,660
+A an ideal of
+
+323
+00:35:16,660 --> 00:35:28,980
+R، then R modulo A is a field if and only if
+
+324
+00:35:28,980 --> 00:35:38,060
+and only if A is maximal، لغاية A is maximal
+
+325
+00:35:38,060 --> 00:35:42,720
+لغاية
+
+326
+00:35:42,720 --> 00:35:51,880
+الproof بدي
+
+327
+00:35:51,880 --> 00:35:58,420
+أصير برضه في اتجاهين، بسبب الـ if and only if، يبقى
+
+328
+00:35:58,420 --> 00:36:08,680
+بدرجة أقوله:  Let A be a maximal ideal، R modulo A is a field، يبقى
+
+329
+00:36:08,680 --> 00:36:17,560
+a field، طبعاً بدي أثبت أن الـ A  is maximal، يبقى
+
+330
+00:36:17,560 --> 00:36:37,110
+we want to show that إن الـ A is maximal، يبدأ
+
+331
+00:36:37,110 --> 00:36:44,050
+يقول: افترض أن الـ B يكون
+
+332
+00:36:44,050 --> 00:36:52,050
+ideal of R بحيث
+
+333
+00:36:52,050 --> 00:37:02,010
+أن الـ A اللي عندنا subset من الـ B ولا يساوي، والـ
+
+334
+00:37:02,010 --> 00:37:08,070
+B subset من R، و
+
+335
+00:37:08,070 --> 00:37:13,730
+الـ B subset من R، طيب
+
+336
+00:37:13,730 --> 00:37:20,570
+مرة ثانية،  قلنا R modulo A عبارة عن field، بتبين أن
+
+337
+00:37:20,570 --> 00:37:25,030
+الـ A maximal، لو روحت لتعريف الـ maximal، وشفت أنه
+
+338
+00:37:25,030 --> 00:37:31,110
+عندي ideal ثاني B، بحيث الـ A subset من B ولا يساوي
+
+339
+00:37:31,110 --> 00:37:36,850
+والـ B subset من R، إذا أثبتوا إنه B يساوي الـ R،
+
+340
+00:37:36,850 --> 00:37:42,310
+بيصير هذا الـ maximal، أو إذا أثبتوا إن الـ unity هو
+
+341
+00:37:42,310 --> 00:37:47,690
+الموجود في B، يبقى بيصير الـ A عبارة عن maximal
+
+342
+00:37:47,690 --> 00:37:51,430
+ideal. بيصير الـ B يساوي الـ R، وبالتالي الـ A is
+
+343
+00:37:51,430 --> 00:38:00,330
+maximal. بيقولوا: خلينا نقول: الـ B موجودة في B، بقى
+
+344
+00:38:00,330 --> 00:38:09,370
+ولكن الـ B مش موجودة في A، إيش صفّت من B ولا يساوي،
+
+345
+00:38:09,370 --> 00:38:15,410
+في عناصر موجودة في B ومش موجودة وين؟ في A، أخدت عنصر
+
+346
+00:38:15,410 --> 00:38:25,040
+موجود في B، وهذا العنصر مش موجود في A، الـ B زائد الـ A
+
+347
+00:38:25,040 --> 00:38:32,280
+بينفع أقول يساوي الـ A هنا؟ لأ، يفجأة لا يساوي الـ
+
+348
+00:38:32,280 --> 00:38:37,340
+A، يعني بيساويش الـ zero element، يفجأة الـ B زائد
+
+349
+00:38:37,340 --> 00:38:43,380
+الـ A is a non-zero element، يفجأة هذا بده يعطينا
+
+350
+00:38:43,380 --> 00:38:51,320
+أن الـ B زائد الـ A is a non-zero element
+
+351
+00:38:53,810 --> 00:39:00,090
+إن الـ R مديول A، يبقى
+
+352
+00:39:00,090 --> 00:39:08,130
+هذا عنصر غير صفري، وأنا فرضت R
+
+353
+00:39:08,130 --> 00:39:12,290
+مديول A field، يبقى هذا العنصر إذا كان غير صفري إيش
+
+354
+00:39:12,290 --> 00:39:18,190
+بده يكون؟ unit، لأن في الـ field أي عنصر غير الصفر
+
+355
+00:39:18,190 --> 00:39:25,870
+يكون unit، هذا بده يعطينا أن الـ B زائد الـ A is a
+
+356
+00:39:25,870 --> 00:39:33,550
+unit، تمام؟ يعني معنى هذا الكلام أن there exists
+
+357
+00:39:33,550 --> 00:39:43,430
+عنصر C زائد الـ A موجود في الـ R modulo A such that
+
+358
+00:39:43,430 --> 00:39:51,630
+بحيث أن حاصل ضربهما بده يساوي الـ unity، مظبوط؟ يعني
+
+359
+00:39:51,630 --> 00:39:57,790
+بده يكون الـ B زائد الـ A في هذا الـ element اللي هو
+
+360
+00:39:57,790 --> 00:40:03,790
+C زائد الـ A بده يساوي الـ unity اللي هو واحد زائد الـ
+
+361
+00:40:03,790 --> 00:40:13,710
+A، يعني إيش معنى هذا الكلام؟ معناه إن الـ B C زائد الـ
+
+362
+00:40:13,710 --> 00:40:23,570
+A يساوي واحد زائد الـ A، أو لو جينا أضفنا للطرفين سالب
+
+363
+00:40:23,570 --> 00:40:33,430
+B C، بيظل الـ A بده يساوي واحد ناقص B C زائد الـ A
+
+364
+00:40:33,430 --> 00:40:40,190
+هذا إيش معناه؟ أن الـ element هذا وين موجود؟ موجود
+
+365
+00:40:40,190 --> 00:40:46,650
+في الـ A، يبقى هذا معناه أن الواحد ناقص الـ B C
+
+366
+00:40:46,650 --> 00:40:52,980
+موجود في الـ A، طب الـ A subset من B ولا لأ؟ يبقى الـ
+
+367
+00:40:52,980 --> 00:40:57,300
+element هذا موجود في B ولا لأ؟ يبقى هذا اللي
+
+368
+00:40:57,300 --> 00:41:06,420
+بيعطيكي علاقة للخاطر أن واحد ناقص B C موجود في B
+
+369
+00:41:06,420 --> 00:41:17,310
+because إن الـ A subset من B ولا يساوي،  الخلاصة الـ
+
+370
+00:41:17,310 --> 00:41:22,870
+element هذا موجود وين يا بنات؟ في B، السؤال لكم؟
+
+371
+00:41:22,870 --> 00:41:33,770
+Pause، الـ B، الـ B، الـ C موجود في B ولا لأ؟ لأن الـ B
+
+372
+00:41:33,770 --> 00:41:39,280
+موجود في B، و الـ C أي element موجود في A، يبقى الـ B
+
+373
+00:41:39,280 --> 00:41:44,920
+موجود في B، و الـ B is an ideal، أو اضرب بالـ B في أي
+
+374
+00:41:44,920 --> 00:41:49,480
+عنصر من عناصر الـ ring، بده يكون موجود في هذا الـ
+
+375
+00:41:49,480 --> 00:42:01,500
+ideal also، هنا because الـ B موجود في الـ B، and الـ B
+
+376
+00:42:01,500 --> 00:42:06,880
+موجود في الـ B، and الـ B ideal
+
+377
+00:42:10,590 --> 00:42:18,530
+طيب الآن لو جيت جمعت اثنين مع بعض، وين بده يكون؟ في
+
+378
+00:42:18,530 --> 00:42:28,590
+نفسه، يبقى هنا  واحد ناقص B C زائد B C موجود
+
+379
+00:42:28,590 --> 00:42:35,510
+في B، يعني معنى هذا الكلام أن الواحد
+
+380
+00:42:37,740 --> 00:42:44,480
+موجود في B، يبقى الـ unity تبع الـ ring الأصلية طلع
+
+381
+00:42:44,480 --> 00:42:51,620
+موجود في B، هذا معناته أن B تساوي،  بدها تساوي R
+
+382
+00:42:51,620 --> 00:42:58,280
+itself، يبقى الـ ideal A عبارة عن؟ عن maximal، عن
+
+383
+00:42:58,280 --> 00:43:04,240
+maximal، هذه طلع المساواة هنا، يبقى هذا يعطيني أن الـ
+
+384
+00:43:04,240 --> 00:43:13,150
+A is maximal in R
+
+385
+00:43:13,150 --> 00:43:19,690
+يبقى هذا لإتجاه الأول، الأهم يجي لإتجاه الثاني
+
+386
+00:43:38,170 --> 00:43:47,290
+يبقى باجي بقوله: conversely، افترضنا
+
+387
+00:43:47,290 --> 00:43:52,370
+فيه، وأثبتنا أنه إيه؟ maximal، يبقى بدأ أفترض أنه
+
+388
+00:43:52,370 --> 00:43:57,650
+إيه؟ maximal، ونثبت أن الـ R modulo A is إيه؟ field
+
+389
+00:43:57,650 --> 00:44:01,470
+يبقى هنا باجي بقوله: assume
+
+390
+00:44:05,020 --> 00:44:15,600
+that إن الـ A  a maximal ideal
+
+391
+00:44:15,600 --> 00:44:19,960
+of R،
+
+392
+00:44:19,960 --> 00:44:32,140
+إيش اللي بدنا نثبته؟  We want to show that الـ R
+
+393
+00:44:34,040 --> 0
+
+445
+00:51:37,860 --> 00:51:44,520
+الـ S A1 Ring الأصلي، هل هو commutative أم لا؟
+
+446
+00:51:44,520 --> 00:51:52,880
+بقدر أعمل خاصية الإبدال هنا، يبقى  يده بده يساوي BSR1
+
+447
+00:51:52,880 --> 00:52:01,500
+زائد الـ S A1، هذه أين موجودة يا بنات؟ في R، هذه
+
+448
+00:52:01,500 --> 00:52:08,200
+موجودة أين؟ في A، لأن الـ A يحتوي على A1 و الـ
+
+449
+00:52:08,200 --> 00:52:13,780
+S موجودة في R، اضرب أي عنصر من عناصر R في أي عنصر
+
+450
+00:52:13,780 --> 00:52:18,800
+من عناصر A، بده يكون موجود في الـ A، يبقى هذا موجود في
+
+451
+00:52:18,800 --> 00:52:25,200
+الـA. إذا كل هذا موجود أين؟ في الـB. Similarly,
+
+452
+00:52:25,200 --> 00:52:28,740
+Similarly,
+
+453
+00:52:28,740 --> 00:52:37,940
+أن الـ X في S موجودة كذلك في B، يبقى Thus، وهكذا أن
+
+454
+00:52:37,940 --> 00:52:50,320
+الـ B is an ideal of R، كويسة. يبقى حتى الآن أثبتنا
+
+455
+00:52:50,320 --> 00:52:55,420
+أن B عبارة عن Ideal of R. ما استخدمناش خاصية الـ
+
+456
+00:52:55,420 --> 00:52:59,920
+maximality التي فرضناها من عند الـ conversion.
+
+457
+00:53:00,600 --> 00:53:03,980
+يعني حتى الآن ما استخدمناها، بس جاها دورها الحين.
+
+458
+00:53:04,540 --> 00:53:14,180
+يبقى أثبتنا أن B is an ideal, not that. السؤال هو: هل
+
+459
+00:53:14,180 --> 00:53:20,400
+الـ A subset من B؟ هي
+
+460
+00:53:20,400 --> 00:53:28,860
+التعريف: هذا الـ element موجود في A، وهذا element
+
+461
+00:53:28,860 --> 00:53:35,580
+زيادة عليه، يبقى هل هي subset من B أم لا؟ يساوي؟ لا
+
+462
+00:53:35,580 --> 00:53:46,790
+ولا يساوي، والـ B في حد ذاته subset من من؟ من R. طب
+
+463
+00:53:46,790 --> 00:53:52,390
+هذا لا يمكن أن يساوي هذا، إذا الـ B بده يساوي الـ R
+
+464
+00:53:52,390 --> 00:53:57,790
+لأن الـ A is maximum، صح أم لا؟ مش هيك التعريف؟ هذا
+
+465
+00:53:57,790 --> 00:54:06,130
+معناه أن الـ B بده يساوي الـ R، because الـ A is
+
+466
+00:54:06,130 --> 00:54:12,930
+maximum حسب ما احنا فرضينه. هي تحتي خط. مدام الـ P بده
+
+467
+00:54:12,930 --> 00:54:21,010
+يساوي الـ R، هذا معناته أن الـ 1 موجود في الـ P، مش
+
+468
+00:54:21,010 --> 00:54:25,750
+الـ P هي بقى، والـ R فيها الـ unity، يبقى الـ 1
+
+469
+00:54:25,750 --> 00:54:32,530
+موجود في P. طب إيه شكل الـ 1 بده يكون؟ إيه يبقى
+
+470
+00:54:32,530 --> 00:54:42,480
+بده يكون PA مثلاً، أو PR1 زائد A على سبيل المثال
+
+471
+00:54:42,480 --> 00:54:47,140
+والله يا شرطة، بلاش تقول مين هذا، إيش ما تكون الـ a
+
+472
+00:54:47,140 --> 00:54:54,360
+أي عنصر من a، يبقى هذا شكله. طيب كويس، لو جيت قلت لكم
+
+473
+00:54:54,360 --> 00:54:59,400
+الـ unity عندنا اللي قلنا عليه 1 زائد a قبل شوية
+
+474
+00:54:59,400 --> 00:55:07,880
+يبقى لو جيت قلت 1 زائد a بده يساوي b أولاً زائد a
+
+475
+00:55:07,880 --> 00:55:14,510
+prime زائد الـ a. يبقى بناءً على إيه؟ صار الواحد زائد
+
+476
+00:55:14,510 --> 00:55:19,770
+الـ A، والباقي الـ A'، موجودة في الـ R أم لا؟ يبقى
+
+477
+00:55:19,770 --> 00:55:29,210
+بضل بس b R1 زائد الـ A، تمام. يبقى صار عند مين؟
+
+478
+00:55:29,210 --> 00:55:37,950
+الواحد زائد الـ A يساوي b زائد الـ A مضروب في الـ R1
+
+479
+00:55:37,950 --> 00:55:45,630
+زائد الـ A. طب إيش تفسيركم للعبارة هذه؟ آه، حاصل ضرب
+
+480
+00:55:45,630 --> 00:55:52,850
+عنصرين يساوي اليونيتي، b زائد a is a unit، احنا
+
+481
+00:55:52,850 --> 00:55:58,370
+قلنا هنا لو قدرنا نثبت أن الـ b زائد a is a unit
+
+482
+00:55:58,370 --> 00:56:07,620
+خلصنا، يبقى هذا بيكون الـ b زائد a is a unit، يبقى
+
+483
+00:56:07,620 --> 00:56:13,140
+صار عندي أي عنصر غير صفري b زائد a في الـ R
+
+484
+00:56:13,140 --> 00:56:19,500
+modulo a is a unit، يعني يبقى الـ R modulo a is a field
+
+485
+00:56:19,500 --> 00:56:29,340
+هذا بيعطيك أن الـ R modulo a is a field، تمام؟ وهو
+
+486
+00:56:29,340 --> 00:56:30,480
+المطلوب
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..24d50bc3f7c52768e5dbe62b0781ff82c227abe8
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_postprocess.srt
@@ -0,0 +1,1944 @@
+1
+00:00:21,080 --> 00:00:25,780
+بسم الله الرحمن الرحيم عودنا على بدأ المرة اللي
+
+2
+00:00:25,780 --> 00:00:30,000
+فاتت بجينا نتكلم على ال prime ideals و ال maximal
+
+3
+00:00:30,000 --> 00:00:36,600
+ideals تمام و أعطينا على ذلك بعض الأمثلة مع ال
+
+4
+00:00:36,600 --> 00:00:41,260
+factoring كذلك المثال رقم 5 بيقول show that the
+
+5
+00:00:41,260 --> 00:00:45,260
+ideal ال principle ideal generated by X ترمية
+
+6
+00:00:45,260 --> 00:00:51,080
+زواحد is maximal in R of Xإذا بدنا نثبت ان هذا ال
+
+7
+00:00:51,080 --> 00:00:55,800
+ideal هو maximal way in our operation لو راجعنا
+
+8
+00:00:55,800 --> 00:01:01,200
+بالذاكرة الى الوراق قليلا مشان نثبت ال maximality
+
+9
+00:01:01,200 --> 00:01:07,120
+ليه ideal بفترض ان في عندي ideal أخر و هذا ال
+
+10
+00:01:07,120 --> 00:01:13,420
+ideal subset منه و ال ideal هذا subset من Rيا إما
+
+11
+00:01:13,420 --> 00:01:17,440
+ال ideal اللى عندنا بده يسوى ال ideal المقترح يا
+
+12
+00:01:17,440 --> 00:01:22,480
+إما ال ideal المقترح بده يسوى أي واحدة منهم، تمام؟
+
+13
+00:01:22,480 --> 00:01:34,120
+إذا احنا بدنا نفرض هنا assume that ال A is an
+
+14
+00:01:34,120 --> 00:01:40,300
+ideal such that .. ideal of
+
+15
+00:01:42,090 --> 00:01:49,750
+of X such that بحيث ان ال principle ideal
+
+16
+00:01:49,750 --> 00:01:56,570
+generated by X تربيعه plus one subset من ال A ولا
+
+17
+00:01:56,570 --> 00:02:06,870
+يساوي وال A معروف هو subset من من ال ring A إذا
+
+18
+00:02:06,870 --> 00:02:13,410
+حيال الآن بيسويش ال A يبقى مطلوب نسبة 8إن ال A بده
+
+19
+00:02:13,410 --> 00:02:23,010
+يسوى من ال R يبقى value بيقول if we show that إذا
+
+20
+00:02:23,010 --> 00:02:32,090
+جدنا نثبت إن ال A بده يسوى ال R itself then ال A
+
+21
+00:02:32,090 --> 00:02:39,350
+is maximal طيب also
+
+22
+00:02:41,510 --> 00:02:50,590
+و كذلك if we show that إذا جدرنا نبين إن الواحد أو
+
+23
+00:02:50,590 --> 00:03:00,490
+ال unity موجود في A then ال A is maximum مش هذا
+
+24
+00:03:00,490 --> 00:03:06,230
+مثال سابق خدناه المحلقة الماضية إنه لو أخدت أي من
+
+25
+00:03:06,230 --> 00:03:09,610
+ال ring R اللي بتبقى commutative ring with unity
+
+26
+00:03:09,990 --> 00:03:13,950
+ولاقيت ال unity موجود في ال ID اللي يبقى ال ID
+
+27
+00:03:13,950 --> 00:03:18,330
+اللي بده يسمى من R و أثبتناها عمليا معاكم طبعا هو
+
+28
+00:03:18,330 --> 00:03:22,350
+سؤال في التمريم احنا أعطينا مثال و بدنا نعتمد عليه
+
+29
+00:03:22,350 --> 00:03:32,730
+هنا في اثبات هذا ال لسات مين هي ال A؟ ال A فرض
+
+30
+00:03:32,730 --> 00:03:38,380
+من عندي؟ اهمش احنا .. احنا الموجود عند مين X
+
+31
+00:03:38,380 --> 00:03:42,860
+التربيع زي الواحد صح هذا ال ideal مُعطى هذا اللي
+
+32
+00:03:42,860 --> 00:03:47,900
+بدي أثبت انه maximum من تعريف ال maximal اللي عندك
+
+33
+00:03:47,900 --> 00:03:54,480
+بنقول هذا maximal إذا جدلت ألاقي ideal تاني بحيث
+
+34
+00:03:54,480 --> 00:03:59,640
+هذا subset منهم وال ideal التاني طبعا subset من R
+
+35
+00:03:59,640 --> 00:04:05,600
+فهو طبيعيإن حدث ذلك، يا إما هذا بتساوي الـA، يا
+
+36
+00:04:05,600 --> 00:04:09,320
+إما الـA بتساوي الـA، مش هيك التعريف اللي مكتوب
+
+37
+00:04:09,320 --> 00:04:12,320
+عندك المرة دي، التعريف المكتمه الـideal، أيوة،
+
+38
+00:04:12,320 --> 00:04:16,200
+احنا
+
+39
+00:04:16,200 --> 00:04:20,260
+مانقولك ideal، نتكلمش set، set لسه بجدوح تتبت من
+
+40
+00:04:20,260 --> 00:04:26,180
+أول و جديد، هذا ideal، وفرقت الـA، ideal تاني، إذا
+
+41
+00:04:26,180 --> 00:04:32,720
+هذا ال ideal هو subset من A ولا يساوييبقى إجباري
+
+42
+00:04:32,720 --> 00:04:36,700
+مشان يكون maximum لازم أثبت ان ال A بده ساوة مين؟
+
+43
+00:04:36,700 --> 00:04:42,360
+بده ساوة ال R طبعا يبقى هنا قولنا إذا قدرنا نبين
+
+44
+00:04:42,360 --> 00:04:46,120
+ان ال A بده ساوة R يبقى ال A بصير maximum طبق
+
+45
+00:04:46,120 --> 00:04:51,120
+التعريف طبق المثال اللي فات إذا قدرت أثبت ان
+
+46
+00:04:51,120 --> 00:04:55,500
+الواحد موجود في ال A يبقى ال A بده ساوة ال R يبقى
+
+47
+00:04:55,500 --> 00:05:02,780
+ال A maximum عادي مظبوط ايه؟ بقول كويسطيب بدنا
+
+48
+00:05:02,780 --> 00:05:07,460
+نحاول نثبت ان هذا ال a maximum او الواحد موجود
+
+49
+00:05:07,460 --> 00:05:15,560
+وين؟ موجود في ال a لذلك بروح اخد element موجود في
+
+50
+00:05:15,560 --> 00:05:20,720
+ال ring او اخده موجود في a ومش موجود في ال
+
+51
+00:05:20,720 --> 00:05:25,260
+principle ideal generated by a يبقى باجي بقوله
+
+52
+00:05:25,260 --> 00:05:32,210
+افترح ان عندي ال element f of xموجود في الـ Ideal
+
+53
+00:05:32,210 --> 00:05:39,570
+I and الـ F of X مش موجود في الـ Principle Ideal
+
+54
+00:05:39,570 --> 00:05:44,710
+Generated by X ترفيه أزاى الواحدة إذا أخدت element
+
+55
+00:05:44,710 --> 00:05:49,870
+موجود هنا ومش موجود هنا هذا subset قد يسوي وقد لا
+
+56
+00:05:49,870 --> 00:05:55,250
+يسوي على فرض لا يسوي إذا ممكن ألاقي عناصر هنا مش
+
+57
+00:05:55,250 --> 00:06:00,150
+موجودة هنا تماملكن كل العناصر اللي هنا موجودة وين
+
+58
+00:06:00,150 --> 00:06:05,590
+موجودة وين هذا إجبال يبقى أخد ال F of X موجودة في
+
+59
+00:06:05,590 --> 00:06:10,450
+إيه أن ال F of X مش موجودة في ال principle ID
+
+60
+00:06:10,450 --> 00:06:18,370
+generated by X تربيع زاد واحد السؤال هو ال F of X
+
+61
+00:06:18,370 --> 00:06:24,870
+بقدر أكتبها بصورة أخرى أو بطريقة أخرى السؤال هو ما
+
+62
+00:06:24,870 --> 00:06:35,740
+هذه الصورةبنقول له then ال F of X بدها تساوي هذي
+
+63
+00:06:35,740 --> 00:06:42,340
+أنا ماخدها وين؟ ماخدها فيهين يبقى مش موجودة فيهين
+
+64
+00:06:42,340 --> 00:06:47,820
+يبقى الدرجة تبعتها هتكون أعلى من الدرجة الثانية،
+
+65
+00:06:47,820 --> 00:06:51,060
+التالتة، الرابعة، العاشرة، العشرة، جد ما تكون،
+
+66
+00:06:51,060 --> 00:06:58,200
+ماعندا مشكلة إذا لو روحت جسم يسمى مطولةالـ F of X
+
+67
+00:06:58,200 --> 00:07:03,160
+جسمتها على الـ polynomial X تربيه زائد واحد، ايش
+
+68
+00:07:03,160 --> 00:07:10,460
+بدي يطلع؟ بدي يطلع Q of X، polynomial في X، X
+
+69
+00:07:10,460 --> 00:07:17,880
+تربيه زائد واحد زائد الباقي اللي هو الـ R of X،
+
+70
+00:07:17,880 --> 00:07:22,540
+تمام؟ اه استرستلنا شوية، بدي انا فاهمها هذه،
+
+71
+00:07:22,540 --> 00:07:27,580
+بفهمها بسيط جدا، ولا حاجةكيف أفهمه بسيط بقول ما
+
+72
+00:07:27,580 --> 00:07:33,020
+ياتي لما نكسب كثيرة حدود على كثيرة حدود يمكن ننتهي
+
+73
+00:07:33,020 --> 00:07:38,440
+بأصفار يبقى جسم على بعض بدون باقي يبقى بيكون ال R
+
+74
+00:07:38,440 --> 00:07:46,480
+of X جده ب Zero تمام و ممكن يزيد شيء لكن لما يزيد
+
+75
+00:07:46,480 --> 00:07:50,820
+شيء درجته تبقى أقل من ال extra بيها زائد واحد
+
+76
+00:07:50,820 --> 00:07:55,160
+مظبوطتمام لأن لو كان أكتر من X تربيه زي الواحد
+
+77
+00:07:55,160 --> 00:08:00,400
+الصلبات لل term اللي عندنا هذا طيب كويس هنا بنقول
+
+78
+00:08:00,400 --> 00:08:07,620
+where؟ بدي أخد ال R of X does not equal to zero مش
+
+79
+00:08:07,620 --> 00:08:18,040
+Zero and ال degree لمن؟ لل R of X أقل من اتنينلأن
+
+80
+00:08:18,040 --> 00:08:22,400
+لو صارت اتنين بدها صير مع ال Q of X اللي مضروبة في
+
+81
+00:08:22,400 --> 00:08:26,300
+X تربية زي واحدة لأن بقول في ال polynomial نقسم
+
+82
+00:08:26,300 --> 00:08:31,320
+polynomial درجة البصر قد درجة المقام أو أكبر منه
+
+83
+00:08:31,320 --> 00:08:36,140
+بقسم جسمه مطولة لكن لو كانت درجة البصر أقل من درجة
+
+84
+00:08:36,140 --> 00:08:41,420
+المقام بقدر أقسم جسمه مطولة؟ لا بقدرش تمام؟ إذن
+
+85
+00:08:41,420 --> 00:08:46,780
+صار عند ال R of X بتاخدها بتسويش Zero يبقى معضمون
+
+86
+00:08:47,220 --> 00:08:52,320
+لازم ألاقي function في ال R of X درجته أقل من 100
+
+87
+00:08:52,320 --> 00:08:57,460
+من اتنين يعني من الدرجة الأولى صح ولا لا يبقى من
+
+88
+00:08:57,460 --> 00:09:03,340
+الدرجة الأولى طيب ممتازة اذا بدي اكتب ال R of X
+
+89
+00:09:03,340 --> 00:09:11,460
+على الصيغة التالية F of X ناقص ل Q of X في X تربيه
+
+90
+00:09:11,460 --> 00:09:15,380
+زائد واحد تمام
+
+91
+00:09:16,060 --> 00:09:20,160
+طيب انا اتهدف و فيكس وين موجودة؟ موجودة في الاه في
+
+92
+00:09:20,160 --> 00:09:28,900
+الاه في الاه طيب و هذه؟ برضه في الاه برضه في الاه
+
+93
+00:09:28,900 --> 00:09:35,100
+لماذا؟ لأنه في الاه جيلاراتر و هذي كسافراتر هذي
+
+94
+00:09:35,100 --> 00:09:45,400
+موجودة في الاه؟ عشانها اناأي element
+
+95
+00:09:45,400 --> 00:09:50,280
+هنا موجود هنا و أي element هنا على الصيغة اللي
+
+96
+00:09:50,280 --> 00:09:55,780
+قلناها تعريف ال principle ID هو الـ generated by A
+
+97
+00:09:55,780 --> 00:10:02,000
+هو الـ A مضروبة في R بحيث الـ R في R و الـ A يبقى
+
+98
+00:10:02,000 --> 00:10:11,440
+هذاليش هذه؟ because ان ال principle ideal gene او
+
+99
+00:10:11,440 --> 00:10:18,940
+because ال X تربيع زائد واحد موجودة فيه تمام؟ يبقى
+
+100
+00:10:18,940 --> 00:10:23,700
+ضربته في أي function من ال R of X موجودة فيه إذا
+
+101
+00:10:23,700 --> 00:10:31,860
+صار R of X موجودة فيه طب مين هي ال R of X؟ ال R of
+
+102
+00:10:31,860 --> 00:10:39,120
+Xبدها الصيغة درجتها قلل من اتنين يبقى number of x
+
+103
+00:10:39,120 --> 00:10:49,200
+بالصيغة على الصيغة a x زائد b صح ؟ وهذه كلها
+
+104
+00:10:49,200 --> 00:10:54,000
+موجودة في ايه؟ وهذه موجودة في ايه؟ يبقى ال term كل
+
+105
+00:10:54,000 --> 00:11:02,810
+هذا موجود هنا واضح حالك اكتر يبقى هذابدي أعطيك ما
+
+106
+00:11:02,810 --> 00:11:11,810
+ياتي ال R of X تساوي ال F of X ناقص ل Q of X في ال
+
+107
+00:11:11,810 --> 00:11:19,850
+X تربيع زائد واحد كلها موجودة في A طيب ال R of X
+
+108
+00:11:19,850 --> 00:11:26,230
+درجتها أقل من الدرجة الثانية يبقى درجة الأول يبقى
+
+109
+00:11:26,230 --> 00:11:37,790
+بصير عند ال AXأو الـ R of X تساوي الـ AX زائد B
+
+110
+00:11:37,790 --> 00:11:46,190
+اللي هي هذه اللي هي موجودة وين؟ موجودة في A طيب،
+
+111
+00:11:46,190 --> 00:11:54,710
+بدي أسألكوا السؤال التالي Now لو أخدت ال AX زائد
+
+112
+00:11:54,710 --> 00:12:04,420
+ال B وضربتها في AXناقص ال B هل هذه موجودة في A؟ في
+
+113
+00:12:04,420 --> 00:12:12,400
+A؟ اه موجودة في A؟ اه موجودة ليش؟ لأن هذا ال
+
+114
+00:12:12,400 --> 00:12:18,720
+element موجود في A وال A ID وضربيه في أي function
+
+115
+00:12:18,720 --> 00:12:23,560
+من ال R of X بدي يكون موجود في A صحيح ولا لأ؟ إذا
+
+116
+00:12:23,560 --> 00:12:33,210
+ال هذي كذلكموجودة في a because ال a is an ideal
+
+117
+00:12:33,210 --> 00:12:39,250
+اللي بيحصل ضربه هناك موجود في ال a طيب الان لو جيت
+
+118
+00:12:39,250 --> 00:12:44,430
+ضربت هذول في بعض الفرق بين المرقعين يبقى a تربيع x
+
+119
+00:12:44,430 --> 00:12:50,730
+تربيع ناقص b تربيع موجود وين؟ موجود في ال a
+
+120
+00:12:58,850 --> 00:13:07,110
+الان بدي اجيب كمان شغلة تانية و نشوف هاها موجودة
+
+121
+00:13:07,110 --> 00:13:17,410
+في a ولا لا لو جيت قلتلك بط ال a ترابيع في ال x
+
+122
+00:13:17,410 --> 00:13:25,720
+ترابيع زائد واحد هل هذه موجودة في aأكس تربية زي
+
+123
+00:13:25,720 --> 00:13:28,460
+الواحد موجودة في ال principle و ال principle
+
+124
+00:13:28,460 --> 00:13:33,300
+subset من a إذا هذا ال element موجود في a هو و
+
+125
+00:13:33,300 --> 00:13:39,160
+مضاعفاته يبقى ال a تربية في ال x تربية زي الواحد
+
+126
+00:13:39,160 --> 00:13:46,060
+لو بدنا نسوي a تربية x تربية زائد a تربية موجود في
+
+127
+00:13:46,060 --> 00:13:53,090
+ال a كذلك طب لو جمعتهم بيكون موجود في ال aطب لو
+
+128
+00:13:53,090 --> 00:14:00,790
+طرحتهم طب لو طرحناهم يبقى سوء ال a تربيع x تربيع
+
+129
+00:14:00,790 --> 00:14:09,450
+زائد ال a تربيع ناقص ال a تربيع x تربيع ناقص ال b
+
+130
+00:14:09,450 --> 00:14:16,110
+تربيع كل هذا بيكون موجود في a لو طرحناهم و لا تشبه
+
+131
+00:14:16,110 --> 00:14:22,950
+ال a تربيع زائد b تربيع موجودة في aيبقى طالع عندي
+
+132
+00:14:22,950 --> 00:14:28,550
+دالة ثابتة، اللي هي مين؟ A تربيع زائد B تربيع
+
+133
+00:14:28,550 --> 00:14:33,770
+موجودة وين؟ موجودة في إيه؟ طيب مقلوبة موجودة في
+
+134
+00:14:33,770 --> 00:14:40,970
+إيه ولا لا؟ دالة مقلوبة، R of X كل ال functions
+
+135
+00:14:40,970 --> 00:14:48,200
+تبعها ترية، تمام؟ يبقى هذا يبدأ يعطينا إنه واحدعلى
+
+136
+00:14:48,200 --> 00:14:55,160
+A تربيع زائد B تربيع موجودة في A كذلك طب لو ضربهم
+
+137
+00:14:55,160 --> 00:15:01,960
+في بعض لو أخدت ال A تربيع زائد B تربيع ضرب واحد
+
+138
+00:15:01,960 --> 00:15:10,620
+على A تربيع زائد B تربيع فهو موجود في A يبقى هدف
+
+139
+00:15:10,620 --> 00:15:16,920
+يعطينا أن الواحد موجود في Aيبقى بناء عليه الـ A كم
+
+140
+00:15:16,920 --> 00:15:23,680
+بده يساوي R. It says يبقى هذا معناته الـ A بده
+
+141
+00:15:23,680 --> 00:15:31,800
+يساوي الـ R وهذا previous example مثال سابق من
+
+142
+00:15:31,800 --> 00:15:36,960
+المحاضرة الماضية. مدام طلع الـ A بده يساوي الـ R
+
+143
+00:15:36,960 --> 00:15:46,890
+يبقى الـ A is maximal وندهينا من هذا المثال.تمام؟
+
+144
+00:15:46,890 --> 00:15:53,750
+كذا نبلغ من الآن فصاعدا كل كثير .. كل الدول
+
+145
+00:15:53,750 --> 00:15:59,070
+المعرفة للمعاملات تبعتها أعداد حقيقية وهي
+
+146
+00:15:59,070 --> 00:16:04,210
+polynomial ال X تربيع زائد واحد ل principle ideal
+
+147
+00:16:04,210 --> 00:16:08,750
+generated by X تربيع زائد واحد يمثل maximum ideal
+
+148
+00:16:08,750 --> 00:16:15,400
+في من؟ في ال R of Xطيب نعطي كمان مثال صغير مش زي
+
+149
+00:16:15,400 --> 00:16:27,080
+هذا طويل يبقى مثال ستة اجزام كذا ستة .. مين اللي
+
+150
+00:16:27,080 --> 00:16:32,720
+بيحكي؟ كيف؟
+
+151
+00:16:32,720 --> 00:16:36,520
+انت
+
+152
+00:16:36,520 --> 00:16:42,330
+كتب so is maximumهذا اخر اخر صور اللي هي ال X
+
+153
+00:16:42,330 --> 00:16:49,310
+ترابيع plus one بالشكل هذا هي ال maximum صحيح لان
+
+154
+00:16:49,310 --> 00:16:55,890
+هذا اللي احنا بنسبته بنجيب ID التاني تبعك كده مانع
+
+155
+00:16:55,890 --> 00:17:01,610
+واحد تبتمل ال A من ال A is maximum فاضح فاضح فاضح
+
+156
+00:17:01,610 --> 00:17:11,100
+فاضح فاضح فاضح فاضح فاضح فاضحهنا؟ أول
+
+157
+00:17:11,100 --> 00:17:16,740
+السؤال؟ تالت وربع سطر تالت وربع سطر تالت وربع سطر
+
+158
+00:17:16,740 --> 00:17:18,900
+تالت وربع سطر تالت وربع سطر تالت وربع سطر تالت
+
+159
+00:17:18,900 --> 00:17:19,060
+وربع سطر تالت وربع سطر تالت وربع سطر تالت وربع سطر
+
+160
+00:17:19,060 --> 00:17:19,640
+تالت وربع سطر تالت وربع سطر تالت وربع سطر تالت
+
+161
+00:17:19,640 --> 00:17:23,320
+تالت وربع سطر تالت وربع سطر تالت وربع سطر تالت
+
+162
+00:17:23,320 --> 00:17:32,640
+وربع سطر تالت وربع سطر تالت وربع سطر تالت وربع سط
+
+163
+00:17:39,930 --> 00:17:45,070
+إذا أثبتنا أن الـ A يساوي الـ R يساوي الـ A يصبح
+
+164
+00:17:45,070 --> 00:17:50,030
+الـ A ماكسيمال حسب التعريف اللي عنه الماكسيمالية،
+
+165
+00:17:50,030 --> 00:17:57,060
+مظبوط؟ طيب أنا عشان أثبت هذا الـ A يساوي Rبقول لو
+
+166
+00:17:57,060 --> 00:18:02,080
+قدرت أثبت أن الواحد موجود في مصير الـA يساوي
+
+167
+00:18:02,080 --> 00:18:05,420
+الأربع بالثالث كيف؟ الـA و لا ال principle ideal
+
+168
+00:18:05,420 --> 00:18:06,640
+الـA و لا ال principle ideal الـA و لا ال
+
+169
+00:18:06,640 --> 00:18:07,960
+principle ideal الـA و لا ال principle ideal الـA
+
+170
+00:18:07,960 --> 00:18:08,480
+و لا ال principle ideal الـA و لا ال principle
+
+171
+00:18:08,480 --> 00:18:09,040
+ideal الـA و لا ال principle ideal الـA و لا ال
+
+172
+00:18:09,040 --> 00:18:09,900
+principle ideal الـA و لا ال principle ideal الـA
+
+173
+00:18:09,900 --> 00:18:10,540
+و لا ال principle ideal الـA و لا ال principle
+
+174
+00:18:10,540 --> 00:18:11,160
+ideal الـA و لا ال principle ideal الـA و لا ال
+
+175
+00:18:11,160 --> 00:18:12,780
+principle ideal الـA و لا ال principle ideal الـA
+
+176
+00:18:12,780 --> 00:18:13,120
+و لا ال principle ideal الـA و لا ال principle
+
+177
+00:18:13,120 --> 00:18:15,940
+ideal الـA و لا ال principle ideal الـA و لا ال
+
+178
+00:18:15,940 --> 00:18:16,480
+و لا ال principle ideal الـA و لا ال principle
+
+179
+00:18:16,480 --> 00:18:19,520
+ideal الـA و لا ال principle ideal الـA و لا ال
+
+180
+00:18:19,520 --> 00:18:25,530
+principle ideal الـالـ X تربيه زائد واحد ثالث is
+
+181
+00:18:25,530 --> 00:18:29,610
+maximal ideal، هذا اللي احنا بنفتحه صحيح معاكم كل
+
+182
+00:18:29,610 --> 00:18:37,050
+الحاجة طيب المثال الأخير قبل أن نبدأ النظريات
+
+183
+00:18:37,050 --> 00:18:44,990
+بيقول لي ال ideal ال principle ideal generated by
+
+184
+00:18:44,990 --> 00:18:48,030
+X تربيه زائد واحد is
+
+185
+00:18:50,870 --> 00:19:08,770
+A' is not a prime in Z2 of X نحن
+
+186
+00:19:08,770 --> 00:19:13,870
+ندّعي أن الـ I دي هذا ما هو ماشي prime in Z2 من
+
+187
+00:19:13,870 --> 00:19:21,640
+عناصر Z2 ياباناأنا صفر و واحد صفر و واحد ممتاز جدا
+
+188
+00:19:21,640 --> 00:19:27,860
+طب لو قلت اتنين تعني صفر لو قلت تلاتة تعني واحد و
+
+189
+00:19:27,860 --> 00:19:33,860
+هكذا طيب انا بقول ان ال ideal هذا ما هو شفراي في
+
+190
+00:19:33,860 --> 00:19:37,840
+ال ring اللي عنده هذا مش في ال R of X الأولانية
+
+191
+00:19:37,840 --> 00:19:42,020
+يعني كأنه أخدنا حالة خاصة اللي هو ال ring اللي
+
+192
+00:19:42,020 --> 00:19:46,170
+عندنا و أخدنا نفس ال ideal في هذه ال ringطيب لو
+
+193
+00:19:46,170 --> 00:19:52,210
+جيت قولتلك ال X زائد واحد هل موجود في ال Z two of
+
+194
+00:19:52,210 --> 00:20:02,390
+X؟ موجود هنا ولا هنا؟ ممتاز طيب خط ده أخدت ال X
+
+195
+00:20:02,390 --> 00:20:09,710
+زائد واحد في ال X زائد واحد العنصر ضربته في نفسه،
+
+196
+00:20:09,710 --> 00:20:16,420
+شو بدي أقينها؟x تربيع زائد نية x زائد واحد جداش
+
+197
+00:20:16,420 --> 00:20:26,540
+هذه تساوي في z2 of x؟ Zero يبدأ هذه Zero in z2 of
+
+198
+00:20:26,540 --> 00:20:33,300
+x جداش الناتج بدي يكون؟ x تربيع زائد واحد اللي هو
+
+199
+00:20:33,300 --> 00:20:38,960
+موجود وين؟ موجود في ال x تربيع زائد واحد ال
+
+200
+00:20:38,960 --> 00:20:43,900
+principal idealgenerated by X تربية زايدة طب
+
+201
+00:20:43,900 --> 00:20:52,040
+يطلعون هنا الآن حاصل ضربة عنصرين موجود في ال ID
+
+202
+00:20:52,040 --> 00:20:58,380
+اللي عندنا هنا لشان يكون إقرأي يبقى واحد منهم بدي
+
+203
+00:20:58,380 --> 00:21:03,260
+يكون هنا موجود واحد من قصين هدول بدي يكون موجود
+
+204
+00:21:03,260 --> 00:21:08,740
+هناك صح ولا لا؟ لأنه إما قصي الأولموجود في هذا ال
+
+205
+00:21:08,740 --> 00:21:13,840
+ideal أو القوس التاني موجود في هذا ال ideal لكن هل
+
+206
+00:21:13,840 --> 00:21:19,840
+اي من القوسين الموجود هنا لأ يبقى حافظا ضارب ما
+
+207
+00:21:19,840 --> 00:21:27,240
+موجود but ولكن ال X زائد واحد does not belong لل
+
+208
+00:21:27,240 --> 00:21:31,120
+principle ideal generated by X تلوية زائد واحد
+
+209
+00:21:31,120 --> 00:21:36,120
+يبقى بناء عليه هذا ما هو shape prime لأن تعريف ال
+
+210
+00:21:36,120 --> 00:21:43,520
+primeلما تلاقي عنصرين موجودات في مين لل ID بدي
+
+211
+00:21:43,520 --> 00:21:49,440
+يكون على الأقل أحدهم أو واحد منهم موجود، أي حاصل
+
+212
+00:21:49,440 --> 00:21:55,380
+ضربهم موجود، لكن ولا واحد من اتنين موجود وين في ال
+
+213
+00:21:55,380 --> 00:22:02,740
+X تربية، يبقى هذا ما هو ايش ال prime ID،
+
+214
+00:22:02,740 --> 00:22:08,710
+ليش ايش؟ ال X زائد واحد كدههاتيلي element تاني
+
+215
+00:22:08,710 --> 00:22:19,250
+غيرها و اريني اشوف اقترفيها اقترفيها بطلت
+
+216
+00:22:19,250 --> 00:22:28,780
+احنا مقيادين مقيادين بال X تربية و زائد واحدنزلنا
+
+217
+00:22:28,780 --> 00:22:33,520
+بطل يصير موجود في ال X تربية زي دوها طالعنا بقدر
+
+218
+00:22:33,520 --> 00:22:37,480
+أكتبه زي ما كتبت واسعى Q of X في ال X تربية زي
+
+219
+00:22:37,480 --> 00:22:42,140
+دوها ازاى وزاى اقرأة of X مظبوط يبقى نشتغل على هذا
+
+220
+00:22:42,140 --> 00:22:53,040
+الأساس طيب نيجي لأول نضاهية في الموضوع KOM let
+
+221
+00:22:53,040 --> 00:23:06,510
+ال A بيa commutative ..
+
+222
+00:23:06,510 --> 00:23:17,810
+commutative ring with unity little
+
+223
+00:23:17,810 --> 00:23:24,690
+a be an ideal
+
+224
+00:23:26,600 --> 00:23:39,120
+أو R ، أفضل من R ثم الـ R موديولو A هو مجموعة
+
+225
+00:23:39,120 --> 00:23:45,100
+انتقالية
+
+226
+00:23:45,100 --> 00:23:53,880
+F اندولي F F اندولي F الـ A صحيح
+
+227
+00:23:55,030 --> 00:24:03,930
+لو كان الـA الـPrime
+
+228
+00:24:03,930 --> 00:24:10,870
+فا
+
+229
+00:24:10,870 --> 00:24:14,330
+نعرف بقى الكمية احنا عالنا R كمية ت bring with
+
+230
+00:24:14,330 --> 00:24:19,810
+unity والـA ايديل في R يبقى بيقول الـR modulo A
+
+231
+00:24:19,810 --> 00:24:23,990
+بتبقى integral domain إذا كان الـA prime ايديل
+
+232
+00:24:24,550 --> 00:24:29,710
+وكلمة F انتقل يفتعني ان البرمانس سيصير في
+
+233
+00:24:29,710 --> 00:24:36,690
+الاتجاهين لذلك الاتجاه الأول بدي افترض ان ال R
+
+234
+00:24:36,690 --> 00:24:47,790
+module A is an integral domain تمام؟
+
+235
+00:24:47,790 --> 00:24:53,920
+مشان أثبت ان ال A is a primeبدي أخد عنصرين من ال
+
+236
+00:24:53,920 --> 00:24:59,560
+ring A و أفترض أن حاصل ضربه ما موجود وين في ال
+
+237
+00:24:59,560 --> 00:25:04,600
+ideal A إذا قدرت أثبت أن واحد منهم موجود في ال A
+
+238
+00:25:04,600 --> 00:25:10,580
+يكون ال A is a prime ideal مقتقل لل definition
+
+239
+00:25:10,580 --> 00:25:18,760
+يبقى بدي أقوله افترض ان ال A و ال B موجودات في A
+
+240
+00:25:18,760 --> 00:25:29,450
+such thatبحيث ان ال A في ال B موجود في ال A طبعا؟
+
+241
+00:25:29,450 --> 00:25:34,750
+مدام ال A بي موجود في ال A يبقى ال A بي زائد ال A
+
+242
+00:25:34,750 --> 00:25:43,450
+جداش مدى سوابه انها ال A itself طبعا؟ طيب مدام هذا
+
+243
+00:25:43,450 --> 00:25:51,470
+هيك يبقى معناته مات مرة تانيةأخدت عمصري الموجودات
+
+244
+00:25:51,470 --> 00:26:00,770
+في R بحيث ان حاصل ضربهما موجود في A بدي احاول اوصل
+
+245
+00:26:00,770 --> 00:26:06,530
+لشغله انه يا اما ال A موجود في ال A يا اما ال B
+
+246
+00:26:06,530 --> 00:26:14,650
+موجود في ال A هذا معناه انه ان
+
+247
+00:26:14,650 --> 00:26:24,470
+ال A زائد ال Aمضروب في الـ B زائد الـ A بدي ساوي
+
+248
+00:26:24,470 --> 00:26:32,670
+الـ A السؤال هو الـ A في حد ذاته إيش تمثل بالنسبة
+
+249
+00:26:32,670 --> 00:26:40,230
+لل factor group R modulo A؟ شو اسم العمصر هذا؟ A
+
+250
+00:26:40,230 --> 00:26:47,650
+في factor group R modulo A؟ Zero element ممتازيبقى
+
+251
+00:26:47,650 --> 00:26:50,950
+الـ zero element في الـ R مُد يقوله إيه اللي بده
+
+252
+00:26:50,950 --> 00:26:56,490
+يسوي إيش الأفاريه؟ ان الـ R إيه؟ Integral Domain
+
+253
+00:26:56,490 --> 00:27:03,350
+مدام Integral Domain اصطلع عندي حاصل ضرب عنصرين من
+
+254
+00:27:03,350 --> 00:27:08,090
+ال ring اللي عندنا هذا أعطاني ال zero يبقى واحد
+
+255
+00:27:08,090 --> 00:27:13,270
+فيهم بده يكون ب zero صح ولا لا؟ يبقى هذا بده
+
+256
+00:27:13,270 --> 00:27:19,750
+يعطينايا إما ال A زائد ال A بده يساوي ال A يا إما
+
+257
+00:27:19,750 --> 00:27:26,430
+ال B زائد ال A بده يساوي ال A itself يفجأ هذا إيش
+
+258
+00:27:26,430 --> 00:27:31,250
+معناه؟ لما أقول A زايد ال A يساوي ال A معناته ال A
+
+259
+00:27:31,250 --> 00:27:37,830
+وين موجود؟ في ال A هذا معناه إن ال A موجود في ال A
+
+260
+00:27:37,830 --> 00:27:46,970
+or ال B موجود في ال Aيبقى هذا معناه مين؟ حاصل ضرب
+
+261
+00:27:46,970 --> 00:27:52,250
+عنصرين موجود في A أثبت له أن الأول في A أو الـ B
+
+262
+00:27:52,250 --> 00:27:58,810
+في A يبقى هذا معناه أن الـ A is A' ID يبقى هذا
+
+263
+00:27:58,810 --> 00:28:07,410
+معناه أن الـ A is A' ID يبقى
+
+264
+00:28:07,410 --> 00:28:10,410
+أثبتنا الاتجاه الأول، بنجي الاتجاه الثاني
+
+265
+00:28:10,410 --> 00:28:11,850
+Conversely
+
+266
+00:28:15,260 --> 00:28:23,600
+Assume that ان الـ A is A' ID.
+
+267
+00:28:25,900 --> 00:28:35,840
+One to show one to show that
+
+268
+00:28:35,840 --> 00:28:44,240
+بدنا نحاول ندبد ان الـ R modulo Ais an integral
+
+269
+00:28:44,240 --> 00:28:50,040
+domain طيب
+
+270
+00:28:50,040 --> 00:28:54,760
+و اكتشف اقدر احكم على الست انها integral domain
+
+271
+00:28:54,760 --> 00:29:02,760
+اذا تحقق شرطان شرط الاول اذا تبقى الست هذي
+
+272
+00:29:02,760 --> 00:29:07,800
+commutative ring with unity اثنان مش فيها zero
+
+273
+00:29:07,800 --> 00:29:13,160
+divisorsأو لو وجدت حاصل ضرب عنصرين منها بدي يساوي
+
+274
+00:29:13,160 --> 00:29:18,420
+ال zero بدي أثبتهم ان على الأقل واحد فيهم بدي
+
+275
+00:29:18,420 --> 00:29:24,520
+يساوي ال zero ممتاز جدا يبقى انا ازعم ان ال R
+
+276
+00:29:24,520 --> 00:29:36,200
+modulo A is a commutative ring with unity
+
+277
+00:29:38,710 --> 00:29:47,650
+قدش ال unity؟ ال a قولنا zero element يبقى واحد
+
+278
+00:29:47,650 --> 00:29:57,610
+زائد a طب ليش هذا الكلام؟ because من
+
+279
+00:29:57,610 --> 00:30:02,330
+نص النظرية قال ال R commutative ring with unity
+
+280
+00:30:02,330 --> 00:30:06,370
+يبقى ال R مديونية commutative ring with unity
+
+281
+00:30:06,890 --> 00:30:23,650
+because الـR is commutative ring with unity تمام؟
+
+282
+00:30:23,650 --> 00:30:30,010
+طيب الآن أنا بدي أثبت إن الـR عبارة عن integral
+
+283
+00:30:30,010 --> 00:30:36,190
+domain integral domain يعني لو أخدت عمصرينوضربتهم
+
+284
+00:30:36,190 --> 00:30:42,730
+في بعض بدي أثبت انه على الأقل واحد فيهم مانع بده
+
+285
+00:30:42,730 --> 00:30:48,510
+ساوي زيرو يبقى أخدنا a prime id بدنا نثبت هذا
+
+286
+00:30:48,510 --> 00:30:53,950
+integral domain أثبتنا الشرط الأول وهو ان ال R
+
+287
+00:30:53,950 --> 00:31:00,370
+modulo a is a commutative ring with unit تمام؟
+
+288
+00:31:00,370 --> 00:31:08,880
+الان بدي أجي أخدحاصل ضرب عنصرين فيهم وافترض ان هذا
+
+289
+00:31:08,880 --> 00:31:14,140
+الكلام بده يساوي مين؟ بده يساوي Zero بالضبط تماما
+
+290
+00:31:14,140 --> 00:31:25,380
+يبقى بده افترض ان عندي عنصرين ل ال A زائد ال A و
+
+291
+00:31:25,380 --> 00:31:35,870
+ال B زائد و ال B زائد ال Aموجودة في الـ R مديون A
+
+292
+00:31:35,870 --> 00:31:45,910
+such that بحيث أن الـ A زائد الـ A مضروب في الـ B
+
+293
+00:31:45,910 --> 00:31:55,310
+زائد الـ A بدي يسوى الـ Zero Element تمام؟
+
+294
+00:31:55,310 --> 00:31:59,670
+يبقى then اللي
+
+295
+00:31:59,670 --> 00:32:07,460
+هو من الـ AB زائد ال A بده سوى مين؟ ال A itself
+
+296
+00:32:07,460 --> 00:32:10,840
+مظبوط؟
+
+297
+00:32:10,840 --> 00:32:20,020
+طيب، هذا إيش معناه؟ هذا معناه إن ال A بي موجودة في
+
+298
+00:32:20,020 --> 00:32:24,700
+ال A كويس؟
+
+299
+00:32:24,700 --> 00:32:31,620
+يبقى ال A بي موجودة في ال Aمدام ال A بي موجودة في
+
+300
+00:32:31,620 --> 00:32:36,880
+ال A تعالى نشوف في شغل احنا مااستفدناش منها وهي ان
+
+301
+00:32:36,880 --> 00:32:41,900
+هذا prime ideal مدام ال prime ideal يبقى هذا
+
+302
+00:32:41,900 --> 00:32:48,360
+معناته ان ال A موجودة في ال A or ال B موجودة في ال
+
+303
+00:32:48,360 --> 00:32:59,940
+A السبب because ان ال A is a prime idealيبقى نظرة
+
+304
+00:32:59,940 --> 00:33:04,880
+لإن ال crime قاعدين هذا الكلام صحيح طيب مدام ال A
+
+305
+00:33:04,880 --> 00:33:10,040
+موجودة في A يبقى ال A زائد ال A قداش بده يساوي يا
+
+306
+00:33:10,040 --> 00:33:20,860
+بنات ال A or ال B زائد ال A بده يساوي ال A يبقى
+
+307
+00:33:20,860 --> 00:33:26,780
+أثبت إنه هذا بده يساوي ال zero element أو هذا بده
+
+308
+00:33:26,780 --> 00:33:31,920
+يساوي ال zero elementيبقى هذا إيش معناه؟ إن الـR
+
+309
+00:33:31,920 --> 00:33:37,640
+modulo A is an integral domain لإن أخدت حاصل ضرب
+
+310
+00:33:37,640 --> 00:33:43,640
+عنصرين يساوي الصفر، لجيت واحد فيهم بساوي الصفر،
+
+311
+00:33:43,640 --> 00:33:50,660
+يبقى هذا بده يعطينا إن الـR modulo A is an
+
+312
+00:33:50,660 --> 00:33:53,700
+integral domain.
+
+313
+00:33:59,660 --> 00:34:06,520
+طيب، فيش حد أحسن من حد؟ الناس كلهم سواسي، عشان
+
+314
+00:34:06,520 --> 00:34:12,340
+ماحدش يزعل من التاني. النظرية اتكلمت عن الـ Prime
+
+315
+00:34:12,340 --> 00:34:17,840
+Ideas، ولم تتكلم عنين؟ عن الـ Maximal Ideas،
+
+316
+00:34:17,840 --> 00:34:21,980
+وموضوعنا موضوع الـ Prime والـ Maximal. إذن هناك
+
+317
+00:34:21,980 --> 00:34:29,200
+نظرية مناضرة لها تتحدث عن مين؟ عن مين؟الـ maximal
+
+318
+00:34:29,200 --> 00:34:34,980
+معلاقته مع ال factor ring إذا بروح للنظرية الثانية
+
+319
+00:34:34,980 --> 00:34:43,780
+يبقى ال theorem النظرية التانية بتقول ما يطيب let
+
+320
+00:34:43,780 --> 00:34:56,020
+ال R be a commutative ring with unity
+
+321
+00:34:58,240 --> 00:35:07,140
+community bring with unity and
+
+322
+00:35:07,140 --> 00:35:16,660
+ال A an ideal of
+
+323
+00:35:16,660 --> 00:35:28,980
+R then ال R modulo A is a field if and only iff
+
+324
+00:35:28,980 --> 00:35:38,060
+and only f ال a is maximum لغاية ال a is maximum
+
+325
+00:35:38,060 --> 00:35:42,720
+لغاية
+
+326
+00:35:42,720 --> 00:35:51,880
+ال pro بدي
+
+327
+00:35:51,880 --> 00:35:58,420
+أصير برضه في اتجاهين بسبب ال f and only fيبقى
+
+328
+00:35:58,420 --> 00:36:08,680
+بدرجة اقوله left ال a موضوعه a a b a field يبقى b
+
+329
+00:36:08,680 --> 00:36:17,560
+a field طبعا بدي اثبت ان ال a باله is maximum يبقى
+
+330
+00:36:17,560 --> 00:36:37,110
+one two one two show thatإن ال A is maximum يبدأ
+
+331
+00:36:37,110 --> 00:36:44,050
+يقول افترض ان ال B بيكون
+
+332
+00:36:44,050 --> 00:36:52,050
+ايديل او R بحيث
+
+333
+00:36:52,050 --> 00:37:02,010
+ان ال A اللي عندناsubset من الـ B و لا يساوي و الـ
+
+334
+00:37:02,010 --> 00:37:08,070
+B subset من R و
+
+335
+00:37:08,070 --> 00:37:13,730
+الـ B subset من R طيب
+
+336
+00:37:13,730 --> 00:37:20,570
+مرة تانية قربنا R modulo A عبارة عن فيه بتبين ان
+
+337
+00:37:20,570 --> 00:37:25,030
+الـ A maximum لو روحت لتعريف ال maximumفرأت أنه
+
+338
+00:37:25,030 --> 00:37:31,110
+عندي ideal تاني B بحيث الـA subset من B ولا يساوي
+
+339
+00:37:31,110 --> 00:37:36,850
+و الـB subset من R. إذا أثبتوا إنه B يساوي الـR،
+
+340
+00:37:36,850 --> 00:37:42,310
+بصير هذا الـMaximal أو إذا أثبتوا إن الـUnity هو
+
+341
+00:37:42,310 --> 00:37:47,690
+الموجود في B، يبقى بصير الـA عبارة عن Maximal
+
+342
+00:37:47,690 --> 00:37:51,430
+Ideal. بصير الـB يساوي الـR، وبالتالي الـA is
+
+343
+00:37:51,430 --> 00:38:00,330
+Maximal.بقولوا خيص قولولي ال B موجودة في B بقى
+
+344
+00:38:00,330 --> 00:38:09,370
+ولكن ال B مش موجودة في A ايه صفصت من B ولا يساوي
+
+345
+00:38:09,370 --> 00:38:15,410
+في عناصر موجودة في B ومش موجودة وين في A أخدت عنصر
+
+346
+00:38:15,410 --> 00:38:25,040
+موجود في B وعنصر هذا مش موجود في Aالـ B زائد الـ A
+
+347
+00:38:25,040 --> 00:38:32,280
+بينفع أقول يساوي الـ A هنا؟ لأ يفجأة لا يساوي الـ
+
+348
+00:38:32,280 --> 00:38:37,340
+A يعني بيسويش الـ zero element يفجأة الـ B زائد
+
+349
+00:38:37,340 --> 00:38:43,380
+الـ A is a non zero element يفجأة هذا بده يعطينا
+
+350
+00:38:43,380 --> 00:38:51,320
+أن الـ B زائد الـ A is a non zero element
+
+351
+00:38:53,810 --> 00:39:00,090
+إن ال R مدلويز A يبقى
+
+352
+00:39:00,090 --> 00:39:08,130
+هذا عنصر غير صفري و أنا فارق R
+
+353
+00:39:08,130 --> 00:39:12,290
+مدلويز A field يبقى هذا عنصر إذا كان غير صفري إيش
+
+354
+00:39:12,290 --> 00:39:18,190
+بدي يكون؟ unit لإن في ال field أي عنصر غير الصفر
+
+355
+00:39:18,190 --> 00:39:25,870
+يكون unitهذا بده يعطينا ان الـB زائد الـA is a
+
+356
+00:39:25,870 --> 00:39:33,550
+unit تمام؟ يعني معنى هذا الكلام ان there exist
+
+357
+00:39:33,550 --> 00:39:43,430
+عنصر C زائد الـA موجود في الـR modulo A such that
+
+358
+00:39:43,430 --> 00:39:51,630
+بحيث ان حاصل ضربهما بده يساوي ال unityمظبوط يعني
+
+359
+00:39:51,630 --> 00:39:57,790
+بدي يكون ال B زائد ال A في هذا ال element اللي هو
+
+360
+00:39:57,790 --> 00:40:03,790
+C زائد ال A بدي يسوى ال unity اللي هو واحد زائد ال
+
+361
+00:40:03,790 --> 00:40:13,710
+A يعني إيش معنى هذا الكلام معناه إن ال B C زائد ال
+
+362
+00:40:13,710 --> 00:40:23,570
+A يسوى واحد زائد ال Aأو لو جينا أضفنا للطرفين سالف
+
+363
+00:40:23,570 --> 00:40:33,430
+بي سي بظل ال a بدر ساوي واحد ناقص بي سي زائد ال a
+
+364
+00:40:33,430 --> 00:40:40,190
+هذا ايش معناه ان ال element هذا وين موجود؟ موجود
+
+365
+00:40:40,190 --> 00:40:46,650
+في ال a يبقى هذا معناه ان الواحد ناقص ال بي سي
+
+366
+00:40:46,650 --> 00:40:52,980
+موجود في ال aطب ال A subset من B ولا لأ؟ يبقى ال
+
+367
+00:40:52,980 --> 00:40:57,300
+element هذا موجود في B ولا لأ؟ يبقى هذا اللي
+
+368
+00:40:57,300 --> 00:41:06,420
+بيعطيكي علاقة للخاطر ان واحد ناقص بي سي موجود في B
+
+369
+00:41:06,420 --> 00:41:17,310
+because ان ال A subset من B ولا يسوىالقصار ال
+
+370
+00:41:17,310 --> 00:41:22,870
+element هذا موجود وين يا بنات في B السؤال الكم؟
+
+371
+00:41:22,870 --> 00:41:33,770
+Pause ال B ال B ال C موجود في B و لا لأ؟ لأن ال B
+
+372
+00:41:33,770 --> 00:41:39,280
+موجود في B و ال C أي element موجود في Aيبقى ال B
+
+373
+00:41:39,280 --> 00:41:44,920
+موجود في B و ال B is an ideal أوضر بال B في أي
+
+374
+00:41:44,920 --> 00:41:49,480
+عنصر من عناصر ال ring بدي يكون موجود في هذا ال
+
+375
+00:41:49,480 --> 00:42:01,500
+ideal also هنا because ال B موجود في ال B and ال B
+
+376
+00:42:01,500 --> 00:42:06,880
+موجود في ال B and ال B ID
+
+377
+00:42:10,590 --> 00:42:18,530
+طيب الآن لو جيت جمعت اتنين مع بعض وين بده يكون؟ في
+
+378
+00:42:18,530 --> 00:42:28,590
+نفسه يبقى هنا ساعة واحد نقص ال Vc زائد ال Vc موجود
+
+379
+00:42:28,590 --> 00:42:35,510
+في B يعني معنى هذا الكلام ان الواحد
+
+380
+00:42:37,740 --> 00:42:44,480
+موجود في B يبقى ال unity تبع ال ring الأصلية طلع
+
+381
+00:42:44,480 --> 00:42:51,620
+موجود في B هذا معناته ان بي تسوى جدير تسوى R
+
+382
+00:42:51,620 --> 00:42:58,280
+itself يبقى ال ideal A عبارة عن من؟ عن مكسيم، عن
+
+383
+00:42:58,280 --> 00:43:04,240
+اللغين، هذه طلع المساوية هنا يبقى هذا يعطيني ان ال
+
+384
+00:43:04,240 --> 00:43:13,150
+Ais maximum in الأرض
+
+385
+00:43:13,150 --> 00:43:19,690
+يبقى هذا لإتجاه الأول الأهم يجي لإتجاه الثاني
+
+386
+00:43:38,170 --> 00:43:47,290
+يبقى باجي بقوله conversion افترضنا
+
+387
+00:43:47,290 --> 00:43:52,370
+فيه و اثبتنا انه ايه maximum يبقى بدأ افترض انه
+
+388
+00:43:52,370 --> 00:43:57,650
+ايه maximum و نثبت ان ال R modulo A is ايه فيه
+
+389
+00:43:57,650 --> 00:44:01,470
+يبقى هنا باجي بقوله assume
+
+390
+00:44:05,020 --> 00:44:15,600
+that إن الـA الـA maximum ideal
+
+391
+00:44:15,600 --> 00:44:19,960
+الـR،
+
+392
+00:44:19,960 --> 00:44:32,140
+إيش اللي بننطبته؟ one one to show that الـR
+
+393
+00:44:34,040 --> 00:44:43,500
+Modulo A is A field نحاول
+
+394
+00:44:43,500 --> 00:44:50,860
+نثبت ان ال R Modulo A is A field بقوله كويس مشان
+
+395
+00:44:50,860 --> 00:44:58,280
+ايه؟ بدي قاعد ياخد عنصر غير صفري هنا العنصر غير
+
+396
+00:44:58,280 --> 00:45:04,140
+الصفري لو جدرت اثبت انه معكوس بتم المطلوب ليش؟إن
+
+397
+00:45:04,140 --> 00:45:10,140
+كل أنصار في ال field is a unit يعني بقدر أجد أنصار
+
+398
+00:45:10,140 --> 00:45:14,640
+أضغط فيها يعطيني main أنصار الواحدة يبقى افترض a
+
+399
+00:45:14,640 --> 00:45:20,420
+maximum وين ما يلزم بدي إياها و بدي أحاول أثبت أن
+
+400
+00:45:20,420 --> 00:45:29,340
+ال R مضي له a is a field طيب لو جيت قلت هنا net ال
+
+401
+00:45:29,340 --> 00:45:36,370
+b موجودة أخدنا بيه من قلة ال bموجودة في ال ring A
+
+402
+00:45:36,370 --> 00:45:47,410
+such that بحيث ال B مش موجود في ال A يبقى
+
+403
+00:45:47,410 --> 00:45:53,650
+ال B مش موجود في ال A then ال
+
+404
+00:45:53,650 --> 00:46:01,680
+B زائد ال A بده يساوي ايه يا بنات؟ مش ممكنيبقى لا
+
+405
+00:46:01,680 --> 00:46:07,240
+يمكن أن يساوي 0 يبقى ال B زائد ال A is a non-zero
+
+406
+00:46:07,240 --> 00:46:17,260
+element يبقى هذا ال B زائد ال A is a non-zero
+
+407
+00:46:17,260 --> 00:46:29,560
+element non-zero element in R modulo A مدام أنصر
+
+408
+00:46:29,560 --> 00:46:37,810
+غير صفريبنحاول نثبت ان هذا unit يبقى one to sure
+
+409
+00:46:37,810 --> 00:46:42,770
+that
+
+410
+00:46:42,770 --> 00:46:53,730
+نحاول نثبت ان ال B بصر ال A is a unit ان تم لنا
+
+411
+00:46:53,730 --> 00:47:03,830
+ذلك بصير ال R موديل A is A فيهبنحاول نستفيد من هذا
+
+412
+00:47:03,830 --> 00:47:09,170
+هو عبارة عن maximal ideal حتى الآن لم نستفيد شيئا
+
+413
+00:47:09,170 --> 00:47:15,330
+كلمة maximal بالزمن مين؟ ideal تاني و اللي عندى
+
+414
+00:47:15,330 --> 00:47:19,450
+بده يكون subset منه و هذا ال ideal اللى جاءه بده
+
+415
+00:47:19,450 --> 00:47:25,030
+يكون subset من مين؟ من R تبقى لو جيتكم ت consider
+
+416
+00:47:25,030 --> 00:47:38,680
+the set Dمين هي V؟ هي كل الـP R كل الـP R زائد
+
+417
+00:47:38,680 --> 00:47:50,060
+الـA بحيث الـR موجودة في R والـA موجودة في A ان
+
+418
+00:47:50,060 --> 00:47:59,270
+يزعم ان الـP هي عبارة عن ID ونريد نشوف ليه لأنالـB
+
+419
+00:47:59,270 --> 00:48:08,970
+is an id ليش؟ because تلت
+
+420
+00:48:08,970 --> 00:48:15,630
+نقاط لازم نثبتهم النقطة الأولى ان الـB is non
+
+421
+00:48:15,630 --> 00:48:22,670
+-empty ليش؟ since؟
+
+422
+00:48:22,670 --> 00:48:31,180
+بتجيبها لو عنصر واحد موجود في الـBzero زائد ال a
+
+423
+00:48:31,180 --> 00:48:40,880
+هو عبارة عن ال b في zero زائد ال a صح ولا لأ يبقى
+
+424
+00:48:40,880 --> 00:48:48,160
+هاي ال b عنصر من ال ring زائد عنصر a من ال a مظبوط
+
+425
+00:48:48,160 --> 00:48:55,830
+هكذا هذا موجود وين موجود يبقى هذا non emptyلأنه
+
+426
+00:48:55,830 --> 00:49:01,310
+قدرت أجيبه عنصر واحد موجود في B موجود في B خلصنا
+
+427
+00:49:01,310 --> 00:49:06,690
+النقطة الأولى النقطة الثانية افترض ان X و Y
+
+428
+00:49:06,690 --> 00:49:14,930
+موجودات في B يبقى A شكلهم على الشكل التالي then ال
+
+429
+00:49:14,930 --> 00:49:27,970
+X بقدر أقول هي B R1 زائد A1 and ال YPR2 زائد A2
+
+430
+00:49:27,970 --> 00:49:40,830
+وعندك R1 وR2 موجودة في R وA1 وA2 موجودة في X يبقى
+
+431
+00:49:40,830 --> 00:49:48,630
+R1 وR2 موجودة في R وA1 وA2 موجودة في A بدي أروح
+
+432
+00:49:48,630 --> 00:49:58,540
+أشوف هل ال X ناقص ال Yموجودة في بي ولا لا يبقى بقى
+
+433
+00:49:58,540 --> 00:50:06,860
+جيبا يقول يبقى ال بي R1 بي R1 زائد ال A1 ناقص بي
+
+434
+00:50:06,860 --> 00:50:15,580
+R2 زائد ال A2 يسوى طلعيل العنصر هذا مع العنصر هذا
+
+435
+00:50:15,580 --> 00:50:26,420
+في بي في R1 ناقص R2بظل a1 minus a2 يبقى زائد a1
+
+436
+00:50:26,420 --> 00:50:32,460
+minus a2 هذا في a و
+
+437
+00:50:32,460 --> 00:50:38,540
+هذا في a و هذا في a يبقى هذا على الصيغة اللي قدامي
+
+438
+00:50:38,540 --> 00:50:45,620
+ولا لا يبقى صار هذا ال element كله على بعض هذا a
+
+439
+00:50:45,620 --> 00:50:54,460
+موجود في ال bنجي الآن للنقطة الثالثة بدي انا اخد
+
+440
+00:50:54,460 --> 00:51:02,460
+element من ال ring R يبقى لو جيه تقول F مثلا S
+
+441
+00:51:02,460 --> 00:51:12,680
+موجود في R and ال X اللي يبدأ تساوي PR1 زائد A1
+
+442
+00:51:12,680 --> 00:51:15,780
+موجودة في من؟ في ال B
+
+443
+00:51:18,940 --> 00:51:26,340
+بدا ياخد الـ S في الـ X يبقى بده يساوي الـ S في
+
+444
+00:51:26,340 --> 00:51:37,860
+PR1 زائد الـ A1 هذا الكلام بده يساوي S في PR1 زائد
+
+445
+00:51:37,860 --> 00:51:44,520
+الـ S A1 الـ Ring الأصلي هى commutative ولا لأ إذا
+
+446
+00:51:44,520 --> 00:51:52,880
+بقدر أعمل خاصية الإبدال هنايبقى يده بده يساوي BSR1
+
+447
+00:51:52,880 --> 00:52:01,500
+زائد ال S A1 هدى وين موجودة يا بنات؟ في R هدى
+
+448
+00:52:01,500 --> 00:52:08,200
+موجودة وين؟ في A لإن ال A ايديل A1 موجودة فيه و ال
+
+449
+00:52:08,200 --> 00:52:13,780
+S موجودة في R اضرب اي عنصر من عناصر R في اي عنصر
+
+450
+00:52:13,780 --> 00:52:18,800
+من عناصر A بده يكون موجود في ال Aيبقى هذا موجود في
+
+451
+00:52:18,800 --> 00:52:25,200
+الـA، إذا كل هذا موجود وين؟ في الـB Similarly
+
+452
+00:52:25,200 --> 00:52:28,740
+Similarly
+
+453
+00:52:28,740 --> 00:52:37,940
+ان ال X في S موجودة كذلك في B يبقى Thus و هكذا ان
+
+454
+00:52:37,940 --> 00:52:50,320
+ال B is an ideal of Rكويسة. يبقى حتى الآن أثبتنا
+
+455
+00:52:50,320 --> 00:52:55,420
+ان بي عبارة عن ID الـ VR. ما استخدمناش خاصية ال
+
+456
+00:52:55,420 --> 00:52:59,920
+maximality اللي احنا فرضناها من عند ال conversion.
+
+457
+00:53:00,600 --> 00:53:03,980
+يعني حتى الآن ما استخدمناها، بس جاها دورها الحين.
+
+458
+00:53:04,540 --> 00:53:14,180
+يبقى أثبتنا ان بي is an ID، not that. السؤال هو هل
+
+459
+00:53:14,180 --> 00:53:20,400
+الـ Asubset من B هي
+
+460
+00:53:20,400 --> 00:53:28,860
+التعريف هذا ال element موجود في A و هذا element
+
+461
+00:53:28,860 --> 00:53:35,580
+زيادة عليه يبقى لها subset من B ولا لا؟ يساوي؟ لا
+
+462
+00:53:35,580 --> 00:53:46,790
+ولا يساوي و ال B في حد ذاته subset من مين؟من R طب
+
+463
+00:53:46,790 --> 00:53:52,390
+هذا لا يمكن ان يساوي هذا إذا ال B بده يساوي ال R
+
+464
+00:53:52,390 --> 00:53:57,790
+لأن ال A is maximum صح ولا لا؟ مش هيك التعريف؟ هذا
+
+465
+00:53:57,790 --> 00:54:06,130
+معناه ان ال B بده يساوي ال R because ال A is
+
+466
+00:54:06,130 --> 00:54:12,930
+maximum حسب ما احنا فرضينه هي تحتي خطمدام ال P بده
+
+467
+00:54:12,930 --> 00:54:21,010
+يساوي ال R هذا معناته ان ال واحد موجود في ال P مش
+
+468
+00:54:21,010 --> 00:54:25,750
+ال P هي بقى و ال R فيها ال unity يبقى ال واحد
+
+469
+00:54:25,750 --> 00:54:32,530
+موجود في P طب ايه شكل ال واحد بده يكون؟ ايه يبقى
+
+470
+00:54:32,530 --> 00:54:42,480
+بده يكون PA مثلا او PR1 زائد Aعلى سبيل المثال
+
+471
+00:54:42,480 --> 00:54:47,140
+والله يا شرطة بلاش تقول مين هذا ايش ما تكون ال a
+
+472
+00:54:47,140 --> 00:54:54,360
+أي عنصر من a يبقى هاي شكله طيب كويس لو جيت قلتلكوا
+
+473
+00:54:54,360 --> 00:54:59,400
+ال unity عندنا اللي يقول عليه واحد زائد a قبل شوية
+
+474
+00:54:59,400 --> 00:55:07,880
+يبقى لو جيت قلت واحد زائد a بده يساوي ب أول زائد a
+
+475
+00:55:07,880 --> 00:55:14,510
+prime زائد ال aيبقى بناءً عن ايه؟ صار الواحد زائد
+
+476
+00:55:14,510 --> 00:55:19,770
+ال A بالبشرة ال A' موجودة في اللغة ولا لا؟ يبقى
+
+477
+00:55:19,770 --> 00:55:29,210
+بضل بس بي R1 زائد ال A تمام، يبقى صار عند مين؟
+
+478
+00:55:29,210 --> 00:55:37,950
+الواحد زائد ال A يساوي بي زائد ال A مضروب في ال R1
+
+479
+00:55:37,950 --> 00:55:45,630
+زائد ال Aطب ايش تفسيركوا للعبارة هذه؟ اه حاصل ضرب
+
+480
+00:55:45,630 --> 00:55:52,850
+عنصرين يساوي اليونيتي بزايد ال a is a unit احنا
+
+481
+00:55:52,850 --> 00:55:58,370
+قلنا هنا لو قدرنا نثبت ان ال b زايد ال a is a unit
+
+482
+00:55:58,370 --> 00:56:07,620
+خلصنا يبقى هذا بيكون ال b زايد ال a is a unitيبقى
+
+483
+00:56:07,620 --> 00:56:13,140
+صار عندى any non zero element b plus a في ال R
+
+484
+00:56:13,140 --> 00:56:19,500
+modulo a is a يعني يبقى ال R modulo a is a field
+
+485
+00:56:19,500 --> 00:56:29,340
+هذا بيعطيلك ان ال R modulo a is a field تمام؟ وهو
+
+486
+00:56:29,340 --> 00:56:30,480
+المطلوب
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a3aae0257066d69edeb973fe316bad70bb9a74c6
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_raw.srt
@@ -0,0 +1,1952 @@
+1
+00:00:21,080 --> 00:00:25,780
+بسم الله الرحمن الرحيم عودنا على بدأ المرة اللي
+
+2
+00:00:25,780 --> 00:00:30,000
+فاتت بجينا نتكلم على ال prime ideals و ال maximal
+
+3
+00:00:30,000 --> 00:00:36,600
+ideals تمام و أعطينا على ذلك بعض الأمثلة مع ال
+
+4
+00:00:36,600 --> 00:00:41,260
+factoring كذلك المثال رقم 5 بيقول show that the
+
+5
+00:00:41,260 --> 00:00:45,260
+ideal ال principle ideal generated by X ترمية
+
+6
+00:00:45,260 --> 00:00:51,080
+زواحد is maximal in R of Xإذا بدنا نثبت ان هذا ال
+
+7
+00:00:51,080 --> 00:00:55,800
+ideal هو maximal way in our operation لو راجعنا
+
+8
+00:00:55,800 --> 00:01:01,200
+بالذاكرة الى الوراق قليلا مشان نثبت ال maximality
+
+9
+00:01:01,200 --> 00:01:07,120
+ليه ideal بفترض ان في عندي ideal أخر و هذا ال
+
+10
+00:01:07,120 --> 00:01:13,420
+ideal subset منه و ال ideal هذا subset من Rيا إما
+
+11
+00:01:13,420 --> 00:01:17,440
+ال ideal اللى عندنا بده يسوى ال ideal المقترح يا
+
+12
+00:01:17,440 --> 00:01:22,480
+إما ال ideal المقترح بده يسوى أي واحدة منهم، تمام؟
+
+13
+00:01:22,480 --> 00:01:34,120
+إذا احنا بدنا نفرض هنا assume that ال A is an
+
+14
+00:01:34,120 --> 00:01:40,300
+ideal such that .. ideal of
+
+15
+00:01:42,090 --> 00:01:49,750
+of X such that بحيث ان ال principle ideal
+
+16
+00:01:49,750 --> 00:01:56,570
+generated by X تربيعه plus one subset من ال A ولا
+
+17
+00:01:56,570 --> 00:02:06,870
+يساوي وال A معروف هو subset من من ال ring A إذا
+
+18
+00:02:06,870 --> 00:02:13,410
+حيال الآن بيسويش ال A يبقى مطلوب نسبة 8إن ال A بده
+
+19
+00:02:13,410 --> 00:02:23,010
+يسوى من ال R يبقى value بيقول if we show that إذا
+
+20
+00:02:23,010 --> 00:02:32,090
+جدنا نثبت إن ال A بده يسوى ال R itself then ال A
+
+21
+00:02:32,090 --> 00:02:39,350
+is maximal طيب also
+
+22
+00:02:41,510 --> 00:02:50,590
+و كذلك if we show that إذا جدرنا نبين إن الواحد أو
+
+23
+00:02:50,590 --> 00:03:00,490
+ال unity موجود في A then ال A is maximum مش هذا
+
+24
+00:03:00,490 --> 00:03:06,230
+مثال سابق خدناه المحلقة الماضية إنه لو أخدت أي من
+
+25
+00:03:06,230 --> 00:03:09,610
+ال ring R اللي بتبقى commutative ring with unity
+
+26
+00:03:09,990 --> 00:03:13,950
+ولاقيت ال unity موجود في ال ID اللي يبقى ال ID
+
+27
+00:03:13,950 --> 00:03:18,330
+اللي بده يسمى من R و أثبتناها عمليا معاكم طبعا هو
+
+28
+00:03:18,330 --> 00:03:22,350
+سؤال في التمريم احنا أعطينا مثال و بدنا نعتمد عليه
+
+29
+00:03:22,350 --> 00:03:32,730
+هنا في اثبات هذا ال لسات مين هي ال A؟ ال A فرض
+
+30
+00:03:32,730 --> 00:03:38,380
+من عندي؟ اهمش احنا .. احنا الموجود عند مين X
+
+31
+00:03:38,380 --> 00:03:42,860
+التربيع زي الواحد صح هذا ال ideal مُعطى هذا اللي
+
+32
+00:03:42,860 --> 00:03:47,900
+بدي أثبت انه maximum من تعريف ال maximal اللي عندك
+
+33
+00:03:47,900 --> 00:03:54,480
+بنقول هذا maximal إذا جدلت ألاقي ideal تاني بحيث
+
+34
+00:03:54,480 --> 00:03:59,640
+هذا subset منهم وال ideal التاني طبعا subset من R
+
+35
+00:03:59,640 --> 00:04:05,600
+فهو طبيعيإن حدث ذلك، يا إما هذا بتساوي الـA، يا
+
+36
+00:04:05,600 --> 00:04:09,320
+إما الـA بتساوي الـA، مش هيك التعريف اللي مكتوب
+
+37
+00:04:09,320 --> 00:04:12,320
+عندك المرة دي، التعريف المكتمه الـideal، أيوة،
+
+38
+00:04:12,320 --> 00:04:16,200
+احنا
+
+39
+00:04:16,200 --> 00:04:20,260
+مانقولك ideal، نتكلمش set، set لسه بجدوح تتبت من
+
+40
+00:04:20,260 --> 00:04:26,180
+أول و جديد، هذا ideal، وفرقت الـA، ideal تاني، إذا
+
+41
+00:04:26,180 --> 00:04:32,720
+هذا ال ideal هو subset من A ولا يساوييبقى إجباري
+
+42
+00:04:32,720 --> 00:04:36,700
+مشان يكون maximum لازم أثبت ان ال A بده ساوة مين؟
+
+43
+00:04:36,700 --> 00:04:42,360
+بده ساوة ال R طبعا يبقى هنا قولنا إذا قدرنا نبين
+
+44
+00:04:42,360 --> 00:04:46,120
+ان ال A بده ساوة R يبقى ال A بصير maximum طبق
+
+45
+00:04:46,120 --> 00:04:51,120
+التعريف طبق المثال اللي فات إذا قدرت أثبت ان
+
+46
+00:04:51,120 --> 00:04:55,500
+الواحد موجود في ال A يبقى ال A بده ساوة ال R يبقى
+
+47
+00:04:55,500 --> 00:05:02,780
+ال A maximum عادي مظبوط ايه؟ بقول كويسطيب بدنا
+
+48
+00:05:02,780 --> 00:05:07,460
+نحاول نثبت ان هذا ال a maximum او الواحد موجود
+
+49
+00:05:07,460 --> 00:05:15,560
+وين؟ موجود في ال a لذلك بروح اخد element موجود في
+
+50
+00:05:15,560 --> 00:05:20,720
+ال ring او اخده موجود في a ومش موجود في ال
+
+51
+00:05:20,720 --> 00:05:25,260
+principle ideal generated by a يبقى باجي بقوله
+
+52
+00:05:25,260 --> 00:05:32,210
+افترح ان عندي ال element f of xموجود في الـ Ideal
+
+53
+00:05:32,210 --> 00:05:39,570
+I and الـ F of X مش موجود في الـ Principle Ideal
+
+54
+00:05:39,570 --> 00:05:44,710
+Generated by X ترفيه أزاى الواحدة إذا أخدت element
+
+55
+00:05:44,710 --> 00:05:49,870
+موجود هنا ومش موجود هنا هذا subset قد يسوي وقد لا
+
+56
+00:05:49,870 --> 00:05:55,250
+يسوي على فرض لا يسوي إذا ممكن ألاقي عناصر هنا مش
+
+57
+00:05:55,250 --> 00:06:00,150
+موجودة هنا تماملكن كل العناصر اللي هنا موجودة وين
+
+58
+00:06:00,150 --> 00:06:05,590
+موجودة وين هذا إجبال يبقى أخد ال F of X موجودة في
+
+59
+00:06:05,590 --> 00:06:10,450
+إيه أن ال F of X مش موجودة في ال principle ID
+
+60
+00:06:10,450 --> 00:06:18,370
+generated by X تربيع زاد واحد السؤال هو ال F of X
+
+61
+00:06:18,370 --> 00:06:24,870
+بقدر أكتبها بصورة أخرى أو بطريقة أخرى السؤال هو ما
+
+62
+00:06:24,870 --> 00:06:35,740
+هذه الصورةبنقول له then ال F of X بدها تساوي هذي
+
+63
+00:06:35,740 --> 00:06:42,340
+أنا ماخدها وين؟ ماخدها فيهين يبقى مش موجودة فيهين
+
+64
+00:06:42,340 --> 00:06:47,820
+يبقى الدرجة تبعتها هتكون أعلى من الدرجة الثانية،
+
+65
+00:06:47,820 --> 00:06:51,060
+التالتة، الرابعة، العاشرة، العشرة، جد ما تكون،
+
+66
+00:06:51,060 --> 00:06:58,200
+ماعندا مشكلة إذا لو روحت جسم يسمى مطولةالـ F of X
+
+67
+00:06:58,200 --> 00:07:03,160
+جسمتها على الـ polynomial X تربيه زائد واحد، ايش
+
+68
+00:07:03,160 --> 00:07:10,460
+بدي يطلع؟ بدي يطلع Q of X، polynomial في X، X
+
+69
+00:07:10,460 --> 00:07:17,880
+تربيه زائد واحد زائد الباقي اللي هو الـ R of X،
+
+70
+00:07:17,880 --> 00:07:22,540
+تمام؟ اه استرستلنا شوية، بدي انا فاهمها هذه،
+
+71
+00:07:22,540 --> 00:07:27,580
+بفهمها بسيط جدا، ولا حاجةكيف أفهمه بسيط بقول ما
+
+72
+00:07:27,580 --> 00:07:33,020
+ياتي لما نكسب كثيرة حدود على كثيرة حدود يمكن ننتهي
+
+73
+00:07:33,020 --> 00:07:38,440
+بأصفار يبقى جسم على بعض بدون باقي يبقى بيكون ال R
+
+74
+00:07:38,440 --> 00:07:46,480
+of X جده ب Zero تمام و ممكن يزيد شيء لكن لما يزيد
+
+75
+00:07:46,480 --> 00:07:50,820
+شيء درجته تبقى أقل من ال extra بيها زائد واحد
+
+76
+00:07:50,820 --> 00:07:55,160
+مظبوطتمام لأن لو كان أكتر من X تربيه زي الواحد
+
+77
+00:07:55,160 --> 00:08:00,400
+الصلبات لل term اللي عندنا هذا طيب كويس هنا بنقول
+
+78
+00:08:00,400 --> 00:08:07,620
+where؟ بدي أخد ال R of X does not equal to zero مش
+
+79
+00:08:07,620 --> 00:08:18,040
+Zero and ال degree لمن؟ لل R of X أقل من اتنينلأن
+
+80
+00:08:18,040 --> 00:08:22,400
+لو صارت اتنين بدها صير مع ال Q of X اللي مضروبة في
+
+81
+00:08:22,400 --> 00:08:26,300
+X تربية زي واحدة لأن بقول في ال polynomial نقسم
+
+82
+00:08:26,300 --> 00:08:31,320
+polynomial درجة البصر قد درجة المقام أو أكبر منه
+
+83
+00:08:31,320 --> 00:08:36,140
+بقسم جسمه مطولة لكن لو كانت درجة البصر أقل من درجة
+
+84
+00:08:36,140 --> 00:08:41,420
+المقام بقدر أقسم جسمه مطولة؟ لا بقدرش تمام؟ إذن
+
+85
+00:08:41,420 --> 00:08:46,780
+صار عند ال R of X بتاخدها بتسويش Zero يبقى معضمون
+
+86
+00:08:47,220 --> 00:08:52,320
+لازم ألاقي function في ال R of X درجته أقل من 100
+
+87
+00:08:52,320 --> 00:08:57,460
+من اتنين يعني من الدرجة الأولى صح ولا لا يبقى من
+
+88
+00:08:57,460 --> 00:09:03,340
+الدرجة الأولى طيب ممتازة اذا بدي اكتب ال R of X
+
+89
+00:09:03,340 --> 00:09:11,460
+على الصيغة التالية F of X ناقص ل Q of X في X تربيه
+
+90
+00:09:11,460 --> 00:09:15,380
+زائد واحد تمام
+
+91
+00:09:16,060 --> 00:09:20,160
+طيب انا اتهدف و فيكس وين موجودة؟ موجودة في الاه في
+
+92
+00:09:20,160 --> 00:09:28,900
+الاه في الاه طيب و هذه؟ برضه في الاه برضه في الاه
+
+93
+00:09:28,900 --> 00:09:35,100
+لماذا؟ لأنه في الاه جيلاراتر و هذي كسافراتر هذي
+
+94
+00:09:35,100 --> 00:09:45,400
+موجودة في الاه؟ عشانها اناأي element
+
+95
+00:09:45,400 --> 00:09:50,280
+هنا موجود هنا و أي element هنا على الصيغة اللي
+
+96
+00:09:50,280 --> 00:09:55,780
+قلناها تعريف ال principle ID هو الـ generated by A
+
+97
+00:09:55,780 --> 00:10:02,000
+هو الـ A مضروبة في R بحيث الـ R في R و الـ A يبقى
+
+98
+00:10:02,000 --> 00:10:11,440
+هذاليش هذه؟ because ان ال principle ideal gene او
+
+99
+00:10:11,440 --> 00:10:18,940
+because ال X تربيع زائد واحد موجودة فيه تمام؟ يبقى
+
+100
+00:10:18,940 --> 00:10:23,700
+ضربته في أي function من ال R of X موجودة فيه إذا
+
+101
+00:10:23,700 --> 00:10:31,860
+صار R of X موجودة فيه طب مين هي ال R of X؟ ال R of
+
+102
+00:10:31,860 --> 00:10:39,120
+Xبدها الصيغة درجتها قلل من اتنين يبقى number of x
+
+103
+00:10:39,120 --> 00:10:49,200
+بالصيغة على الصيغة a x زائد b صح ؟ وهذه كلها
+
+104
+00:10:49,200 --> 00:10:54,000
+موجودة في ايه؟ وهذه موجودة في ايه؟ يبقى ال term كل
+
+105
+00:10:54,000 --> 00:11:02,810
+هذا موجود هنا واضح حالك اكتر يبقى هذابدي أعطيك ما
+
+106
+00:11:02,810 --> 00:11:11,810
+ياتي ال R of X تساوي ال F of X ناقص ل Q of X في ال
+
+107
+00:11:11,810 --> 00:11:19,850
+X تربيع زائد واحد كلها موجودة في A طيب ال R of X
+
+108
+00:11:19,850 --> 00:11:26,230
+درجتها أقل من الدرجة الثانية يبقى درجة الأول يبقى
+
+109
+00:11:26,230 --> 00:11:37,790
+بصير عند ال AXأو الـ R of X تساوي الـ AX زائد B
+
+110
+00:11:37,790 --> 00:11:46,190
+اللي هي هذه اللي هي موجودة وين؟ موجودة في A طيب،
+
+111
+00:11:46,190 --> 00:11:54,710
+بدي أسألكوا السؤال التالي Now لو أخدت ال AX زائد
+
+112
+00:11:54,710 --> 00:12:04,420
+ال B وضربتها في AXناقص ال B هل هذه موجودة في A؟ في
+
+113
+00:12:04,420 --> 00:12:12,400
+A؟ اه موجودة في A؟ اه موجودة ليش؟ لأن هذا ال
+
+114
+00:12:12,400 --> 00:12:18,720
+element موجود في A وال A ID وضربيه في أي function
+
+115
+00:12:18,720 --> 00:12:23,560
+من ال R of X بدي يكون موجود في A صحيح ولا لأ؟ إذا
+
+116
+00:12:23,560 --> 00:12:33,210
+ال هذي كذلكموجودة في a because ال a is an ideal
+
+117
+00:12:33,210 --> 00:12:39,250
+اللي بيحصل ضربه هناك موجود في ال a طيب الان لو جيت
+
+118
+00:12:39,250 --> 00:12:44,430
+ضربت هذول في بعض الفرق بين المرقعين يبقى a تربيع x
+
+119
+00:12:44,430 --> 00:12:50,730
+تربيع ناقص b تربيع موجود وين؟ موجود في ال a
+
+120
+00:12:58,850 --> 00:13:07,110
+الان بدي اجيب كمان شغلة تانية و نشوف هاها موجودة
+
+121
+00:13:07,110 --> 00:13:17,410
+في a ولا لا لو جيت قلتلك بط ال a ترابيع في ال x
+
+122
+00:13:17,410 --> 00:13:25,720
+ترابيع زائد واحد هل هذه موجودة في aأكس تربية زي
+
+123
+00:13:25,720 --> 00:13:28,460
+الواحد موجودة في ال principle و ال principle
+
+124
+00:13:28,460 --> 00:13:33,300
+subset من a إذا هذا ال element موجود في a هو و
+
+125
+00:13:33,300 --> 00:13:39,160
+مضاعفاته يبقى ال a تربية في ال x تربية زي الواحد
+
+126
+00:13:39,160 --> 00:13:46,060
+لو بدنا نسوي a تربية x تربية زائد a تربية موجود في
+
+127
+00:13:46,060 --> 00:13:53,090
+ال a كذلك طب لو جمعتهم بيكون موجود في ال aطب لو
+
+128
+00:13:53,090 --> 00:14:00,790
+طرحتهم طب لو طرحناهم يبقى سوء ال a تربيع x تربيع
+
+129
+00:14:00,790 --> 00:14:09,450
+زائد ال a تربيع ناقص ال a تربيع x تربيع ناقص ال b
+
+130
+00:14:09,450 --> 00:14:16,110
+تربيع كل هذا بيكون موجود في a لو طرحناهم و لا تشبه
+
+131
+00:14:16,110 --> 00:14:22,950
+ال a تربيع زائد b تربيع موجودة في aيبقى طالع عندي
+
+132
+00:14:22,950 --> 00:14:28,550
+دالة ثابتة، اللي هي مين؟ A تربيع زائد B تربيع
+
+133
+00:14:28,550 --> 00:14:33,770
+موجودة وين؟ موجودة في إيه؟ طيب مقلوبة موجودة في
+
+134
+00:14:33,770 --> 00:14:40,970
+إيه ولا لا؟ دالة مقلوبة، R of X كل ال functions
+
+135
+00:14:40,970 --> 00:14:48,200
+تبعها ترية، تمام؟ يبقى هذا يبدأ يعطينا إنه واحدعلى
+
+136
+00:14:48,200 --> 00:14:55,160
+A تربيع زائد B تربيع موجودة في A كذلك طب لو ضربهم
+
+137
+00:14:55,160 --> 00:15:01,960
+في بعض لو أخدت ال A تربيع زائد B تربيع ضرب واحد
+
+138
+00:15:01,960 --> 00:15:10,620
+على A تربيع زائد B تربيع فهو موجود في A يبقى هدف
+
+139
+00:15:10,620 --> 00:15:16,920
+يعطينا أن الواحد موجود في Aيبقى بناء عليه الـ A كم
+
+140
+00:15:16,920 --> 00:15:23,680
+بده يساوي R. It says يبقى هذا معناته الـ A بده
+
+141
+00:15:23,680 --> 00:15:31,800
+يساوي الـ R وهذا previous example مثال سابق من
+
+142
+00:15:31,800 --> 00:15:36,960
+المحاضرة الماضية. مدام طلع الـ A بده يساوي الـ R
+
+143
+00:15:36,960 --> 00:15:46,890
+يبقى الـ A is maximal وندهينا من هذا المثال.تمام؟
+
+144
+00:15:46,890 --> 00:15:53,750
+كذا نبلغ من الآن فصاعدا كل كثير .. كل الدول
+
+145
+00:15:53,750 --> 00:15:59,070
+المعرفة للمعاملات تبعتها أعداد حقيقية وهي
+
+146
+00:15:59,070 --> 00:16:04,210
+polynomial ال X تربيع زائد واحد ل principle ideal
+
+147
+00:16:04,210 --> 00:16:08,750
+generated by X تربيع زائد واحد يمثل maximum ideal
+
+148
+00:16:08,750 --> 00:16:15,400
+في من؟ في ال R of Xطيب نعطي كمان مثال صغير مش زي
+
+149
+00:16:15,400 --> 00:16:27,080
+هذا طويل يبقى مثال ستة اجزام كذا ستة .. مين اللي
+
+150
+00:16:27,080 --> 00:16:32,720
+بيحكي؟ كيف؟
+
+151
+00:16:32,720 --> 00:16:36,520
+انت
+
+152
+00:16:36,520 --> 00:16:42,330
+كتب so is maximumهذا اخر اخر صور اللي هي ال X
+
+153
+00:16:42,330 --> 00:16:49,310
+ترابيع plus one بالشكل هذا هي ال maximum صحيح لان
+
+154
+00:16:49,310 --> 00:16:55,890
+هذا اللي احنا بنسبته بنجيب ID التاني تبعك كده مانع
+
+155
+00:16:55,890 --> 00:17:01,610
+واحد تبتمل ال A من ال A is maximum فاضح فاضح فاضح
+
+156
+00:17:01,610 --> 00:17:11,100
+فاضح فاضح فاضح فاضح فاضح فاضحهنا؟ أول
+
+157
+00:17:11,100 --> 00:17:16,740
+السؤال؟ تالت وربع سطر تالت وربع سطر تالت وربع سطر
+
+158
+00:17:16,740 --> 00:17:18,900
+تالت وربع سطر تالت وربع سطر تالت وربع سطر تالت
+
+159
+00:17:18,900 --> 00:17:19,060
+وربع سطر تالت وربع سطر تالت وربع سطر تالت وربع سطر
+
+160
+00:17:19,060 --> 00:17:19,640
+تالت وربع سطر تالت وربع سطر تالت وربع سطر تالت
+
+161
+00:17:19,640 --> 00:17:19,640
+وربع سطر تالت وربع سطر تالت وربع سطر تالت وربع سطر
+
+162
+00:17:19,640 --> 00:17:23,320
+تالت وربع سطر تالت وربع سطر تالت وربع سطر تالت
+
+163
+00:17:23,320 --> 00:17:32,640
+وربع سطر تالت وربع سطر تالت وربع سطر تالت وربع سط
+
+164
+00:17:39,930 --> 00:17:45,070
+إذا أثبتنا أن الـ A يساوي الـ R يساوي الـ A يصبح
+
+165
+00:17:45,070 --> 00:17:50,030
+الـ A ماكسيمال حسب التعريف اللي عنه الماكسيمالية،
+
+166
+00:17:50,030 --> 00:17:57,060
+مظبوط؟ طيب أنا عشان أثبت هذا الـ A يساوي Rبقول لو
+
+167
+00:17:57,060 --> 00:18:02,080
+قدرت أثبت أن الواحد موجود في مصير الـA يساوي
+
+168
+00:18:02,080 --> 00:18:05,420
+الأربع بالثالث كيف؟ الـA و لا ال principle ideal
+
+169
+00:18:05,420 --> 00:18:06,640
+الـA و لا ال principle ideal الـA و لا ال
+
+170
+00:18:06,640 --> 00:18:07,960
+principle ideal الـA و لا ال principle ideal الـA
+
+171
+00:18:07,960 --> 00:18:08,480
+و لا ال principle ideal الـA و لا ال principle
+
+172
+00:18:08,480 --> 00:18:09,040
+ideal الـA و لا ال principle ideal الـA و لا ال
+
+173
+00:18:09,040 --> 00:18:09,900
+principle ideal الـA و لا ال principle ideal الـA
+
+174
+00:18:09,900 --> 00:18:10,540
+و لا ال principle ideal الـA و لا ال principle
+
+175
+00:18:10,540 --> 00:18:11,160
+ideal الـA و لا ال principle ideal الـA و لا ال
+
+176
+00:18:11,160 --> 00:18:12,780
+principle ideal الـA و لا ال principle ideal الـA
+
+177
+00:18:12,780 --> 00:18:13,120
+و لا ال principle ideal الـA و لا ال principle
+
+178
+00:18:13,120 --> 00:18:15,940
+ideal الـA و لا ال principle ideal الـA و لا ال
+
+179
+00:18:15,940 --> 00:18:15,940
+principle ideal الـA و لا ال principle ideal الـA
+
+180
+00:18:15,940 --> 00:18:16,480
+و لا ال principle ideal الـA و لا ال principle
+
+181
+00:18:16,480 --> 00:18:19,520
+ideal الـA و لا ال principle ideal الـA و لا ال
+
+182
+00:18:19,520 --> 00:18:25,530
+principle ideal الـالـ X تربيه زائد واحد ثالث is
+
+183
+00:18:25,530 --> 00:18:29,610
+maximal ideal، هذا اللي احنا بنفتحه صحيح معاكم كل
+
+184
+00:18:29,610 --> 00:18:37,050
+الحاجة طيب المثال الأخير قبل أن نبدأ النظريات
+
+185
+00:18:37,050 --> 00:18:44,990
+بيقول لي ال ideal ال principle ideal generated by
+
+186
+00:18:44,990 --> 00:18:48,030
+X تربيه زائد واحد is
+
+187
+00:18:50,870 --> 00:19:08,770
+A' is not a prime in Z2 of X نحن
+
+188
+00:19:08,770 --> 00:19:13,870
+ندّعي أن الـ I دي هذا ما هو ماشي prime in Z2 من
+
+189
+00:19:13,870 --> 00:19:21,640
+عناصر Z2 ياباناأنا صفر و واحد صفر و واحد ممتاز جدا
+
+190
+00:19:21,640 --> 00:19:27,860
+طب لو قلت اتنين تعني صفر لو قلت تلاتة تعني واحد و
+
+191
+00:19:27,860 --> 00:19:33,860
+هكذا طيب انا بقول ان ال ideal هذا ما هو شفراي في
+
+192
+00:19:33,860 --> 00:19:37,840
+ال ring اللي عنده هذا مش في ال R of X الأولانية
+
+193
+00:19:37,840 --> 00:19:42,020
+يعني كأنه أخدنا حالة خاصة اللي هو ال ring اللي
+
+194
+00:19:42,020 --> 00:19:46,170
+عندنا و أخدنا نفس ال ideal في هذه ال ringطيب لو
+
+195
+00:19:46,170 --> 00:19:52,210
+جيت قولتلك ال X زائد واحد هل موجود في ال Z two of
+
+196
+00:19:52,210 --> 00:20:02,390
+X؟ موجود هنا ولا هنا؟ ممتاز طيب خط ده أخدت ال X
+
+197
+00:20:02,390 --> 00:20:09,710
+زائد واحد في ال X زائد واحد العنصر ضربته في نفسه،
+
+198
+00:20:09,710 --> 00:20:16,420
+شو بدي أقينها؟x تربيع زائد نية x زائد واحد جداش
+
+199
+00:20:16,420 --> 00:20:26,540
+هذه تساوي في z2 of x؟ Zero يبدأ هذه Zero in z2 of
+
+200
+00:20:26,540 --> 00:20:33,300
+x جداش الناتج بدي يكون؟ x تربيع زائد واحد اللي هو
+
+201
+00:20:33,300 --> 00:20:38,960
+موجود وين؟ موجود في ال x تربيع زائد واحد ال
+
+202
+00:20:38,960 --> 00:20:43,900
+principal idealgenerated by X تربية زايدة طب
+
+203
+00:20:43,900 --> 00:20:52,040
+يطلعون هنا الآن حاصل ضربة عنصرين موجود في ال ID
+
+204
+00:20:52,040 --> 00:20:58,380
+اللي عندنا هنا لشان يكون إقرأي يبقى واحد منهم بدي
+
+205
+00:20:58,380 --> 00:21:03,260
+يكون هنا موجود واحد من قصين هدول بدي يكون موجود
+
+206
+00:21:03,260 --> 00:21:08,740
+هناك صح ولا لا؟ لأنه إما قصي الأولموجود في هذا ال
+
+207
+00:21:08,740 --> 00:21:13,840
+ideal أو القوس التاني موجود في هذا ال ideal لكن هل
+
+208
+00:21:13,840 --> 00:21:19,840
+اي من القوسين الموجود هنا لأ يبقى حافظا ضارب ما
+
+209
+00:21:19,840 --> 00:21:27,240
+موجود but ولكن ال X زائد واحد does not belong لل
+
+210
+00:21:27,240 --> 00:21:31,120
+principle ideal generated by X تلوية زائد واحد
+
+211
+00:21:31,120 --> 00:21:36,120
+يبقى بناء عليه هذا ما هو shape prime لأن تعريف ال
+
+212
+00:21:36,120 --> 00:21:43,520
+primeلما تلاقي عنصرين موجودات في مين لل ID بدي
+
+213
+00:21:43,520 --> 00:21:49,440
+يكون على الأقل أحدهم أو واحد منهم موجود، أي حاصل
+
+214
+00:21:49,440 --> 00:21:55,380
+ضربهم موجود، لكن ولا واحد من اتنين موجود وين في ال
+
+215
+00:21:55,380 --> 00:22:02,740
+X تربية، يبقى هذا ما هو ايش ال prime ID،
+
+216
+00:22:02,740 --> 00:22:08,710
+ليش ايش؟ ال X زائد واحد كدههاتيلي element تاني
+
+217
+00:22:08,710 --> 00:22:19,250
+غيرها و اريني اشوف اقترفيها اقترفيها بطلت
+
+218
+00:22:19,250 --> 00:22:28,780
+احنا مقيادين مقيادين بال X تربية و زائد واحدنزلنا
+
+219
+00:22:28,780 --> 00:22:33,520
+بطل يصير موجود في ال X تربية زي دوها طالعنا بقدر
+
+220
+00:22:33,520 --> 00:22:37,480
+أكتبه زي ما كتبت واسعى Q of X في ال X تربية زي
+
+221
+00:22:37,480 --> 00:22:42,140
+دوها ازاى وزاى اقرأة of X مظبوط يبقى نشتغل على هذا
+
+222
+00:22:42,140 --> 00:22:53,040
+الأساس طيب نيجي لأول نضاهية في الموضوع KOM let
+
+223
+00:22:53,040 --> 00:23:06,510
+ال A بيa commutative ..
+
+224
+00:23:06,510 --> 00:23:17,810
+commutative ring with unity little
+
+225
+00:23:17,810 --> 00:23:24,690
+a be an ideal
+
+226
+00:23:26,600 --> 00:23:39,120
+أو R ، أفضل من R ثم الـ R موديولو A هو مجموعة
+
+227
+00:23:39,120 --> 00:23:45,100
+انتقالية
+
+228
+00:23:45,100 --> 00:23:53,880
+F اندولي F F اندولي F الـ A صحيح
+
+229
+00:23:55,030 --> 00:24:03,930
+لو كان الـA الـPrime
+
+230
+00:24:03,930 --> 00:24:10,870
+فا
+
+231
+00:24:10,870 --> 00:24:14,330
+نعرف بقى الكمية احنا عالنا R كمية ت bring with
+
+232
+00:24:14,330 --> 00:24:19,810
+unity والـA ايديل في R يبقى بيقول الـR modulo A
+
+233
+00:24:19,810 --> 00:24:23,990
+بتبقى integral domain إذا كان الـA prime ايديل
+
+234
+00:24:24,550 --> 00:24:29,710
+وكلمة F انتقل يفتعني ان البرمانس سيصير في
+
+235
+00:24:29,710 --> 00:24:36,690
+الاتجاهين لذلك الاتجاه الأول بدي افترض ان ال R
+
+236
+00:24:36,690 --> 00:24:47,790
+module A is an integral domain تمام؟
+
+237
+00:24:47,790 --> 00:24:53,920
+مشان أثبت ان ال A is a primeبدي أخد عنصرين من ال
+
+238
+00:24:53,920 --> 00:24:59,560
+ring A و أفترض أن حاصل ضربه ما موجود وين في ال
+
+239
+00:24:59,560 --> 00:25:04,600
+ideal A إذا قدرت أثبت أن واحد منهم موجود في ال A
+
+240
+00:25:04,600 --> 00:25:10,580
+يكون ال A is a prime ideal مقتقل لل definition
+
+241
+00:25:10,580 --> 00:25:18,760
+يبقى بدي أقوله افترض ان ال A و ال B موجودات في A
+
+242
+00:25:18,760 --> 00:25:29,450
+such thatبحيث ان ال A في ال B موجود في ال A طبعا؟
+
+243
+00:25:29,450 --> 00:25:34,750
+مدام ال A بي موجود في ال A يبقى ال A بي زائد ال A
+
+244
+00:25:34,750 --> 00:25:43,450
+جداش مدى سوابه انها ال A itself طبعا؟ طيب مدام هذا
+
+245
+00:25:43,450 --> 00:25:51,470
+هيك يبقى معناته مات مرة تانيةأخدت عمصري الموجودات
+
+246
+00:25:51,470 --> 00:26:00,770
+في R بحيث ان حاصل ضربهما موجود في A بدي احاول اوصل
+
+247
+00:26:00,770 --> 00:26:06,530
+لشغله انه يا اما ال A موجود في ال A يا اما ال B
+
+248
+00:26:06,530 --> 00:26:14,650
+موجود في ال A هذا معناه انه ان
+
+249
+00:26:14,650 --> 00:26:24,470
+ال A زائد ال Aمضروب في الـ B زائد الـ A بدي ساوي
+
+250
+00:26:24,470 --> 00:26:32,670
+الـ A السؤال هو الـ A في حد ذاته إيش تمثل بالنسبة
+
+251
+00:26:32,670 --> 00:26:40,230
+لل factor group R modulo A؟ شو اسم العمصر هذا؟ A
+
+252
+00:26:40,230 --> 00:26:47,650
+في factor group R modulo A؟ Zero element ممتازيبقى
+
+253
+00:26:47,650 --> 00:26:50,950
+الـ zero element في الـ R مُد يقوله إيه اللي بده
+
+254
+00:26:50,950 --> 00:26:56,490
+يسوي إيش الأفاريه؟ ان الـ R إيه؟ Integral Domain
+
+255
+00:26:56,490 --> 00:27:03,350
+مدام Integral Domain اصطلع عندي حاصل ضرب عنصرين من
+
+256
+00:27:03,350 --> 00:27:08,090
+ال ring اللي عندنا هذا أعطاني ال zero يبقى واحد
+
+257
+00:27:08,090 --> 00:27:13,270
+فيهم بده يكون ب zero صح ولا لا؟ يبقى هذا بده
+
+258
+00:27:13,270 --> 00:27:19,750
+يعطينايا إما ال A زائد ال A بده يساوي ال A يا إما
+
+259
+00:27:19,750 --> 00:27:26,430
+ال B زائد ال A بده يساوي ال A itself يفجأ هذا إيش
+
+260
+00:27:26,430 --> 00:27:31,250
+معناه؟ لما أقول A زايد ال A يساوي ال A معناته ال A
+
+261
+00:27:31,250 --> 00:27:37,830
+وين موجود؟ في ال A هذا معناه إن ال A موجود في ال A
+
+262
+00:27:37,830 --> 00:27:46,970
+or ال B موجود في ال Aيبقى هذا معناه مين؟ حاصل ضرب
+
+263
+00:27:46,970 --> 00:27:52,250
+عنصرين موجود في A أثبت له أن الأول في A أو الـ B
+
+264
+00:27:52,250 --> 00:27:58,810
+في A يبقى هذا معناه أن الـ A is A' ID يبقى هذا
+
+265
+00:27:58,810 --> 00:28:07,410
+معناه أن الـ A is A' ID يبقى
+
+266
+00:28:07,410 --> 00:28:10,410
+أثبتنا الاتجاه الأول، بنجي الاتجاه الثاني
+
+267
+00:28:10,410 --> 00:28:11,850
+Conversely
+
+268
+00:28:15,260 --> 00:28:23,600
+Assume that ان الـ A is A' ID.
+
+269
+00:28:25,900 --> 00:28:35,840
+One to show one to show that
+
+270
+00:28:35,840 --> 00:28:44,240
+بدنا نحاول ندبد ان الـ R modulo Ais an integral
+
+271
+00:28:44,240 --> 00:28:50,040
+domain طيب
+
+272
+00:28:50,040 --> 00:28:54,760
+و اكتشف اقدر احكم على الست انها integral domain
+
+273
+00:28:54,760 --> 00:29:02,760
+اذا تحقق شرطان شرط الاول اذا تبقى الست هذي
+
+274
+00:29:02,760 --> 00:29:07,800
+commutative ring with unity اثنان مش فيها zero
+
+275
+00:29:07,800 --> 00:29:13,160
+divisorsأو لو وجدت حاصل ضرب عنصرين منها بدي يساوي
+
+276
+00:29:13,160 --> 00:29:18,420
+ال zero بدي أثبتهم ان على الأقل واحد فيهم بدي
+
+277
+00:29:18,420 --> 00:29:24,520
+يساوي ال zero ممتاز جدا يبقى انا ازعم ان ال R
+
+278
+00:29:24,520 --> 00:29:36,200
+modulo A is a commutative ring with unity
+
+279
+00:29:38,710 --> 00:29:47,650
+قدش ال unity؟ ال a قولنا zero element يبقى واحد
+
+280
+00:29:47,650 --> 00:29:57,610
+زائد a طب ليش هذا الكلام؟ because من
+
+281
+00:29:57,610 --> 00:30:02,330
+نص النظرية قال ال R commutative ring with unity
+
+282
+00:30:02,330 --> 00:30:06,370
+يبقى ال R مديونية commutative ring with unity
+
+283
+00:30:06,890 --> 00:30:23,650
+because الـR is commutative ring with unity تمام؟
+
+284
+00:30:23,650 --> 00:30:30,010
+طيب الآن أنا بدي أثبت إن الـR عبارة عن integral
+
+285
+00:30:30,010 --> 00:30:36,190
+domain integral domain يعني لو أخدت عمصرينوضربتهم
+
+286
+00:30:36,190 --> 00:30:42,730
+في بعض بدي أثبت انه على الأقل واحد فيهم مانع بده
+
+287
+00:30:42,730 --> 00:30:48,510
+ساوي زيرو يبقى أخدنا a prime id بدنا نثبت هذا
+
+288
+00:30:48,510 --> 00:30:53,950
+integral domain أثبتنا الشرط الأول وهو ان ال R
+
+289
+00:30:53,950 --> 00:31:00,370
+modulo a is a commutative ring with unit تمام؟
+
+290
+00:31:00,370 --> 00:31:08,880
+الان بدي أجي أخدحاصل ضرب عنصرين فيهم وافترض ان هذا
+
+291
+00:31:08,880 --> 00:31:14,140
+الكلام بده يساوي مين؟ بده يساوي Zero بالضبط تماما
+
+292
+00:31:14,140 --> 00:31:25,380
+يبقى بده افترض ان عندي عنصرين ل ال A زائد ال A و
+
+293
+00:31:25,380 --> 00:31:35,870
+ال B زائد و ال B زائد ال Aموجودة في الـ R مديون A
+
+294
+00:31:35,870 --> 00:31:45,910
+such that بحيث أن الـ A زائد الـ A مضروب في الـ B
+
+295
+00:31:45,910 --> 00:31:55,310
+زائد الـ A بدي يسوى الـ Zero Element تمام؟
+
+296
+00:31:55,310 --> 00:31:59,670
+يبقى then اللي
+
+297
+00:31:59,670 --> 00:32:07,460
+هو من الـ AB زائد ال A بده سوى مين؟ ال A itself
+
+298
+00:32:07,460 --> 00:32:10,840
+مظبوط؟
+
+299
+00:32:10,840 --> 00:32:20,020
+طيب، هذا إيش معناه؟ هذا معناه إن ال A بي موجودة في
+
+300
+00:32:20,020 --> 00:32:24,700
+ال A كويس؟
+
+301
+00:32:24,700 --> 00:32:31,620
+يبقى ال A بي موجودة في ال Aمدام ال A بي موجودة في
+
+302
+00:32:31,620 --> 00:32:36,880
+ال A تعالى نشوف في شغل احنا مااستفدناش منها وهي ان
+
+303
+00:32:36,880 --> 00:32:41,900
+هذا prime ideal مدام ال prime ideal يبقى هذا
+
+304
+00:32:41,900 --> 00:32:48,360
+معناته ان ال A موجودة في ال A or ال B موجودة في ال
+
+305
+00:32:48,360 --> 00:32:59,940
+A السبب because ان ال A is a prime idealيبقى نظرة
+
+306
+00:32:59,940 --> 00:33:04,880
+لإن ال crime قاعدين هذا الكلام صحيح طيب مدام ال A
+
+307
+00:33:04,880 --> 00:33:10,040
+موجودة في A يبقى ال A زائد ال A قداش بده يساوي يا
+
+308
+00:33:10,040 --> 00:33:20,860
+بنات ال A or ال B زائد ال A بده يساوي ال A يبقى
+
+309
+00:33:20,860 --> 00:33:26,780
+أثبت إنه هذا بده يساوي ال zero element أو هذا بده
+
+310
+00:33:26,780 --> 00:33:31,920
+يساوي ال zero elementيبقى هذا إيش معناه؟ إن الـR
+
+311
+00:33:31,920 --> 00:33:37,640
+modulo A is an integral domain لإن أخدت حاصل ضرب
+
+312
+00:33:37,640 --> 00:33:43,640
+عنصرين يساوي الصفر، لجيت واحد فيهم بساوي الصفر،
+
+313
+00:33:43,640 --> 00:33:50,660
+يبقى هذا بده يعطينا إن الـR modulo A is an
+
+314
+00:33:50,660 --> 00:33:53,700
+integral domain.
+
+315
+00:33:59,660 --> 00:34:06,520
+طيب، فيش حد أحسن من حد؟ الناس كلهم سواسي، عشان
+
+316
+00:34:06,520 --> 00:34:12,340
+ماحدش يزعل من التاني. النظرية اتكلمت عن الـ Prime
+
+317
+00:34:12,340 --> 00:34:17,840
+Ideas، ولم تتكلم عنين؟ عن الـ Maximal Ideas،
+
+318
+00:34:17,840 --> 00:34:21,980
+وموضوعنا موضوع الـ Prime والـ Maximal. إذن هناك
+
+319
+00:34:21,980 --> 00:34:29,200
+نظرية مناضرة لها تتحدث عن مين؟ عن مين؟الـ maximal
+
+320
+00:34:29,200 --> 00:34:34,980
+معلاقته مع ال factor ring إذا بروح للنظرية الثانية
+
+321
+00:34:34,980 --> 00:34:43,780
+يبقى ال theorem النظرية التانية بتقول ما يطيب let
+
+322
+00:34:43,780 --> 00:34:56,020
+ال R be a commutative ring with unity
+
+323
+00:34:58,240 --> 00:35:07,140
+community bring with unity and
+
+324
+00:35:07,140 --> 00:35:16,660
+ال A an ideal of
+
+325
+00:35:16,660 --> 00:35:28,980
+R then ال R modulo A is a field if and only iff
+
+326
+00:35:28,980 --> 00:35:38,060
+and only f ال a is maximum لغاية ال a is maximum
+
+327
+00:35:38,060 --> 00:35:42,720
+لغاية
+
+328
+00:35:42,720 --> 00:35:51,880
+ال pro بدي
+
+329
+00:35:51,880 --> 00:35:58,420
+أصير برضه في اتجاهين بسبب ال f and only fيبقى
+
+330
+00:35:58,420 --> 00:36:08,680
+بدرجة اقوله left ال a موضوعه a a b a field يبقى b
+
+331
+00:36:08,680 --> 00:36:17,560
+a field طبعا بدي اثبت ان ال a باله is maximum يبقى
+
+332
+00:36:17,560 --> 00:36:37,110
+one two one two show thatإن ال A is maximum يبدأ
+
+333
+00:36:37,110 --> 00:36:44,050
+يقول افترض ان ال B بيكون
+
+334
+00:36:44,050 --> 00:36:52,050
+ايديل او R بحيث
+
+335
+00:36:52,050 --> 00:37:02,010
+ان ال A اللي عندناsubset من الـ B و لا يساوي و الـ
+
+336
+00:37:02,010 --> 00:37:08,070
+B subset من R و
+
+337
+00:37:08,070 --> 00:37:13,730
+الـ B subset من R طيب
+
+338
+00:37:13,730 --> 00:37:20,570
+مرة تانية قربنا R modulo A عبارة عن فيه بتبين ان
+
+339
+00:37:20,570 --> 00:37:25,030
+الـ A maximum لو روحت لتعريف ال maximumفرأت أنه
+
+340
+00:37:25,030 --> 00:37:31,110
+عندي ideal تاني B بحيث الـA subset من B ولا يساوي
+
+341
+00:37:31,110 --> 00:37:36,850
+و الـB subset من R. إذا أثبتوا إنه B يساوي الـR،
+
+342
+00:37:36,850 --> 00:37:42,310
+بصير هذا الـMaximal أو إذا أثبتوا إن الـUnity هو
+
+343
+00:37:42,310 --> 00:37:47,690
+الموجود في B، يبقى بصير الـA عبارة عن Maximal
+
+344
+00:37:47,690 --> 00:37:51,430
+Ideal. بصير الـB يساوي الـR، وبالتالي الـA is
+
+345
+00:37:51,430 --> 00:38:00,330
+Maximal.بقولوا خيص قولولي ال B موجودة في B بقى
+
+346
+00:38:00,330 --> 00:38:09,370
+ولكن ال B مش موجودة في A ايه صفصت من B ولا يساوي
+
+347
+00:38:09,370 --> 00:38:15,410
+في عناصر موجودة في B ومش موجودة وين في A أخدت عنصر
+
+348
+00:38:15,410 --> 00:38:25,040
+موجود في B وعنصر هذا مش موجود في Aالـ B زائد الـ A
+
+349
+00:38:25,040 --> 00:38:32,280
+بينفع أقول يساوي الـ A هنا؟ لأ يفجأة لا يساوي الـ
+
+350
+00:38:32,280 --> 00:38:37,340
+A يعني بيسويش الـ zero element يفجأة الـ B زائد
+
+351
+00:38:37,340 --> 00:38:43,380
+الـ A is a non zero element يفجأة هذا بده يعطينا
+
+352
+00:38:43,380 --> 00:38:51,320
+أن الـ B زائد الـ A is a non zero element
+
+353
+00:38:53,810 --> 00:39:00,090
+إن ال R مدلويز A يبقى
+
+354
+00:39:00,090 --> 00:39:08,130
+هذا عنصر غير صفري و أنا فارق R
+
+355
+00:39:08,130 --> 00:39:12,290
+مدلويز A field يبقى هذا عنصر إذا كان غير صفري إيش
+
+356
+00:39:12,290 --> 00:39:18,190
+بدي يكون؟ unit لإن في ال field أي عنصر غير الصفر
+
+357
+00:39:18,190 --> 00:39:25,870
+يكون unitهذا بده يعطينا ان الـB زائد الـA is a
+
+358
+00:39:25,870 --> 00:39:33,550
+unit تمام؟ يعني معنى هذا الكلام ان there exist
+
+359
+00:39:33,550 --> 00:39:43,430
+عنصر C زائد الـA موجود في الـR modulo A such that
+
+360
+00:39:43,430 --> 00:39:51,630
+بحيث ان حاصل ضربهما بده يساوي ال unityمظبوط يعني
+
+361
+00:39:51,630 --> 00:39:57,790
+بدي يكون ال B زائد ال A في هذا ال element اللي هو
+
+362
+00:39:57,790 --> 00:40:03,790
+C زائد ال A بدي يسوى ال unity اللي هو واحد زائد ال
+
+363
+00:40:03,790 --> 00:40:13,710
+A يعني إيش معنى هذا الكلام معناه إن ال B C زائد ال
+
+364
+00:40:13,710 --> 00:40:23,570
+A يسوى واحد زائد ال Aأو لو جينا أضفنا للطرفين سالف
+
+365
+00:40:23,570 --> 00:40:33,430
+بي سي بظل ال a بدر ساوي واحد ناقص بي سي زائد ال a
+
+366
+00:40:33,430 --> 00:40:40,190
+هذا ايش معناه ان ال element هذا وين موجود؟ موجود
+
+367
+00:40:40,190 --> 00:40:46,650
+في ال a يبقى هذا معناه ان الواحد ناقص ال بي سي
+
+368
+00:40:46,650 --> 00:40:52,980
+موجود في ال aطب ال A subset من B ولا لأ؟ يبقى ال
+
+369
+00:40:52,980 --> 00:40:57,300
+element هذا موجود في B ولا لأ؟ يبقى هذا اللي
+
+370
+00:40:57,300 --> 00:41:06,420
+بيعطيكي علاقة للخاطر ان واحد ناقص بي سي موجود في B
+
+371
+00:41:06,420 --> 00:41:17,310
+because ان ال A subset من B ولا يسوىالقصار ال
+
+372
+00:41:17,310 --> 00:41:22,870
+element هذا موجود وين يا بنات في B السؤال الكم؟
+
+373
+00:41:22,870 --> 00:41:33,770
+Pause ال B ال B ال C موجود في B و لا لأ؟ لأن ال B
+
+374
+00:41:33,770 --> 00:41:39,280
+موجود في B و ال C أي element موجود في Aيبقى ال B
+
+375
+00:41:39,280 --> 00:41:44,920
+موجود في B و ال B is an ideal أوضر بال B في أي
+
+376
+00:41:44,920 --> 00:41:49,480
+عنصر من عناصر ال ring بدي يكون موجود في هذا ال
+
+377
+00:41:49,480 --> 00:42:01,500
+ideal also هنا because ال B موجود في ال B and ال B
+
+378
+00:42:01,500 --> 00:42:06,880
+موجود في ال B and ال B ID
+
+379
+00:42:10,590 --> 00:42:18,530
+طيب الآن لو جيت جمعت اتنين مع بعض وين بده يكون؟ في
+
+380
+00:42:18,530 --> 00:42:28,590
+نفسه يبقى هنا ساعة واحد نقص ال Vc زائد ال Vc موجود
+
+381
+00:42:28,590 --> 00:42:35,510
+في B يعني معنى هذا الكلام ان الواحد
+
+382
+00:42:37,740 --> 00:42:44,480
+موجود في B يبقى ال unity تبع ال ring الأصلية طلع
+
+383
+00:42:44,480 --> 00:42:51,620
+موجود في B هذا معناته ان بي تسوى جدير تسوى R
+
+384
+00:42:51,620 --> 00:42:58,280
+itself يبقى ال ideal A عبارة عن من؟ عن مكسيم، عن
+
+385
+00:42:58,280 --> 00:43:04,240
+اللغين، هذه طلع المساوية هنا يبقى هذا يعطيني ان ال
+
+386
+00:43:04,240 --> 00:43:13,150
+Ais maximum in الأرض
+
+387
+00:43:13,150 --> 00:43:19,690
+يبقى هذا لإتجاه الأول الأهم يجي لإتجاه الثاني
+
+388
+00:43:38,170 --> 00:43:47,290
+يبقى باجي بقوله conversion افترضنا
+
+389
+00:43:47,290 --> 00:43:52,370
+فيه و اثبتنا انه ايه maximum يبقى بدأ افترض انه
+
+390
+00:43:52,370 --> 00:43:57,650
+ايه maximum و نثبت ان ال R modulo A is ايه فيه
+
+391
+00:43:57,650 --> 00:44:01,470
+يبقى هنا باجي بقوله assume
+
+392
+00:44:05,020 --> 00:44:15,600
+that إن الـA الـA maximum ideal
+
+393
+00:44:15,600 --> 00:44:19,960
+الـR،
+
+394
+00:44:19,960 --> 00:44:32,140
+إيش اللي بننطبته؟ one one to show that الـR
+
+395
+00:44:34,040 --> 00:44:43,500
+Modulo A is A field نحاول
+
+396
+00:44:43,500 --> 00:44:50,860
+نثبت ان ال R Modulo A is A field بقوله كويس مشان
+
+397
+00:44:50,860 --> 00:44:58,280
+ايه؟ بدي قاعد ياخد عنصر غير صفري هنا العنصر غير
+
+398
+00:44:58,280 --> 00:45:04,140
+الصفري لو جدرت اثبت انه معكوس بتم المطلوب ليش؟إن
+
+399
+00:45:04,140 --> 00:45:10,140
+كل أنصار في ال field is a unit يعني بقدر أجد أنصار
+
+400
+00:45:10,140 --> 00:45:14,640
+أضغط فيها يعطيني main أنصار الواحدة يبقى افترض a
+
+401
+00:45:14,640 --> 00:45:20,420
+maximum وين ما يلزم بدي إياها و بدي أحاول أثبت أن
+
+402
+00:45:20,420 --> 00:45:29,340
+ال R مضي له a is a field طيب لو جيت قلت هنا net ال
+
+403
+00:45:29,340 --> 00:45:36,370
+b موجودة أخدنا بيه من قلة ال bموجودة في ال ring A
+
+404
+00:45:36,370 --> 00:45:47,410
+such that بحيث ال B مش موجود في ال A يبقى
+
+405
+00:45:47,410 --> 00:45:53,650
+ال B مش موجود في ال A then ال
+
+406
+00:45:53,650 --> 00:46:01,680
+B زائد ال A بده يساوي ايه يا بنات؟ مش ممكنيبقى لا
+
+407
+00:46:01,680 --> 00:46:07,240
+يمكن أن يساوي 0 يبقى ال B زائد ال A is a non-zero
+
+408
+00:46:07,240 --> 00:46:17,260
+element يبقى هذا ال B زائد ال A is a non-zero
+
+409
+00:46:17,260 --> 00:46:29,560
+element non-zero element in R modulo A مدام أنصر
+
+410
+00:46:29,560 --> 00:46:37,810
+غير صفريبنحاول نثبت ان هذا unit يبقى one to sure
+
+411
+00:46:37,810 --> 00:46:42,770
+that
+
+412
+00:46:42,770 --> 00:46:53,730
+نحاول نثبت ان ال B بصر ال A is a unit ان تم لنا
+
+413
+00:46:53,730 --> 00:47:03,830
+ذلك بصير ال R موديل A is A فيهبنحاول نستفيد من هذا
+
+414
+00:47:03,830 --> 00:47:09,170
+هو عبارة عن maximal ideal حتى الآن لم نستفيد شيئا
+
+415
+00:47:09,170 --> 00:47:15,330
+كلمة maximal بالزمن مين؟ ideal تاني و اللي عندى
+
+416
+00:47:15,330 --> 00:47:19,450
+بده يكون subset منه و هذا ال ideal اللى جاءه بده
+
+417
+00:47:19,450 --> 00:47:25,030
+يكون subset من مين؟ من R تبقى لو جيتكم ت consider
+
+418
+00:47:25,030 --> 00:47:38,680
+the set Dمين هي V؟ هي كل الـP R كل الـP R زائد
+
+419
+00:47:38,680 --> 00:47:50,060
+الـA بحيث الـR موجودة في R والـA موجودة في A ان
+
+420
+00:47:50,060 --> 00:47:59,270
+يزعم ان الـP هي عبارة عن ID ونريد نشوف ليه لأنالـB
+
+421
+00:47:59,270 --> 00:48:08,970
+is an id ليش؟ because تلت
+
+422
+00:48:08,970 --> 00:48:15,630
+نقاط لازم نثبتهم النقطة الأولى ان الـB is non
+
+423
+00:48:15,630 --> 00:48:22,670
+-empty ليش؟ since؟
+
+424
+00:48:22,670 --> 00:48:31,180
+بتجيبها لو عنصر واحد موجود في الـBzero زائد ال a
+
+425
+00:48:31,180 --> 00:48:40,880
+هو عبارة عن ال b في zero زائد ال a صح ولا لأ يبقى
+
+426
+00:48:40,880 --> 00:48:48,160
+هاي ال b عنصر من ال ring زائد عنصر a من ال a مظبوط
+
+427
+00:48:48,160 --> 00:48:55,830
+هكذا هذا موجود وين موجود يبقى هذا non emptyلأنه
+
+428
+00:48:55,830 --> 00:49:01,310
+قدرت أجيبه عنصر واحد موجود في B موجود في B خلصنا
+
+429
+00:49:01,310 --> 00:49:06,690
+النقطة الأولى النقطة الثانية افترض ان X و Y
+
+430
+00:49:06,690 --> 00:49:14,930
+موجودات في B يبقى A شكلهم على الشكل التالي then ال
+
+431
+00:49:14,930 --> 00:49:27,970
+X بقدر أقول هي B R1 زائد A1 and ال YPR2 زائد A2
+
+432
+00:49:27,970 --> 00:49:40,830
+وعندك R1 وR2 موجودة في R وA1 وA2 موجودة في X يبقى
+
+433
+00:49:40,830 --> 00:49:48,630
+R1 وR2 موجودة في R وA1 وA2 موجودة في A بدي أروح
+
+434
+00:49:48,630 --> 00:49:58,540
+أشوف هل ال X ناقص ال Yموجودة في بي ولا لا يبقى بقى
+
+435
+00:49:58,540 --> 00:50:06,860
+جيبا يقول يبقى ال بي R1 بي R1 زائد ال A1 ناقص بي
+
+436
+00:50:06,860 --> 00:50:15,580
+R2 زائد ال A2 يسوى طلعيل العنصر هذا مع العنصر هذا
+
+437
+00:50:15,580 --> 00:50:26,420
+في بي في R1 ناقص R2بظل a1 minus a2 يبقى زائد a1
+
+438
+00:50:26,420 --> 00:50:32,460
+minus a2 هذا في a و
+
+439
+00:50:32,460 --> 00:50:38,540
+هذا في a و هذا في a يبقى هذا على الصيغة اللي قدامي
+
+440
+00:50:38,540 --> 00:50:45,620
+ولا لا يبقى صار هذا ال element كله على بعض هذا a
+
+441
+00:50:45,620 --> 00:50:54,460
+موجود في ال bنجي الآن للنقطة الثالثة بدي انا اخد
+
+442
+00:50:54,460 --> 00:51:02,460
+element من ال ring R يبقى لو جيه تقول F مثلا S
+
+443
+00:51:02,460 --> 00:51:12,680
+موجود في R and ال X اللي يبدأ تساوي PR1 زائد A1
+
+444
+00:51:12,680 --> 00:51:15,780
+موجودة في من؟ في ال B
+
+445
+00:51:18,940 --> 00:51:26,340
+بدا ياخد الـ S في الـ X يبقى بده يساوي الـ S في
+
+446
+00:51:26,340 --> 00:51:37,860
+PR1 زائد الـ A1 هذا الكلام بده يساوي S في PR1 زائد
+
+447
+00:51:37,860 --> 00:51:44,520
+الـ S A1 الـ Ring الأصلي هى commutative ولا لأ إذا
+
+448
+00:51:44,520 --> 00:51:52,880
+بقدر أعمل خاصية الإبدال هنايبقى يده بده يساوي BSR1
+
+449
+00:51:52,880 --> 00:52:01,500
+زائد ال S A1 هدى وين موجودة يا بنات؟ في R هدى
+
+450
+00:52:01,500 --> 00:52:08,200
+موجودة وين؟ في A لإن ال A ايديل A1 موجودة فيه و ال
+
+451
+00:52:08,200 --> 00:52:13,780
+S موجودة في R اضرب اي عنصر من عناصر R في اي عنصر
+
+452
+00:52:13,780 --> 00:52:18,800
+من عناصر A بده يكون موجود في ال Aيبقى هذا موجود في
+
+453
+00:52:18,800 --> 00:52:25,200
+الـA، إذا كل هذا موجود وين؟ في الـB Similarly
+
+454
+00:52:25,200 --> 00:52:28,740
+Similarly
+
+455
+00:52:28,740 --> 00:52:37,940
+ان ال X في S موجودة كذلك في B يبقى Thus و هكذا ان
+
+456
+00:52:37,940 --> 00:52:50,320
+ال B is an ideal of Rكويسة. يبقى حتى الآن أثبتنا
+
+457
+00:52:50,320 --> 00:52:55,420
+ان بي عبارة عن ID الـ VR. ما استخدمناش خاصية ال
+
+458
+00:52:55,420 --> 00:52:59,920
+maximality اللي احنا فرضناها من عند ال conversion.
+
+459
+00:53:00,600 --> 00:53:03,980
+يعني حتى الآن ما استخدمناها، بس جاها دورها الحين.
+
+460
+00:53:04,540 --> 00:53:14,180
+يبقى أثبتنا ان بي is an ID، not that. السؤال هو هل
+
+461
+00:53:14,180 --> 00:53:20,400
+الـ Asubset من B هي
+
+462
+00:53:20,400 --> 00:53:28,860
+التعريف هذا ال element موجود في A و هذا element
+
+463
+00:53:28,860 --> 00:53:35,580
+زيادة عليه يبقى لها subset من B ولا لا؟ يساوي؟ لا
+
+464
+00:53:35,580 --> 00:53:46,790
+ولا يساوي و ال B في حد ذاته subset من مين؟من R طب
+
+465
+00:53:46,790 --> 00:53:52,390
+هذا لا يمكن ان يساوي هذا إذا ال B بده يساوي ال R
+
+466
+00:53:52,390 --> 00:53:57,790
+لأن ال A is maximum صح ولا لا؟ مش هيك التعريف؟ هذا
+
+467
+00:53:57,790 --> 00:54:06,130
+معناه ان ال B بده يساوي ال R because ال A is
+
+468
+00:54:06,130 --> 00:54:12,930
+maximum حسب ما احنا فرضينه هي تحتي خطمدام ال P بده
+
+469
+00:54:12,930 --> 00:54:21,010
+يساوي ال R هذا معناته ان ال واحد موجود في ال P مش
+
+470
+00:54:21,010 --> 00:54:25,750
+ال P هي بقى و ال R فيها ال unity يبقى ال واحد
+
+471
+00:54:25,750 --> 00:54:32,530
+موجود في P طب ايه شكل ال واحد بده يكون؟ ايه يبقى
+
+472
+00:54:32,530 --> 00:54:42,480
+بده يكون PA مثلا او PR1 زائد Aعلى سبيل المثال
+
+473
+00:54:42,480 --> 00:54:47,140
+والله يا شرطة بلاش تقول مين هذا ايش ما تكون ال a
+
+474
+00:54:47,140 --> 00:54:54,360
+أي عنصر من a يبقى هاي شكله طيب كويس لو جيت قلتلكوا
+
+475
+00:54:54,360 --> 00:54:59,400
+ال unity عندنا اللي يقول عليه واحد زائد a قبل شوية
+
+476
+00:54:59,400 --> 00:55:07,880
+يبقى لو جيت قلت واحد زائد a بده يساوي ب أول زائد a
+
+477
+00:55:07,880 --> 00:55:14,510
+prime زائد ال aيبقى بناءً عن ايه؟ صار الواحد زائد
+
+478
+00:55:14,510 --> 00:55:19,770
+ال A بالبشرة ال A' موجودة في اللغة ولا لا؟ يبقى
+
+479
+00:55:19,770 --> 00:55:29,210
+بضل بس بي R1 زائد ال A تمام، يبقى صار عند مين؟
+
+480
+00:55:29,210 --> 00:55:37,950
+الواحد زائد ال A يساوي بي زائد ال A مضروب في ال R1
+
+481
+00:55:37,950 --> 00:55:45,630
+زائد ال Aطب ايش تفسيركوا للعبارة هذه؟ اه حاصل ضرب
+
+482
+00:55:45,630 --> 00:55:52,850
+عنصرين يساوي اليونيتي بزايد ال a is a unit احنا
+
+483
+00:55:52,850 --> 00:55:58,370
+قلنا هنا لو قدرنا نثبت ان ال b زايد ال a is a unit
+
+484
+00:55:58,370 --> 00:56:07,620
+خلصنا يبقى هذا بيكون ال b زايد ال a is a unitيبقى
+
+485
+00:56:07,620 --> 00:56:13,140
+صار عندى any non zero element b plus a في ال R
+
+486
+00:56:13,140 --> 00:56:19,500
+modulo a is a يعني يبقى ال R modulo a is a field
+
+487
+00:56:19,500 --> 00:56:29,340
+هذا بيعطيلك ان ال R modulo a is a field تمام؟ وهو
+
+488
+00:56:29,340 --> 00:56:30,480
+المطلوب
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e15f3a75fe91f6cbc4e59b625ac1a550be30ac8d
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew_postprocess.srt
@@ -0,0 +1,1896 @@
+1
+00:00:20,700 --> 00:00:24,800
+بسم الله الرحمن الرحيم نكمل ما ابتدأناه في المرة
+
+2
+00:00:24,800 --> 00:00:30,660
+الماضية من حل المسائل على شكتر خمستاشر طبعا احنا
+
+3
+00:00:30,660 --> 00:00:36,980
+في المرة الماضية على ما قلت حلنا المسائل له تمانية
+
+4
+00:00:36,980 --> 00:00:42,520
+وعشرة واثمانة اللي انا قلنا اربعتاشر اربعتاشر
+
+5
+00:00:42,520 --> 00:00:47,580
+روتيني بدي اعطيك ال function او ال math وانت لحالك
+
+6
+00:00:47,580 --> 00:00:51,580
+تفتيهاهذه المرة هذه لأنه جاي واحدة زيها برضه
+
+7
+00:00:51,580 --> 00:00:56,980
+مصفوفة بعد قليل بنفس الطريقة ايضا السؤال الاربعتاج
+
+8
+00:00:56,980 --> 00:01:07,260
+هاكيلك كل فكرة فقط اللي في المعرفة من يهو ال z of
+
+9
+00:01:07,260 --> 00:01:13,880
+جدر اتنين من ال z of جدر اتنين هي كل العناصر على
+
+10
+00:01:13,880 --> 00:01:21,690
+صيغة a زائد b جدر اتنينبحيث ال A و ال B belong to
+
+11
+00:01:21,690 --> 00:01:31,210
+Z ماذا هذي؟ بدنا نثبت ال isomorphic لل H و ال H هي
+
+12
+00:01:31,210 --> 00:01:39,890
+كل المصففة اللي على الصيغة A2BBA بحيث ال A و ال B
+
+13
+00:01:39,890 --> 00:01:47,580
+كذلك موجودة في Z قللي شهدات فاجز isomorphismالـ
+
+14
+00:01:47,580 --> 00:01:54,120
+Phi هذه أنا بدي أعزفها على إنها Phi of A زائد B
+
+15
+00:01:54,120 --> 00:02:01,540
+جانير اتنين فالمتأثر على هذا ال element الصورة
+
+16
+00:02:01,540 --> 00:02:07,040
+تبعته بدي أخليها A2BDA
+
+17
+00:02:07,040 --> 00:02:15,760
+بتبتيلي إن Phi isomorphism شو بينيلي إن Phi
+
+18
+00:02:17,100 --> 00:02:20,200
+Isomorphism طبعا هو ماعطكيش ال function يعطاك
+
+19
+00:02:20,200 --> 00:02:24,200
+يقالك فيه homomorphism من ال ring الأولى لل ring
+
+20
+00:02:24,200 --> 00:02:27,860
+التانية تثبت علي انه isomorphism احنا عطناك ال
+
+21
+00:02:27,860 --> 00:02:31,680
+function ويقولك يالله اتفضلي زي ما سوينا كل ال
+
+22
+00:02:31,680 --> 00:02:35,960
+functions قبل ذلك تثبتلي انه homomorphism و تثبت
+
+23
+00:02:35,960 --> 00:02:40,400
+انها one to one او one to one هو كل شغل مباشر لا
+
+24
+00:02:40,400 --> 00:02:45,400
+في لف ولا في دوران مباشر دورطيب ننتقل الى السؤال
+
+25
+00:02:45,400 --> 00:02:52,080
+الذى دالى يليه وهو سؤال يتنين وعشرين تمنتاشر
+
+26
+00:02:52,080 --> 00:02:58,380
+تمنتاشر بيقول لي is the mapping من Z عشرة given by
+
+27
+00:02:58,380 --> 00:03:04,460
+is a ring homomorphism ولا لأ تمام قال لي هاي
+
+28
+00:03:04,460 --> 00:03:16,790
+تمنتاشر هل كل الفاية من Z عشرةالى z عشرة من z عشرة
+
+29
+00:03:16,790 --> 00:03:27,810
+الى z عشرة defined by defined by اللي هو five of x
+
+30
+00:03:27,810 --> 00:03:32,370
+يسوى اتنين x هل هي ring homomorphism ولا لأ
+
+31
+00:03:32,370 --> 00:03:37,630
+الاجابة لأ تبعت الجمع مظبوط مية لمية بس تبعت
+
+32
+00:03:37,630 --> 00:03:48,370
+الضاربة لأيبقى الإجابة انه because انه five of ال
+
+33
+00:03:48,370 --> 00:03:56,790
+X في Y يسوى اتنين XY ليه يسوى اتنين X في اتنين Y
+
+34
+00:03:56,790 --> 00:04:02,450
+اللي هي five of X في five of A هذا الشرط الثاني من
+
+35
+00:04:02,450 --> 00:04:07,250
+شروط ال homomorphism غير متحقق يبقى هذا very easy
+
+36
+00:04:07,250 --> 00:04:15,390
+مش محتاج شغلطيب إذا بروح لسؤال 22 سؤال 22 بيقول
+
+37
+00:04:15,390 --> 00:04:25,390
+بده كل ring isomorphism من ZN إلى ZN يبقى fine
+
+38
+00:04:25,390 --> 00:04:34,170
+بدنا نجيه five اللي من ZN إلى ZN بحيث تكون هذه
+
+39
+00:04:34,170 --> 00:04:41,890
+isomorphism such thatالـ Phi is isomorphism
+
+40
+00:04:41,890 --> 00:04:48,490
+solution لو
+
+41
+00:04:48,490 --> 00:04:54,430
+رجعتوا الى سؤال تمانية أول سؤال حلناه كان من Z in
+
+42
+00:04:54,430 --> 00:05:03,270
+إلى Z in كان Phi of X يساوي A X أثبتناه همومورفيزم
+
+43
+00:05:03,270 --> 00:05:07,820
+بظلت علينا قصة ال one to one and one to oneمظبوط
+
+44
+00:05:07,820 --> 00:05:13,960
+يبقى بقى دي بقولك from exercises
+
+45
+00:05:13,960 --> 00:05:23,420
+8 اللي حد قال مرة اللي فاتت we have ان ال 5 of x
+
+46
+00:05:23,420 --> 00:05:31,180
+بده يساوي ax is a homomorphism
+
+47
+00:05:35,730 --> 00:05:42,430
+طيب احنا فرضين هنا Phi ما له isomorphism طيب هذا
+
+48
+00:05:42,430 --> 00:05:48,510
+كان مع الشرط إذا بتلقوا ان ال A ترابيع يساوي ال A
+
+49
+00:05:48,510 --> 00:05:56,090
+يعني معناته ان ال A في ال A بده يساوي ال A صح؟
+
+50
+00:05:56,090 --> 00:06:04,630
+يعني معناته ان Phi of A في ال A بده يساوي Phi of A
+
+51
+00:06:05,140 --> 00:06:12,480
+يعني معناه ان ال five of a في ال five of a بده
+
+52
+00:06:12,480 --> 00:06:21,760
+ساوي ال five of a يعني معناه ان ال five of one في
+
+53
+00:06:21,760 --> 00:06:31,780
+ال five of one بده ساوي ال five of one أكيد؟ أكيد
+
+54
+00:06:31,780 --> 00:06:37,890
+يعنيطيب تعالى نرجع بالذاكرة قليلا هو بيقول الـ Phi
+
+55
+00:06:37,890 --> 00:06:45,490
+isomorphism صح؟ مظبوط؟ صورة ال identity element
+
+56
+00:06:45,490 --> 00:06:49,530
+بدها تروح لمين؟ لل identity element في حالة ال
+
+57
+00:06:49,530 --> 00:06:56,810
+isomorphism بقوله but ولكن اللي هو ال Phi of one
+
+58
+00:06:56,810 --> 00:07:01,870
+بده يساوي ال one لأن ال Phi عبارة عن isomorphism
+
+59
+00:07:02,350 --> 00:07:09,790
+بناء عليه هذا الكلام بده يخللي ان ال five of one
+
+60
+00:07:09,790 --> 00:07:17,810
+بده يساوي ال one طبعا طيب تعالى نشوف احنا عندنا
+
+61
+00:07:17,810 --> 00:07:24,570
+five of x بده يساوي ال ax هذا بده يخليلك ان ال
+
+62
+00:07:24,570 --> 00:07:31,970
+five of one بده يساوي ال a في ال one صحيح؟يعني هذا
+
+63
+00:07:31,970 --> 00:07:40,150
+بده يخلّيه لإنه فاي of one بده يساوي ال a مظبوط؟
+
+64
+00:07:40,150 --> 00:07:46,790
+طيب من الإتنين هدول مع بعض إيش بتستنتجي؟ ال a بده
+
+65
+00:07:46,790 --> 00:07:52,490
+يساوي واحد هذا بيساوي هذا يبقى ال a بدها تساوي
+
+66
+00:07:52,490 --> 00:08:00,380
+واحد يبقى صارت هذه ال function الآن فاي of xبدي
+
+67
+00:08:00,380 --> 00:08:07,020
+يساوي الواحد في ال X يبقى ال Phi of X يساوي مين ال
+
+68
+00:08:07,020 --> 00:08:12,480
+X؟ مين هي هذه يا بنات؟ شو اسمها في لغة الرياضيات؟
+
+69
+00:08:12,480 --> 00:08:16,780
+ال identity function، مظبوط؟ طب ال identity
+
+70
+00:08:16,780 --> 00:08:23,820
+function one to one and unto؟ اي identity function
+
+71
+00:08:23,820 --> 00:08:31,810
+is one to one and unto يبقى هذه واتشis the
+
+72
+00:08:31,810 --> 00:08:37,430
+identity function
+
+73
+00:08:37,430 --> 00:08:45,810
+هذا بده يقيل انه مدام هال identity يبقى فاي is one
+
+74
+00:08:45,810 --> 00:08:56,530
+to one and unto and unto so فاي is an isomorphism
+
+75
+00:08:58,130 --> 00:09:04,290
+يبقى يا بنات لا يوجد عندى isomorphisms من الـZ in
+
+76
+00:09:04,290 --> 00:09:10,570
+إلى الـZ in إلا ال identity functions لدلة الوحدة
+
+77
+00:09:10,570 --> 00:09:15,870
+بقيتنا نقول عليها Phi of X يسوى X Phi of M يسوى M
+
+78
+00:09:15,870 --> 00:09:22,890
+Phi of Y تسوى Y إلى آخرى تمام؟ يبقى هذا شكل ال
+
+79
+00:09:22,890 --> 00:09:30,070
+function أو شكل ال homomorphisms من الـZن الى ز ان
+
+80
+00:09:30,070 --> 00:09:42,030
+هذا سؤال اللي هو 22 سؤال 24 و 25 مع بعض سؤال 25 في
+
+81
+00:09:42,030 --> 00:09:51,810
+الأول بدنا ال homomorphism من ز plus او ال direct
+
+82
+00:09:51,810 --> 00:09:57,960
+sum مع ز الى ز Direct sum مع زد.
+
+83
+00:10:00,500 --> 00:10:14,380
+تتوقعوا أكم همومورفزيوم؟ يلّا واحد، نين، خمساش،
+
+84
+00:10:14,380 --> 00:10:20,560
+أيوة، يلّا شوفوا القرقر، مال النهاية مثلًا؟ One
+
+85
+00:10:20,560 --> 00:10:27,680
+dollar.انت عندك هو قطير واحد فانت تسوي التبديلات
+
+86
+00:10:27,680 --> 00:10:36,300
+الممكنة كده يعني التبديلات؟ مش تمانية؟
+
+87
+00:10:36,300 --> 00:10:39,940
+تسعة
+
+88
+00:10:39,940 --> 00:10:45,960
+همومورفزيومز من هم تعالى نشوف الهمومورفزيومز
+
+89
+00:10:45,960 --> 00:10:54,840
+الممكنة هي Phi of A وBبدي اخد عنصر من z direct sum
+
+90
+00:10:54,840 --> 00:11:02,420
+ع z الاحتمال الاول انه يطلع a وb صح؟ اه بالسلب
+
+91
+00:11:02,420 --> 00:11:05,920
+الموجة كمان سبيكيم سلب يعني مين ما يكون الرقم يكون
+
+92
+00:11:05,920 --> 00:11:10,060
+سلب موجة بصفره مابتفرقش عندي خلاص انا خدت element
+
+93
+00:11:10,060 --> 00:11:15,740
+من ال direct sum الهكومة الفجرية التانية phi of a
+
+94
+00:11:15,740 --> 00:11:27,160
+وb ممكن يكون b وfمصبوح؟ طيب التالت Phi of A و B
+
+95
+00:11:27,160 --> 00:11:36,640
+ممكن يكون A و A الرابع Phi of A و B ممكن يكون B و
+
+96
+00:11:36,640 --> 00:11:48,660
+B Phi أربعة Phi of A و B ممكن يكون A و Zerofive of
+
+97
+00:11:48,660 --> 00:11:59,720
+a و b ممكن يكون zero و a five of a و b ممكن يكون
+
+98
+00:11:59,720 --> 00:12:15,900
+zero و b five of a و b ممكن يكون b و zero five of
+
+99
+00:12:15,900 --> 00:12:19,910
+a و b ممكن يكون b و zeroالذي هو الـ Zero Function.
+
+100
+00:12:20,770 --> 00:12:26,190
+الحين كل واحد من هذول همومورفزم، في غيره؟ لا يوجد
+
+101
+00:12:26,190 --> 00:12:32,630
+غيرهم، تسعة، مش أربع ولا تمانية ولا خمستاشر زي ما
+
+102
+00:12:32,630 --> 00:12:36,490
+قلنا ولا مالورية، يبقى هم التسعة لا يوجد غيرهم.
+
+103
+00:12:36,990 --> 00:12:41,490
+تقدر في الدارة براحتك عشوائيا، حط إيدك على أي واحد
+
+104
+00:12:41,490 --> 00:12:45,670
+من التسعة و تبتيه انه همومورفزم. تمام؟ نتبته بكل
+
+105
+00:12:45,670 --> 00:12:50,950
+سهولة.طب بدنا نيجي نطبق سؤال 24 اللي هو سؤال
+
+106
+00:12:50,950 --> 00:12:58,030
+الوزير سؤال 24 جالي ما هي الاحتمالات الممكنة لل
+
+107
+00:12:58,030 --> 00:13:02,550
+Phi of 1 و 0؟
+
+108
+00:13:02,550 --> 00:13:10,110
+موجودة و بيبي Zero من الاحتمالات الممكنة هلا بقول
+
+109
+00:13:10,110 --> 00:13:19,700
+ممكن تكون Zero و Zero آخر واحدصح؟ وممكن يتكون واحد
+
+110
+00:13:19,700 --> 00:13:29,500
+وواحد صح؟ وممكن يتكون واحد وزيرو اللي هو identity
+
+111
+00:13:29,500 --> 00:13:35,460
+وممكن يتكون zero واحد، في غير هيكل؟ لأ، يبقى
+
+112
+00:13:35,460 --> 00:13:41,260
+ماعنديش الا اربعة homomorphism لأ خامسة لأ هذا ال
+
+113
+00:13:41,260 --> 00:13:46,820
+zero homomorphism هذا اللي هوالوين هذا هو ال
+
+114
+00:13:46,820 --> 00:13:51,240
+identity homomorphism واتنين هذول هي الأربعة لا
+
+115
+00:13:51,240 --> 00:13:55,520
+أيوجد غيرها. رغم ان هو المتبادل من الذول بيقول
+
+116
+00:13:55,520 --> 00:13:58,440
+الزد فيها مالة نقية من العناصر ومالة نهاية من
+
+117
+00:13:58,440 --> 00:14:02,940
+العناصر والزد ذلك صمع زد فيها مريض ممكن يكون مالة
+
+118
+00:14:02,940 --> 00:14:06,960
+نهاية ولا مالة نهاية ولا حاجة التبديلات الممكنة
+
+119
+00:14:06,960 --> 00:14:12,680
+للأربعة عناصر الموجودة فقط لا ريحةيبقى هذا اربعة و
+
+120
+00:14:12,680 --> 00:14:16,880
+عشرين اللي كان مطلوب و زيادة عليه سؤال خمسة و
+
+121
+00:14:16,880 --> 00:14:20,720
+عشرين خمسة و عشرين و بعدين كل سؤال اتنين و تلاتين
+
+122
+00:14:20,720 --> 00:14:27,700
+مش هاد اللي هو القسمة على الاحداشر يبقى بيجي لسؤال
+
+123
+00:14:27,700 --> 00:14:35,160
+اتنين و تلاتين بيقول ال N positive integer و اثبت
+
+124
+00:14:35,160 --> 00:14:46,890
+ال proof ان ال N is divisibleby A11 if and only if
+
+125
+00:14:46,890 --> 00:14:55,370
+if and only if الـ A9 ناقص الـ A1 زائد الـ A2 ناقص
+
+126
+00:14:55,370 --> 00:15:04,710
+زائد ناقص واحد to the power K للـ AK is divisible
+
+127
+00:15:04,710 --> 00:15:10,970
+by 11 تمام؟
+
+128
+00:15:11,810 --> 00:15:16,850
+طيب، احنا أخدنا سؤال تفعى الـDivision من بقى تسعة،
+
+129
+00:15:16,850 --> 00:15:22,830
+مظبط؟ طيب، احنا هذا مش هنحله، هنعطيك المفتاح ونروح
+
+130
+00:15:22,830 --> 00:15:26,630
+لسؤال أربعة وثلاثين اللي يجيب سؤاله يقول تسعة
+
+131
+00:15:26,630 --> 00:15:30,210
+وسؤاله يقول إحتاشر اتنين بسؤال الواحد، يقول
+
+132
+00:15:30,210 --> 00:15:36,250
+خلاصنا، وبنمرنك كيفية عملية الحسابات من سؤال أربعة
+
+133
+00:15:36,250 --> 00:15:40,940
+دنيا، خلّينا مع هذا.طيب هذا لما أخدنا ايه المثال
+
+134
+00:15:40,940 --> 00:15:45,040
+السابق دي باسم البرتصال كان كل العلاصر هذه موجبة
+
+135
+00:15:45,040 --> 00:15:50,540
+صح؟ من أين أتت هذه السالبة هذا اللي بدنا نجاوب
+
+136
+00:15:50,540 --> 00:15:55,800
+عليه؟ نقوله بسيطة، مشان نثبت هذا الكلام بدنا نعرف
+
+137
+00:15:55,800 --> 00:16:04,080
+في من Z إلى Z11 بالنياد شرع ال homomorphism اللي
+
+138
+00:16:04,080 --> 00:16:10,970
+على الشكل التاليفاي اف اكس بده يساوي ال X موديولو
+
+139
+00:16:10,970 --> 00:16:15,390
+11 مش هذا ال natural homomorphism اللي عرفناه في
+
+140
+00:16:15,390 --> 00:16:19,050
+حالة التسعة ماجينا نقول فاي اف اكس بيساوي X
+
+141
+00:16:19,050 --> 00:16:24,630
+موديولو 9 هنا X موديولو main 11 أي integer ان
+
+142
+00:16:24,630 --> 00:16:31,130
+حاطناه على الصيغة ا ك عشر أقصى ك زاد ا كمنصة عشر
+
+143
+00:16:31,130 --> 00:16:36,270
+أقصى ك minus one زاد زاد ا one في عشرة زاد ا نود
+
+144
+00:16:36,600 --> 00:16:44,200
+تذكروا؟ اه مظبوط يفجأى اي ان عندى هنا بتعمله بنفس
+
+145
+00:16:44,200 --> 00:16:49,580
+الطريقة مع مراحظة ما يأتي فى زد عشر فى زد احداش يا
+
+146
+00:16:49,580 --> 00:16:56,880
+بناة الاحداش قداش تساوي ازيرة يعني معنى هذا الكلام
+
+147
+00:16:56,880 --> 00:17:02,440
+ان العشرة تساوي قداش يفجأى الان اللى حطناها بده
+
+148
+00:17:02,440 --> 00:17:06,740
+يشيل كل عشرة ويحط مكانهاسالب واحد بيصير سالب واحد
+
+149
+00:17:06,740 --> 00:17:10,180
+قصة واحد بسالب واحد سالب واحد تربيه بالموجب سالب
+
+150
+00:17:10,180 --> 00:17:13,980
+واحد تكييف السالب قصة اربعة موجب قصة خمسة سالب من
+
+151
+00:17:13,980 --> 00:17:18,940
+هنا سيظهر هذا سالب موجب موجب سالب الى اتنين عرفنا
+
+152
+00:17:18,940 --> 00:17:25,440
+من وين هذه بدأ تطلع من هذه طبعا احنا قلنا سابقا ان
+
+153
+00:17:25,440 --> 00:17:34,680
+ال N تساوي AK عشر عوز K زي AK minus ال oneعشرة أوس
+
+154
+00:17:34,680 --> 00:17:40,600
+كي ماينوس ال one زائد a one في عشرة زائد a نص
+
+155
+00:17:40,600 --> 00:17:46,600
+تذكرون؟ طيب ممتاز لنا، بدي أشيل كل عشرة هذه و أحط
+
+156
+00:17:46,600 --> 00:17:51,440
+مكانها سالب واحد، بصي لنا سالب موجب، سالب موجب،
+
+157
+00:17:51,440 --> 00:17:52,900
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+158
+00:17:52,900 --> 00:17:55,280
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+159
+00:17:55,280 --> 00:17:56,340
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+160
+00:17:56,340 --> 00:17:57,300
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+161
+00:17:57,300 --> 00:18:01,080
+سالب، سالب، سالب،
+
+162
+00:18:02,410 --> 00:18:06,990
+مع السؤال اللي خدناه في المحاضرة اتنين بسؤال واحد
+
+163
+00:18:06,990 --> 00:18:12,450
+و هو سؤال اربعة و تلاتين يعني بدك تسوي التفتيك
+
+164
+00:18:12,450 --> 00:18:17,570
+اللي هنا بنات مثل المثال حرفيا بس بده يشيل كل عشر
+
+165
+00:18:17,570 --> 00:18:23,490
+و يحط مكانها سالب واحد وبالتالي عرف طريقة القسم
+
+166
+00:18:23,490 --> 00:18:28,830
+على مين على الاحداشر سؤال اربعة و تلاتين بيقول ما
+
+167
+00:18:28,830 --> 00:18:35,330
+يقتينسؤال اربعة و تلاتين قولي show them the number
+
+168
+00:18:35,330 --> 00:18:43,490
+ال number ان اللي هو بده يساوي بده يساوي تسعة
+
+169
+00:18:43,490 --> 00:18:52,570
+تمانية تسعة سبعة تمانية تسعة سبعة ستة خمسة اربعة
+
+170
+00:18:52,570 --> 00:19:00,830
+ستة خمسة اربعة خمسة اتنين سبعة خمسة اتنين سبعةو
+
+171
+00:19:00,830 --> 00:19:17,510
+609 609 و 805 805 is divisible by 99 يبقى هذا is
+
+172
+00:19:17,510 --> 00:19:28,450
+divisible by 99 خلّيني أبدا أشوف بيكسب على ال 11
+
+173
+00:19:28,450 --> 00:19:34,300
+ولا لأ؟إذا قسم على الـ11 وقسم على الـ9، يعني أنا
+
+174
+00:19:34,300 --> 00:19:39,520
+بقسم على الـ99، صح ولا لا؟ يبقى قصتنا بسيطة، إذا
+
+175
+00:19:39,520 --> 00:19:43,820
+أثبت أن هذا الرقم اليوم دي اللي ما شاء الله عليه،
+
+176
+00:19:43,820 --> 00:19:48,100
+بقى ست عشر رقم ولا جدش، واحد، اتنين، تلاتة، اربع،
+
+177
+00:19:48,100 --> 00:19:53,800
+خمس، خمساشر، ست عشر رقم، مليارات، هه، هه، وكيف أنت
+
+178
+00:19:53,800 --> 00:19:56,620
+تقسمها؟ إذا حُط على ال calculator وضع اقسم عادي،
+
+179
+00:19:56,620 --> 00:20:02,110
+يعني قصة طويلة.لأ بدنا نروح يا بناتي نعرف function
+
+180
+00:20:02,110 --> 00:20:13,810
+دي فاي فاي من زد إلى زد احداشر باي فاي of X يساوي
+
+181
+00:20:13,810 --> 00:20:20,110
+X modulo 11 اللي هو 100 اللي عندنا هنا تمام؟ الحين
+
+182
+00:20:20,110 --> 00:20:25,550
+مش هكتب المقام ده هكتب بداله in يبقى بروح بقوله
+
+183
+00:20:25,550 --> 00:20:37,790
+هنا ال in isdivisible by 11 if and only if ال N
+
+184
+00:20:37,790 --> 00:20:45,390
+تقسم ال 11 إذا كانت ال N تسوى 11 برقم if and only
+
+185
+00:20:45,390 --> 00:20:57,820
+if ال N تساوي 11 M و ال M هذا رقم موجود في ذلكيبقى
+
+186
+00:20:57,820 --> 00:21:04,060
+هذا الكلام صحيح if and only if الـ Phi of N بدي
+
+187
+00:21:04,060 --> 00:21:15,100
+ساوي ال Phi of 11M ال Phi of 11M طبقا للتعريف
+
+188
+00:21:15,100 --> 00:21:27,930
+يساوي 11M modulo M يعني قداشر داشر Mموديول 11 يعني
+
+189
+00:21:27,930 --> 00:21:34,590
+موديول 11 صحيح موديول 11 يبقى ناتج جدار يساوي zero
+
+190
+00:21:34,590 --> 00:21:40,370
+إذا وصلنا هنا بنات ال five of n بدها ساوي zero if
+
+191
+00:21:40,370 --> 00:21:45,390
+and only if هاي ال elements اللي علنا يبقى بدها
+
+192
+00:21:45,390 --> 00:21:50,370
+ابدا بال a node من الخلف يبقى بداجي يقول if and
+
+193
+00:21:50,370 --> 00:21:58,080
+only if اللي همين خمسة خمسةسالف Zero زائد تمانية
+
+194
+00:21:58,080 --> 00:22:06,060
+سالف تسعة زائد Zero ناقص ستة زائد سبعة ناقص اتنين
+
+195
+00:22:06,060 --> 00:22:16,220
+زائد خمسة زائد خمسة سبعة اتنين خمسة ناقص اربعة
+
+196
+00:22:16,220 --> 00:22:25,820
+زائد خمسة ناقص ستة زائد سبعةنقص تسعة زائد تمانية
+
+197
+00:22:25,820 --> 00:22:35,740
+ناقص تسعة كدهش هدول مجموعة يبقى
+
+198
+00:22:35,740 --> 00:22:40,220
+هذا طيب ويقول يبقى سوى إذا كان هذا كله سوى كدهش؟
+
+199
+00:22:40,220 --> 00:22:43,900
+Zero هده بيسوي Zero ولا لا؟ I speak within a
+
+200
+00:22:43,900 --> 00:22:49,280
+uniform spectrum يبقى هذا الكلام كله بيبقى سوى
+
+201
+00:22:49,280 --> 00:22:58,750
+Zeroطيب الان ال zero او if and only if خلينا نشي
+
+202
+00:22:58,750 --> 00:23:09,950
+ترتيب اذا كان هذا الرقم is divisible by 11 طبعا؟
+
+203
+00:23:09,950 --> 00:23:16,330
+طيب هذا كلام if and only if مجموعهم كلهم zero is
+
+204
+00:23:16,330 --> 00:23:20,970
+divisible by 11
+
+205
+00:23:23,190 --> 00:23:30,530
+زيرو بنقسم بال 11 ولا لا؟ اه بيقسم بدون باقل يفجأه
+
+206
+00:23:30,530 --> 00:23:34,910
+يسأله الف زيرو is divisible by 11 يفجأه بناء عليه
+
+207
+00:23:34,910 --> 00:23:42,830
+رقم ان بصير يقسم بمن؟ بال 11 يفجأه هنا الان الرقم
+
+208
+00:23:42,830 --> 00:23:52,570
+الكبير هذا is divisible by 11بالمثل بدنا نروح
+
+209
+00:23:52,570 --> 00:23:58,450
+للتسعة بس التسعة مافيش فيها زائد وناقص كله بالزائد
+
+210
+00:23:58,450 --> 00:24:03,390
+طيب الان بقى بنفس الطريقة بدنا نعرف function من z
+
+211
+00:24:03,390 --> 00:24:11,530
+ل z تسعة يبقى بالداخل اقوله define a
+
+212
+00:24:11,530 --> 00:24:22,710
+function f من z الى z تسعة by اللي همينfive of x
+
+213
+00:24:22,710 --> 00:24:29,350
+يساوي ال X modulo تسعة ماتيش ابدأ كل الشغل اشتغال
+
+214
+00:24:29,350 --> 00:24:34,230
+فبدا ابدأ من هنا دول يبقى او بدا اقول ان ال N is
+
+215
+00:24:34,230 --> 00:24:38,810
+divisible و اخش على هدول دول اللي يبقى باجي بقوله
+
+216
+00:24:38,810 --> 00:24:49,960
+ال N is divisible by تسعة F عنده الفمجموعهم بدي
+
+217
+00:24:49,960 --> 00:24:56,260
+يقسم بواسطة 9 يبقى بدي اقول if and only if اللي هو
+
+218
+00:24:56,260 --> 00:25:12,160
+9 زائد 8 زائد 9 زائد 7 زائد 6 5 4 6 زائد 5 زائد 4
+
+219
+00:25:12,160 --> 00:25:21,070
+زائدخمسة اتنين سبعة خمسة زائد اتنين زائد سابعة هو
+
+220
+00:25:21,070 --> 00:25:26,590
+ستة صفر تسعة زائد ستة زائد صفر زائد تسعة زائد
+
+221
+00:25:26,590 --> 00:25:33,110
+تمانية زائد zero زائد خمسة يبقى هاي المجموع بتبعهم
+
+222
+00:25:33,110 --> 00:25:38,110
+بالضبط تماما زي ما قلنا هذا الكلام is divisible by
+
+223
+00:25:38,110 --> 00:25:41,370
+تسعة هذا الكلام is
+
+224
+00:25:43,710 --> 00:25:49,730
+divisible by 9 هذا الكلام يمكن ان تقوله اذا كتش
+
+225
+00:25:49,730 --> 00:25:57,390
+مجموعة هذه البنات تسعين يبقى التسعين is divisible
+
+226
+00:25:57,390 --> 00:26:05,470
+by 9 طب هذي تقسم بالتسعة ولا لا صح يبقى بتقسم
+
+227
+00:26:05,470 --> 00:26:10,810
+والنتج يسوى عشرة معناته ان ال N هذي is divisible
+
+228
+00:26:10,810 --> 00:26:22,620
+by 9يبقى so ال N is divisible by 9 هذه رقم اتنين
+
+229
+00:26:22,620 --> 00:26:33,180
+وهذه رقم واحد طيب اذا from واحد
+
+230
+00:26:33,180 --> 00:26:40,460
+and اتنين ال N is divisible
+
+231
+00:26:41,490 --> 00:26:51,390
+by both 11 and 9 تقسم بيلي اتنين يبقى تقسم بحاصل
+
+232
+00:26:51,390 --> 00:26:59,790
+ضاربينها هذا بده يعطينا ان ال in is divisible by
+
+233
+00:26:59,790 --> 00:27:06,690
+تسعة وتسعين وانتهينا من المسألة يبقى هذه المسألة
+
+234
+00:27:06,690 --> 00:27:11,080
+جبت القسم على تسعة وجبت القسم على احدانقسم على
+
+235
+00:27:11,080 --> 00:27:15,660
+تسعة مثال في المحاضرة المرة قبل الماضية والاحدى
+
+236
+00:27:15,660 --> 00:27:20,260
+عشرين في محاضرة اليوم السؤال اتنين و تلاتين
+
+237
+00:27:20,260 --> 00:27:29,760
+هيطبقناه على سؤال اربع و تلاتين بعد ذلك بنجي لسؤال
+
+238
+00:27:29,760 --> 00:27:37,180
+اتنين واربعين جالي كل ring homomorphism سؤال اتنين
+
+239
+00:27:37,180 --> 00:27:38,100
+واربعين
+
+240
+00:27:41,570 --> 00:27:49,130
+الرنج homomorphisms في من ال six rational number
+
+241
+00:27:49,130 --> 00:27:57,590
+للست rational number بتعرف مين هم ؟
+
+242
+00:27:57,590 --> 00:28:07,990
+مين ؟ يالا حد حلت فيك السؤال ؟ يعني
+
+243
+00:28:07,990 --> 00:28:12,020
+ال identity functionبس بدنا نثبت انها ال identity
+
+244
+00:28:12,020 --> 00:28:17,660
+function اه انا اظهر صحيح ان كلامي مظبوط هو ال
+
+245
+00:28:17,660 --> 00:28:23,500
+identity function ولا يوجد غيرها كيف كالتالي؟ خلوي
+
+246
+00:28:23,500 --> 00:28:31,380
+ولا كده solution milligrams
+
+247
+00:28:31,380 --> 00:28:37,820
+five of one بده يساوي ال one مظبوط؟ طيب الان لو
+
+248
+00:28:37,820 --> 00:28:46,570
+جيت اخدتالـ N موجودة في Z والـ Z صاحب 6 من 100 من
+
+249
+00:28:46,570 --> 00:28:55,650
+الـ Q يبقى الـ N موجودة في الـ Q ثم Phi of N بقدر
+
+250
+00:28:55,650 --> 00:29:02,070
+اكتبها Phi of واحد زائد واحد زائد واحد اكمرة بنات
+
+251
+00:29:02,070 --> 00:29:11,970
+اكمرة in Piطيب الفي أنا بقول انه homomorphism طبعا
+
+252
+00:29:11,970 --> 00:29:16,390
+وانا فرض انه في عبارة عن homomorphism يبقى هذا
+
+253
+00:29:16,390 --> 00:29:22,030
+الكلام بده يساوي في of one زائد في of one زائد
+
+254
+00:29:22,030 --> 00:29:31,150
+زائد في of one كمان قداش in times يبقى هذا معناه
+
+255
+00:29:31,150 --> 00:29:40,600
+ان الفي of inيساوي N في ال 5 of 1 فال 5 of 1 يبقى
+
+256
+00:29:40,600 --> 00:29:46,280
+داشر يبقى واحد يبقى هذا بده يعطينا انه 5 of N
+
+257
+00:29:46,280 --> 00:29:53,560
+يساوي ال N في واحد هذا بده يعطينا ال 5 of N بده
+
+258
+00:29:53,560 --> 00:30:02,300
+ساوي ال N بده ساوي ال N يبقى صارت هذه ال identity
+
+259
+00:30:02,300 --> 00:30:09,600
+mapو هذه كمان هي ال identity map بس هدول على مين؟
+
+260
+00:30:09,600 --> 00:30:16,140
+على الأعداد الصحيحة بدنا نشوف الأعداد rational
+
+261
+00:30:16,140 --> 00:30:22,340
+اللي بتكون على شكل قصور اعتيادية طبعا احنا عندنا
+
+262
+00:30:22,340 --> 00:30:27,300
+set of rational numbers AQ كل الأعداد اللي على
+
+263
+00:30:27,300 --> 00:30:34,010
+صيغة M على N بحيث ال M و ال N موجودة في ال Zو ال N
+
+264
+00:30:34,010 --> 00:30:46,670
+لا تساوي زي ما يبقى
+
+265
+00:30:46,670 --> 00:30:51,090
+أثبتنا ان ال homomorphisms على الأعداد الصحية هي
+
+266
+00:30:51,090 --> 00:30:55,690
+identity function نيجي على القصور اللي ماهياش
+
+267
+00:30:55,690 --> 00:31:05,330
+أعداد صحية يبقى أنا بتاخد Phi of M على Mأليست Phi
+
+268
+00:31:05,330 --> 00:31:17,150
+of M في N أس ناقص واحد صح ؟ طيب أليست هذه Phi of M
+
+269
+00:31:17,150 --> 00:31:28,210
+في Phi of N أس ناقص واحد صحيح طيب نرجع لل groups
+
+270
+00:31:28,210 --> 00:31:36,150
+لو رجعنا لل groups هذه Phi of Mفي Phi of N أُس
+
+271
+00:31:36,150 --> 00:31:44,270
+هالي واحد طب ال Phi of M مش هي ال M من العلاقة
+
+272
+00:31:44,270 --> 00:31:50,170
+اللي عندنا هذه لإنه integers وهذه اللي هو main
+
+273
+00:31:50,170 --> 00:31:57,270
+وهذه Phi of N اللي هو ال N أُس ناقص واحد يبقى صارة
+
+274
+00:31:57,270 --> 00:32:05,880
+ال M على Nيبقى Phi of M على N هي M على N يبقى هنا
+
+275
+00:32:05,880 --> 00:32:15,720
+Phi of Q بدها تساوي الـ Q لكل Q اللي موجودة في
+
+276
+00:32:15,720 --> 00:32:21,600
+كبتلة Q مين هي ال function هذه ال identity
+
+277
+00:32:21,600 --> 00:32:27,910
+function كما زعمت زميلتكم قبل قليليبقى هذه الـ
+
+278
+00:32:27,910 --> 00:32:39,450
+Identity Map أو الـ Identity Homomorphism طبعا؟
+
+279
+00:32:39,450 --> 00:32:47,670
+إذا قبل قليل من ZN إلى ZN مالجيناش أي زومورفزم إلا
+
+280
+00:32:47,670 --> 00:32:53,780
+الـ Identity Mapوهنا من ال EQ للي EQ مالاجيناش إلا
+
+281
+00:32:53,780 --> 00:33:00,200
+ال identity homomorphism هذا سؤال اتنين واربعين
+
+282
+00:33:00,200 --> 00:33:04,620
+أظن كان معانا سبعة واربعين؟ هذا محلول عندك في
+
+283
+00:33:04,620 --> 00:33:11,180
+الكتاب تفصيليا يبقى خلالك روحي راجعي وكتبيه الآن
+
+284
+00:33:11,180 --> 00:33:15,620
+أهم سؤال عندي على جد اللواجت ضايل سؤال ستة وستين
+
+285
+00:33:15,620 --> 00:33:24,420
+اللي هو خمسة مطالبتمام وبيشمل الفكرة تبعت سؤال 14
+
+286
+00:33:24,420 --> 00:33:29,900
+اللي تركناه وقلنا لك جايب إذا بدي أروح لسؤال 66
+
+287
+00:33:29,900 --> 00:33:33,160
+سؤال
+
+288
+00:33:33,160 --> 00:33:42,680
+66 بيقول ليش احنا ring اعطيه كل المصرفات اللي على
+
+289
+00:33:42,680 --> 00:33:52,220
+الشكل a,b,b,aبحيث ان ال A و ال B موجودات في الستة
+
+290
+00:33:52,220 --> 00:34:03,000
+انتجات وعندنا Phi معرفة من ال A B D A تساوي ال A
+
+291
+00:34:03,000 --> 00:34:12,140
+ناقص ال B طلب المطلوب الأول نمرأ A show Phi is
+
+292
+00:34:12,140 --> 00:34:16,360
+homomorphism والله يشوف لأ homomorphism
+
+293
+00:34:20,790 --> 00:34:28,730
+خلّي بالك هنا يبقى بدي أخد الحالة الأولى وهي نصف
+
+294
+00:34:28,730 --> 00:34:33,570
+الأول من ال homomorphism تبع الجمع يبقى بدي أخد
+
+295
+00:34:33,570 --> 00:34:42,970
+Phi of مجموع مصرفتين موجودتين في R والتكن A B B A
+
+296
+00:34:42,970 --> 00:34:54,130
+زائد C D D C و7 يعرف جديشجدفة يقول جمع المصفوفات
+
+297
+00:34:54,130 --> 00:35:00,430
+حسب ما تعلمته في الجبر الخاطى كل عنصر لعنى غيره
+
+298
+00:35:00,430 --> 00:35:09,590
+تطلع المصفوفة التالية A زائد ال C بي زائد ال D بي
+
+299
+00:35:09,590 --> 00:35:18,690
+زائد ال D بي زائد ال D ال A زائد ال C جسرت مصفوفة
+
+300
+00:35:18,690 --> 00:35:25,080
+واحدةحسب ال definition اللى عندنا بده يساوي ال A
+
+301
+00:35:25,080 --> 00:35:32,360
+ناقص ال B يفجأ هذا بده يساوي ال A زي ال C ناقص ال
+
+302
+00:35:32,360 --> 00:35:39,840
+B زي ال D اللى بقدر اكتبها على الشكل التالف ال A
+
+303
+00:35:39,840 --> 00:35:49,940
+ناقص ال B زي ال C ناقص ال D حسب ال definitionفاي
+
+304
+00:35:49,940 --> 00:35:57,680
+of المصوفة هذه يبقى هذا فاي of المصوفة a b b a
+
+305
+00:35:57,680 --> 00:36:06,540
+زائد فاي of المصوفة الثانية فاي of ال b .. ال ..
+
+306
+00:36:06,540 --> 00:36:24,910
+ال c b ال c b ال c d c dDC and يبقى بالنسبة للجمعة
+
+307
+00:36:24,910 --> 00:36:30,370
+مباشرة لا في لف ولا في دوران ولا في صعوبة بتاخد
+
+308
+00:36:30,370 --> 00:36:40,290
+Phi of حاصل الضرب A B B A في مين في C D D C ويسوي
+
+309
+00:36:40,290 --> 00:36:47,540
+Phi ofضرب المصفات الصف الأول في العمود الأول لو
+
+310
+00:36:47,540 --> 00:36:57,120
+نجمع بيعطينا العمصر الأول يبقى AC زائد BD يبقى AC
+
+311
+00:36:57,120 --> 00:37:04,300
+زائد BD هذا العمصر الأول في العمود الأول الصف
+
+312
+00:37:04,300 --> 00:37:09,230
+الأول في العمود التاني بيعطينا العمصر الثانييبقى
+
+313
+00:37:09,230 --> 00:37:18,390
+AD زائد BC يبقى AD زائد BC الصف الثاني في العمود
+
+314
+00:37:18,390 --> 00:37:28,210
+الأول بيعطينا AD زائد BC والعنصر الأخير AC زائد BD
+
+315
+00:37:28,210 --> 00:37:35,310
+طيب صارت كلها مصفوفة واحدة مش مصفوفتينحسب التعريف
+
+316
+00:37:35,310 --> 00:37:39,270
+اللى عندنا يبقى ال element اللى فى الصفر الاول
+
+317
+00:37:39,270 --> 00:37:44,490
+ناقص ال element اللى فى الصفر الثانى يبقى هذه بده
+
+318
+00:37:44,490 --> 00:37:53,930
+يعطينا ميمو ال AC زي دي ال BD ناقص ال AD ناقص ال
+
+319
+00:37:53,930 --> 00:38:01,850
+BC اعتبريلي هذه المعادلة رقم واحد بدي اجي اخد Phi
+
+320
+00:38:02,920 --> 00:38:12,400
+of ال A P B A في Phi of C D D C by yourself هذه يا
+
+321
+00:38:12,400 --> 00:38:20,340
+بناد اللي همين ال A ناقص ال B و هذه ال C ناقص ال D
+
+322
+00:38:20,340 --> 00:38:30,160
+بدي أضرب القوشين في بعض يبقى هذه ب A C A C ناقص
+
+323
+00:38:30,160 --> 00:38:44,210
+فناقص بزائدBD ناقص B ناقص ال A D ناقص ال B C B C
+
+324
+00:38:44,210 --> 00:38:53,270
+طلع يشوف ايه هذه هيها ها هيها بالحرف الواحد يبقى
+
+325
+00:38:53,270 --> 00:39:03,210
+هذه اتنين يبقى بروح بقوله هنا from واحد ان اتنينWe
+
+326
+00:39:03,210 --> 00:39:10,370
+have ان الـ Phi of ABDA
+
+327
+00:39:10,370 --> 00:39:25,750
+مضروبة في CDDC بتشاوي Phi of ABDA في Phi of CDDC
+
+328
+00:39:25,750 --> 00:39:29,450
+وبالتالي Phi is homomorphism
+
+329
+00:39:45,400 --> 00:39:55,480
+المصمم الثاني خلصنا ايه قال بيه بده find الكرن
+
+330
+00:39:55,480 --> 00:40:05,520
+الالفاية بقوله الكرن الالفاية هو كل المصفوفات a,
+
+331
+00:40:05,860 --> 00:40:11,120
+d, b, a, f,
+
+332
+00:40:14,230 --> 00:40:20,890
+بحيث ان ال file of a, b, b, a بده يساوي zero
+
+333
+00:40:20,890 --> 00:40:28,290
+مظبوط؟ مش هيك التعريف؟ طيب، هذا الكلام معناه مين؟
+
+334
+00:40:28,290 --> 00:40:36,350
+كل المصفات a, b, b, a صدش ده صورة هذا العنصر هو a
+
+335
+00:40:36,350 --> 00:40:43,940
+ناقص ال b يبقى ال a ناقص ال b بده يساوي zeroيبقى
+
+336
+00:40:43,940 --> 00:40:51,700
+هذا الكلام كل المصروفات a,b,b,a such ذات ال a
+
+337
+00:40:51,700 --> 00:40:57,520
+تساوي ال b إذا انا هشيل كل b و أحط مكانها a أو
+
+338
+00:40:57,520 --> 00:41:04,440
+أشيل كل a و أحط مكانها b يبقى هذا الكلام بده يساوي
+
+339
+00:41:04,440 --> 00:41:11,820
+كل المصروفات اللي ع الشكل a,a,a,a بحيث ال a موجود
+
+340
+00:41:11,820 --> 00:41:18,560
+وينموجود فيه زر يبقى الكيرن التابع هذه ال function
+
+341
+00:41:18,560 --> 00:41:24,400
+كل المصفوفات اللي نظامها اتنين في اتنين واللي جميع
+
+342
+00:41:24,400 --> 00:41:30,220
+أنصارها متساوية قال لي بعد ذلك المطلوب التالت
+
+343
+00:41:30,220 --> 00:41:41,920
+نمرسي قال لي شو؟ لأ ان ال R Modular Kern لل Phi
+
+344
+00:41:42,290 --> 00:41:50,890
+Isomorphic لمين؟ Isomorphic to Z Solution
+
+345
+00:41:50,890 --> 00:41:59,610
+هذه
+
+346
+00:41:59,610 --> 00:42:06,600
+مرت علينا في نظرية من نظريات خلال هذا الشهر داإيش
+
+347
+00:42:06,600 --> 00:42:10,640
+اسمها؟ الـ first isomorphism ممتاز جدا، يبقى أنا
+
+348
+00:42:10,640 --> 00:42:16,380
+بدأ أروح على ال first isomorphism theorem ونقارنها
+
+349
+00:42:16,380 --> 00:42:20,980
+مع مين؟ مع المطلوب، يمكن تصبط ويمكن ما تصبطش الله
+
+350
+00:42:20,980 --> 00:42:27,600
+أعلم، طب الله بقول هنا from أو قبل هيك، we know
+
+351
+00:42:27,600 --> 00:42:28,240
+that
+
+352
+00:42:31,630 --> 00:42:40,230
+إن الكيرن الـ alpha is an ideal of R.مظبوط يا
+
+353
+00:42:40,230 --> 00:42:46,150
+عزيزي؟ الكيرن الـ ideal. أثبتنا نظرية كذلك خلال
+
+354
+00:42:46,150 --> 00:42:56,010
+هذا الشرطة.طيب بروح بقول هنا by the isomorphism
+
+355
+00:42:56,010 --> 00:43:05,590
+theorem. We haveحدة بيذكراها في Ego ان R موديول
+
+356
+00:43:05,590 --> 00:43:14,010
+الكرن لـ Phi ايزو مورفك لميه؟ لا Phi of R Phi of R
+
+357
+00:43:14,010 --> 00:43:22,210
+طب هو ايش المطلوب؟ اثبت ايزو مورفك لـ Z بنقول إذا
+
+358
+00:43:22,210 --> 00:43:29,710
+قدرنا نثبت ان Phi of R ايزو مورفك لـ Z بتم المطلوب
+
+359
+00:43:30,380 --> 00:43:35,980
+والأسهل من ذلك انه نثبت ان ال five of R هي Z
+
+360
+00:43:35,980 --> 00:43:41,680
+itself إذا قدرنا نثبت هذا الكلام يقول خلصنا تمام
+
+361
+00:43:41,680 --> 00:43:50,400
+يبقى فاجب أقوله F we show them إذا قدرنا نثبت ان
+
+362
+00:43:50,400 --> 00:44:01,930
+ال five of R تساوي Z يبقى then wehave the result
+
+363
+00:44:01,930 --> 00:44:08,730
+يكون خلصنا، حصلنا على النتيجة لذلك بدي أحاول أثبت
+
+364
+00:44:08,730 --> 00:44:14,090
+أنه كل واحدة فيهم subset من التالية يبقى بروح
+
+365
+00:44:14,090 --> 00:44:23,370
+بقوله little x موجودة في الـPhi of R تمام؟
+
+366
+00:44:23,370 --> 00:44:38,030
+then ال Xتساوي فاي of مصروف من R will تكون A1 B1
+
+367
+00:44:38,030 --> 00:44:45,650
+B1 A1 فاي
+
+368
+00:44:45,650 --> 00:44:51,210
+of هذه X موجودة في فاي of عريب X تساوي فاي of
+
+369
+00:44:51,210 --> 00:44:57,640
+element من R من ما يكون يكونطيب هذا مشوعي عبارة عن
+
+370
+00:44:57,640 --> 00:45:04,080
+a1 ناقص b1 طب a1 و b1 وين موجوداتها دول؟ في z
+
+371
+00:45:04,080 --> 00:45:08,860
+الفرق بينها موجود في z لأن هذول الفرق بين any two
+
+372
+00:45:08,860 --> 00:45:16,440
+integers is an integer يبقى هذا موجود في z يبقى
+
+373
+00:45:16,440 --> 00:45:24,040
+sir phi of a subset من مين؟ subset من zنعمل
+
+374
+00:45:24,040 --> 00:45:32,500
+العملية العكسية on the other hand let
+
+375
+00:45:32,500 --> 00:45:40,320
+ال X موجودة في Z إذا قدرنا نثبت إن ال X موجودة في
+
+376
+00:45:40,320 --> 00:45:46,240
+Phi R، يكون خلاص تم المطلوب تمام؟ يبقى افترضنا إن
+
+377
+00:45:46,240 --> 00:45:56,000
+X موجودة في Z then ال X تساويممكن احطها فرق بين
+
+378
+00:45:56,000 --> 00:46:02,460
+any two انتجارات بدون مشاكل حتى لو كانت zero ممكن
+
+379
+00:46:02,460 --> 00:46:06,600
+احطها zero ناقص zero ممكن احطها خمسة ناقص خمسة مية
+
+380
+00:46:06,600 --> 00:46:11,980
+ناقص هادى جدا يبقى ال element اللى أخدته فاقدر
+
+381
+00:46:11,980 --> 00:46:18,500
+احطه كفرق بين two انتجارات يبقى then ال X بده يقول
+
+382
+00:46:18,500 --> 00:46:27,490
+ايه ناقص ال B مثلاقبل A نقص ال V مش هي عبارة عن
+
+383
+00:46:27,490 --> 00:46:40,950
+Phi of A,B,B,A وهذه موجودة في Phi of A صح؟
+
+384
+00:46:40,950 --> 00:46:47,930
+فهذه موجودة في Phi of A يبقى ال element اللي خدته
+
+385
+00:46:47,930 --> 00:46:56,250
+في Z لجته موجود وين؟ في Phi of Aيبقى هنا سا اللي
+
+386
+00:46:56,250 --> 00:47:06,670
+هو ال z subject من five of a سميلي الأولى رقم واحد
+
+387
+00:47:06,670 --> 00:47:14,450
+وسميلي هذه رقم اتنين فبنروح نقوله from واحد and
+
+388
+00:47:14,450 --> 00:47:25,030
+اتنين we have ان ال five of aتساوي الـ Z itself
+
+389
+00:47:25,030 --> 00:47:28,350
+طيب
+
+390
+00:47:28,350 --> 00:47:45,050
+ليش وصلنا؟
+
+391
+00:47:45,050 --> 00:47:48,350
+يبقى
+
+392
+00:47:48,350 --> 00:47:54,190
+صاروا اتنين دول متساوياتين ساعةالـR موديول الكيرني
+
+393
+00:47:54,190 --> 00:48:00,350
+للـPhi أيزو مورفك لـPhi of R اللي بتساوي مينا منها
+
+394
+00:48:00,350 --> 00:48:08,030
+Z إذا معنى هذا الكلام أنه R موديول الكيرني للـPhi
+
+395
+00:48:08,030 --> 00:48:15,950
+أيزو مورفك لمين؟ لـZ بسأله
+
+396
+00:48:15,950 --> 00:48:20,510
+كمان سؤال، الحين كم سؤال سؤال؟ تلاتة سؤال الرابع
+
+397
+00:48:21,250 --> 00:48:30,430
+المرأة دي بقول هل الكيرن ال ال5 is a prime ideal
+
+398
+00:48:30,430 --> 00:48:34,490
+ولا لا؟
+
+399
+00:48:34,490 --> 00:48:43,690
+سمع، بنفع، طيب، وده بتبدأ بطريقتنا، طريقتنا
+
+400
+00:48:43,690 --> 00:48:48,210
+الأخرى، يا إما بوسطة ال definition، يا إما
+
+401
+00:48:48,210 --> 00:48:54,630
+بالنظريةبتاعة الار موديولو موديولو مين؟ موديولو
+
+402
+00:48:54,630 --> 00:49:00,950
+الكيرنل تبقى integral domain إذا كان الكيرنل ال
+
+403
+00:49:00,950 --> 00:49:07,250
+prime صح ولا لأ؟ اه يعني إيش ممكن أعمل؟ يعني ممكن
+
+404
+00:49:07,250 --> 00:49:14,530
+أخد mass of تين موجودات في الأرض بحيث حصل ضربهم
+
+405
+00:49:14,530 --> 00:49:18,950
+يكون في الكيرنلو أثبت يا الأولى في ال kernel يا
+
+406
+00:49:18,950 --> 00:49:23,090
+التانية في ال kernel إيه الحدث ذلك؟ بقوله يبقى هذا
+
+407
+00:49:23,090 --> 00:49:28,330
+prime ideal هذا الطريقة الأولى طويلة شوية مية
+
+408
+00:49:28,330 --> 00:49:32,050
+المية بس طويلة شوية اللي أقصر منها احنا قولنا
+
+409
+00:49:32,050 --> 00:49:37,630
+isomorphic لمين؟ لزد لما نقول في عندي ring
+
+410
+00:49:37,630 --> 00:49:41,370
+isomorphic ل ring التانية يبقى ال ring الأولى
+
+411
+00:49:41,370 --> 00:49:46,560
+والتانية كلهم لهم نفس الخواصة الرياضيةطب الـ z is
+
+412
+00:49:46,560 --> 00:49:50,740
+an integral domain؟ انتجرال دومينة خدناها قبل ذلك
+
+413
+00:49:50,740 --> 00:49:59,580
+يبقى بالي بقوله since بما ان ال z is an integral
+
+414
+00:49:59,580 --> 00:50:12,600
+domain we have ان ال R modulo الكرمي لل 5 is an
+
+415
+00:50:12,600 --> 00:50:24,690
+integraldomain طيب هذا بده يعطيني by a previous
+
+416
+00:50:24,690 --> 00:50:34,890
+theorem by a previous theorem by
+
+417
+00:50:34,890 --> 00:50:39,550
+a previous theorem هذه integral domain
+
+418
+00:50:43,640 --> 00:50:51,740
+الـ prime ideal و هو المطلوب خلصنا من دين جيل
+
+419
+00:50:51,740 --> 00:51:00,220
+الريب بيسأل هل هذا maximal ولا لا؟ يبقى أزة اللي
+
+420
+00:51:00,220 --> 00:51:07,940
+هو ال kern اللوفاية maximum ideal ولا لا؟
+
+421
+00:51:11,030 --> 00:51:16,870
+بس الاسئلة التالية هل ال z فيه؟ يبقى لا يمكن ال R
+
+422
+00:51:16,870 --> 00:51:21,190
+موديل الكون ان انا اكون فيه يبقى لا يمكن الكون ان
+
+423
+00:51:21,190 --> 00:51:27,490
+انا اكون ماكسيما هذي احد الطرق تمام؟ يبقى value
+
+424
+00:51:27,490 --> 00:51:42,040
+بيقوله since بيبقى ان ال z ال z عندى is notA field
+
+425
+00:51:42,040 --> 00:51:47,580
+ليش؟ لأنه مش كل أنصار له معكوث. مش هو ال unity.
+
+426
+00:51:47,720 --> 00:51:52,340
+اتنين والتلاتة والاربعة ولا واحد له معكوث في ذاته.
+
+427
+00:51:52,740 --> 00:52:00,300
+That is not a field. We have in our modular kernel
+
+428
+00:52:00,300 --> 00:52:08,910
+الفائض is not a field.يبقى هذا يقدر يعطيك الكيرن
+
+429
+00:52:08,910 --> 00:52:18,730
+اللي الفاي is not maximal طيب
+
+430
+00:52:18,730 --> 00:52:25,970
+أنا ماجدتش في بالي النظرية لكن تعريف الفيل ان اي
+
+431
+00:52:25,970 --> 00:52:32,910
+عنصر له معكوس طب لو كده اثبت او ااخد و لو عنصر
+
+432
+00:52:32,910 --> 00:52:37,130
+واحد مالاقيش عنصر غير صفري بسمايكونش لو ماكوش
+
+433
+00:52:37,130 --> 00:52:39,750
+بيبقى اللي يصير فيه دول وبالتالي بيبقى اللي يصير
+
+434
+00:52:39,750 --> 00:52:46,070
+هذا maximal ID مظهر؟ طيب تعالى نشوف بدنا طريقة
+
+435
+00:52:46,070 --> 00:52:56,030
+ثانية للورهام يبقى بداخل let اللي هو main let مثلا
+
+436
+00:52:56,030 --> 00:53:04,280
+خمسة اتنين اتنين خمسة زائد الكرن لل fiveموجودة في
+
+437
+00:53:04,280 --> 00:53:11,120
+الار موديول الكيرني للفارق بدي
+
+438
+00:53:11,120 --> 00:53:19,660
+أبيل ان هذا عنصر غير صفري تمام؟ then هذا شو بده
+
+439
+00:53:19,660 --> 00:53:27,620
+يساوي؟ الخمسة اتنين اتنين خمسة زائد الكيرني للفارق
+
+440
+00:53:27,620 --> 00:53:35,120
+يساوي تلاتة Zero Zeroثلاث، اتنين، اتنين، اتنين
+
+441
+00:53:35,120 --> 00:53:42,660
+زائد الكيرن للـ Phi صحيح ؟ مجموع
+
+442
+00:53:42,660 --> 00:53:46,900
+المصفوفة هناك تتطلع هذه طب هذا موجود في الكيرن
+
+443
+00:53:46,900 --> 00:53:53,980
+المصفوفة هذه لأن الكيرن الـAAA موجود في الكيرن
+
+444
+00:53:53,980 --> 00:53:59,320
+يبقى ما يسهل عليها الطير يولد مع الكيرنيبقى بقول
+
+445
+00:53:59,320 --> 00:54:08,480
+هذا الكلام بدي يسوى 3003 زي الكرن الالفاية هل هذا
+
+446
+00:54:08,480 --> 00:54:16,980
+بيسوى الكرن الالفاية؟ لا يسوى الكرن الالفاية يبقى
+
+447
+00:54:16,980 --> 00:54:24,520
+هذا اضمان a zero element يبقى هنا ساعة اللي هو من
+
+448
+00:54:24,520 --> 00:54:27,480
+3003
+
+449
+00:54:27,930 --> 00:54:38,070
+زائد الكائن اللى الفاية is a non zero n بدى افترض
+
+450
+00:54:38,070 --> 00:54:46,190
+انه يلو معكوس طبعا طيب لما يلو معكوس بدى اشوف هل
+
+451
+00:54:46,190 --> 00:54:52,670
+بوصل الى تناقض والله بصير كلامي صحيح انا فضالي
+
+452
+00:54:52,670 --> 00:54:57,030
+بقولهم as you want that
+
+453
+00:54:58,690 --> 00:55:09,050
+إنه تلاتة Zero Zero تلاتة زادة كيرن للفاي مضروف A
+
+454
+00:55:09,050 --> 00:55:20,850
+B B A زادة كيرن للفاي كل هذا مضروف هذا بده يساوي
+
+455
+00:55:20,850 --> 00:55:26,270
+ال unity من ال unity واحد Zero Zero واحد اللي هو
+
+456
+00:55:26,270 --> 00:55:37,550
+موجود في A1001 زائد الكيرن للـ 5 يبقى
+
+457
+00:55:37,550 --> 00:55:49,370
+هذا معناته يا بنات ان التلاتة 003 في ال A B B A
+
+458
+00:55:49,370 --> 00:56:01,420
+سبب واحد 001 مظبوط؟ عشان اكترطيب هذا معناه هو
+
+459
+00:56:01,420 --> 00:56:06,920
+المصروف التالي الصف الأول في العمود الأول تلاتة A
+
+460
+00:56:06,920 --> 00:56:13,640
+و هنا تلاتة B و هنا تلاتة B و هنا تلاتة A بدها
+
+461
+00:56:13,640 --> 00:56:20,100
+تساوي واحد Zero واحد طيب هذا ايش معناه ان تلاتة A
+
+462
+00:56:20,100 --> 00:56:27,320
+بدها تساوي واحديعني ايه تسوى كده؟ هل التوتس موجود
+
+463
+00:56:27,320 --> 00:56:33,740
+في Z؟ يبقى هذا does not belong to Z يبقى فرض اللي
+
+464
+00:56:33,740 --> 00:56:38,660
+فرضته هذا غلط ولا صح؟ غلط يعني معناه أن العنصر هذا
+
+465
+00:56:38,660 --> 00:56:44,760
+مالوش معكوس عنصر غير صفري مالوش معكوس يبقى لا يمكن
+
+466
+00:56:44,760 --> 00:56:49,840
+أن يكون هذا فيل لإن الفيل كل عنصر غير صفري لهو
+
+467
+00:56:49,840 --> 00:56:59,630
+معكوسطيب كويس مش موجود في 6 الخمسة اتنين اتنين
+
+468
+00:56:59,630 --> 00:57:06,650
+خمسة زائد الكيرن اللي ال five has no
+
+469
+00:57:06,650 --> 00:57:11,070
+multiplicative
+
+470
+00:57:11,070 --> 00:57:20,450
+inverse هذا بده يعطينا ان ال RModular Kernel لـ
+
+471
+00:57:20,450 --> 00:57:29,150
+Phi is not a field مدام ما هوش فين يبقى ال Kernel
+
+472
+00:57:29,150 --> 00:57:38,610
+لـ Phi is not maximal يبقى عندك طريقتين لإثبات
+
+473
+00:57:38,610 --> 00:57:44,110
+الـPrime وعندك طريقتين لإثبات نين لإثبات ال
+
+474
+00:57:44,110 --> 00:57:47,510
+maximum أعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c62e23949a305fafa129ffaf8c7a7d4240d78255
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc.srt
@@ -0,0 +1,1322 @@
+1
+00:00:20,670 --> 00:00:26,050
+بسم الله الرحمن الرحيم. عوضنا على بدأ، إحنا بدأنا في
+
+2
+00:00:26,050 --> 00:00:30,790
+ring homomorphism المرة الماضية، وكتبنا نص نظرية
+
+3
+00:00:30,790 --> 00:00:35,710
+طبعًا الكتاب ما برهَنْشي و قال زي تبعت الـ group، و
+
+4
+00:00:35,710 --> 00:00:39,670
+إحنا مش هنقول زي مجلة، لأ، بدنا نروح نبرهن هذه
+
+5
+00:00:39,670 --> 00:00:45,590
+النظرية. ثمان نقاط هذه النظرية، النقطة الأولى بقول
+
+6
+00:00:45,590 --> 00:00:51,620
+لو كان الـ n is a positive integer، والـ R موجود في
+
+7
+00:00:51,620 --> 00:00:58,420
+R، بدنا نثبت أن الـ φ(nR) = n φ(R)
+
+8
+00:00:58,420 --> 00:01:03,740
+وكذلك نثبت أن φ(R)<sup>n</sup> = φ(R<sup>n</sup>) يعني بقى الـ proof الثاني
+
+9
+00:01:03,740 --> 00:01:08,400
+بدي أبدأ بالنقطة الأولى. φ(nR) هذه بقدر
+
+10
+00:01:08,400 --> 00:01:14,700
+أكتبها للشكل الثاني. φ(
+
+11
+00:01:14,700 --> 00:01:19,810
+1 + 1 + 1 ...إلى آخره) يبقى 1 +
+
+12
+00:01:19,810 --> 00:01:24,510
+1 + 1 + ... إلى آخره، يبقى 1 +
+
+13
+00:01:24,510 --> 00:01:31,010
+1 + ... + 1، كل هذا في R اللي برا اللي
+
+14
+00:01:31,010 --> 00:01:37,490
+عندنا هنا، تمام؟ هذا الكلام يساوي، من حسب قانون
+
+15
+00:01:37,490 --> 00:01:42,690
+التوزيع، الـ distributive law، هذه بيصير 1 في R
+
+16
+00:01:42,690 --> 00:01:51,240
+اللي هي بـ R، تمام؟ والثانية بـ R، والثالثة بـ R، والآخرة
+
+17
+00:01:51,240 --> 00:01:57,020
+واحدة اللي هي بـ R. طبعًا عددهم هذول كده؟ كم واحد؟
+
+18
+00:01:57,020 --> 00:02:04,440
+يبقى n φ(R). يبقى n من المرات. هذول عددهم كذلك n من
+
+19
+00:02:04,440 --> 00:02:08,880
+المرات. الآن في رأس النظرية قال لي φ is a
+
+20
+00:02:08,880 --> 00:02:15,680
+homomorphism. إذًا هذا الكلام بيساوي φ(R) +
+
+21
+00:02:15,680 --> 00:02:24,640
+φ(R) + ... + φ(R). هذول كذلك n من
+
+22
+00:02:24,640 --> 00:02:32,760
+المرات. يبقى كلهم زي بعض، يبقى n في عددهم، يبقى n في
+
+23
+00:02:32,760 --> 00:02:37,180
+φ(R). أظن، وهو المطلوب. انتهينا من النقطة
+
+24
+00:02:37,180 --> 00:02:43,920
+الأولى. الآن بتأجي للنقطة الثانية. φ(R<sup>n</sup>)
+
+25
+00:02:43,920 --> 00:02:54,240
+بتساوي φ(R × R × R ... كذلك عددهم n). φ
+
+26
+00:02:54,240 --> 00:02:59,940
+homomorphism، إذًا هتدخل على كل واحدة منهم. φ(R)
+
+27
+00:02:59,940 --> 00:03:07,900
+× φ(R) × φ(R) ... عددهم كم؟ n من المرات
+
+28
+00:03:07,900 --> 00:03:15,800
+ومكرر، يبقى φ(R)<sup>n</sup>، وهو المطلوب.
+
+29
+00:03:15,800 --> 00:03:25,720
+النقطة الثانية. بيقول لي φ(A) = {φ(a) |
+
+30
+00:03:25,720 --> 00:03:35,100
+كل العناصر φ(a) such that وبحيث أن a موجود
+
+31
+00:03:35,100 --> 00:03:46,230
+في الـ A is a subring of S، يبقى هذا is a subring of
+
+32
+00:03:46,230 --> 00:03:52,850
+S. طبعًا إحنا معانا من رأس النظرية φ: R → S is a
+
+33
+00:03:52,850 --> 00:03:58,110
+homomorphism، والـ A عبارة عن subring، والـ B عبارة
+
+34
+00:03:58,110 --> 00:04:03,150
+عن ideal. هي نص النظرية اللي مكتوبة معاكم من المرة
+
+35
+00:04:03,150 --> 00:04:10,320
+الماضية. الآن بدنا نثبت هذا عبارة عن subring. بنقوله
+
+36
+00:04:10,320 --> 00:04:15,540
+بسيطة خالص. يبقى النقطة الأولى من إثبات الـ subring
+
+37
+00:04:15,540 --> 00:04:24,260
+بقوله φ(A) is non-empty. ليش؟ because
+
+38
+00:04:24,260 --> 00:04:33,920
+الـ A is non-empty. اللي هي subring. طيب،
+
+39
+00:04:33,920 --> 00:04:43,590
+نقطة ثانية، بدي آخد عنصرين، وليكن x و y موجودين في φ
+
+40
+00:04:43,590 --> 00:04:53,590
+(A). يبقى ممكن يكون شكلهم هذا. يقدر يعطينا أن x
+
+41
+00:04:53,590 --> 00:05:09,960
+تساوي φ(a) و y تساوي φ(b). هذا الكلام for some a و b
+
+42
+00:05:09,960 --> 00:05:18,420
+اللي موجودة في subring A. كويس، بنشوف الفرق في
+
+43
+00:05:18,420 --> 00:05:26,260
+ما بينهما. يبقى x - y = φ(a) -
+
+44
+00:05:26,260 --> 00:05:33,120
+φ(b). هذا بده يعطينا الآن. φ homomorphism. إذًا
+
+45
+00:05:33,120 --> 00:05:42,310
+x - y = φ(a - b). ليش؟ لأن φ
+
+46
+00:05:42,310 --> 00:05:49,670
+is a homomorphism. طيب، هذا الكلام إيش بيعطينا؟
+
+47
+00:05:49,670 --> 00:05:56,230
+بيعطينا أن x - y موجودة. هذا a - b
+
+48
+00:05:56,230 --> 00:06:02,750
+وين موجود؟ في الـ subring A، تمام؟ في الـ sub
+
+49
+00:06:02,750 --> 00:06:08,800
+ring A. يبقى معنا هذا الكلام موجود في φ(A).
+
+50
+00:06:08,800 --> 00:06:12,880
+أثبتنا الـ condition التالي من الـ subring. الـ
+
+51
+00:06:12,880 --> 00:06:18,720
+condition التالي. بدي آخد عنصرين من الـ subring. بدي
+
+52
+00:06:18,720 --> 00:06:23,580
+أثبت أن حاصل ضربهما موجود داخل الـ subring اللي
+
+53
+00:06:23,580 --> 00:06:35,500
+عندنا. يبقى let x و y موجودة في φ(A). الـ x بده
+
+54
+00:06:35,500 --> 00:06:46,620
+تساوي φ(a) و الـ y بده يساوي φ(b) for some a و b
+
+55
+00:06:46,620 --> 00:06:54,920
+اللي موجودة في الـ subring A. بدي آخد حاصل
+
+56
+00:06:54,920 --> 00:07:03,520
+الضرب x في y. يبقى هذا الكلام بده يساوي φ(a) في
+
+57
+00:07:03,520 --> 00:07:10,320
+φ(b). φ homomorphism، إذًا هذا الكلام بتساوي φ
+
+58
+00:07:10,320 --> 00:07:20,360
+(ab). هذه موجودة في φ(A) ولا لأ؟ ليش؟ لأن a
+
+59
+00:07:20,360 --> 00:07:26,860
+في b موجودة في الـ subring A. يبقى هنا موجودة في
+
+60
+00:07:26,860 --> 00:07:40,530
+φ(A). يبقى إذًا، وهكذا، φ(A) is a subring of S.
+
+61
+00:07:40,530 --> 00:07:48,210
+هذا النقطة الثانية. النقطة الثالثة. النقطة
+
+62
+00:07:48,210 --> 00:07:53,050
+الثالثة بتقول لي لو كان الـ A ideal، يبقى بتبطل الـ A
+
+63
+00:07:53,050 --> 00:07:59,670
+بتصير subring. بدنا نفترضها أنها ideal، يبقى الـ A
+
+64
+00:07:59,670 --> 00:08:08,560
+ideal، تمام؟ هذه المعطيات الأولى في المثل. Ideal of A
+
+65
+00:08:08,560 --> 00:08:17,800
+وفي نفس الوقت، φ is onto. والـ φ is onto. الـ
+
+66
+00:08:17,800 --> 00:08:24,440
+φ is onto. يبقى φ(A) is an ideal. يبقى هذا
+
+67
+00:08:24,440 --> 00:08:33,880
+يريحنا. أن φ(A) is an ideal of ... اسم هذا اللي بنا
+
+68
+00:08:33,880 --> 00:08:43,760
+نثبته. الـ proof.  فَالّي باركوا يعني أن الـ A في رأس
+
+69
+00:08:43,760 --> 00:08:48,460
+النظرية، بيقول subring هنا. افترض هي إيش؟ ideal. لو
+
+70
+00:08:48,460 --> 00:08:53,820
+كانت ideal و φ كانت onto، يعني غطت جميع عناصر اسمه
+
+71
+00:08:53,820 --> 00:08:59,730
+باستثناء، أو الـ range ساوي الـ codomain اللي هو S،
+
+72
+00:08:59,730 --> 00:09:04,130
+يبقى φ(A) بداية بتفتح أنه عبارة عن إيش؟ ideal.
+
+73
+00:09:04,130 --> 00:09:11,770
+طب السؤال هو: هل φ(A) Sub-range؟
+
+74
+00:09:11,770 --> 00:09:19,130
+نعم. نقطة ثانية، إيه باجي بقول لك from part
+
+75
+00:09:19,130 --> 00:09:31,810
+two. φ(A) is a subring of S. يبقى لنا بس
+
+76
+00:09:31,810 --> 00:09:37,350
+آخر شرط من شروط الـ ideal. يبقى الـ φ(A) non-empty، و
+
+77
+00:09:37,350 --> 00:09:42,310
+الفرق بين أي عنصرين موجود فيه. لما كان الـ subring، باقي لنا
+
+78
+00:09:42,310 --> 00:09:47,910
+ناخد عنصرين من نفس الـ set. لكن هنا لأ، بدي آخد عنصر من
+
+79
+00:09:47,910 --> 00:09:53,250
+الـ set وعنصر من الـ ring الأصلية. بدي أحصل ضربهما يكون
+
+80
+00:09:53,250 --> 00:10:02,670
+موجود في φ(A). إن حدث ذلك، بقول φ(A) is an
+
+81
+00:10:02,670 --> 00:10:05,410
+ideal of S. لذلك
+
+82
+00:10:13,750 --> 00:10:22,250
+الـ x موجودة في الـ φ(A). يبقى آخد element
+
+83
+00:10:22,250 --> 00:10:26,270
+موجود في الـ set اللي عندنا، و element موجود في
+
+84
+00:10:26,270 --> 00:10:31,530
+الـ ring الأصلية. يبقى
+
+85
+00:10:31,530 --> 00:10:41,840
+إذن، الـ r موجودة في الـ R، و الـ x بده يساوي φ
+
+86
+00:10:41,840 --> 00:10:54,380
+(a) for some a اللي موجودة في A. then بدي
+
+87
+00:10:54,380 --> 00:11:03,080
+آخد الـ r x. بدي أثبت أن الـ r x هذه موجودة وين؟
+
+88
+00:11:03,240 --> 00:11:09,540
+موجودة في الـ φ(A). طب استنوا شوية، أنا ما آخد r
+
+89
+00:11:09,540 --> 00:11:14,520
+لكن لا لا لا، استنى. بدنا نأخذ. بدنا نطبق هذا
+
+90
+00:11:14,520 --> 00:11:20,120
+على الـ subring من مين؟ من الـ S. يبقى هذا يا بنات مش
+
+91
+00:11:20,120 --> 00:11:30,600
+صحيحة هذه. بدي آخد مثلًا t موجودة في S. لأن φ(A)
+
+92
+00:11:30,600 --> 00:11:35,290
+element في S، وأنا بدي أثبت أن φ(A)
+
+93
+00:11:35,290 --> 00:11:42,490
+هو ideal في من؟ في الـ S. لأن φ(A) موجودة في S. طيب،
+
+94
+00:11:42,490 --> 00:11:48,290
+كويس. الآن t موجودة في S، و الـ φ is ... أنتم، يبقى
+
+95
+00:11:48,290 --> 00:11:55,470
+إيه؟ له أصل في الـ ring R ولا لأ؟ يبقى هنا بدي أجي
+
+96
+00:11:55,470 --> 00:12:05,970
+أقول له since، بما أن، since φ is onto، و t
+
+97
+00:12:05,970 --> 00:12:14,150
+موجودة في S، there exists r موجودة في الـ R such
+
+98
+00:12:14,150 --> 00:12:23,930
+that بحيث أن t تساوي φ(r). نظرًا
+
+99
+00:12:23,930 --> 00:12:29,290
+لأن φ is onto، يبقى أي element آخذه من الـ code
+
+100
+00:12:29,290 --> 00:12:35,140
+main هنجد له أصل في الـ domain اللي هو R. t تساوي φ
+
+101
+00:12:35,140 --> 00:12:43,860
+(r). طيب أنا بدي أثبت الآن أنه t x موجودة
+
+102
+00:12:43,860 --> 00:12:50,460
+وين؟ في φ(A). صح ولا لأ؟ مش هنفضل يعني. بدي
+
+103
+00:12:50,460 --> 00:12:56,460
+أثبت φ(A) is an ideal. إذًا بدي آخد الآن t x
+
+104
+00:12:56,460 --> 00:13:05,420
+يساوي الـ t عندي بمين؟ φ(r)، والـ x عندي φ(a)
+
+105
+00:13:05,420 --> 00:13:14,840
+فيهم homomorphism، يبقى هذا الكلام φ(ra). طيب
+
+106
+00:13:14,840 --> 00:13:23,020
+السؤال هو: هل هذا الـ element موجود في A؟ اه. ليش؟ لأنه
+
+107
+00:13:23,020 --> 00:13:29,990
+افترضنا A ideal، وهذا element موجود في الـ ideal، يبقى
+
+108
+00:13:29,990 --> 00:13:34,650
+هذا element موجود في الـ ring A. يبقى حاصل ضربهما
+
+109
+00:13:34,650 --> 00:13:43,770
+يكون موجود. يبقى هذا موجود في φ(A). ليش؟ because
+
+110
+00:13:43,770 --> 00:13:55,290
+الـ a موجود في الـ A، و الـ A is an ideal. يبقى اللي
+
+111
+00:13:55,290 --> 00:14:05,160
+حصل هنا. الـ tx موجودة في φ(A).
+
+112
+00:14:05,160 --> 00:14:14,320
+بنفس الطريقة، Similarly، بنفس الطريقة، الـ xt موجودة
+
+113
+00:14:14,320 --> 00:14:21,700
+في φ(A). إذًا اتحققت شروط الـ ideal. صحيح؟ يبقى
+
+114
+00:14:21,700 --> 00:14:35,780
+بقوله Therefore، ولهذا، φ(A) is an ideal of S. هذا
+
+115
+00:14:35,780 --> 00:14:41,380
+النقطة الثالثة. النقطة الرابعة. النقطة الرابعة دي
+
+116
+00:14:41,380 --> 00:14:50,440
+بيقول لي φ<sup>-1</sup>(B). بدنا نثبت أن φ<sup>-1</sup>
+
+117
+00:14:50,440 --> 00:14:56,300
+(B)، اللي هو عبارة عن كل العناصر r الموجودة في الـ
+
+118
+00:14:56,300 --> 00:15:06,330
+ring R، بحكي أن φ(r) موجودة في B. إيش بنا نثبته؟
+
+119
+00:15:06,330 --> 00:15:14,410
+هذا. نثبت هذه. φ<sup>-1</sup>(B) is an ideal is an ideal
+
+120
+00:15:14,410 --> 00:15:20,430
+of R. خلينا
+
+121
+00:15:20,430 --> 00:15:30,430
+نلقي هنا. إحنا بنقول: φ من الـ R إلى S، هذا
+
+122
+00:15:30,430 --> 00:15:35,910
+معروف homomorphism. مظبوط؟ طب الـ φ<sup>-1</sup> بدي يكون
+
+123
+00:15:35,910 --> 00:15:40,490
+من وين؟ من S إلى R. من S إلى R. يبقى لو كان
+
+124
+00:15:40,490 --> 00:15:45,070
+هذا one to one and onto، يبقى φ<sup>-1</sup> exist
+
+125
+00:15:45,070 --> 00:15:51,990
+وبدي يكون من الـ S لغاية R. ممتاز جدًا. طيب هو قال لي
+
+126
+00:15:51,990 --> 00:15:59,440
+أصلًا الـ B ideal في مين؟ في S. طلع نص النظرية من
+
+127
+00:15:59,440 --> 00:16:06,480
+البداية. جالي A subring من R، و الـ B ideal من S، و
+
+128
+00:16:06,480 --> 00:16:15,400
+عندنا هنا الـ B ideal of S. جالي أثبت أن φ
+
+129
+00:16:15,400 --> 00:16:20,880
+<sup>-1</sup>(B) موجود. وأن في S يبقى φ<sup>-1</sup> لما
+
+130
+00:16:20,880 --> 00:16:26,500
+تأثر على الـ ideal بترجع لمين؟ ترجع لـ A. يبقى بدنا
+
+131
+00:16:26,500 --> 00:16:32,460
+نثبت أن φ<sup>-1</sup> لما يأثر على B بيعطيني عناصر
+
+132
+00:16:32,460 --> 00:16:38,980
+من الـ ring R، من هم اللي هم صورهم موجودة في الـ
+
+133
+00:16:38,980 --> 00:16:43,340
+ideal B. إيش بدنا نثبت الـ φ<sup>-1</sup>(B)؟ بدنا
+
+134
+00:16:43,340 --> 00:16:49,340
+نثبت أنه ideal. يعني بدنا نثبت الشروط الثلاثة اللي
+
+135
+00:16:49,340 --> 00:16:54,620
+أثبتناهم هنا. واحد، اثنين، ثلاثة. هنا أثبتنا أن φ
+
+136
+00:16:54,620 --> 00:17:01,960
+(A) subring، وبعد هيك حولنا لمين؟ للـ ideal. طيب الآن
+
+137
+00:17:01,960 --> 00:17:07,560
+بتدخل الشرط الأول من شروط الـ ideal. بقول لهم φ
+
+138
+00:17:07,560 --> 00:17:15,080
+<sup>-1</sup>(B) is non-empty. معقول؟ إيش السبب؟
+
+139
+00:17:15,080 --> 00:17:19,480
+because الـ B is non-empty.
+
+140
+00:17:22,200 --> 00:17:28,660
+لأن الـ B عبارة عن Ideal، والـ Ideal non-empty. طيب،
+
+141
+00:17:28,660 --> 00:17:33,060
+النقطة الثانية، بدنا نأخذ عنصرين في الـ φ
+
+142
+00:17:33,060 --> 00:17:39,720
+<sup>-1</sup>(B). يبقى بالذات يقول له: افترض الـ x والـ y
+
+143
+00:17:39,720 --> 00:17:45,540
+موجودة في الـ φ<sup>-1</sup>(B). بدي أثبت أن الفرق
+
+144
+00:17:45,540 --> 00:17:50,480
+فيما بينهما موجود وين؟ في الـ φ<sup>-1</sup>(B). إن
+
+145
+00:17:50,480 --> 00:17:54,520
+حدث ذلك، بكون انتهيت من الشرط التالي. وبيقى عليه
+
+146
+00:17:54,520 --> 00:18:00,940
+مايعني الشرط التالي. كون هذول موجودات هنا، معناه هذا
+
+147
+00:18:00,940 --> 00:18:10,320
+الكلام أن x = φ<sup>-1</sup>(عنصر من عناصر الـ ideal
+
+148
+00:18:10,320 --> 00:18:17,580
+B). صحيح ولا لأ؟ x موجودة هنا، إيش ممكن يكون شكلها؟
+
+149
+00:18:17,580 --> 00:18:26,230
+يبقى x = φ<sup>-1</sup>(b<sub>1</sub>)، و الـ y بيكون φ<sup>-1</sup>
+
+150
+00:18:26,230 --> 00:18:38,690
+(b<sub>2</sub>) for some b<sub>1</sub> و b<sub>2</sub> اللي موجودة في B. طيب، الجميل
+
+151
+00:18:38,690 --> 00:18:44,830
+هذا بيعطي لبنات مين؟ لو أثرت على الطرفين بـ φ،
+
+152
+00:18:44,830 --> 00:18:56,820
+بيصير φ(x) بيكون بيساوي الـ b<sub>1</sub>، و φ(y) بده
+
+153
+00:18:56,820 --> 00:19:05,860
+يساوي b<sub>2</sub>. فبكيس الآن، لو جيت جمعت الاتنين هدول مع
+
+154
+00:19:05,860 --> 00:19:11,740
+بعض، والله إحنا بدنا نطرح! لا نطرح ولا يهمك، يبقى هذا
+
+155
+00:19:11,740 --> 00:19:19,930
+الكلام بده يعطينا φ(x) - φ(y) = b<sub>1</sub>
+
+156
+00:19:19,930 --> 00:19:26,190
+- b<sub>2</sub>. لكن φ عبارة عن إيه يا عزيزي؟ homomorphism.
+
+157
+00:19:26,190 --> 00:19:33,890
+نظرًا لأن homomorphism، هذا بده يعطينا أن φ(x) -
+
+158
+00:19:33,890 --> 00:19:42,930
+y بده يساوي b<sub>1</sub> - b<sub>2</sub>. بده يؤثر بـ φ<sup>-1</sup> على
+
+159
+00:19:42,930 --> 00:19:49,910
+الطرفين. لو أثرنا بـ φ<sup>-1</sup> على الطرفين، هذا بيعطينا
+
+160
+00:19:49,910 --> 00:19:59,050
+أن x - y = φ<sup>-1</sup>(b<sub>1</sub> - b<sub>2</sub>).
+
+161
+00:19:59,050 --> 00:20:05,650
+هذا b<sub>1</sub> - b<sub>2</sub> موجود وين؟ في B اللي هو
+
+162
+00:20:05,650 --> 00:20:11,210
+ideal، تمام؟ من شروط الـ ideal، لو أخدت عنصرين فيه
+
+163
+00:20:11,210 --> 00:20:15,660
+وطرحتم من بعض يكون موجود وين؟ في نفس الـ ideal. إذًا هذا
+
+164
+00:20:15,660 --> 00:20:23,940
+موجود في الـ ideal B. يبقى هذا بده يعطينا أن
+
+165
+00:20:23,940 --> 00:20:31,4
+
+223
+00:28:12,940 --> 00:28:20,340
+five is unto أن حدث ذلك، و الـ five is one هذا بده
+
+224
+00:28:20,340 --> 00:28:34,280
+يعطينا أن الـ five of one is the unity of this. يبقى
+
+225
+00:28:34,280 --> 00:28:42,660
+هذا هو الـ unity of this. طيب،
+
+226
+00:28:42,660 --> 00:28:50,120
+يعطينا ثلاث معقيات، ومطلوب مين؟ مطلوب واحد، بس يبقى
+
+227
+00:28:50,120 --> 00:28:55,920
+يعطيني الـ R هيظهر على الـ ring with unity. عندنا الـ
+
+228
+00:28:55,920 --> 00:29:05,720
+S لا تساوي Zero، يعني الـ S لا تساوي Zero as a set
+
+229
+00:29:05,720 --> 00:29:10,420
+ما تساويش الست اللي هي Zero، ومعطينا المعطيات
+
+230
+00:29:10,420 --> 00:29:16,040
+الثالثة أن Phi is onto، نظرة لهذه المعطيات التي
+
+231
+00:29:16,040 --> 00:29:20,760
+تُلخص بأن Phi of one هو الـ unity تبع من؟ تبع
+
+232
+00:29:20,760 --> 00:29:27,010
+ring S. نقولها بسيطة إذا جئنا أثبتنا أن five of one
+
+233
+00:29:27,010 --> 00:29:32,610
+ضرب أي element من S من اليمين ومن الشمال بيُعطيني الـ
+
+234
+00:29:32,610 --> 00:29:36,350
+element اللي فيه S، بيصير five of one هو الـ unity.
+
+235
+00:29:39,550 --> 00:29:49,330
+صح؟ طيب، الآن بدي أقوله only the small s موجودة
+
+236
+00:29:49,330 --> 00:29:57,520
+في capital S. تمام؟ طيب الـ Phi قال لي إيش؟ قال لي on
+
+237
+00:29:57,520 --> 00:30:05,860
+to. إيش يعني on to؟ يعني كل عنصر في S له أصل وين؟
+
+238
+00:30:05,860 --> 00:30:16,500
+في R، صح ولا لأ؟ يبقى then there exist R موجود في R
+
+239
+00:30:16,500 --> 00:30:25,030
+such that وبحيث أن الـ S هذه، الـ S small اللي عندها
+
+240
+00:30:25,030 --> 00:30:34,770
+بدها تساوي Phi of R. طيب خلينا نيجي ناخد الآن Phi of
+
+241
+00:30:34,770 --> 00:30:45,030
+1 مضروبة في S. Phi of 1 عنصر وين؟ في S؟ إذا بدي
+
+242
+00:30:45,030 --> 00:30:51,050
+أضربه في مين؟ في عنصر ثاني من S. هذا الكلام يساوي
+
+243
+00:30:51,050 --> 00:30:59,310
+فاي of one في الـ S. سوّيناها، صارت أن فاي of R، يبقى
+
+244
+00:30:59,310 --> 00:31:07,390
+فاي of R، يبقى في homomorphism، يبقى في of واحد مضروب
+
+245
+00:31:07,390 --> 00:31:14,610
+من الـ R، الـ unity من R، لما أضربه في عنصر من
+
+246
+00:31:14,610 --> 00:31:20,400
+عناصر R بيعطيني نفس العنصر. يبقى هذا بيعطيني Phi
+
+247
+00:31:20,400 --> 00:31:26,960
+of R. Phi of R هي مين؟ هي S. يبقى لما ضرب Phi of 1
+
+248
+00:31:26,960 --> 00:31:31,340
+في S طلع الـ S. تشوف الشجرة الثانية أو الاتجاه
+
+249
+00:31:31,340 --> 00:31:41,780
+الآخر. لو أخدت S، S small مضروبة في مين؟ في Phi، Phi
+
+250
+00:31:41,780 --> 00:31:50,610
+of 1، أشوف إيش تساوي. الـ S هي Phi of 1 of R مضروبة
+
+251
+00:31:50,610 --> 00:31:57,310
+في Phi of 1. الـ Phi عبارة عن homomorphism، إذًا هذه
+
+252
+00:31:57,310 --> 00:32:03,190
+Phi of R مضروبة في 1. الـ R والـ 1 elements من
+
+253
+00:32:03,190 --> 00:32:10,230
+عناصر الـ ring. إذًا هذا يعتبر Phi of R، لأن الـ unity
+
+254
+00:32:10,230 --> 00:32:15,050
+تبع الـ ring اللي هو واحد. طيب Phi of R هو عبارة عن
+
+255
+00:32:15,050 --> 00:32:21,350
+مين؟ عن الـ S. من هذا الكلام إيش ما أقدر استنتج أنه
+
+256
+00:32:21,350 --> 00:32:26,510
+five one of S يساوي S of five one يساوي الـ S. إيش
+
+257
+00:32:26,510 --> 00:32:32,350
+معنى هذا الكلام؟ أن five of one هو الـ unity تبع الـ
+
+258
+00:32:32,350 --> 00:32:42,390
+S. هذا بده يعطينا أن five of one is the unity of S.
+
+259
+00:32:42,390 --> 00:32:45,350
+تمام.
+
+260
+00:32:45,800 --> 00:32:50,960
+هذه النقطة قد إيش؟ السادسة. النقطة السابعة، النقطة
+
+261
+00:32:50,960 --> 00:32:56,720
+السابعة بتقول لي Phi is an isomorphism. Phi is
+
+262
+00:32:56,720 --> 00:33:06,440
+an isomorphism if and only if الـ Phi is on to، and
+
+263
+00:33:06,440 --> 00:33:12,960
+الكرنل للفاي هو
+
+264
+00:33:12,960 --> 00:33:21,710
+الست المكوّنة فقط من العنصر الصفري. تمام؟ ما فيش غيره.
+
+265
+00:33:21,710 --> 00:33:26,390
+طيب if and only if، معناه القول بده يصير وين؟ في
+
+266
+00:33:26,390 --> 00:33:35,070
+الاتجاهين. يبقى بالبداية أقول له:  Assume، افترض
+
+267
+00:33:35,070 --> 00:33:44,930
+that الـ Phi is an isomorphism. إيش يعني؟ يعني الـ
+
+268
+00:33:44,930 --> 00:33:50,570
+Phi homomorphism، Phi is one to one، Phi is one...
+
+269
+00:33:50,570 --> 00:33:57,850
+مظبوط؟ هذا معناه، يبقى هذا معناه أن Phi is
+
+270
+00:33:57,850 --> 00:34:10,350
+a homomorphism and one to one and... and onto. تمام؟
+
+271
+00:34:10,350 --> 00:34:15,110
+طيب إذا أثبتنا هذا المطلوب ولا لا؟ طيب بس مثل
+
+272
+00:34:15,110 --> 00:34:20,370
+ما طول ما نثبت له مين؟ أن الكيرنل لـ Phi يساوي الست التي
+
+273
+00:34:20,370 --> 00:34:28,010
+لا تحتوي إلا على الصفر. طيب سؤال: إذا أثبتت أن هذه
+
+274
+00:34:28,010 --> 00:34:33,310
+subset من هذه، وهذه subset من هذه، مش بيكون المطلوب
+
+275
+00:34:33,310 --> 00:34:42,190
+تم؟ طب السؤال هو: هل الـ zero subset من الكيرنل لـ Phi؟
+
+276
+00:34:43,280 --> 00:34:52,860
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى هذا
+
+277
+00:34:52,860 --> 00:34:57,660
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى هذا
+
+278
+00:34:57,660 --> 00:34:58,160
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى هذا
+
+279
+00:34:58,160 --> 00:34:59,360
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى هذا
+
+280
+00:34:59,360 --> 00:35:00,460
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى هذا
+
+281
+00:35:00,460 --> 00:35:03,260
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى هذا
+
+282
+00:35:03,260 --> 00:35:06,560
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى هذا
+
+283
+00:35:06,560 --> 00:35:10,140
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى هذا
+
+284
+00:35:10,140 --> 00:35:13,820
+صحيح، لأن فاي أوف زيرو موجود في الـ kernel، يبقى بده
+
+285
+00:35:13,820 --> 00:35:19,060
+يساوي Zero. يبقى هذا بدي اعتبره النقطة رقم واحد.
+
+286
+00:35:19,060 --> 00:35:25,480
+بدي للنقطة رقم اثنين، بدي أقول: افترض أن X موجود
+
+287
+00:35:25,480 --> 00:35:32,200
+في kernel الفاي. إذا قدرت أثبت أن X موجود هنا، بيكون
+
+288
+00:35:32,200 --> 00:35:37,200
+تم المطلوب، يكون خلصنا من الشغل هذا. يبقى then
+
+289
+00:35:37,200 --> 00:35:49,770
+الفاي of X بده يساوي Zero. في  
+
+290
+00:35:49,770 --> 00:35:53,530
+Phi of X بده يساوي Zero، لأنها موجودة في الـ kernel من
+
+291
+00:35:53,530 --> 00:35:57,250
+تعريف الـ kernel. كل العناصر اللي موجودة في الـ ring
+
+292
+00:35:57,250 --> 00:36:01,770
+اللي صارت صورتها Zero. مظبوط؟ إذا أنا استخدمت تعريف
+
+293
+00:36:01,770 --> 00:36:08,390
+على كأنه، يبقى... يبقى أنا استخدمت التعريف تبع الـ
+
+294
+00:36:08,390 --> 00:36:14,790
+kernel. كيرنل الـ Phi. كل العناصر اللي في R بحيث Phi
+
+295
+00:36:14,790 --> 00:36:19,410
+of R بده يساوي Zero. يبقى أنا أخدت X موجودة في الكيرنل
+
+296
+00:36:19,410 --> 00:36:23,310
+اللي هي، يبقى صورة هذا الـ X بده تساوي مين؟ بده تساوي
+
+297
+00:36:23,310 --> 00:36:32,150
+Zero. طيب أليس هذا هو Phi of Zero؟ صح؟ طيب يبقى
+
+298
+00:36:32,150 --> 00:36:38,360
+الصورة عند مين؟ صورتين متساويتين. Phi of X بده يساوي
+
+299
+00:36:38,360 --> 00:36:44,840
+فاي of زيرو، والفاي هذه مالها؟ one to one. يبقى إذا
+
+300
+00:36:44,840 --> 00:36:49,420
+كانت الـ function one to one، ولقيت صورتين متساويتين،
+
+301
+00:36:49,420 --> 00:36:56,100
+بده يكون الأصل متساوي. يبقى هذا معناه أن الـ X بده
+
+302
+00:36:56,100 --> 00:37:05,120
+يساوي اللي هو الـ zero، because Phi is one to one.
+
+303
+00:37:05,730 --> 00:37:12,910
+مدام الـ X بدها تساوي Zero، معناته أن الـ X موجودة في
+
+304
+00:37:12,910 --> 00:37:18,490
+الست التي لا يوجد فيها إلا العنصر الصفري. طب ماشي.
+
+305
+00:37:18,490 --> 00:37:25,410
+اللي عملتها؟ أخدت X موجودة في الـ kernel. لجأت الـ X
+
+306
+00:37:25,410 --> 00:37:31,410
+موجودة وين؟ في الـ Zero. يبقى بناء عليه، So الـ
+
+307
+00:37:31,410 --> 00:37:37,730
+kernel للـ Phi صار ست من مين؟ من الست اللي عندها هذه
+
+308
+00:37:37,730 --> 00:37:43,790
+و هذه العلاقة رقم اثنين. إذا بروح أقول له: if from
+
+309
+00:37:43,790 --> 00:37:56,490
+واحد and اثنين، we have أن الكيرنل للـ Phi بده
+
+310
+00:37:56,490 --> 00:38:02,530
+يساوي فقط الست المكونة من element واحد، وهذا الـ
+
+311
+00:38:02,530 --> 00:38:08,610
+element هو العنصر الصفري. خلصنا النقطة هذه؟ خلاص؟
+
+312
+00:38:08,610 --> 00:38:10,810
+خلصنا نصها.
+
+313
+00:38:13,210 --> 00:38:20,890
+ليش؟ بسبب وجود الـ if and only if. يبقى بسبب وجود الـ
+
+314
+00:38:20,890 --> 00:38:26,770
+if and only if، يبقى بدنا نروح نمشي الاتجاه الثاني.
+
+315
+00:38:31,690 --> 00:38:34,630
+يبقى بدنا نروح أقول لك: Converse.
+
+316
+00:38:39,350 --> 00:38:44,110
+هي اللي عندها Phi is an isomorphism. عشان لو  
+
+317
+00:38:44,110 --> 00:38:49,810
+Phi is onto، يبقى أنا بدي افترض أن Phi is onto، و الـ
+
+318
+00:38:49,810 --> 00:38:54,350
+kernel اللي بده يساوي zero، وبده أثبت أن Phi هذه
+
+319
+00:38:54,350 --> 00:38:59,970
+عبارة عن isomorphism. يبقى بدي آجي وأقول له: assume
+
+320
+00:38:59,970 --> 00:39:15,440
+that فاي من R إلى S is... أنتم ترون، هؤلاء ما طلبوها والـ
+
+321
+00:39:15,440 --> 00:39:25,000
+kernel يساوي زيرو، و الـ kernel للفاي بده يساوي ست
+
+322
+00:39:25,000 --> 00:39:33,260
+زيرو. want to show that
+
+323
+00:39:33,260 --> 00:39:42,720
+Phi is an isomorphism. مش هلا أثبت أنه Phi
+
+324
+00:39:42,720 --> 00:39:48,000
+Isomorphism، بالذات بالتلات شغلات: أنه homomorphism، و
+
+325
+00:39:48,000 --> 00:39:53,860
+one to one، وأنتم... طب احنا فرضنا أنه أنتم ومرسى
+
+326
+00:39:53,860 --> 00:40:01,420
+المثل isomorphism، ضال إيش؟ one to one. مظبوط؟ يبقى
+
+327
+00:40:01,420 --> 00:40:14,010
+بعدين بقول: since Phi من R إلى S، من R إلى S، is
+
+328
+00:40:14,010 --> 00:40:25,610
+homomorphic، and الـ Phi is onto. أحنا فرضنا Assume
+
+329
+00:40:25,610 --> 00:40:31,230
+that هي onto، ومن رأس المثلث فرضنا أنه homomorphic.
+
+330
+00:40:31,230 --> 00:40:36,640
+إيش ضال علينا؟ بس أثبت أنه one to one. إذا قدرت أثبت
+
+331
+00:40:36,640 --> 00:40:41,400
+أنه one to one، بكون خلصنا، بيصير الفاي عبارة عن إيش؟
+
+332
+00:40:41,400 --> 00:40:48,000
+isomorphism. يبقى بعدين بقوله هنا حكاية الـ one to
+
+333
+00:40:48,000 --> 00:40:56,900
+one، بدنا نستفيد من الشغل أن الكيرنل يساوي zero. يبقى
+
+334
+00:40:56,900 --> 00:41:05,660
+بعدين بقوله: let x و y موجودة في الكيرنل للـ Phi.
+
+335
+00:41:09,360 --> 00:41:18,280
+Then الـ Phi of X بده يساوي Zero، and الـ Phi of Y
+
+336
+00:41:18,280 --> 00:41:19,640
+بده يساوي Zero.
+
+337
+00:41:22,740 --> 00:41:29,680
+صحيح؟ يبقى هذا إيش بيعطينا يا بنات؟ أن الـ Phi of X
+
+338
+00:41:29,680 --> 00:41:36,560
+بده يساوي الـ Phi of Y. صحيح ولا لا؟ لكل الـ X والـ Y
+
+339
+00:41:36,560 --> 00:41:40,980
+اللي موجودة وين؟ اللي موجودة في الـ kernel. تمام؟
+
+340
+00:41:40,980 --> 00:41:49,060
+يبقى أخدت صورتين متساويتين. إذا قدرت أثبت أنه الأصل
+
+341
+00:41:49,060 --> 00:41:53,420
+تبعهم متساوي، بيصير إنت و أنا بكون خلصنا من الشغل
+
+342
+00:41:53,420 --> 00:42:00,280
+مظبوط؟ طيب احنا عندنا Phi of X يساوي Phi of Y. يبقى
+
+343
+00:42:00,280 --> 00:42:07,260
+Phi of X ناقص Phi of Y بده يساوي صفر. Phi
+
+344
+00:42:07,260 --> 00:42:14,540
+homomorphism، يبقى هذا بده يعطينا أن Phi of X ناقص
+
+345
+00:42:14,540 --> 00:42:22,040
+الـ Y بده يساوي Zero. طيب هذا معناه أن الـ X ناقص الـ Y
+
+346
+00:42:22,040 --> 00:42:32,240
+موجودة في kernel لـ Phi. صح؟ طب قد إيش kernel لـ Phi؟ هو Zero.
+
+347
+00:42:32,240 --> 00:42:37,440
+صحيح ولا لا؟ احنا فرضناها هي، يبقى هذا كده بده
+
+348
+00:42:37,440 --> 00:42:44,000
+يساوي؟ Zero. هذا معناته أن الـ X ناقص الـ Y بده يساوي
+
+349
+00:42:44,000 --> 00:42:50,920
+Zero. هذا معناته أن الـ X بده يساوي الـ Y. يبقى So
+
+350
+00:42:50,920 --> 00:42:59,600
+الـ Phi is one to one. Thus، وهكذا الـ Phi is
+
+351
+00:43:01,640 --> 00:43:07,380
+an isomorphism. ضالة النقطة الأخيرة. النقطة الأخيرة
+
+352
+00:43:07,380 --> 00:43:15,260
+بتقول ما يأتي: لو كانت الـ Phi isomorphism، then الـ Phi
+
+353
+00:43:15,260 --> 00:43:23,760
+inverse is an isomorphism. if الـ Phi is an isomorphism،
+
+354
+00:43:23,760 --> 00:43:30,120
+then الـ Phi inverse is an isomorphism.
+
+355
+00:43:31,020 --> 00:43:34,760
+طبعًا هو كاتب لك onto،  onto، ما هو الـ
+
+356
+00:43:34,760 --> 00:43:40,220
+isomorphism تعني one to one and onto. يبقى كاتبها
+
+357
+00:43:40,220 --> 00:43:45,740
+و الله ما كاتبهاش. سَيّان، تفرّج عندنا ليش؟ لأن الـ
+
+358
+00:43:45,740 --> 00:43:52,600
+isomorphism في حد ذاته هو homomorphism وهو one to
+
+359
+00:43:52,600 --> 00:43:59,510
+one and onto في نفس الوقت. طيب يبقى أنا بدي افترض
+
+360
+00:43:59,510 --> 00:44:07,690
+أن الـ Phi هذا isomorphism.  Assume
+
+361
+00:44:07,690 --> 00:44:20,390
+that أن الـ Phi is an isomorphism. طيب
+
+362
+00:44:20,390 --> 00:44:26,320
+يعني الـ Phi is one to one and onto. صح؟ يبقى هذا بده
+
+363
+00:44:26,320 --> 00:44:34,540
+يعطينا Phi is one to one and onto. نرجع لمبادئ
+
+364
+00:44:34,540 --> 00:44:39,560
+الرياضية، principle of mathematics. تمام؟ بجرأة نقول
+
+365
+00:44:39,560 --> 00:44:44,420
+و الله ده الـ function one to one and onto، يبقى الـ
+
+366
+00:44:44,420 --> 00:44:49,180
+inverse exist، وفي نفس الوقت one to one and onto،
+
+367
+00:44:49,180 --> 00:44:54,790
+وفي كل کلاس بيه، في أول section قلنا الـ existence
+
+368
+00:44:54,790 --> 00:45:00,150
+للمعكوس أن تكون الدالة one to one. صح ولا لأ؟ هذا
+
+369
+00:45:00,150 --> 00:45:05,330
+شرط وجود المعكوس. مدام الـ Phi one to one and onto،
+
+370
+00:45:05,330 --> 00:45:13,590
+هذا بده يُعطينا أن الـ Phi inverse exist، and الـ Phi
+
+371
+00:45:13,590 --> 00:45:22,010
+inverse is one to one and onto. إيش ضال علينا؟ نثبت
+
+372
+00:45:22,010 --> 00:45:32,930
+أنه homomorphism. يبقى it remains that، ضال علينا
+
+373
+00:45:32,930 --> 00:45:42,030
+نثبت أن الـ Phi inverse is a homomorphism. why؟
+
+374
+00:45:42,030 --> 00:45:46,110
+يبقى بده أروح آخذ Phi inverse، بده يكون من وين لوين؟
+
+375
+00:45:46,110 --> 00:45:57,310
+من S لـ R، من S إلى R، يعني من R إلى S، يبقى Phi inverse
+
+376
+00:45:57,310 --> 00:46:06,530
+من S إلى R. يبقى بدي أقول له: let S واحد و S
+
+377
+00:46:06,530 --> 00:46:14,290
+اثنين موجودة في S. طيب هنا عندنا الـ Phi one to one
+
+378
+00:46:14,290 --> 00:46:20,630
+and onto، يبقى الـ S واحد والـ S اثنين أصلهما وين؟ في R.
+
+379
+00:46:21,350 --> 00:46:30,810
+يبقى then الـ S واحد بده يساوي اللي هو Phi of R
+
+380
+00:46:30,810 --> 00:46:40,670
+واحد، and S اثنين بده يساوي Phi of R اثنين. كويس.
+
+381
+00:46:40,670 --> 00:46:48,470
+إذا لو جيت أخدت S واحد زائد S اثنين، يبقى بده يساوي
+
+382
+00:46:48,470 --> 00:46:57,040
+Phi of R واحد زائد Phi of R اثنين. هذا هو مورفزيوم، يبقى
+
+383
+00:46:57,040 --> 00:47:05,220
+Phi of R واحد زائد R اثنين. احنا بدنا الـ Phi inverse، يبقى
+
+384
+00:47:05,220 --> 00:47:11,140
+بروح بقوله: الـ Phi inverse لما يأثر على مجموعة الـ
+
+385
+00:47:11,140 --> 00:47:17,460
+two elements اللي موجودات في S، بده يساوي الـ Phi
+
+386
+00:47:17,460 --> 00:47:24,880
+inverse للـ Phi of R واحد زائد R اثنين. الـ function ومعكوسها
+
+387
+00:47:24,880 --> 00:47:30,800
+بتلغي بعضها، لما كل عنصر هذا في domainها. يبقى الـ R واحد
+
+388
+00:47:30,800 --> 00:47:36,320
+زائد
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9b383c585f084c1afb67f388e166f043b2b4161b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_postprocess.srt
@@ -0,0 +1,1632 @@
+1
+00:00:20,670 --> 00:00:26,050
+بسم الله الرحمن الرحيم عوضنا على بدأ احنا بدأنا في
+
+2
+00:00:26,050 --> 00:00:30,790
+ring homomorphism المرة الماضية و كتبنا نص نظرية
+
+3
+00:00:30,790 --> 00:00:35,710
+طبعا الكتاب مابرهنشيشي و قال زي تبعت ال group و
+
+4
+00:00:35,710 --> 00:00:39,670
+احنا مش هنقول زي مجلة لأ بدنا نروح نبرهن هذه
+
+5
+00:00:39,670 --> 00:00:45,590
+النظرية ثمان نقاط هذه النظرية النقطة الأولى بقول
+
+6
+00:00:45,590 --> 00:00:51,620
+لو كان ال in is a positive integerوالـ R موجود في
+
+7
+00:00:51,620 --> 00:00:58,420
+R بدنا نثبت انه الـ Phi in R بيسوي N في Phi of R
+
+8
+00:00:58,420 --> 00:01:03,740
+وكذلك نثبت انه Phi of R to the power N بيسوي Phi
+
+9
+00:01:03,740 --> 00:01:08,400
+of R كلها to the power N يعني بقى ال proof التاني
+
+10
+00:01:08,400 --> 00:01:14,700
+بدي أبدأ بالنقطة الأولى Phi of الـ N في R هذه بقدر
+
+11
+00:01:14,700 --> 00:01:19,810
+أكتبها للشكل تاني Phi ofالان يا بنات واحد وارتوبها
+
+12
+00:01:19,810 --> 00:01:24,510
+واحد زائد واحد زائد واحد الى اخرى يبقى واحد زائد
+
+13
+00:01:24,510 --> 00:01:31,010
+واحد زائد زائد واحد كل هذا في R اللي برا اللي
+
+14
+00:01:31,010 --> 00:01:37,490
+عندنا هنا تمام هذا الكلام يساوي من حسب قانون
+
+15
+00:01:37,490 --> 00:01:42,690
+التوزيع ال distributive law هذه بيصير واحد في R
+
+16
+00:01:42,690 --> 00:01:51,240
+اللي هي ب R تماموالثانية بـR والثالثة بـR والاخر
+
+17
+00:01:51,240 --> 00:01:57,020
+واحدة اللي هي بـA. طبعا عددهم هذول كده؟ كم واحد؟
+
+18
+00:01:57,020 --> 00:02:04,440
+يبقى N Phi. يبقى N من المرات. هذول عددهم كذلك N من
+
+19
+00:02:04,440 --> 00:02:08,880
+المرات. الآن في راسي النظرية قال لي Phi is a
+
+20
+00:02:08,880 --> 00:02:15,680
+homomorphism. إذاً هذا الكلام بيساوي Phi of R.زائد
+
+21
+00:02:15,680 --> 00:02:24,640
+Phi of R زائد زائد Phi of R هذول كذلك M times M من
+
+22
+00:02:24,640 --> 00:02:32,760
+المرات يبقى كلهم زي بعض يبقى M في عددهم يبقى M في
+
+23
+00:02:32,760 --> 00:02:37,180
+Phi of R أظن و هو المطلوب انتهينا من النقطة
+
+24
+00:02:37,180 --> 00:02:43,920
+الأولى. الآن بتاجي للنقطة ثانية Phi of R to the
+
+25
+00:02:43,920 --> 00:02:54,240
+power Mبتساوي Phi of R في R في R كذلك عددهم M Phi
+
+26
+00:02:54,240 --> 00:02:59,940
+homomorphism إذا هتدخل على كل واحدة منهم Phi of R
+
+27
+00:02:59,940 --> 00:03:07,900
+في Phi of R في Phi of R عددهم كم؟ M من المرات
+
+28
+00:03:07,900 --> 00:03:15,800
+ومكرر يبقى Phi of R كله to the power Mوهو المطلوب
+
+29
+00:03:15,800 --> 00:03:25,720
+النقطة الثانية بيقول لي Phi of A Phi of A اللي هو
+
+30
+00:03:25,720 --> 00:03:35,100
+كل العناصر Phi of A such that وبحيث ان ال A موجود
+
+31
+00:03:35,100 --> 00:03:46,230
+في ال A is a subring of Sيبقى هذا is a subring of
+
+32
+00:03:46,230 --> 00:03:52,850
+S طبعا احنا معانا من رأس النظرية Phi من R إلى S is
+
+33
+00:03:52,850 --> 00:03:58,110
+homomorphism و ال A عبارة عن subring و ال B عبارة
+
+34
+00:03:58,110 --> 00:04:03,150
+عن ideal هي كنص النظرية اللي مكتوب معاكم من المرة
+
+35
+00:04:03,150 --> 00:04:10,320
+الماضية الآن بدنا نثبت هذا عبارة عن subringبنقوله
+
+36
+00:04:10,320 --> 00:04:15,540
+بسيطة خالص يبقى النقطة الأولى من إثبات ال subring
+
+37
+00:04:15,540 --> 00:04:24,260
+بقوله Phi of A is non-empty non-empty ليش؟ because
+
+38
+00:04:24,260 --> 00:04:33,920
+ال A is non-empty is non-empty اللي هي subring طيب
+
+39
+00:04:33,920 --> 00:04:43,590
+نقطة ثانية بدي أخد عنصرينوليكن X وY موجود في Phi
+
+40
+00:04:43,590 --> 00:04:53,590
+of A يبقى ممكن يكون شكلهم هذا يقدر يعطينا ان X
+
+41
+00:04:53,590 --> 00:05:09,960
+تساوي Phi of A وY تساوي Phi of B هذا الكلام forSum
+
+42
+00:05:09,960 --> 00:05:18,420
+a وb اللى موجودة فى subring a كويس، بتشوف الفرق فى
+
+43
+00:05:18,420 --> 00:05:26,260
+ما بينهما يبجى ال X ناقص ال Y لسبب Phi of a ناقص
+
+44
+00:05:26,260 --> 00:05:33,120
+Phi of b هذا بده يعطينا الان Phi homomorphism إذا
+
+45
+00:05:33,120 --> 00:05:42,310
+ال X ناقص ال Yيساوي Phi of A ناقص B، ليش؟ لأن Phi
+
+46
+00:05:42,310 --> 00:05:49,670
+is a homomorphism طيب، هذا الكلام إيش بيعطينا؟
+
+47
+00:05:49,670 --> 00:05:56,230
+بيعطينا إن ال X ناقص ال Y موجودة هذا ال A ناقص ال
+
+48
+00:05:56,230 --> 00:06:02,750
+B وين موجود؟ في ال sub ring A، تمام؟ في ال sub
+
+49
+00:06:02,750 --> 00:06:08,800
+ring Aيبقى معنا هذا الكلام موجود في Phi of A
+
+50
+00:06:08,800 --> 00:06:12,880
+أثبتنا ال condition التالي من ال sub ring ال
+
+51
+00:06:12,880 --> 00:06:18,720
+condition التالي بدي أخد عنصرين من ال sub ring بدي
+
+52
+00:06:18,720 --> 00:06:23,580
+أثبت أن حاصل ضربهما موجود داخل ال sub ring اللي
+
+53
+00:06:23,580 --> 00:06:35,500
+عندنا يبقى let X وY موجودة في Phi of Aالـ X بده
+
+54
+00:06:35,500 --> 00:06:46,620
+تساوي في of A و ال Y بده يساوي في of B for some A
+
+55
+00:06:46,620 --> 00:06:54,920
+و B اللي موجودة في ال sub ring A بده أخد حاصل
+
+56
+00:06:54,920 --> 00:07:03,520
+الضرب X في Y يبقى هذا الكلام بده يساوي في of Aفي
+
+57
+00:07:03,520 --> 00:07:10,320
+Phi of B Phi homomorphism إذا هذا الكلام بتسوي Phi
+
+58
+00:07:10,320 --> 00:07:20,360
+of AB هذه موجودة في Phi of A ولا لا؟ ليش؟ لإن ال A
+
+59
+00:07:20,360 --> 00:07:26,860
+في B موجودة في ال sub ring A يبقى هنا موجودة في
+
+60
+00:07:26,860 --> 00:07:40,530
+Phi A يبقى ضص وهكذا ال Phiof A is a subring of S
+
+61
+00:07:40,530 --> 00:07:48,210
+هذا النقطة الثانية النقطة التالتة النقطة
+
+62
+00:07:48,210 --> 00:07:53,050
+التالتة بتقولي لو كان ال A ideal يبقى بطلة ال A
+
+63
+00:07:53,050 --> 00:07:59,670
+صير subring بدنا نفترضها انها ايdeal يبقى ال A
+
+64
+00:07:59,670 --> 00:08:08,560
+idealتمام؟ هذه المعطيات الأولى في المثل Ideal of A
+
+65
+00:08:08,560 --> 00:08:17,800
+وفي نفس الوقت الـ Phi is unto والـ Phi is unto ال
+
+66
+00:08:17,800 --> 00:08:24,440
+Phi is unto يبقى Phi of A is an ideal يبقى هذا
+
+67
+00:08:24,440 --> 00:08:33,880
+يريحنا أن Phi of A is anideal of اسم هذا اللي بنا
+
+68
+00:08:33,880 --> 00:08:43,760
+نثبه ال proof فالي باركوا يعنى ان ال a في رأس
+
+69
+00:08:43,760 --> 00:08:48,460
+النظرية يقول لصبرينج هنا افترض هي ايش؟ ideal لو
+
+70
+00:08:48,460 --> 00:08:53,820
+كانت ideal و Phi كانت onto يعني غطت جميع عناصر اسم
+
+71
+00:08:53,820 --> 00:08:59,730
+بلاستثناءأو الـ Range ساوى الـ Codomain اللي هو S
+
+72
+00:08:59,730 --> 00:09:04,130
+يبقى الـ Phi of A بداية تفتح انه عبارة عن ايش؟ ID
+
+73
+00:09:04,130 --> 00:09:11,770
+طب السؤال هو هل ال Phi of A Sub-Range؟
+
+74
+00:09:11,770 --> 00:09:19,130
+نعم، نقطة ثانية، ايه باجي بقولك from part
+
+75
+00:09:19,130 --> 00:09:31,810
+two ال Phi of Ais a subring of الـ S يبقى لنا بس
+
+76
+00:09:31,810 --> 00:09:37,350
+أخر شرط من شروط ال ID يبقى ال file non-empty و
+
+77
+00:09:37,350 --> 00:09:42,310
+الفرق بين أي عصر موجود فيهالما كان الصبرينج باقينا
+
+78
+00:09:42,310 --> 00:09:47,910
+ناخد عنصرين من نفس الست لكن هنا لأ بدي أخد عنصر من
+
+79
+00:09:47,910 --> 00:09:53,250
+الست و عنصر من ال ring الأصلية بدي أحصل ضربهم يكون
+
+80
+00:09:53,250 --> 00:10:02,670
+موجود في في او اي ان حدث ذلك بقول في او اي is an
+
+81
+00:10:02,670 --> 00:10:05,410
+ideal of S لذلك
+
+82
+00:10:13,750 --> 00:10:22,250
+الـ X موجودة في الـ Phi of A يبقى أخد Element
+
+83
+00:10:22,250 --> 00:10:26,270
+موجود في الـ6 اللي عندنا و Element موجود في
+
+84
+00:10:26,270 --> 00:10:31,530
+الـRing الأصلية يبقى
+
+85
+00:10:31,530 --> 00:10:41,840
+ذنبالـ R موجودة في الـ R and ال X بده يساوي Phi of
+
+86
+00:10:41,840 --> 00:10:54,380
+A for some A اللي موجودة في A then بده
+
+87
+00:10:54,380 --> 00:11:03,080
+أخد ال همين بده أثبت أن ال R في X هذه موجودة وين؟
+
+88
+00:11:03,240 --> 00:11:09,540
+موجودة في الـPhi of A طب استنوا شوية انا ماخد R
+
+89
+00:11:09,540 --> 00:11:14,520
+لكن لا لا لا استنى بدنا ناخد بدنا نطبق هذا
+
+90
+00:11:14,520 --> 00:11:20,120
+فالsubring من مين من ال S يبقى هذا يا بنات مش
+
+91
+00:11:20,120 --> 00:11:30,600
+صحيحة هذي بدى اخد مثلا T موجودة في S لأن Phi of A
+
+92
+00:11:30,600 --> 00:11:35,290
+element في Sوانا بدي أثبت ان الـ Phi of A capital
+
+93
+00:11:35,290 --> 00:11:42,490
+هو ideal في من؟ في ال S لأن Phi A موجودة في S طيب
+
+94
+00:11:42,490 --> 00:11:48,290
+كويس الان T موجودة في S و ال Phi is .. انتوا يبقى
+
+95
+00:11:48,290 --> 00:11:55,470
+إيه له أصل في ال ring R ولا لا؟ يبقى هنا بدي أجي
+
+96
+00:11:55,470 --> 00:12:05,970
+أقول له since بما أن since ال Phiis onto and ات
+
+97
+00:12:05,970 --> 00:12:14,150
+موجود في الاسم there exist r موجود في الار such
+
+98
+00:12:14,150 --> 00:12:23,930
+that بحيث ان ات تساوي five of r نظرا
+
+99
+00:12:23,930 --> 00:12:29,290
+لان five is onto يبقى اي element اخده من ال code
+
+100
+00:12:29,290 --> 00:12:35,140
+mainهنجيله أصل في ال domain اللي هو R T تساوي Phi
+
+101
+00:12:35,140 --> 00:12:43,860
+of R طيب أنا بدي أثبت الآن أنه A T في ال X موجودة
+
+102
+00:12:43,860 --> 00:12:50,460
+وين في ال Phi of A صح ولا لأ مش هنفدل يعني بدي
+
+103
+00:12:50,460 --> 00:12:56,460
+أثبت Phi of A is an ideal إذا بدي أخد الآن T في X
+
+104
+00:12:56,460 --> 00:13:05,420
+يساوي ال T عندي بمين؟فاي of R وال X عندي في of A
+
+105
+00:13:05,420 --> 00:13:14,840
+فيهومومورفزم يبقى هذا الكلام في of R في A طيب
+
+106
+00:13:14,840 --> 00:13:23,020
+السؤال هو هل هذا ال element موجود في A؟ اه ليش انه
+
+107
+00:13:23,020 --> 00:13:29,990
+فرضين A ايديل وهذا element موجود في ال idealيبقى
+
+108
+00:13:29,990 --> 00:13:34,650
+هذا element موجود في ال ring A يبقى حاصل ضربهما
+
+109
+00:13:34,650 --> 00:13:43,770
+يكون موجود يبقى هذا موجود في Phi of A ليش؟ because
+
+110
+00:13:43,770 --> 00:13:55,290
+ال A موجود في ال A and ال A is an ideal يبقاش اللي
+
+111
+00:13:55,290 --> 00:14:05,160
+حصل هنا ال T في Xموجودة في Phi of A في Phi of A
+
+112
+00:14:05,160 --> 00:14:14,320
+بنفس الطريقة Similarly بنفس الطريقة ال XT موجودة
+
+113
+00:14:14,320 --> 00:14:21,700
+في Phi of A إذا انتحققت شروط ال ideal صحيح يبقى
+
+114
+00:14:21,700 --> 00:14:35,780
+بقوله Therefore ولهذا Phi of Ais an ideal of S هذا
+
+115
+00:14:35,780 --> 00:14:41,380
+النقطة التالتة النقطة الرابعة النقطة الرابعة دي
+
+116
+00:14:41,380 --> 00:14:50,440
+يقولي Phi inverse of B بينا نثبت ان Phi inverse of
+
+117
+00:14:50,440 --> 00:14:56,300
+B اللي هو عبارة عن كل العناصر I الموجودة في ال
+
+118
+00:14:56,300 --> 00:15:06,330
+ring Rبحكي ان فاي of R موجودة في بيه ايش بنا نسبته
+
+119
+00:15:06,330 --> 00:15:14,410
+هذا اثبت هذه فاي inverse is an ideal is an ideal
+
+120
+00:15:14,410 --> 00:15:20,430
+of R خلينا
+
+121
+00:15:20,430 --> 00:15:30,430
+نلقي هنا احنا بنا كالنا فاي منالار الى اس هذا
+
+122
+00:15:30,430 --> 00:15:35,910
+معروف homomorphism مظبوط طب الفاي انفرست بدى يكون
+
+123
+00:15:35,910 --> 00:15:40,490
+من و لا و لا من اس لأ ار من اس لأ ار يبقى لو كان
+
+124
+00:15:40,490 --> 00:15:45,070
+هذا one to one and one to two يبقى في انفرست exist
+
+125
+00:15:45,070 --> 00:15:51,990
+وبدى يكون من الاس لغاية ار ممتاز جدا طيب هو قاللي
+
+126
+00:15:51,990 --> 00:15:59,440
+اصلا ال بي ايديل في مين؟فى S طلع نص النظرية من
+
+127
+00:15:59,440 --> 00:16:06,480
+البداية جالى A subring من R و ال B ideal من S و
+
+128
+00:16:06,480 --> 00:16:15,400
+عندنا هنا ال B ideal of S جالى اثبت انه Phi
+
+129
+00:16:15,400 --> 00:16:20,880
+inverse يبقى B موجود وان فى S يبقى Phi inverse لما
+
+130
+00:16:20,880 --> 00:16:26,500
+اتأثر على ال ideal بترجع لمين؟ ترجع ال Aيبقى بدنا
+
+131
+00:16:26,500 --> 00:16:32,460
+نثبت انه Phi inverse لما يأثر على P بيعطيني عناصر
+
+132
+00:16:32,460 --> 00:16:38,980
+من ال ring R من هم اللي هم صورهم موجودة في ال
+
+133
+00:16:38,980 --> 00:16:43,340
+ideal P ايش بدنا نثبت ال Phi inverse of P؟ بدنا
+
+134
+00:16:43,340 --> 00:16:49,340
+نثبت انه ideal يعني بدنا نثبت الشروب التلاتة اللي
+
+135
+00:16:49,340 --> 00:16:54,620
+أثبتناهم هنا واحد اتنين تلاتةهنا اثبتنا ان فاي of
+
+136
+00:16:54,620 --> 00:17:01,960
+a sub ring و بعد هيك حولنا لمين لل ideal طيب الآن
+
+137
+00:17:01,960 --> 00:17:07,560
+بتدجل الشرط الأول من شروط ال ideal بقول لهم فاي
+
+138
+00:17:07,560 --> 00:17:15,080
+inverse of b is non empty معقول؟ ايش السبب؟
+
+139
+00:17:15,080 --> 00:17:19,480
+because ال b is non empty
+
+140
+00:17:22,200 --> 00:17:28,660
+لأن الـ B عبارة عن Ideal والـ Ideal non-empty طيب،
+
+141
+00:17:28,660 --> 00:17:33,060
+النقطة الثانية، بدنا ناخد عنصرين في الـ Phi
+
+142
+00:17:33,060 --> 00:17:39,720
+inverse of B يبقى بالذات يقولّه افترض الـ X والـ Y
+
+143
+00:17:39,720 --> 00:17:45,540
+موجودة في الـ Phi inverse of B بدي أثبت أن الفرق
+
+144
+00:17:45,540 --> 00:17:50,480
+فيما بينهما موجود وين في الـ Phi inverse of B، إن
+
+145
+00:17:50,480 --> 00:17:54,520
+حدث ذلكبكون انتهيت من الشرط التالي و بيبقى عليه
+
+146
+00:17:54,520 --> 00:18:00,940
+مايعني الشرط التالي كون هذول موجودات هنا معناه هذا
+
+147
+00:18:00,940 --> 00:18:10,320
+الكلام ان X بيساوي في انفرس of عنصر من عناصر ال ID
+
+148
+00:18:10,320 --> 00:18:17,580
+ال B صحيح ولا لأ X موجودة هنا ايش ممكن يكون شكلها
+
+149
+00:18:17,580 --> 00:18:26,230
+يبقى X بيساوي في انفرس of P1والـ y بيكون فاي انفرس
+
+150
+00:18:26,230 --> 00:18:38,690
+of b2 for some b1 وb2 اللي موجودة في b طيب الجميل
+
+151
+00:18:38,690 --> 00:18:44,830
+هذا بيعطي لبنات مين؟ لو أثرت على الطرفين بفاي
+
+152
+00:18:44,830 --> 00:18:56,820
+بيصير فاي of x بيكون بيساوي ال b1and Phi of Y بده
+
+153
+00:18:56,820 --> 00:19:05,860
+يساوي P2 فبكيس الان لو جيت جمعت الاتنين هدول مع
+
+154
+00:19:05,860 --> 00:19:11,740
+بعض والله احنا بدنا اطرح لا اطرح ولا يهمك يبقى هذا
+
+155
+00:19:11,740 --> 00:19:19,930
+الكلام بده يعطينا Phi of X ناقص Phi of Yيساوي B1
+
+156
+00:19:19,930 --> 00:19:26,190
+ناقص B2 لكن في عبارة عن ايه يا عزيزي همومورفزم
+
+157
+00:19:26,190 --> 00:19:33,890
+نظرا لان همومورفزم هذا بده يعطينا ان في X ناقص ال
+
+158
+00:19:33,890 --> 00:19:42,930
+Y بده يساوي B1 ناقص ال B2 بده يؤثر بفي انفرس على
+
+159
+00:19:42,930 --> 00:19:49,910
+الطرفينلو أثرنا بفاي انفرس على الطرفين هذا بيعطينا
+
+160
+00:19:49,910 --> 00:19:59,050
+ان X ناقص ال Y بيساوي فاي انفرس of B1 ناقص ال B2
+
+161
+00:19:59,050 --> 00:20:05,650
+هذا B1 ناقص B2 موجود وين؟ في capital B اللي هو
+
+162
+00:20:05,650 --> 00:20:11,210
+ideal تمام؟ من شروط ال ideal لو أخدت عنصرين فيه
+
+163
+00:20:11,210 --> 00:20:15,660
+وطرحتم من بعض يكون موجود وين؟و نفس الواضح إذا هذا
+
+164
+00:20:15,660 --> 00:20:23,940
+موجود one في ال ideal P يبقى هذا بده يعطينا إن ال
+
+165
+00:20:23,940 --> 00:20:31,420
+X ناقص ال Y موجود في Phi inverse of P يبقى انتهينا
+
+166
+00:20:31,420 --> 00:20:35,940
+من ال condition الثاني بدنا نروح لل condition
+
+167
+00:20:35,940 --> 00:20:37,560
+التالت
+
+168
+00:20:45,070 --> 00:20:49,350
+يبقى ال condition التالت والأخير مشان أثبت انه هذا
+
+169
+00:20:49,350 --> 00:20:56,850
+I دي فاي انفرست بيه هذا موجود في ال S ولا في ال R؟
+
+170
+00:20:56,850 --> 00:21:02,010
+في ال R طبعا يبقى في انفرست بيه عندما يؤثر عليه
+
+171
+00:21:02,010 --> 00:21:08,250
+بيوديه لوين؟ لل R يبقى بيروح أخر element موجود هنا
+
+172
+00:21:08,250 --> 00:21:14,790
+و element موجود وين؟ في ال R طبعايبقى بالضبط اقول
+
+173
+00:21:14,790 --> 00:21:25,830
+هنا let ال X موجود في ال Phi inverse of B and ال R
+
+174
+00:21:25,830 --> 00:21:36,010
+موجودة في ال R يبقى ال R أخدتها موجودة في ال R هو
+
+175
+00:21:36,010 --> 00:21:43,830
+Phi inverse ال element اللي فيهاالـ domain تبعها
+
+176
+00:21:43,830 --> 00:21:51,450
+مين هو؟ S واللي بدي أثبت انه Phi inverse of B صح؟
+
+177
+00:21:51,450 --> 00:21:56,290
+بدي أثبت Phi inverse of B عبارة عن ideal يبقى بدي
+
+178
+00:21:56,290 --> 00:22:03,530
+أخد element من مين؟ من Phi inverse of B و بدي أخد
+
+179
+00:22:03,530 --> 00:22:09,290
+element من ال ring اللي هو موجود فيها من ال ring
+
+180
+00:22:09,290 --> 00:22:18,170
+اللي موجود فيها؟ R ولا S؟سكت الشعب وصرت اقتراحات
+
+181
+00:22:18,170 --> 00:22:23,370
+بديش اقتراحات بدنا كلام مليان سؤال مرة تانية صح
+
+182
+00:22:23,370 --> 00:22:28,410
+بقى معايا كويسة احنا الان بدنا نثبت ان فاي انفرس
+
+183
+00:22:28,410 --> 00:22:36,770
+عبارة عن مين؟ شوف فاي انفرس ايديل of A ندخل عنصر
+
+184
+00:22:36,770 --> 00:22:43,400
+من R وعنصر من فاي انفرس of B هي خدناعنصر من Phi
+
+185
+00:22:43,400 --> 00:22:53,260
+inverse of B هو عنصر موجود في R بدأ جهازي اخد Phi
+
+186
+00:22:53,260 --> 00:23:04,200
+of X A لو جهت هنا اخد Phi of X A خديلي هذا يعني ان
+
+187
+00:23:04,200 --> 00:23:13,910
+X بده يساوي Phi inverse of Bالـ R موجودة في R هذا
+
+188
+00:23:13,910 --> 00:23:23,190
+يعني ان الـ Phi of X بده يساوي B and الـ R موجودة
+
+189
+00:23:23,190 --> 00:23:33,150
+فيها صحيح؟ صحيح الان بده ياخد Phi of X في R Phi
+
+190
+00:23:33,150 --> 00:23:41,420
+of X في R هذا الكلام بده يساوي Phi of Xفي Phi of A
+
+191
+00:23:41,420 --> 00:23:49,820
+هذا الكلام يساوي Phi of X بقدرش بيه بيه و هذا Phi
+
+192
+00:23:49,820 --> 00:23:57,700
+of A طب بيه وين موجود بيه
+
+193
+00:23:57,700 --> 00:24:02,980
+بيه هذا لحاله وين موجود بيه بيه يعني هذا belongs
+
+194
+00:24:02,980 --> 00:24:05,280
+to بيه هذا وين موجود
+
+195
+00:24:27,220 --> 00:24:33,800
+يبقى هذا موجود في بي لأن بي عبارة عن ideal يبقى
+
+196
+00:24:33,800 --> 00:24:42,010
+معنى هذا الكلام ان ال XR موجودفي Phi inverse of P
+
+197
+00:24:42,010 --> 00:24:48,690
+مظبوط يبقى أخدت element من ال ring و element من
+
+198
+00:24:48,690 --> 00:24:53,270
+Phi inverse of P وجدت حصل ضربه ما موجود في Phi
+
+199
+00:24:53,270 --> 00:25:03,010
+inverse of P بقوله هنا similarly ال Rx موجود في
+
+200
+00:25:03,010 --> 00:25:09,210
+Phi inverse of Pإذا اتحققت الشروط التالتة يا بنات
+
+201
+00:25:09,210 --> 00:25:15,710
+هذا من هنا هو الشرط التالف اتحققت الشروط التالتة
+
+202
+00:25:15,710 --> 00:25:23,170
+ده يبقى بروح بقول الله اص و هكذا five inverse of B
+
+203
+00:25:23,170 --> 00:25:33,370
+is an ideal of A هذا نقطة رقم كم؟ اربعة نقطة رقم
+
+204
+00:25:33,370 --> 00:25:39,950
+خمسةالنقطة رقم خمسة من هذه النظرية بتقول لي ان لو
+
+205
+00:25:39,950 --> 00:25:45,550
+كانت ال R is commutative يبقى صورتها في S is
+
+206
+00:25:45,550 --> 00:25:53,730
+commutative يبقى هنا ال R is commutative
+
+207
+00:25:53,730 --> 00:26:01,330
+implies ان ال Phi of R is commutative
+
+208
+00:26:04,580 --> 00:26:09,260
+هي اللي بدنا نثب طيب
+
+209
+00:26:09,260 --> 00:26:17,360
+ال R is commutative شو معناها يبقى ن approve ال R
+
+210
+00:26:17,360 --> 00:26:29,140
+is commutative هذا يتطلب ايه يتطلب ان ال X في Y
+
+211
+00:26:29,560 --> 00:26:36,060
+بتساوي ال Y في X لكل ال X و Y اللي موجودة في R
+
+212
+00:26:36,060 --> 00:26:44,660
+بلاستيكنات تمام شو رايك أثر على الطرفين بفاي يبقى
+
+213
+00:26:44,660 --> 00:26:55,600
+هذا يعني ان فاي X Y بيساوي فاي و Y في X فمن راسي
+
+214
+00:26:55,600 --> 00:27:00,350
+المسألة فوق في عبارة عنHomomorphism مدام
+
+215
+00:27:00,350 --> 00:27:08,070
+Homomorphism يبقى Phi of X في Phi of Y بده سوى Phi
+
+216
+00:27:08,070 --> 00:27:17,790
+of Y في Phi of X يبقى هذا ايش معناه ان Phi of R is
+
+217
+00:27:17,790 --> 00:27:25,990
+commutative يبقى هذا معناته ان Phi of R is
+
+218
+00:27:29,440 --> 00:27:35,260
+Commutative انت هنا من النقطة الخامسة بالضرورة
+
+219
+00:27:35,260 --> 00:27:53,440
+الوحدة النقطة السادسة طيب
+
+220
+00:27:53,440 --> 00:28:00,100
+النقطة السادسةالنقطة السادسة بتقول ما يتيح لو كانت
+
+221
+00:28:00,100 --> 00:28:05,860
+ال R has a unity الواحد موجود في ال R اللي هو ال
+
+222
+00:28:05,860 --> 00:28:12,940
+unity و ال S مابتسويش ال zero وزيادة على ذلك ال
+
+223
+00:28:12,940 --> 00:28:20,340
+five is unto ان حدث ذلك و ال five is one هذا بده
+
+224
+00:28:20,340 --> 00:28:34,280
+يعطينا ان ال five of oneis the unity of this.يبقى
+
+225
+00:28:34,280 --> 00:28:42,660
+هذا هو ال unity of this.طيب،
+
+226
+00:28:42,660 --> 00:28:50,120
+يعطينا ثلاث معقيات ومطلوب مين؟ مطلوب واحد، بس يبقى
+
+227
+00:28:50,120 --> 00:28:55,920
+يعطيني الـR هيظهر على ال ring with unity.عندنا الـ
+
+228
+00:28:55,920 --> 00:29:05,720
+S لا تساوي Zero يعني الـ S لا تساوي Zero as a set
+
+229
+00:29:05,720 --> 00:29:10,420
+ما تساويش الست اللي هي Zero ومعطينا المعطيات
+
+230
+00:29:10,420 --> 00:29:16,040
+التالتة انه Phi is onto نظرة لهذه المعطيات التي
+
+231
+00:29:16,040 --> 00:29:20,760
+تلت ريشه ان Phi of one هو ال unity تبع من؟ تبع
+
+232
+00:29:20,760 --> 00:29:27,010
+ring S نقوله بسيطة إذا جدرنانثبت انه five of one
+
+233
+00:29:27,010 --> 00:29:32,610
+ضرب أي element من S من اليمين ومن الشمال بيقين ال
+
+234
+00:29:32,610 --> 00:29:36,350
+element اللي فيه S بيصير five of one هو ال unity.
+
+235
+00:29:39,550 --> 00:29:49,330
+صح؟ طيب، الآن بدكي أقوله only the small s موجودة
+
+236
+00:29:49,330 --> 00:29:57,520
+في capital S. تمام؟طيب الفي قال لي إيش؟ قال لي on
+
+237
+00:29:57,520 --> 00:30:05,860
+to إيش يعني on to؟ يعني كل عنصر في S له أصل وين؟
+
+238
+00:30:05,860 --> 00:30:16,500
+في R صح ولا لأ يبقى then there exist R موجود في R
+
+239
+00:30:16,500 --> 00:30:25,030
+such that وبحيث أن ال S هذهالـ S Small اللي عندها
+
+240
+00:30:25,030 --> 00:30:34,770
+بدها ساوي Phi of R طيب خلينا نيجي ناخد الآن Phi of
+
+241
+00:30:34,770 --> 00:30:45,030
+1 مضروبة في S Phi of 1 عنصر وين؟ في S؟ إذا بدي
+
+242
+00:30:45,030 --> 00:30:51,050
+أضربه في مين؟ في عنصر تاني من Sهذا الكلام يساوي
+
+243
+00:30:51,050 --> 00:30:59,310
+فاي of one فيه ال S سوينها صارت ان فاي of ار يبقى
+
+244
+00:30:59,310 --> 00:31:07,390
+فاي of ار يبقى في همومورفيزم يبقى في of واحد مضروف
+
+245
+00:31:07,390 --> 00:31:14,610
+من في الار ال unity من ار لما اضربه في عنصر من
+
+246
+00:31:14,610 --> 00:31:20,400
+عناصر ار بيعطيني نفسي العنصريبقى هذا بيعطيني Phi
+
+247
+00:31:20,400 --> 00:31:26,960
+of R Phi of R هي مين؟ هي S يبقى لما ضرب Phi of 1
+
+248
+00:31:26,960 --> 00:31:31,340
+في S طلع الـ S تشوف الشجرة التانية أو الاتجاه
+
+249
+00:31:31,340 --> 00:31:41,780
+الآخر لو أخدت S S small مضروبة في مين؟ في Phi Phi
+
+250
+00:31:41,780 --> 00:31:50,610
+of 1 أشوف إيش تساويالـ S هي Phi of 1 of R مضروبة
+
+251
+00:31:50,610 --> 00:31:57,310
+في Phi of 1 الـ Phi عبارة عن همومورفيزم إذاً هذه
+
+252
+00:31:57,310 --> 00:32:03,190
+Phi of R مضروبة في 1 الـ R والـ 1 elements من
+
+253
+00:32:03,190 --> 00:32:10,230
+عناصر ال ring إذاً هذا يعتبر Phi of R لأن ال unity
+
+254
+00:32:10,230 --> 00:32:15,050
+تبع ال ring اللي هو واحد طيب Phi of R هو عبارة عن
+
+255
+00:32:15,050 --> 00:32:21,350
+مين؟عن ال S من هذا الكلام ايش ما اقدر استنتج انه
+
+256
+00:32:21,350 --> 00:32:26,510
+five one of S يساوي S of five one يساوي ال S ايش
+
+257
+00:32:26,510 --> 00:32:32,350
+معنى هذا الكلام انه five of one هو ال unity تبع ال
+
+258
+00:32:32,350 --> 00:32:42,390
+S هذا بده يعطينا انه five of one is the unity of S
+
+259
+00:32:42,390 --> 00:32:45,350
+تمام
+
+260
+00:32:45,800 --> 00:32:50,960
+هذا النقطة قدش السادسة النقطة السابعة النقطة
+
+261
+00:32:50,960 --> 00:32:56,720
+السابعة بتقول لي فاي is an isomorphism فاي is
+
+262
+00:32:56,720 --> 00:33:06,440
+isomorphism if and only if الفاي is on two and
+
+263
+00:33:06,440 --> 00:33:12,960
+الكرنل للفاي هو
+
+264
+00:33:12,960 --> 00:33:21,710
+الستالمكوّنة فقط من العمصر A صفري تمام؟ مافيش غيره
+
+265
+00:33:21,710 --> 00:33:26,390
+طيب if and don't if معناه القرهان بده يسير وين؟ في
+
+266
+00:33:26,390 --> 00:33:35,070
+التجاهين يبقى بالدرجة أقوله لـPro Assume افترض
+
+267
+00:33:35,070 --> 00:33:44,930
+that الـPhi is an isomorphism إيش يعني؟يعني الـ
+
+268
+00:33:44,930 --> 00:33:50,570
+Phi homomorphism Phi is one to one Phi is one ..
+
+269
+00:33:50,570 --> 00:33:57,850
+مظبوط؟ هذا معناه يبقى هذا معناه ان Phi is
+
+270
+00:33:57,850 --> 00:34:10,350
+homomorphism and one to one and .. and on تمام؟
+
+271
+00:34:10,350 --> 00:34:15,110
+طيب إذا أثبتنا له هذا المطلوب ولا لا؟طيب بس مثل
+
+272
+00:34:15,110 --> 00:34:20,370
+طول نثبتله مين؟ ان الكيرن لـ Phi يساوي الست التي
+
+273
+00:34:20,370 --> 00:34:28,010
+لا تحتوي الا على الصفر طيب سؤال اذا اثبتت ان هذه
+
+274
+00:34:28,010 --> 00:34:33,310
+subset من هذه و هذه subset من هذه مش بتم المطلوب
+
+275
+00:34:33,310 --> 00:34:42,190
+طب السؤال هو هل ال zero subset من الكيرن لـ Phi؟
+
+276
+00:34:43,280 --> 00:34:52,860
+صحيح لإن فاي اف زيرو موجود في ال kernel يبقى هذا
+
+277
+00:34:52,860 --> 00:34:57,660
+صحيح لإن فاي اف زيرو موجود في ال kernel يبقى هذا
+
+278
+00:34:57,660 --> 00:34:58,160
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+279
+00:34:58,160 --> 00:34:59,360
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+280
+00:34:59,360 --> 00:35:00,460
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+281
+00:35:00,460 --> 00:35:03,260
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+282
+00:35:03,260 --> 00:35:06,560
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+283
+00:35:06,560 --> 00:35:10,140
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+284
+00:35:10,140 --> 00:35:13,820
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقىبدو
+
+285
+00:35:13,820 --> 00:35:19,060
+يساوي Zero يبقى هذا بدي اعتبره النقطة رقم واحد
+
+286
+00:35:19,060 --> 00:35:25,480
+بدالي للنقطة رقم اتنين بدي اقول افترض ان X موجود
+
+287
+00:35:25,480 --> 00:35:32,200
+في كيرنل الفاية اذا كدرت اثبت ان X موجود هنا بيكون
+
+288
+00:35:32,200 --> 00:35:37,200
+تم المطلوب يكون خلصنا من هالشغل هذا يبقى then
+
+289
+00:35:37,200 --> 00:35:49,770
+الفاية of X بدو يساوي Zeroفى I
+
+290
+00:35:49,770 --> 00:35:53,530
+of X بده يساوي Zero لإنها موجودة في ال kernel من
+
+291
+00:35:53,530 --> 00:35:57,250
+تعريف ال kernel كل العناصر اللي موجودة في ال ring
+
+292
+00:35:57,250 --> 00:36:01,770
+اللي صاروا تم Zero مظبوط؟ إذا أنا استخدمت تخالب
+
+293
+00:36:01,770 --> 00:36:08,390
+على كأنة يبقى .. يبقى أنا استخدمت التعريف تبع ال
+
+294
+00:36:08,390 --> 00:36:14,790
+kernelكيرن للـ Phi كل العناصر اللي في R بحيث Phi
+
+295
+00:36:14,790 --> 00:36:19,410
+of R بده سوى Zero يبقى أنا أخد X موجودة في الكيرن
+
+296
+00:36:19,410 --> 00:36:23,310
+اللي هيبقى صورة هذا ال X بده تسوى مين؟ بده تسوى
+
+297
+00:36:23,310 --> 00:36:32,150
+Zero طيب أليس هذا هو Phi of Zero؟ صح؟ طيب يبقى
+
+298
+00:36:32,150 --> 00:36:38,360
+الصورة عند مين؟ صورتين متساويتين Phi of Xبدي يساوي
+
+299
+00:36:38,360 --> 00:36:44,840
+فاي of زيرو والفاي هذه مالها one to one يبقى إذا
+
+300
+00:36:44,840 --> 00:36:49,420
+كانت ال function one to one وخات صوتين متساويتين
+
+301
+00:36:49,420 --> 00:36:56,100
+بدي يكون الأصل متساوي يبقى هذا معناه إن ال X بدي
+
+302
+00:36:56,100 --> 00:37:05,120
+يساوي اللي هو ال zero because فاي is one to one
+
+303
+00:37:05,730 --> 00:37:12,910
+مدام ال X بدها تساوي Zero معناته ان ال X موجودة في
+
+304
+00:37:12,910 --> 00:37:18,490
+الست التي لا يوجد فيها الا العنصر الصفري طب ماش
+
+305
+00:37:18,490 --> 00:37:25,410
+اللي عاملتها؟ أخدت X موجودة في ال kernel لجأت ال X
+
+306
+00:37:25,410 --> 00:37:31,410
+موجودة وين؟ في ال Zero يبقى بلاءً عليه So ال
+
+307
+00:37:31,410 --> 00:37:37,730
+kernel لل Phi صار ست من مين؟من الست اللي عندها هذه
+
+308
+00:37:37,730 --> 00:37:43,790
+و هذه العلاقة رقم اتنين اذا بروح اقوله if from
+
+309
+00:37:43,790 --> 00:37:56,490
+واحد and اتنين we have ان ال kernel لل file بده
+
+310
+00:37:56,490 --> 00:38:02,530
+يساوي فقط الست المكونة من element واحد وهذا ال
+
+311
+00:38:02,530 --> 00:38:08,610
+element هو العمصر الصفريخلصنا النقطة هذه؟ خلاص؟
+
+312
+00:38:08,610 --> 00:38:10,810
+خلصنا نصها.
+
+313
+00:38:13,210 --> 00:38:20,890
+ليش؟ بسبب وجود ال F and only F. يبقى بسبب وجود ال
+
+314
+00:38:20,890 --> 00:38:26,770
+F and only F يبقى بدنا نروح نمشي الاتجاه الثاني.
+
+315
+00:38:31,690 --> 00:38:34,630
+يبقى بدنا نروح أقولك Converse.
+
+316
+00:38:39,350 --> 00:38:44,110
+هي اللي عندها فاي is an isomorphism عشان لو لفت
+
+317
+00:38:44,110 --> 00:38:49,810
+فاي is onto يبقى انا بده افترض ان فاي is onto و ال
+
+318
+00:38:49,810 --> 00:38:54,350
+kern اللي بده يساوي zero و بده اثبت ان فاي هذي
+
+319
+00:38:54,350 --> 00:38:59,970
+عبارة عن isomorphism يبقى بده اجي و اقوله assume
+
+320
+00:38:59,970 --> 00:39:15,440
+that فاي من R الى S isانتوا ترى دول ماطلوة وال
+
+321
+00:39:15,440 --> 00:39:25,000
+كيرنل يساوي زيرو and الكيرنل للفاي بده يساوي ست
+
+322
+00:39:25,000 --> 00:39:33,260
+زيرو want to show that
+
+323
+00:39:33,260 --> 00:39:42,720
+فاي is aIsomorphism مش هلا اثبت انه Phi
+
+324
+00:39:42,720 --> 00:39:48,000
+Isomorphism بالذات بالتلت شغلات انه homomorphism و
+
+325
+00:39:48,000 --> 00:39:53,860
+one to one و أنتوا طب احنا فرضين انه أنتوا و مرسى
+
+326
+00:39:53,860 --> 00:40:01,420
+المثل Isomorphism ضال إيه؟ one to one مظبوط؟ يبقى
+
+327
+00:40:01,420 --> 00:40:14,010
+بعدى بقول since Phiمن R إلى S من R إلى S is
+
+328
+00:40:14,010 --> 00:40:25,610
+homomorphic and الـ Phi is Onto أحنا فرضينه Assume
+
+329
+00:40:25,610 --> 00:40:31,230
+that هي Onto ومن رأس المثلة فرضين أنه homomorphic
+
+330
+00:40:31,230 --> 00:40:36,640
+إيش ضلالينا؟بس اثبت انه one to one اذا قدرت اثبت
+
+331
+00:40:36,640 --> 00:40:41,400
+انه one to one بكون خلصنا بصير الفاى عبارة عن ايه؟
+
+332
+00:40:41,400 --> 00:40:48,000
+isomorphism يبقى بعدي بقوله هنا احكاية ال one to
+
+333
+00:40:48,000 --> 00:40:56,900
+one بدنا نستفيد من الشغل ان الكيرن يساوي zero يبقى
+
+334
+00:40:56,900 --> 00:41:05,660
+بعدي بقوله let x و yموجودة في الكيرن للـ Phi.
+
+335
+00:41:09,360 --> 00:41:18,280
+Then الـ Phi of X بده يساوي Zero and ال Phi of Y
+
+336
+00:41:18,280 --> 00:41:19,640
+بده يساوي Zero.
+
+337
+00:41:22,740 --> 00:41:29,680
+صحيح؟ يبقى هذا إيش بيعطينا يا بنات؟ إن ال Phi of X
+
+338
+00:41:29,680 --> 00:41:36,560
+بده يساوي ال Phi of Y.صحيح ولا لا؟ لكل ال X وال Y
+
+339
+00:41:36,560 --> 00:41:40,980
+اللي موجودة وين؟ اللي موجودة في ال kernel تمام؟
+
+340
+00:41:40,980 --> 00:41:49,060
+يبقى أخد صورتين متساويتين إذا قررت أثبت أنه الأصل
+
+341
+00:41:49,060 --> 00:41:53,420
+تبعهم متساوي بصير وانت وانا بكون خلصها من هالشغل
+
+342
+00:41:53,420 --> 00:42:00,280
+مظبوط؟ طيب احنا عندنا Phi of X يسوى Phi of Y يبقى
+
+343
+00:42:00,280 --> 00:42:07,260
+Phi of Xنقص Phi of Y بدي سوى مان Zero Phi
+
+344
+00:42:07,260 --> 00:42:14,540
+homomorphism يبقى هذا بدي اعطيلك ان Phi of X نقص
+
+345
+00:42:14,540 --> 00:42:22,040
+ال Y بدي سوى Zero طيب هذا معناه ان ال X نقص ال Y
+
+346
+00:42:22,040 --> 00:42:32,240
+موجودة في كيرن لفاي صح؟ طب قدش كيرن لفاي؟هو Zero
+
+347
+00:42:32,240 --> 00:42:37,440
+صحيح ولا لا؟ احنا فرضينه هى يبقى هذا كده بده
+
+348
+00:42:37,440 --> 00:42:44,000
+يساوي؟ Zero هذا معناته ان ال X ناقص ال Y بده يساوي
+
+349
+00:42:44,000 --> 00:42:50,920
+Zero هذا معناته ان ال X بده يساوي 100 ال Y يبقى So
+
+350
+00:42:50,920 --> 00:42:59,600
+ال Phi is one to one Thus وهكذا ال Phi is
+
+351
+00:43:01,640 --> 00:43:07,380
+isomorphism ضالة النقطة الأخيرة النقطة الأخيرة
+
+352
+00:43:07,380 --> 00:43:15,260
+بتقول ما ياتي لو كانت الفاي isomorphism then الفاي
+
+353
+00:43:15,260 --> 00:43:23,760
+انفرست is isomorphism if الفاي is isomorphism
+
+354
+00:43:23,760 --> 00:43:30,120
+then الفاي انفرست is isomorphism
+
+355
+00:43:31,020 --> 00:43:34,760
+طبعا هو كتبلك on two تنتين on two ما هو ال
+
+356
+00:43:34,760 --> 00:43:40,220
+isomorphism تعني one to one and on two يبقى كتبها
+
+357
+00:43:40,220 --> 00:43:45,740
+و الله ما كتبهاش سيان تفرجش عندنا ليش؟ لأن ال
+
+358
+00:43:45,740 --> 00:43:52,600
+isomorphism في حد ذاته هو homomorphism وهو one to
+
+359
+00:43:52,600 --> 00:43:59,510
+one and on two في نفس الوقت طيبيبقى انا بدي افترض
+
+360
+00:43:59,510 --> 00:44:07,690
+ان الـ Phi هذا ايزو مورفيزيوم ال approved assume
+
+361
+00:44:07,690 --> 00:44:20,390
+that ان ال Phi is an isomorphism طيب
+
+362
+00:44:20,390 --> 00:44:26,320
+يعني ال Phi is one to one and unto صح؟يبقى هذا بده
+
+363
+00:44:26,320 --> 00:44:34,540
+يعطينا فاي is one to one and unto نرجع لمبادئ
+
+364
+00:44:34,540 --> 00:44:39,560
+الرياضية principle of mathematics تمام؟ بجرر نقول
+
+365
+00:44:39,560 --> 00:44:44,420
+والله ده ال function one to one and unto يبقى ال
+
+366
+00:44:44,420 --> 00:44:49,180
+inverse exist وفي نفس الوقت one to one and unto
+
+367
+00:44:49,180 --> 00:44:54,790
+وفي كل كلاص بيه في أول sectionقلنا ال existence
+
+368
+00:44:54,790 --> 00:45:00,150
+للمعكوس ان تكون الدالة one to one صح ولا لأ؟ هذا
+
+369
+00:45:00,150 --> 00:45:05,330
+شرط وجوده المعكوس مدام ال Phi one to one and unto
+
+370
+00:45:05,330 --> 00:45:13,590
+هذا بده يقينا ان ال Phi inverse exist and ال Phi
+
+371
+00:45:13,590 --> 00:45:22,010
+inverse is one to one and unto ايش ضايل علينا؟نثبت
+
+372
+00:45:22,010 --> 00:45:32,930
+ان هو homomorphism يبقى it remains that ضايل علينا
+
+373
+00:45:32,930 --> 00:45:42,030
+نثبت ان الـ Phi inverse is a homomorphism why؟
+
+374
+00:45:42,030 --> 00:45:46,110
+يبقى بده روح اخد Phi inverse بده يكون من وين لوين
+
+375
+00:45:46,110 --> 00:45:57,310
+من S لRمن S إلى R يعني من R إلى S يبقى Phi inverse
+
+376
+00:45:57,310 --> 00:46:06,530
+من S إلى R يبقى بدالي أقول له let له S واحد و S
+
+377
+00:46:06,530 --> 00:46:14,290
+اتنين موجودة في S طيب هنا عندنا ال Phi one to one
+
+378
+00:46:14,290 --> 00:46:20,630
+and onto يبقى ال S واحد و ال S اتنين أصلا وين في R
+
+379
+00:46:21,350 --> 00:46:30,810
+يبقى then ال S واحد بده يساوي اللي هو Phi of R
+
+380
+00:46:30,810 --> 00:46:40,670
+واحد and S اتنين بده يساوي Phi of R اتنين كويس
+
+381
+00:46:40,670 --> 00:46:48,470
+اذا لو جيت اخدت S واحد زائد S اتنين يبقى بده يساوي
+
+382
+00:46:48,470 --> 00:46:57,040
+Phi of R واحدزائد Phi of R2 هذا هو مورفزيوم يبقى
+
+383
+00:46:57,040 --> 00:47:05,220
+Phi of R1 زائد R2 احنا بدنا ال Phi inverse يبقى
+
+384
+00:47:05,220 --> 00:47:11,140
+بروح بقوله ال Phi inverse لما يأثر على مجموعة ال
+
+385
+00:47:11,140 --> 00:47:17,460
+two elements اللي موجودات في S بده يساوي ال Phi
+
+386
+00:47:17,460 --> 00:47:24,880
+inverse لل Phi of R1زائد R2 الـ function و معكوسها
+
+387
+00:47:24,880 --> 00:47:30,800
+تلغي بعضها لما كل عنصر هذا في domainها يبقى ال R1
+
+388
+00:47:30,800 --> 00:47:36,320
+زائد R2 طب ال R1 يا بنات من هنا مين هو؟ Phi
+
+389
+00:47:36,320 --> 00:47:45,840
+inverse of S1 يبقى هذا Phi inverse of S1 زائد Phi
+
+390
+00:47:45,840 --> 00:47:52,820
+inverse of S2يبقى هاي أثبتنا ال condition الأول من
+
+391
+00:47:52,820 --> 00:47:57,340
+ال two conditions تبعات ال homomorphism بدنا ال
+
+392
+00:47:57,340 --> 00:48:04,660
+condition التاني يبقى and بدي أخد من؟ بدي أخد
+
+393
+00:48:04,660 --> 00:48:15,680
+element من S ولكن S مثلا YS او بدي أخد ال phi of
+
+394
+00:48:15,680 --> 00:48:17,020
+S1
+
+395
+00:48:23,030 --> 00:48:30,450
+5 of S1 ال condition التاني بدك تاخد element من ال
+
+396
+00:48:30,450 --> 00:48:35,870
+ring مش احنا بدنا نثبت ان ال homomorphism بدي اخد
+
+397
+00:48:35,870 --> 00:48:40,890
+اتنين من ال ring و اخد حاصل دور بيهم هقوله كويس
+
+398
+00:48:40,890 --> 00:48:48,440
+يعني بدي اخد اما انا اتنين بدي اخد S1 S2يبقى هذا
+
+399
+00:48:48,440 --> 00:48:55,740
+بدل يساوي Phi of R1 في Phi of R2 ال Phi
+
+400
+00:48:55,740 --> 00:49:02,340
+همومورفيزيوم يبقى Phi of R1 R2 فبدي أثر على
+
+401
+00:49:02,340 --> 00:49:08,140
+الطرفين ب Phi inverse يبقى بيصير Phi inverse of S1
+
+402
+00:49:08,140 --> 00:49:17,630
+S2 بدل يساوي Phi inverse ل Phi of R1 R2هذا الكلاب
+
+403
+00:49:17,630 --> 00:49:29,190
+بده يساوي R1 R2 مين ال R1؟ Phi inverse of S1 يبقى
+
+404
+00:49:29,190 --> 00:49:36,790
+يساوي Phi inverse of S1 ب Phi inverse of S2 plus
+
+405
+00:49:36,790 --> 00:49:44,230
+وهكذا ال Phi inverse is a homomorphism وهذا بده
+
+406
+00:49:44,230 --> 00:49:45,150
+يخلينا
+
+407
+00:49:50,900 --> 00:49:57,980
+عن إيه خلصنا النظرية فقط هذه لا غير ومرة جاية
+
+408
+00:49:57,980 --> 00:50:00,320
+بنكمل اعطاك العالم
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..9004927dc7993e6a82da89e5df88af2a53ade8a4
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_raw.json
@@ -0,0 +1 @@
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"word": " الار", "probability": 0.79541015625}, {"start": 733.25, "end": 734.15, "word": " such", "probability": 0.91748046875}, {"start": 734.15, "end": 735.09, "word": " that", "probability": 0.93994140625}, {"start": 735.09, "end": 736.05, "word": " بحيث", "probability": 0.9764404296875}, {"start": 736.05, "end": 736.51, "word": " ان", "probability": 0.8955078125}, {"start": 736.51, "end": 737.71, "word": " ات", "probability": 0.85791015625}, {"start": 737.71, "end": 738.85, "word": " تساوي", "probability": 0.8525390625}, {"start": 738.85, "end": 739.81, "word": " five", "probability": 0.60400390625}, {"start": 739.81, "end": 740.19, "word": " of", "probability": 0.96142578125}, {"start": 740.19, "end": 740.73, "word": " r", "probability": 0.7587890625}, {"start": 740.73, "end": 743.93, "word": " نظرا", "probability": 0.955078125}, {"start": 743.93, "end": 744.33, "word": " لان", "probability": 0.561279296875}, {"start": 744.33, "end": 744.93, "word": " five", "probability": 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وين في ال Phi of A صح ولا لأ مش هنفدل يعني بدي أثبت Phi of A is an ideal إذا بدي أخد الآن T في X يساوي ال T عندي بمين؟", "tokens": [3224, 1863, 7435, 26895, 3224, 5551, 36520, 8978, 2423, 9274, 13672, 1829, 31439, 497, 314, 6055, 3794, 995, 45865, 41435, 295, 497, 23032, 1829, 3555, 41850, 4724, 16254, 5551, 12984, 3555, 2655, 6024, 48506, 14739, 3224, 316, 314, 8978, 2423, 1783, 3714, 29245, 23328, 3660, 4032, 9957, 8978, 2423, 41435, 295, 316, 20328, 5016, 49429, 5296, 10721, 37893, 8032, 1863, 5172, 3215, 1211, 37495, 22653, 4724, 16254, 5551, 12984, 3555, 2655, 41435, 295, 316, 307, 364, 7157, 11933, 15730, 4724, 16254, 5551, 9778, 3215, 6024, 48506, 314, 8978, 1783, 7251, 3794, 995, 45865, 2423, 314, 18871, 16254, 4724, 2304, 9957, 22807], "avg_logprob": -0.30024510446716757, "compression_ratio": 1.6467661691542288, "no_speech_prob": 0.0, "words": [{"start": 750.08, "end": 750.86, "word": "هنجيله", "probability": 0.679931640625}, {"start": 750.86, "end": 751.32, "word": " أصل", 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"probability": 0.59490966796875}, {"start": 788.34, "end": 789.22, "word": " يبقى", "probability": 0.9285888671875}, {"start": 789.22, "end": 789.64, "word": " هذا", "probability": 0.90087890625}, {"start": 789.64, "end": 790.38, "word": " الكلام", "probability": 0.9441731770833334}, {"start": 790.38, "end": 791.56, "word": " في", "probability": 0.857421875}, {"start": 791.56, "end": 792.12, "word": " of", "probability": 0.75732421875}, {"start": 792.12, "end": 793.0, "word": " R", "probability": 0.93408203125}, {"start": 793.0, "end": 793.38, "word": " في", "probability": 0.93408203125}, {"start": 793.38, "end": 793.64, "word": " A", "probability": 0.7314453125}, {"start": 793.64, "end": 794.84, "word": " طيب", "probability": 0.56396484375}, {"start": 794.84, "end": 795.54, "word": " السؤال", "probability": 0.9855143229166666}, {"start": 795.54, "end": 795.94, "word": " هو", "probability": 0.984375}, {"start": 795.94, "end": 797.06, "word": " هل", "probability": 0.970703125}, {"start": 797.06, "end": 797.54, "word": " هذا", "probability": 0.97607421875}, {"start": 797.54, "end": 798.0, "word": " ال", "probability": 0.97509765625}, {"start": 798.0, "end": 798.58, "word": " element", "probability": 0.90283203125}, {"start": 798.58, "end": 799.76, "word": " موجود", "probability": 0.98974609375}, {"start": 799.76, "end": 800.06, "word": " في", "probability": 0.9765625}, {"start": 800.06, "end": 801.36, "word": " A؟", "probability": 0.696044921875}, {"start": 801.36, "end": 802.46, "word": " اه", "probability": 0.53619384765625}, {"start": 802.46, "end": 802.76, "word": " ليش", "probability": 0.74951171875}, {"start": 802.76, "end": 803.02, "word": " انه", "probability": 0.81103515625}, {"start": 803.02, "end": 803.76, "word": " فرضين", "probability": 0.9677734375}, {"start": 803.76, "end": 804.16, "word": " A", "probability": 0.7890625}, {"start": 804.16, "end": 805.06, "word": " ايديل", "probability": 0.476531982421875}, {"start": 805.06, "end": 805.92, "word": " وهذا", "probability": 0.7010498046875}, {"start": 805.92, "end": 806.62, "word": " element", "probability": 0.72314453125}, {"start": 806.62, "end": 807.66, "word": " موجود", "probability": 0.9910481770833334}, {"start": 807.66, "end": 808.02, "word": " في", "probability": 0.9599609375}, {"start": 808.02, "end": 808.2, "word": " ال", "probability": 0.7353515625}, {"start": 808.2, "end": 808.78, "word": " ideal", "probability": 0.56103515625}], "temperature": 1.0}, {"id": 29, "seek": 83879, "start": 809.17, "end": 838.79, "text": "يبقى هذا element موجود في ال ring A يبقى حاصل ضربهما يكون موجود يبقى هذا موجود في Phi of A ليش؟ because ال A موجود في ال A and ال A is an ideal يبقاش اللي حصل هنا ال T في X", "tokens": [1829, 3555, 4587, 7578, 23758, 4478, 3714, 29245, 23328, 8978, 2423, 4875, 316, 7251, 3555, 4587, 7578, 11331, 33546, 1211, 48812, 25513, 3224, 15042, 7251, 30544, 3714, 29245, 23328, 7251, 3555, 4587, 7578, 23758, 3714, 29245, 23328, 8978, 41435, 295, 316, 32239, 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ideal", "probability": 0.82177734375}, {"start": 833.27, "end": 835.07, "word": " يبقاش", "probability": 0.7822265625}, {"start": 835.07, "end": 835.29, "word": " اللي", "probability": 0.908203125}, {"start": 835.29, "end": 835.75, "word": " حصل", "probability": 0.9931640625}, {"start": 835.75, "end": 836.17, "word": " هنا", "probability": 0.986328125}, {"start": 836.17, "end": 836.99, "word": " ال", "probability": 0.196044921875}, {"start": 836.99, "end": 837.87, "word": " T", "probability": 0.9501953125}, {"start": 837.87, "end": 838.37, "word": " في", "probability": 0.96533203125}, {"start": 838.37, "end": 838.79, "word": " X", "probability": 0.94287109375}], "temperature": 1.0}, {"id": 30, "seek": 86826, "start": 839.02, "end": 868.26, "text": "موجودة في Phi of A في Phi of A بنفس الطريقة Similarly بنفس الطريقة ال XT موجودة في Phi of A إذا انتحققت شروط ال ideal صحيح يبقى بقوله Therefore ولهذا Phi of A", "tokens": [2304, 29245, 23328, 3660, 8978, 41435, 295, 316, 8978, 41435, 295, 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985.06, "word": " A", "probability": 0.400390625}], "temperature": 1.0}, {"id": 35, "seek": 101246, "start": 985.68, "end": 1012.46, "text": "يبقى بدنا نثبت انه Phi inverse لما يأثر على P بيعطيني عناصر من ال ring R من هم اللي هم صورهم موجودة في ال ideal P ايش بدنا نثبت ال Phi inverse of P؟ بدنا نثبت انه ideal يعني بدنا نثبت الشروب التلاتة اللي أثبتناهم هنا واحد اتنين تلاتة", "tokens": [1829, 3555, 4587, 7578, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 3224, 41435, 17340, 5296, 15042, 7251, 10721, 49115, 15844, 430, 4724, 40228, 9566, 9957, 1829, 18871, 33546, 2288, 9154, 2423, 4875, 497, 9154, 8032, 2304, 13672, 1829, 8032, 2304, 20328, 13063, 16095, 3714, 29245, 23328, 3660, 8978, 2423, 7157, 430, 1975, 1829, 8592, 47525, 8315, 8717, 12984, 3555, 2655, 2423, 41435, 17340, 295, 430, 22807, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 3224, 7157, 37495, 22653, 47525, 8315, 8717, 12984, 3555, 2655, 25124, 32887, 3555, 16712, 1211, 9307, 3660, 13672, 1829, 5551, 12984, 3555, 2655, 8315, 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حولنا", "probability": 0.8439127604166666}, {"start": 1018.22, "end": 1018.76, "word": " لمين", "probability": 0.697998046875}, {"start": 1018.76, "end": 1019.44, "word": " لل", "probability": 0.54345703125}, {"start": 1019.44, "end": 1020.32, "word": " ideal", "probability": 0.64990234375}, {"start": 1020.32, "end": 1021.36, "word": " طيب", "probability": 0.8606770833333334}, {"start": 1021.36, "end": 1021.96, "word": " الآن", "probability": 0.5906982421875}, {"start": 1021.96, "end": 1022.56, "word": " بتدجل", "probability": 0.456756591796875}, {"start": 1022.56, "end": 1023.24, "word": " الشرط", "probability": 0.9313151041666666}, {"start": 1023.24, "end": 1023.86, "word": " الأول", "probability": 0.82958984375}, {"start": 1023.86, "end": 1024.16, "word": " من", "probability": 0.98779296875}, {"start": 1024.16, "end": 1024.72, "word": " شروط", "probability": 0.9752604166666666}, {"start": 1024.72, "end": 1024.92, "word": " ال", "probability": 0.93017578125}, {"start": 1024.92, "end": 1025.5, "word": " ideal", "probability": 0.95458984375}, {"start": 1025.5, "end": 1026.72, "word": " بقول", "probability": 0.946044921875}, {"start": 1026.72, "end": 1027.02, "word": " لهم", "probability": 0.52801513671875}, {"start": 1027.02, "end": 1027.56, "word": " فاي", "probability": 0.619384765625}, {"start": 1027.56, "end": 1028.22, "word": " inverse", "probability": 0.72314453125}, {"start": 1028.22, "end": 1028.8, "word": " of", "probability": 0.97119140625}, {"start": 1028.8, "end": 1029.2, "word": " b", "probability": 0.5458984375}, {"start": 1029.2, "end": 1029.88, "word": " is", "probability": 0.91259765625}, {"start": 1029.88, "end": 1030.72, "word": " non", "probability": 0.646484375}, {"start": 1030.72, "end": 1031.8, "word": " empty", "probability": 0.62646484375}, {"start": 1031.8, "end": 1033.86, "word": " معقول؟", "probability": 0.5849609375}, {"start": 1033.86, "end": 1034.16, "word": " ايش", "probability": 0.7608235677083334}, {"start": 1034.16, "end": 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بقى معايا كويسة احنا الان بدنا نثبت ان فاي انفرس عبارة عن مين؟ شوف فاي انفرس ايديل of A ندخل عنصر من R وعنصر من فاي انفرس of B هي خدنا", "tokens": [3794, 4117, 2655, 25124, 3615, 3555, 4032, 9381, 43500, 1975, 38149, 23557, 5016, 9307, 4724, 16254, 8592, 1975, 38149, 23557, 5016, 9307, 47525, 8315, 28242, 10943, 3714, 20292, 7649, 8608, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 20328, 5016, 4724, 4587, 7578, 20449, 995, 25528, 9122, 45865, 3794, 3660, 1975, 5016, 8315, 2423, 7649, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 6156, 47302, 16472, 5172, 2288, 3794, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 22807, 13412, 38688, 6156, 47302, 16472, 5172, 2288, 3794, 1975, 1829, 16254, 1211, 295, 316, 8717, 3215, 9778, 1211, 18871, 9381, 2288, 9154, 497, 4032, 3615, 1863, 9381, 2288, 9154, 6156, 47302, 16472, 5172, 2288, 3794, 295, 363, 39896, 16490, 3215, 8315], "avg_logprob": -0.2660256267612816, "compression_ratio": 1.8952879581151831, "no_speech_prob": 0.0, "words": [{"start": 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4724, 1829, 6225, 3555, 9640, 3660, 18871, 7157, 7251, 3555, 4587, 7578, 20449, 1863, 7578, 23758, 2423, 28820, 10943, 16472, 2423, 1783, 49, 3714, 29245, 23328], "avg_logprob": -0.4300781384110451, "compression_ratio": 1.32, "no_speech_prob": 0.0, "words": [{"start": 1467.22, "end": 1468.26, "word": "يبقى", "probability": 0.711151123046875}, {"start": 1468.26, "end": 1469.3, "word": " هذا", "probability": 0.07916259765625}, {"start": 1469.3, "end": 1469.92, "word": " موجود", "probability": 0.9202473958333334}, {"start": 1469.92, "end": 1470.18, "word": " في", "probability": 0.87890625}, {"start": 1470.18, "end": 1470.46, "word": " بي", "probability": 0.475799560546875}, {"start": 1470.46, "end": 1470.98, "word": " لأن", "probability": 0.82568359375}, {"start": 1470.98, "end": 1471.42, "word": " بي", "probability": 0.5919189453125}, {"start": 1471.42, "end": 1472.08, "word": " عبارة", "probability": 0.764007568359375}, {"start": 1472.08, "end": 1472.26, "word": " عن", "probability": 0.9931640625}, {"start": 1472.26, "end": 1472.72, "word": " ideal", "probability": 0.480712890625}, {"start": 1472.72, "end": 1473.8, "word": " يبقى", "probability": 0.83966064453125}, {"start": 1473.8, "end": 1474.32, "word": " معنى", "probability": 0.8092447916666666}, {"start": 1474.32, "end": 1474.6, "word": " هذا", "probability": 0.8955078125}, {"start": 1474.6, "end": 1475.22, "word": " الكلام", "probability": 0.9181315104166666}, {"start": 1475.22, "end": 1475.58, "word": " ان", "probability": 0.462890625}, {"start": 1475.58, "end": 1475.88, "word": " ال", "probability": 0.5185546875}, {"start": 1475.88, "end": 1477.16, "word": " XR", "probability": 0.677978515625}, {"start": 1477.16, "end": 1478.72, "word": " موجود", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 52, "seek": 150575, "start": 1478.89, "end": 1505.75, "text": "في Phi inverse of P مظبوط يبقى أخدت element من ال ring و element من Phi inverse of P وجدت حصل ضربه ما موجود في Phi inverse of P بقوله هنا similarly ال Rx موجود في Phi inverse of P", "tokens": [41185, 41435, 17340, 295, 430, 3714, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 5551, 9778, 3215, 2655, 4478, 9154, 2423, 4875, 4032, 4478, 9154, 41435, 17340, 295, 430, 49610, 3215, 2655, 11331, 36520, 48812, 25513, 3224, 19446, 3714, 29245, 23328, 8978, 41435, 17340, 295, 430, 4724, 39648, 3224, 34105, 14138, 2423, 497, 87, 3714, 29245, 23328, 8978, 41435, 17340, 295, 430], "avg_logprob": -0.237971226847361, "compression_ratio": 1.619047619047619, "no_speech_prob": 0.0, "words": [{"start": 1478.89, "end": 1479.15, "word": "في", "probability": 0.64404296875}, {"start": 1479.15, "end": 1479.85, "word": " Phi", "probability": 0.31494140625}, {"start": 1479.85, "end": 1481.09, "word": " inverse", "probability": 0.7138671875}, {"start": 1481.09, "end": 1481.57, "word": " of", "probability": 0.95654296875}, {"start": 1481.57, "end": 1482.01, "word": " P", "probability": 0.3916015625}, {"start": 1482.01, "end": 1484.67, "word": " مظبوط", "probability": 0.72783203125}, {"start": 1484.67, "end": 1485.23, "word": " يبقى", "probability": 0.76031494140625}, {"start": 1485.23, "end": 1485.77, "word": " أخدت", "probability": 0.779541015625}, {"start": 1485.77, "end": 1486.29, "word": " element", "probability": 0.7744140625}, {"start": 1486.29, "end": 1486.79, "word": " من", "probability": 0.9931640625}, {"start": 1486.79, "end": 1487.07, "word": " ال", "probability": 0.90966796875}, {"start": 1487.07, "end": 1487.39, "word": " ring", "probability": 0.75439453125}, {"start": 1487.39, "end": 1487.95, "word": " و", "probability": 0.830078125}, {"start": 1487.95, "end": 1488.43, "word": " element", "probability": 0.81298828125}, {"start": 1488.43, "end": 1488.69, "word": " من", "probability": 0.9794921875}, {"start": 1488.69, "end": 1488.97, "word": " Phi", "probability": 0.85205078125}, {"start": 1488.97, "end": 1489.51, "word": " inverse", "probability": 0.84765625}, {"start": 1489.51, "end": 1489.87, "word": " of", "probability": 0.9345703125}, {"start": 1489.87, "end": 1490.21, "word": " P", "probability": 0.94677734375}, {"start": 1490.21, "end": 1490.99, "word": " وجدت", "probability": 0.7005208333333334}, {"start": 1490.99, "end": 1491.47, "word": " حصل", "probability": 0.748046875}, {"start": 1491.47, "end": 1492.07, "word": " ضربه", "probability": 0.8567708333333334}, {"start": 1492.07, "end": 1492.29, "word": " ما", "probability": 0.51220703125}, {"start": 1492.29, "end": 1492.73, "word": " موجود", "probability": 0.9791666666666666}, {"start": 1492.73, "end": 1492.89, "word": " في", "probability": 0.9287109375}, {"start": 1492.89, "end": 1493.27, "word": " Phi", "probability": 0.88134765625}, {"start": 1493.27, "end": 1493.71, "word": " inverse", "probability": 0.81982421875}, {"start": 1493.71, "end": 1494.11, "word": " of", "probability": 0.94287109375}, {"start": 1494.11, "end": 1494.47, "word": " P", "probability": 0.9814453125}, {"start": 1494.47, "end": 1495.57, "word": " بقوله", "probability": 0.8284505208333334}, {"start": 1495.57, "end": 1496.05, "word": " هنا", "probability": 0.97314453125}, {"start": 1496.05, "end": 1498.01, "word": " similarly", "probability": 0.46923828125}, {"start": 1498.01, "end": 1500.33, "word": " ال", "probability": 0.6572265625}, {"start": 1500.33, "end": 1501.59, "word": " Rx", "probability": 0.678466796875}, {"start": 1501.59, "end": 1502.77, "word": " موجود", "probability": 0.98388671875}, {"start": 1502.77, "end": 1503.01, "word": " في", "probability": 0.962890625}, {"start": 1503.01, "end": 1503.63, "word": " Phi", "probability": 0.89111328125}, {"start": 1503.63, "end": 1504.75, "word": " inverse", "probability": 0.78466796875}, {"start": 1504.75, "end": 1505.45, "word": " of", "probability": 0.97412109375}, {"start": 1505.45, "end": 1505.75, "word": " P", "probability": 0.9482421875}], "temperature": 1.0}, {"id": 53, "seek": 153425, "start": 1506.21, "end": 1534.25, "text": "إذا اتحققت الشروط التالتة يا بنات هذا من هنا هو الشرط التالف اتحققت الشروط التالتة ده يبقى بروح بقول الله اص و هكذا five inverse of B is an ideal of A هذا نقطة رقم كم؟ اربعة نقطة رقم خمسة", "tokens": [28814, 15730, 1975, 2655, 5016, 4587, 4587, 2655, 25124, 32887, 9566, 16712, 6027, 2655, 3660, 35186, 4724, 8315, 2655, 23758, 9154, 34105, 31439, 25124, 2288, 9566, 16712, 6027, 5172, 1975, 2655, 5016, 4587, 4587, 2655, 25124, 32887, 9566, 16712, 6027, 2655, 3660, 11778, 3224, 7251, 3555, 4587, 7578, 4724, 32887, 5016, 4724, 39648, 21984, 1975, 9381, 4032, 8032, 4117, 15730, 1732, 17340, 295, 363, 307, 364, 7157, 295, 316, 23758, 8717, 47432, 3660, 12602, 4587, 2304, 9122, 2304, 22807, 1975, 25513, 27884, 8717, 47432, 3660, 12602, 4587, 2304, 16490, 2304, 3794, 3660], "avg_logprob": -0.2782258064516129, "compression_ratio": 1.7457627118644068, "no_speech_prob": 0.0, "words": [{"start": 1506.21, "end": 1506.57, "word": "إذا", "probability": 0.7076416015625}, {"start": 1506.57, "end": 1507.39, "word": " اتحققت", "probability": 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الشروط", "probability": 0.9436848958333334}, {"start": 1515.05, "end": 1515.71, "word": " التالتة", "probability": 0.8345947265625}, {"start": 1515.71, "end": 1515.97, "word": " ده", "probability": 0.6278076171875}, {"start": 1515.97, "end": 1517.21, "word": " يبقى", "probability": 0.80029296875}, {"start": 1517.21, "end": 1517.69, "word": " بروح", "probability": 0.9029947916666666}, {"start": 1517.69, "end": 1518.17, "word": " بقول", "probability": 0.760009765625}, {"start": 1518.17, "end": 1518.55, "word": " الله", "probability": 0.390380859375}, {"start": 1518.55, "end": 1519.19, "word": " اص", "probability": 0.3692626953125}, {"start": 1519.19, "end": 1519.45, "word": " و", "probability": 0.53271484375}, {"start": 1519.45, "end": 1520.55, "word": " هكذا", "probability": 0.8409830729166666}, {"start": 1520.55, "end": 1521.35, "word": " five", "probability": 0.107666015625}, {"start": 1521.35, "end": 1522.19, "word": " inverse", "probability": 0.8349609375}, {"start": 1522.19, "end": 1522.69, "word": " of", "probability": 0.97216796875}, {"start": 1522.69, "end": 1523.17, "word": " B", "probability": 0.35400390625}, {"start": 1523.17, "end": 1524.17, "word": " is", "probability": 0.92919921875}, {"start": 1524.17, "end": 1525.05, "word": " an", "probability": 0.8759765625}, {"start": 1525.05, "end": 1526.45, "word": " ideal", "probability": 0.8837890625}, {"start": 1526.45, "end": 1527.81, "word": " of", "probability": 0.947265625}, {"start": 1527.81, "end": 1528.33, "word": " A", "probability": 0.415283203125}, {"start": 1528.33, "end": 1529.45, "word": " هذا", "probability": 0.61083984375}, {"start": 1529.45, "end": 1530.01, "word": " نقطة", "probability": 0.8408203125}, {"start": 1530.01, "end": 1530.57, "word": " رقم", "probability": 0.94580078125}, {"start": 1530.57, "end": 1531.29, "word": " كم؟", "probability": 0.6905924479166666}, {"start": 1531.29, "end": 1531.85, "word": " اربعة", "probability": 0.741455078125}, {"start": 1531.85, "end": 1532.87, "word": " نقطة", "probability": 0.8836263020833334}, {"start": 1532.87, "end": 1533.37, "word": " رقم", "probability": 0.990234375}, {"start": 1533.37, "end": 1534.25, "word": " خمسة", "probability": 0.9691162109375}], "temperature": 1.0}, {"id": 54, "seek": 156133, "start": 1534.95, "end": 1561.33, "text": "النقطة رقم خمسة من هذه النظرية بتقول لي ان لو كانت ال R is commutative يبقى صورتها في S is commutative يبقى هنا ال R is commutative implies ان ال Phi of R is commutative", "tokens": [6027, 1863, 47432, 3660, 12602, 4587, 2304, 16490, 2304, 3794, 3660, 9154, 29538, 28239, 19913, 2288, 10632, 39894, 39648, 32239, 16472, 45164, 25961, 2655, 2423, 497, 307, 800, 325, 1166, 7251, 3555, 4587, 7578, 20328, 13063, 2655, 11296, 8978, 318, 307, 800, 325, 1166, 7251, 3555, 4587, 7578, 34105, 2423, 497, 307, 800, 325, 1166, 18779, 16472, 2423, 41435, 295, 497, 307, 800, 325, 1166], "avg_logprob": -0.1537642040939042, "compression_ratio": 1.6164383561643836, "no_speech_prob": 0.0, "words": [{"start": 1534.95, "end": 1535.67, "word": "النقطة", "probability": 0.9581298828125}, {"start": 1535.67, "end": 1536.01, "word": " رقم", "probability": 0.8430989583333334}, {"start": 1536.01, "end": 1536.59, "word": " خمسة", "probability": 0.84619140625}, {"start": 1536.59, "end": 1536.79, "word": " من", "probability": 0.96337890625}, {"start": 1536.79, "end": 1537.21, "word": " هذه", "probability": 0.97900390625}, {"start": 1537.21, "end": 1537.97, "word": " النظرية", "probability": 0.965576171875}, {"start": 1537.97, "end": 1538.73, "word": " بتقول", "probability": 0.94287109375}, {"start": 1538.73, "end": 1538.99, "word": " لي", "probability": 0.421875}, {"start": 1538.99, "end": 1539.57, "word": " ان", "probability": 0.60888671875}, {"start": 1539.57, "end": 1539.95, "word": " لو", "probability": 0.60595703125}, {"start": 1539.95, "end": 1540.37, "word": " كانت", "probability": 0.64111328125}, {"start": 1540.37, "end": 1540.53, "word": " ال", "probability": 0.88037109375}, {"start": 1540.53, "end": 1540.85, "word": " R", "probability": 0.494873046875}, {"start": 1540.85, "end": 1541.75, "word": " is", "probability": 0.7353515625}, {"start": 1541.75, "end": 1542.79, "word": " commutative", "probability": 0.96826171875}, {"start": 1542.79, "end": 1543.59, "word": " يبقى", "probability": 0.957275390625}, {"start": 1543.59, "end": 1544.39, "word": " صورتها", "probability": 0.9490966796875}, {"start": 1544.39, "end": 1544.69, "word": " في", "probability": 0.943359375}, {"start": 1544.69, "end": 1545.13, "word": " S", "probability": 0.90234375}, {"start": 1545.13, "end": 1545.55, "word": " is", "probability": 0.91943359375}, {"start": 1545.55, "end": 1546.59, "word": " commutative", "probability": 0.9827473958333334}, {"start": 1546.59, "end": 1547.81, "word": " يبقى", "probability": 0.9566650390625}, {"start": 1547.81, "end": 1548.27, "word": " هنا", "probability": 0.9912109375}, {"start": 1548.27, "end": 1548.87, "word": " ال", "probability": 0.8935546875}, {"start": 1548.87, "end": 1549.61, "word": " R", "probability": 0.89794921875}, {"start": 1549.61, "end": 1550.49, "word": " is", "probability": 0.93603515625}, {"start": 1550.49, "end": 1553.73, "word": " commutative", "probability": 0.9851888020833334}, {"start": 1553.73, "end": 1555.63, "word": " implies", "probability": 0.497802734375}, {"start": 1555.63, "end": 1556.53, "word": " ان", "probability": 0.7880859375}, {"start": 1556.53, "end": 1556.87, "word": " ال", "probability": 0.51123046875}, {"start": 1556.87, "end": 1557.47, "word": " Phi", "probability": 0.326171875}, {"start": 1557.47, "end": 1558.11, "word": " of", "probability": 0.8359375}, {"start": 1558.11, "end": 1558.71, "word": " R", "probability": 0.92822265625}, {"start": 1558.71, "end": 1559.69, "word": " is", "probability": 0.95068359375}, {"start": 1559.69, "end": 1561.33, "word": " commutative", "probability": 0.9861653645833334}], "temperature": 1.0}, {"id": 55, "seek": 158914, "start": 1564.58, "end": 1589.14, "text": "هي اللي بدنا نثب طيب ال R is commutative شو معناها يبقى ن approve ال R is commutative هذا يتطلب ايه يتطلب ان ال X في Y", "tokens": [3224, 1829, 13672, 1829, 47525, 8315, 8717, 12984, 3555, 23032, 1829, 3555, 2423, 497, 307, 800, 325, 1166, 13412, 2407, 20449, 8315, 11296, 7251, 3555, 4587, 7578, 8717, 18827, 2423, 497, 307, 800, 325, 1166, 23758, 7251, 2655, 9566, 46152, 1975, 1829, 3224, 7251, 2655, 9566, 46152, 16472, 2423, 1783, 8978, 398], "avg_logprob": -0.28095519317770906, "compression_ratio": 1.4065040650406504, "no_speech_prob": 0.0, "words": [{"start": 1564.58, "end": 1565.0, "word": "هي", "probability": 0.41796875}, {"start": 1565.0, "end": 1565.12, "word": " اللي", "probability": 0.822021484375}, {"start": 1565.12, "end": 1565.5, "word": " بدنا", "probability": 0.9453125}, {"start": 1565.5, "end": 1565.98, "word": " نثب", "probability": 0.7902018229166666}, {"start": 1565.98, "end": 1569.26, "word": " طيب", "probability": 0.6215006510416666}, {"start": 1569.26, "end": 1570.06, "word": " ال", "probability": 0.86181640625}, {"start": 1570.06, "end": 1570.5, "word": " R", "probability": 0.4619140625}, {"start": 1570.5, "end": 1570.92, "word": " is", "probability": 0.81982421875}, {"start": 1570.92, "end": 1571.72, "word": " commutative", "probability": 0.9519856770833334}, {"start": 1571.72, "end": 1572.14, "word": " شو", "probability": 0.885986328125}, {"start": 1572.14, "end": 1572.98, "word": " معناها", "probability": 0.923828125}, {"start": 1572.98, "end": 1573.6, "word": " يبقى", "probability": 0.77667236328125}, {"start": 1573.6, "end": 1573.8, "word": " ن", "probability": 0.7685546875}, {"start": 1573.8, "end": 1574.26, "word": " approve", "probability": 0.12322998046875}, {"start": 1574.26, "end": 1576.8, "word": " ال", "probability": 0.81201171875}, {"start": 1576.8, "end": 1577.36, "word": " R", "probability": 0.94287109375}, {"start": 1577.36, "end": 1578.6, "word": " is", "probability": 0.92626953125}, {"start": 1578.6, "end": 1581.0, "word": " 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{"start": 2206.78, "end": 2207.0, "word": " one", "probability": 0.9580078125}, {"start": 2207.0, "end": 2207.66, "word": " وخات", "probability": 0.642822265625}, {"start": 2207.66, "end": 2208.32, "word": " صوتين", "probability": 0.9378255208333334}, {"start": 2208.32, "end": 2209.42, "word": " متساويتين", "probability": 0.8948974609375}, {"start": 2209.42, "end": 2209.64, "word": " بدي", "probability": 0.712646484375}, {"start": 2209.64, "end": 2209.92, "word": " يكون", "probability": 0.916015625}, {"start": 2209.92, "end": 2210.58, "word": " الأصل", "probability": 0.919189453125}, {"start": 2210.58, "end": 2212.16, "word": " متساوي", "probability": 0.920166015625}, {"start": 2212.16, "end": 2212.9, "word": " يبقى", "probability": 0.9368896484375}, {"start": 2212.9, "end": 2213.38, "word": " هذا", "probability": 0.9833984375}, {"start": 2213.38, "end": 2214.2, "word": " معناه", "probability": 0.9793294270833334}, {"start": 2214.2, "end": 2214.7, "word": " إن", "probability": 0.55078125}, {"start": 2214.7, "end": 2215.0, "word": " ال", "probability": 0.955078125}, {"start": 2215.0, "end": 2215.38, "word": " X", "probability": 0.68115234375}, {"start": 2215.38, "end": 2216.1, "word": " بدي", "probability": 0.91064453125}, {"start": 2216.1, "end": 2216.94, "word": " يساوي", "probability": 0.86962890625}, {"start": 2216.94, "end": 2217.56, "word": " اللي", "probability": 0.956298828125}, {"start": 2217.56, "end": 2218.12, "word": " هو", "probability": 0.9970703125}, {"start": 2218.12, "end": 2218.6, "word": " ال", "probability": 0.74462890625}, {"start": 2218.6, "end": 2219.26, "word": " zero", "probability": 0.66015625}, {"start": 2219.26, "end": 2220.28, "word": " because", "probability": 0.7646484375}, {"start": 2220.28, "end": 2222.92, "word": " فاي", "probability": 0.650634765625}, {"start": 2222.92, "end": 2223.82, "word": " is", "probability": 0.92138671875}, {"start": 2223.82, "end": 2224.5, "word": " one", "probability": 0.96044921875}, {"start": 2224.5, "end": 2224.84, "word": " to", "probability": 0.9765625}, {"start": 2224.84, "end": 2225.12, "word": " one", "probability": 0.95166015625}], "temperature": 1.0}, {"id": 78, "seek": 225557, "start": 2225.73, "end": 2255.57, "text": "مدام ال X بدها تساوي Zero معناته ان ال X موجودة في الست التي لا يوجد فيها الا العنصر الصفري طب ماش اللي عاملتها؟ أخدت X موجودة في ال kernel لجأت ال X موجودة وين؟ في ال Zero يبقى بلاءً عليه So ال kernel لل Phi صار ست من مين؟", "tokens": [2304, 3215, 10943, 2423, 1783, 47525, 11296, 6055, 3794, 995, 45865, 17182, 3714, 3615, 8315, 47395, 16472, 2423, 1783, 3714, 29245, 23328, 3660, 8978, 2423, 14851, 38392, 20193, 7251, 29245, 3215, 8978, 11296, 42963, 18863, 1863, 9381, 2288, 31767, 5172, 16572, 23032, 3555, 19446, 8592, 13672, 1829, 6225, 10943, 1211, 2655, 11296, 22807, 5551, 9778, 3215, 2655, 1783, 3714, 29245, 23328, 3660, 8978, 2423, 28256, 5296, 7435, 10721, 2655, 2423, 1783, 3714, 29245, 23328, 3660, 4032, 9957, 22807, 8978, 2423, 17182, 7251, 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{"start": 2245.41, "end": 2246.09, "word": " موجودة", "probability": 0.9910888671875}, {"start": 2246.09, "end": 2246.79, "word": " وين؟", "probability": 0.7478841145833334}, {"start": 2246.79, "end": 2246.93, "word": " في", "probability": 0.8896484375}, {"start": 2246.93, "end": 2247.09, "word": " ال", "probability": 0.91455078125}, {"start": 2247.09, "end": 2247.53, "word": " Zero", "probability": 0.7255859375}, {"start": 2247.53, "end": 2248.25, "word": " يبقى", "probability": 0.943359375}, {"start": 2248.25, "end": 2248.91, "word": " بلاءً", "probability": 0.60479736328125}, {"start": 2248.91, "end": 2249.55, "word": " عليه", "probability": 0.81494140625}, {"start": 2249.55, "end": 2250.65, "word": " So", "probability": 0.10906982421875}, {"start": 2250.65, "end": 2251.41, "word": " ال", "probability": 0.81884765625}, {"start": 2251.41, "end": 2252.21, "word": " kernel", "probability": 0.80810546875}, {"start": 2252.21, "end": 2252.85, "word": " لل", "probability": 0.6220703125}, {"start": 2252.85, "end": 2253.39, "word": " Phi", "probability": 0.12005615234375}, {"start": 2253.39, "end": 2254.27, "word": " صار", "probability": 0.8193359375}, {"start": 2254.27, "end": 2254.73, "word": " ست", "probability": 0.639404296875}, {"start": 2254.73, "end": 2254.97, "word": " من", "probability": 0.96923828125}, {"start": 2254.97, "end": 2255.57, "word": " مين؟", "probability": 0.90673828125}], "temperature": 1.0}, {"id": 79, "seek": 228489, "start": 2255.71, "end": 2284.89, "text": "من الست اللي عندها هذه و هذه العلاقة رقم اتنين اذا بروح اقوله if from واحد and اتنين we have ان ال kernel لل file بده يساوي فقط الست المكونة من element واحد وهذا ال element هو العمصر الصفري", "tokens": [27842, 2423, 14851, 13672, 1829, 43242, 11296, 29538, 4032, 29538, 18863, 15040, 28671, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 1975, 15730, 4724, 32887, 5016, 1975, 39648, 3224, 498, 490, 36764, 24401, 293, 1975, 2655, 1863, 9957, 321, 362, 16472, 2423, 28256, 24976, 3991, 47525, 3224, 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"probability": 0.9739583333333334}, {"start": 2259.93, "end": 2260.65, "word": " اتنين", "probability": 0.891845703125}, {"start": 2260.65, "end": 2261.37, "word": " اذا", "probability": 0.6240234375}, {"start": 2261.37, "end": 2261.89, "word": " بروح", "probability": 0.9423828125}, {"start": 2261.89, "end": 2262.61, "word": " اقوله", "probability": 0.7017415364583334}, {"start": 2262.61, "end": 2263.19, "word": " if", "probability": 0.560546875}, {"start": 2263.19, "end": 2263.79, "word": " from", "probability": 0.91943359375}, {"start": 2263.79, "end": 2266.01, "word": " واحد", "probability": 0.889892578125}, {"start": 2266.01, "end": 2267.15, "word": " and", "probability": 0.939453125}, {"start": 2267.15, "end": 2268.63, "word": " اتنين", "probability": 0.98095703125}, {"start": 2268.63, "end": 2269.21, "word": " we", "probability": 0.77099609375}, {"start": 2269.21, "end": 2270.19, "word": " have", "probability": 0.96826171875}, {"start": 2270.19, "end": 2272.49, "word": " ان", 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"probability": 0.988525390625}, {"start": 2281.91, "end": 2282.37, "word": " وهذا", "probability": 0.768798828125}, {"start": 2282.37, "end": 2282.53, "word": " ال", "probability": 0.90966796875}, {"start": 2282.53, "end": 2282.95, "word": " element", "probability": 0.93896484375}, {"start": 2282.95, "end": 2283.49, "word": " هو", "probability": 0.9892578125}, {"start": 2283.49, "end": 2284.23, "word": " العمصر", "probability": 0.9444580078125}, {"start": 2284.23, "end": 2284.89, "word": " الصفري", "probability": 0.9152018229166666}], "temperature": 1.0}, {"id": 80, "seek": 231463, "start": 2285.19, "end": 2314.63, "text": "خلصنا النقطة هذه؟ خلاص؟ خلصنا نصها. ليش؟ بسبب وجود ال F and only F. يبقى بسبب وجود ال F and only F يبقى بدنا نروح نمشي الاتجاه الثاني. يبقى بدنا نروح أقولك Converse.", "tokens": [9778, 1211, 9381, 8315, 28239, 47432, 3660, 29538, 22807, 16490, 1211, 33546, 22807, 16490, 1211, 9381, 8315, 8717, 9381, 11296, 13, 32239, 8592, 22807, 4724, 35457, 3555, 49610, 23328, 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"text": "Isomorphism مش هلا اثبت انه Phi Isomorphism بالذات بالتلت شغلات انه homomorphism و one to one و أنتوا طب احنا فرضين انه أنتوا و مرسى المثل Isomorphism ضال إيه؟ one to one مظبوط؟ يبقى بعدى بقول since Phi", "tokens": [40, 539, 76, 18191, 1434, 37893, 8032, 15040, 1975, 12984, 3555, 2655, 16472, 3224, 41435, 286, 539, 76, 18191, 1434, 20666, 8848, 9307, 20666, 2655, 1211, 2655, 13412, 17082, 1211, 9307, 16472, 3224, 3655, 32702, 1434, 4032, 472, 281, 472, 4032, 14739, 2655, 14407, 23032, 3555, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 3224, 14739, 2655, 14407, 4032, 3714, 2288, 3794, 7578, 9673, 12984, 1211, 286, 539, 76, 18191, 1434, 48812, 6027, 11933, 1829, 3224, 22807, 472, 281, 472, 3714, 19913, 3555, 2407, 9566, 22807, 7251, 3555, 4587, 7578, 39182, 7578, 4724, 39648, 1670, 41435], "avg_logprob": -0.32226563431322575, "compression_ratio": 1.6388888888888888, "no_speech_prob": 0.0, "words": [{"start": 2377.92, "end": 2379.28, "word": "Isomorphism", "probability": 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since", "probability": 0.69677734375}, {"start": 2404.48, "end": 2406.12, "word": " Phi", "probability": 0.8486328125}], "temperature": 1.0}, {"id": 84, "seek": 243303, "start": 2406.93, "end": 2433.03, "text": "من R إلى S من R إلى S is homomorphic and الـ Phi is Onto أحنا فرضينه Assume that هي Onto ومن رأس المثلة فرضين أنه homomorphic إيش ضلالينا؟", "tokens": [27842, 497, 30731, 318, 9154, 497, 30731, 318, 307, 3655, 32702, 299, 293, 2423, 39184, 41435, 307, 16980, 78, 5551, 5016, 8315, 6156, 43042, 9957, 3224, 6281, 2540, 300, 39896, 16980, 78, 4032, 27842, 12602, 10721, 3794, 9673, 12984, 37977, 6156, 43042, 9957, 14739, 3224, 3655, 32702, 299, 11933, 1829, 8592, 48812, 1211, 6027, 1829, 8315, 22807], "avg_logprob": -0.356411625599039, "compression_ratio": 1.3566433566433567, "no_speech_prob": 0.0, "words": [{"start": 2406.93, "end": 2407.53, "word": "من", "probability": 0.82666015625}, {"start": 2407.53, "end": 2408.19, "word": " R", "probability": 0.51611328125}, {"start": 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one Thus وهكذا ال Phi is", "tokens": [3224, 2407, 17182, 20328, 5016, 1829, 5016, 49429, 20193, 22807, 1975, 5016, 8315, 6156, 43042, 9957, 3224, 8032, 7578, 7251, 3555, 4587, 7578, 23758, 9122, 3215, 3224, 47525, 3224, 7251, 3794, 995, 45865, 22807, 17182, 23758, 20449, 8315, 47395, 16472, 2423, 1783, 8717, 995, 4587, 9381, 2423, 398, 47525, 3224, 7251, 3794, 995, 45865, 17182, 23758, 20449, 8315, 47395, 16472, 2423, 1783, 47525, 3224, 7251, 3794, 995, 45865, 2319, 2423, 398, 7251, 3555, 4587, 7578, 407, 2423, 41435, 307, 472, 281, 472, 13827, 37037, 4117, 15730, 2423, 41435, 307], "avg_logprob": -0.23906250562932757, "compression_ratio": 1.7976190476190477, "no_speech_prob": 0.0, "words": [{"start": 2551.16, "end": 2551.62, "word": "هو", "probability": 0.849853515625}, {"start": 2551.62, "end": 2552.24, "word": " Zero", "probability": 0.301025390625}, {"start": 2552.24, "end": 2553.04, "word": " صحيح", "probability": 0.9837646484375}, {"start": 2553.04, "end": 2553.22, "word": " 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وهو one to one and on two في نفس الوقت طيب", "tokens": [9566, 3555, 3615, 995, 31439, 9122, 2655, 3555, 23275, 322, 732, 6055, 29399, 9957, 322, 732, 19446, 31439, 2423, 307, 32702, 1434, 6055, 3615, 22653, 472, 281, 472, 293, 322, 732, 7251, 3555, 4587, 7578, 9122, 2655, 3555, 11296, 4032, 21984, 19446, 9122, 2655, 3555, 3224, 33599, 8608, 1829, 7649, 6055, 5172, 47341, 8592, 43242, 8315, 32239, 8592, 22807, 5296, 33456, 2423, 307, 32702, 1434, 8978, 11331, 3215, 29910, 9307, 3224, 31439, 3655, 32702, 1434, 37037, 2407, 472, 281, 472, 293, 322, 732, 8978, 8717, 36178, 2423, 30543, 2655, 23032, 1829, 3555], "avg_logprob": -0.20430107078244608, "compression_ratio": 1.7135135135135136, "no_speech_prob": 0.0, "words": [{"start": 2611.02, "end": 2611.5, "word": "طبعا", "probability": 0.980224609375}, {"start": 2611.5, "end": 2611.64, "word": " هو", "probability": 0.76171875}, {"start": 2611.64, "end": 2612.52, "word": " كتبلك", "probability": 0.875732421875}, {"start": 2612.52, "end": 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"probability": 0.99462890625}, {"start": 2623.7, "end": 2625.2, "word": " ليش؟", "probability": 0.73388671875}, {"start": 2625.2, "end": 2625.54, "word": " لأن", "probability": 0.809326171875}, {"start": 2625.54, "end": 2625.74, "word": " ال", "probability": 0.95263671875}, {"start": 2625.74, "end": 2627.0, "word": " isomorphism", "probability": 0.9158528645833334}, {"start": 2627.0, "end": 2627.24, "word": " في", "probability": 0.9267578125}, {"start": 2627.24, "end": 2627.8, "word": " حد", "probability": 0.94970703125}, {"start": 2627.8, "end": 2628.7, "word": " ذاته", "probability": 0.9933268229166666}, {"start": 2628.7, "end": 2629.72, "word": " هو", "probability": 0.9638671875}, {"start": 2629.72, "end": 2631.12, "word": " homomorphism", "probability": 0.9295247395833334}, {"start": 2631.12, "end": 2631.9, "word": " وهو", "probability": 0.805908203125}, {"start": 2631.9, "end": 2632.26, "word": " one", "probability": 0.96923828125}, {"start": 2632.26, "end": 2632.6, "word": " to", 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"word": " هذا", "probability": 0.376220703125}, {"start": 2640.85, "end": 2641.45, "word": " ايزو", "probability": 0.614959716796875}, {"start": 2641.45, "end": 2642.29, "word": " مورفيزيوم", "probability": 0.78857421875}, {"start": 2642.29, "end": 2643.17, "word": " ال", "probability": 0.52001953125}, {"start": 2643.17, "end": 2643.87, "word": " approved", "probability": 0.044647216796875}, {"start": 2643.87, "end": 2647.69, "word": " assume", "probability": 0.80712890625}, {"start": 2647.69, "end": 2650.49, "word": " that", "probability": 0.90283203125}, {"start": 2650.49, "end": 2651.97, "word": " ان", "probability": 0.80224609375}, {"start": 2651.97, "end": 2652.43, "word": " ال", "probability": 0.8447265625}, {"start": 2652.43, "end": 2653.11, "word": " Phi", "probability": 0.517578125}, {"start": 2653.11, "end": 2654.03, "word": " is", "probability": 0.95166015625}, {"start": 2654.03, "end": 2655.11, "word": " an", "probability": 0.83642578125}, {"start": 2655.11, "end": 2657.07, "word": " isomorphism", "probability": 0.9153645833333334}, {"start": 2657.07, "end": 2660.39, "word": " طيب", "probability": 0.9353841145833334}, {"start": 2660.39, "end": 2660.77, "word": " يعني", "probability": 0.93896484375}, {"start": 2660.77, "end": 2661.05, "word": " ال", "probability": 0.8671875}, {"start": 2661.05, "end": 2661.49, "word": " Phi", "probability": 0.91748046875}, {"start": 2661.49, "end": 2661.85, "word": " is", "probability": 0.88623046875}, {"start": 2661.85, "end": 2662.17, "word": " one", "probability": 0.8671875}, {"start": 2662.17, "end": 2662.47, "word": " to", "probability": 0.90673828125}, {"start": 2662.47, "end": 2662.81, "word": " one", "probability": 0.9501953125}, {"start": 2662.81, "end": 2663.23, "word": " and", "probability": 0.939453125}, {"start": 2663.23, "end": 2663.63, "word": " unto", "probability": 0.30859375}, {"start": 2663.63, "end": 2664.47, "word": " صح؟", "probability": 0.7986653645833334}], "temperature": 1.0}, {"id": 93, "seek": 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0.961669921875}, {"start": 2674.54, "end": 2675.42, "word": " الرياضية", "probability": 0.9105224609375}, {"start": 2675.42, "end": 2676.06, "word": " principle", "probability": 0.288818359375}, {"start": 2676.06, "end": 2676.4, "word": " of", "probability": 0.93701171875}, {"start": 2676.4, "end": 2677.22, "word": " mathematics", "probability": 0.73876953125}, {"start": 2677.22, "end": 2678.84, "word": " تمام؟", "probability": 0.7112630208333334}, {"start": 2678.84, "end": 2679.32, "word": " بجرر", "probability": 0.54364013671875}, {"start": 2679.32, "end": 2679.56, "word": " نقول", "probability": 0.91845703125}, {"start": 2679.56, "end": 2680.24, "word": " والله", "probability": 0.84375}, {"start": 2680.24, "end": 2680.6, "word": " ده", "probability": 0.586669921875}, {"start": 2680.6, "end": 2680.72, "word": " ال", "probability": 0.9755859375}, {"start": 2680.72, "end": 2681.3, "word": " function", "probability": 0.90869140625}, {"start": 2681.3, "end": 2681.7, "word": " one", "probability": 0.84716796875}, {"start": 2681.7, "end": 2682.06, "word": " to", "probability": 0.9697265625}, {"start": 2682.06, "end": 2682.34, "word": " one", "probability": 0.94677734375}, {"start": 2682.34, "end": 2682.78, "word": " and", "probability": 0.95849609375}, {"start": 2682.78, "end": 2683.32, "word": " unto", "probability": 0.96337890625}, {"start": 2683.32, "end": 2684.26, "word": " يبقى", "probability": 0.9632568359375}, {"start": 2684.26, "end": 2684.42, "word": " ال", "probability": 0.97607421875}, {"start": 2684.42, "end": 2684.92, "word": " inverse", "probability": 0.80615234375}, {"start": 2684.92, "end": 2685.82, "word": " exist", "probability": 0.806640625}, {"start": 2685.82, "end": 2686.32, "word": " وفي", "probability": 0.874755859375}, {"start": 2686.32, "end": 2686.66, "word": " نفس", "probability": 0.998046875}, {"start": 2686.66, "end": 2687.26, "word": " الوقت", "probability": 0.98486328125}, {"start": 2687.26, "end": 2687.64, "word": " one", 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"end": 2721.25, "text": "قلنا ال existence للمعكوس ان تكون الدالة one to one صح ولا لأ؟ هذا شرط وجوده المعكوس مدام ال Phi one to one and unto هذا بده يقينا ان ال Phi inverse exist and ال Phi inverse is one to one and unto ايش ضايل علينا؟", "tokens": [4587, 1211, 8315, 2423, 9123, 5296, 19528, 3615, 4117, 41779, 16472, 6055, 30544, 32748, 6027, 3660, 472, 281, 472, 20328, 5016, 49429, 5296, 10721, 22807, 23758, 13412, 2288, 9566, 49610, 23328, 3224, 9673, 3615, 4117, 41779, 3714, 3215, 10943, 2423, 41435, 472, 281, 472, 293, 16521, 23758, 47525, 3224, 7251, 38436, 8315, 16472, 2423, 41435, 17340, 2514, 293, 2423, 41435, 17340, 307, 472, 281, 472, 293, 16521, 1975, 1829, 8592, 48812, 995, 26895, 25894, 8315, 22807], "avg_logprob": -0.2510146088414378, "compression_ratio": 1.6988636363636365, "no_speech_prob": 0.0, "words": [{"start": 2693.21, "end": 2693.65, "word": "قلنا", "probability": 0.74072265625}, {"start": 2693.65, "end": 2693.87, "word": " ال", "probability": 0.8349609375}, {"start": 2693.87, "end": 2694.79, "word": " existence", "probability": 0.91259765625}, {"start": 2694.79, "end": 2696.67, "word": " للمعكوس", "probability": 0.85576171875}, {"start": 2696.67, "end": 2696.83, "word": " ان", "probability": 0.580078125}, {"start": 2696.83, "end": 2697.15, "word": " تكون", "probability": 0.904296875}, {"start": 2697.15, "end": 2697.69, "word": " الدالة", "probability": 0.9327799479166666}, {"start": 2697.69, "end": 2697.91, "word": " one", "probability": 0.8583984375}, {"start": 2697.91, "end": 2698.15, "word": " to", "probability": 0.8974609375}, {"start": 2698.15, "end": 2698.79, "word": " one", "probability": 0.955078125}, {"start": 2698.79, "end": 2699.21, "word": " صح", "probability": 0.949462890625}, {"start": 2699.21, "end": 2699.41, "word": " ولا", "probability": 0.95263671875}, {"start": 2699.41, "end": 2699.93, "word": " لأ؟", "probability": 0.6748860677083334}, {"start": 2699.93, "end": 2700.15, "word": " هذا", "probability": 0.7451171875}, {"start": 2700.15, "end": 2700.69, "word": " شرط", "probability": 0.9396158854166666}, {"start": 2700.69, "end": 2701.21, "word": " وجوده", "probability": 0.8564453125}, {"start": 2701.21, "end": 2701.83, "word": " المعكوس", "probability": 0.872802734375}, {"start": 2701.83, "end": 2702.85, "word": " مدام", "probability": 0.6650390625}, {"start": 2702.85, "end": 2703.07, "word": " ال", "probability": 0.8583984375}, {"start": 2703.07, "end": 2703.31, "word": " Phi", "probability": 0.089111328125}, {"start": 2703.31, "end": 2703.71, "word": " one", "probability": 0.88037109375}, {"start": 2703.71, "end": 2703.99, "word": " to", "probability": 0.96728515625}, {"start": 2703.99, "end": 2704.31, "word": " one", "probability": 0.95947265625}, {"start": 2704.31, "end": 2704.77, "word": " and", "probability": 0.865234375}, {"start": 2704.77, "end": 2705.33, "word": " unto", "probability": 0.29443359375}, {"start": 2705.33, "end": 2706.27, "word": " هذا", "probability": 0.7353515625}, {"start": 2706.27, "end": 2706.89, "word": " بده", "probability": 0.574951171875}, {"start": 2706.89, "end": 2707.61, "word": " يقينا", "probability": 0.7640787760416666}, {"start": 2707.61, "end": 2707.95, "word": " ان", "probability": 0.86767578125}, {"start": 2707.95, "end": 2708.33, "word": " ال", "probability": 0.83447265625}, {"start": 2708.33, "end": 2708.71, "word": " Phi", "probability": 0.93359375}, {"start": 2708.71, "end": 2709.53, "word": " inverse", "probability": 0.869140625}, {"start": 2709.53, "end": 2710.41, "word": " exist", "probability": 0.7177734375}, {"start": 2710.41, "end": 2712.07, "word": " and", "probability": 0.66015625}, {"start": 2712.07, "end": 2712.97, "word": " ال", "probability": 0.77490234375}, {"start": 2712.97, "end": 2713.59, "word": " Phi", "probability": 0.95068359375}, {"start": 2713.59, "end": 2714.55, "word": " inverse", "probability": 0.875}, {"start": 2714.55, "end": 2715.29, "word": " is", "probability": 0.94873046875}, {"start": 2715.29, "end": 2715.77, "word": " one", "probability": 0.962890625}, {"start": 2715.77, "end": 2716.21, "word": " to", "probability": 0.97314453125}, {"start": 2716.21, "end": 2716.79, "word": " one", "probability": 0.955078125}, {"start": 2716.79, "end": 2717.43, "word": " and", "probability": 0.95361328125}, {"start": 2717.43, "end": 2718.27, "word": " unto", "probability": 0.974609375}, {"start": 2718.27, "end": 2720.19, "word": " ايش", "probability": 0.5894368489583334}, {"start": 2720.19, "end": 2720.51, "word": " ضايل", "probability": 0.8990885416666666}, {"start": 2720.51, "end": 2721.25, "word": " علينا؟", "probability": 0.9402669270833334}], "temperature": 1.0}, {"id": 95, "seek": 275085, "start": 2721.53, "end": 2750.85, "text": "نثبت ان هو homomorphism يبقى it remains that ضايل علينا نثبت ان الـ Phi inverse is a homomorphism why؟ يبقى بده روح اخد Phi inverse بده يكون من وين لوين من S لR", "tokens": [1863, 12984, 3555, 2655, 16472, 31439, 3655, 32702, 1434, 7251, 3555, 4587, 7578, 309, 7023, 300, 48812, 995, 26895, 25894, 8315, 8717, 12984, 3555, 2655, 16472, 2423, 39184, 41435, 17340, 307, 257, 3655, 32702, 1434, 983, 22807, 7251, 3555, 4587, 7578, 47525, 3224, 12602, 2407, 5016, 1975, 9778, 3215, 41435, 17340, 47525, 3224, 7251, 30544, 9154, 4032, 9957, 5296, 2407, 9957, 9154, 318, 5296, 49], "avg_logprob": -0.43039772546652594, "compression_ratio": 1.457516339869281, "no_speech_prob": 0.0, "words": [{"start": 2721.53, "end": 2722.01, "word": "نثبت", "probability": 0.7857666015625}, {"start": 2722.01, "end": 2723.21, "word": " ان", "probability": 0.363525390625}, {"start": 2723.21, "end": 2723.45, "word": " هو", "probability": 0.34912109375}, {"start": 2723.45, "end": 2724.89, "word": " homomorphism", "probability": 0.6751708984375}, {"start": 2724.89, "end": 2726.09, "word": " يبقى", "probability": 0.8619384765625}, {"start": 2726.09, "end": 2726.59, "word": " it", "probability": 0.59765625}, {"start": 2726.59, "end": 2729.37, "word": " remains", "probability": 0.6884765625}, {"start": 2729.37, "end": 2731.41, "word": " that", "probability": 0.6123046875}, {"start": 2731.41, "end": 2732.43, "word": " ضايل", "probability": 0.8203125}, {"start": 2732.43, "end": 2732.93, "word": " علينا", "probability": 0.934326171875}, {"start": 2732.93, "end": 2733.55, "word": " نثبت", "probability": 0.86456298828125}, {"start": 2733.55, "end": 2734.07, "word": " ان", "probability": 0.73388671875}, {"start": 2734.07, "end": 2734.41, "word": " الـ", "probability": 0.3424072265625}, {"start": 2734.41, "end": 2734.63, "word": " Phi", "probability": 0.2144775390625}, {"start": 2734.63, "end": 2735.33, "word": " inverse", "probability": 0.6806640625}, {"start": 2735.33, "end": 2736.05, "word": " is", "probability": 0.66064453125}, {"start": 2736.05, "end": 2737.03, "word": " a", "probability": 0.72119140625}, {"start": 2737.03, "end": 2739.81, "word": " homomorphism", "probability": 0.9666341145833334}, {"start": 2739.81, "end": 2742.03, "word": " why؟", "probability": 0.43408203125}, {"start": 2742.03, "end": 2742.41, "word": " يبقى", "probability": 0.963623046875}, {"start": 2742.41, "end": 2742.71, "word": " بده", "probability": 0.419921875}, {"start": 2742.71, "end": 2743.43, "word": " روح", "probability": 0.7327880859375}, {"start": 2743.43, "end": 2744.19, "word": " اخد", "probability": 0.7605794270833334}, {"start": 2744.19, "end": 2744.47, "word": " Phi", "probability": 0.68115234375}, {"start": 2744.47, "end": 2744.83, "word": " inverse", "probability": 0.85986328125}, {"start": 2744.83, "end": 2745.07, "word": " بده", "probability": 0.7313232421875}, {"start": 2745.07, "end": 2745.27, "word": " يكون", "probability": 0.780029296875}, {"start": 2745.27, "end": 2745.41, "word": " من", "probability": 0.984375}, {"start": 2745.41, "end": 2745.61, "word": " وين", "probability": 0.3414306640625}, {"start": 2745.61, "end": 2746.11, "word": " لوين", "probability": 0.5859375}, {"start": 2746.11, "end": 2747.65, "word": " من", 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Phi of R1 في Phi of R2 ال Phi همومورفيزيوم يبقى Phi of R1 R2 فبدي أثر على الطرفين ب Phi inverse يبقى بيصير Phi inverse of S1 S2 بدل يساوي Phi inverse ل Phi of R1 R2", "tokens": [1829, 3555, 4587, 7578, 23758, 47525, 1211, 7251, 3794, 995, 45865, 41435, 295, 497, 16, 8978, 41435, 295, 497, 17, 2423, 41435, 8032, 2304, 20498, 13063, 41185, 11622, 1829, 20498, 7251, 3555, 4587, 7578, 41435, 295, 497, 16, 497, 17, 6156, 3555, 16254, 5551, 49115, 15844, 41950, 28480, 9957, 4724, 41435, 17340, 7251, 3555, 4587, 7578, 4724, 1829, 9381, 13546, 41435, 17340, 295, 318, 16, 318, 17, 47525, 1211, 7251, 3794, 995, 45865, 41435, 17340, 5296, 41435, 295, 497, 16, 497, 17], "avg_logprob": -0.2200677746749786, "compression_ratio": 1.6933333333333334, "no_speech_prob": 0.0, "words": [{"start": 2927.46, "end": 2928.1, "word": "يبقى", "probability": 0.890869140625}, {"start": 2928.1, "end": 2928.44, "word": " هذا", "probability": 0.908203125}, {"start": 2928.44, "end": 2928.84, "word": " بدل", 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0.9744873046875}, {"start": 2945.02, "end": 2945.62, "word": " بيصير", "probability": 0.895263671875}, {"start": 2945.62, "end": 2946.2, "word": " Phi", "probability": 0.95263671875}, {"start": 2946.2, "end": 2946.88, "word": " inverse", "probability": 0.83935546875}, {"start": 2946.88, "end": 2947.22, "word": " of", "probability": 0.93994140625}, {"start": 2947.22, "end": 2948.14, "word": " S1", "probability": 0.978271484375}, {"start": 2948.14, "end": 2949.14, "word": " S2", "probability": 0.928955078125}, {"start": 2949.14, "end": 2949.98, "word": " بدل", "probability": 0.903076171875}, {"start": 2949.98, "end": 2950.6, "word": " يساوي", "probability": 0.9815673828125}, {"start": 2950.6, "end": 2951.18, "word": " Phi", "probability": 0.9404296875}, {"start": 2951.18, "end": 2952.02, "word": " inverse", "probability": 0.83203125}, {"start": 2952.02, "end": 2952.3, "word": " ل", "probability": 0.90625}, {"start": 2952.3, "end": 2952.86, "word": " Phi", "probability": 0.5517578125}, 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diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c1c029477c637c3932752a7cce96ebba84d95520
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4964, "start": 20.82, "end": 49.64, "text": "بسم الله الرحمن الرحيم نكمل النظرية اللي انتهينا منها في المرة الماضية، انتهينا في الشطرة الأول، بقى الشطرة الثانية، فكان باختصار أنها النظرية البردية الـR modulo A is a ring if and only if الـA is an ID، تمام؟", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 24793, 1211, 28239, 19913, 2288, 10632, 13672, 1829, 16472, 47395, 1829, 8315, 9154, 11296, 8978, 9673, 25720, 9673, 46958, 10632, 12399, 16472, 47395, 1829, 8315, 8978, 25124, 9566, 25720, 16247, 12610, 12399, 4724, 4587, 7578, 25124, 9566, 25720, 6024, 104, 7649, 10632, 12399, 6156, 41361, 4724, 47283, 2655, 9381, 9640, 14739, 11296, 28239, 19913, 2288, 10632, 2423, 26890, 3215, 10632, 2423, 39184, 49, 1072, 13455, 316, 307, 257, 4875, 498, 293, 787, 498, 2423, 39184, 32, 307, 364, 7348, 12399, 46811, 10943, 22807], "avg_logprob": -0.21409574690017294, "compression_ratio": 1.7626262626262625, "no_speech_prob": 0.0, 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0.7032470703125}, {"start": 104.4, "end": 104.94, "word": " نمشي", "probability": 0.9969482421875}, {"start": 104.94, "end": 105.12, "word": " في", "probability": 0.9697265625}, {"start": 105.12, "end": 106.06, "word": " الاتجاه", "probability": 0.8966064453125}, {"start": 106.06, "end": 107.12, "word": " المعكس", "probability": 0.86822509765625}], "temperature": 1.0}, {"id": 4, "seek": 13599, "start": 107.51, "end": 135.99, "text": "الجبوح بقوله بنتكمل conversely بعد الشي اللي كتبتيه المرة اللي فاتت بقوله conversely assume that افترضي ان ال R modulo A is a ring شو اللي بدنا نعمله one two sure that", "tokens": [6027, 7435, 3555, 2407, 5016, 4724, 39648, 3224, 4724, 29399, 24793, 1211, 2615, 736, 39182, 25124, 1829, 13672, 1829, 9122, 2655, 3555, 31371, 3224, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 4724, 39648, 3224, 2615, 736, 6552, 300, 1975, 5172, 2655, 43042, 1829, 16472, 2423, 497, 1072, 13455, 316, 307, 257, 4875, 13412, 2407, 13672, 1829, 47525, 8315, 8717, 25957, 43761, 472, 732, 988, 300], "avg_logprob": -0.3037405443010908, "compression_ratio": 1.4610778443113772, "no_speech_prob": 0.0, "words": [{"start": 107.51, "end": 108.35, "word": "الجبوح", "probability": 0.641748046875}, {"start": 108.35, "end": 109.23, "word": " بقوله", "probability": 0.81787109375}, {"start": 109.23, "end": 110.41, "word": " بنتكمل", "probability": 0.66168212890625}, {"start": 110.41, "end": 112.01, "word": " conversely", "probability": 0.65673828125}, {"start": 112.01, "end": 112.77, "word": " بعد", "probability": 0.53076171875}, {"start": 112.77, "end": 113.19, "word": " الشي", "probability": 0.838623046875}, {"start": 113.19, "end": 113.37, "word": " اللي", "probability": 0.731201171875}, {"start": 113.37, "end": 113.97, "word": " كتبتيه", "probability": 0.9439453125}, {"start": 113.97, "end": 114.31, "word": " المرة", "probability": 0.822265625}, {"start": 114.31, "end": 114.51, "word": " اللي", "probability": 0.732666015625}, {"start": 114.51, "end": 114.83, "word": " فاتت", "probability": 0.6184488932291666}, {"start": 114.83, "end": 115.15, "word": " بقوله", "probability": 0.3490804036458333}, {"start": 115.15, "end": 116.31, "word": " conversely", "probability": 0.82080078125}, {"start": 116.31, "end": 118.33, "word": " assume", "probability": 0.7275390625}, {"start": 118.33, "end": 121.39, "word": " that", "probability": 0.85791015625}, {"start": 121.39, "end": 122.93, "word": " افترضي", "probability": 0.86005859375}, {"start": 122.93, "end": 123.57, "word": " ان", "probability": 0.7939453125}, {"start": 123.57, "end": 123.93, "word": " ال", "probability": 0.826171875}, {"start": 123.93, "end": 124.39, "word": " R", "probability": 0.489501953125}, {"start": 124.39, "end": 125.21, "word": " modulo", "probability": 0.785888671875}, {"start": 125.21, "end": 125.67, "word": " A", "probability": 0.7978515625}, {"start": 125.67, "end": 126.47, "word": " is", "probability": 0.80419921875}, {"start": 126.47, "end": 127.05, "word": " a", "probability": 0.7275390625}, {"start": 127.05, "end": 127.73, "word": " ring", "probability": 0.97705078125}, {"start": 127.73, "end": 128.77, "word": " شو", "probability": 0.971435546875}, {"start": 128.77, "end": 128.95, "word": " اللي", "probability": 0.9765625}, {"start": 128.95, "end": 129.29, "word": " بدنا", "probability": 0.9677734375}, {"start": 129.29, "end": 130.09, "word": " نعمله", "probability": 0.994140625}, {"start": 130.09, "end": 131.03, "word": " one", "probability": 0.61767578125}, {"start": 131.03, "end": 132.41, "word": " two", "probability": 0.603515625}, {"start": 132.41, "end": 133.91, "word": " sure", "probability": 0.7607421875}, {"start": 133.91, "end": 135.99, "word": " that", "probability": 0.9462890625}], "temperature": 1.0}, {"id": 5, "seek": 16719, "start": 137.73, "end": 167.19, "text": "إن الـ A is an ID يبقى هذا اللي بنثبته هحاول نثبت أنه A is ID طبعا اتعلمنا في مبادئ الرياضيات أن هناك أكثر من طريقة للبرهان في أنحاج اسمه ال Direct Probe في حيث ال Probe بواسط Contradiction أو Contrapositive هحاول نثبت هذا الكلام بواسط Contradiction", "tokens": [28814, 1863, 2423, 39184, 316, 307, 364, 7348, 7251, 3555, 4587, 7578, 23758, 13672, 1829, 44945, 12984, 3555, 2655, 3224, 8032, 5016, 995, 12610, 8717, 12984, 3555, 2655, 14739, 3224, 316, 307, 7348, 23032, 3555, 3615, 995, 1975, 2655, 3615, 19528, 8315, 8978, 3714, 3555, 18513, 19986, 2423, 16572, 46958, 1829, 9307, 14739, 34105, 4117, 5551, 4117, 49115, 9154, 23032, 16572, 28671, 24976, 26890, 3224, 7649, 8978, 14739, 5016, 26108, 24525, 2304, 3224, 2423, 18308, 1705, 650, 8978, 11331, 1829, 12984, 2423, 1705, 650, 4724, 14407, 3794, 9566, 4839, 6206, 4105, 34051, 4839, 4007, 329, 2187, 8032, 5016, 995, 12610, 8717, 12984, 3555, 2655, 23758, 2423, 28820, 10943, 4724, 14407, 3794, 9566, 4839, 6206, 4105], "avg_logprob": -0.17941809612615356, "compression_ratio": 1.6768558951965065, "no_speech_prob": 0.0, "words": [{"start": 137.73, "end": 138.11, "word": "إن", "probability": 0.6400146484375}, 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0.9934895833333334}, {"start": 153.35, "end": 154.87, "word": " للبرهان", "probability": 0.9117431640625}, {"start": 154.87, "end": 155.05, "word": " في", "probability": 0.69140625}, {"start": 155.05, "end": 155.51, "word": " أنحاج", "probability": 0.7679036458333334}, {"start": 155.51, "end": 155.97, "word": " اسمه", "probability": 0.9329427083333334}, {"start": 155.97, "end": 156.03, "word": " ال", "probability": 0.68115234375}, {"start": 156.03, "end": 156.43, "word": " Direct", "probability": 0.349609375}, {"start": 156.43, "end": 157.19, "word": " Probe", "probability": 0.755126953125}, {"start": 157.19, "end": 157.67, "word": " في", "probability": 0.876953125}, {"start": 157.67, "end": 157.99, "word": " حيث", "probability": 0.9111328125}, {"start": 157.99, "end": 158.19, "word": " ال", "probability": 0.634765625}, {"start": 158.19, "end": 158.69, "word": " Probe", "probability": 0.6630859375}, {"start": 158.69, "end": 159.93, "word": " بواسط", "probability": 0.9130859375}, {"start": 159.93, "end": 161.15, "word": " Contradiction", "probability": 0.74267578125}, {"start": 161.15, "end": 161.51, "word": " أو", "probability": 0.7744140625}, {"start": 161.51, "end": 162.75, "word": " Contrapositive", "probability": 0.81982421875}, {"start": 162.75, "end": 163.77, "word": " هحاول", "probability": 0.9693603515625}, {"start": 163.77, "end": 164.27, "word": " نثبت", "probability": 0.9923095703125}, {"start": 164.27, "end": 164.51, "word": " هذا", "probability": 0.9580078125}, {"start": 164.51, "end": 165.05, "word": " الكلام", "probability": 0.9576822916666666}, {"start": 165.05, "end": 165.79, "word": " بواسط", "probability": 0.987060546875}, {"start": 165.79, "end": 167.19, "word": " Contradiction", "probability": 0.8611653645833334}], "temperature": 1.0}, {"id": 6, "seek": 19406, "start": 167.48, "end": 194.06, "text": "Okay احنا بنقول بدنا نحاول نثبت نبين ان ال A is an ideal of ال ring اللي عندنا هذي of A ده يقوله suppose not افترض ان هذا كلام مش صحيح يبقى suppose not يعني افترض ان هذا مش ideal", "tokens": [8297, 1975, 5016, 8315, 44945, 39648, 47525, 8315, 8717, 5016, 995, 12610, 8717, 12984, 3555, 2655, 8717, 3555, 9957, 16472, 2423, 316, 307, 364, 7157, 295, 2423, 4875, 13672, 1829, 43242, 8315, 8032, 8848, 1829, 295, 316, 11778, 3224, 7251, 39648, 3224, 7297, 406, 1975, 5172, 2655, 43042, 16472, 23758, 28242, 10943, 37893, 20328, 5016, 1829, 5016, 7251, 3555, 4587, 7578, 7297, 406, 37495, 22653, 1975, 5172, 2655, 43042, 16472, 23758, 37893, 7157], "avg_logprob": -0.2493665435829678, "compression_ratio": 1.5730994152046784, "no_speech_prob": 0.0, "words": [{"start": 167.48, "end": 167.88, "word": "Okay", "probability": 0.0638427734375}, {"start": 167.88, "end": 169.04, "word": " احنا", "probability": 0.8987630208333334}, {"start": 169.04, "end": 169.5, "word": " بنقول", "probability": 0.784912109375}, {"start": 169.5, "end": 169.92, "word": " بدنا", "probability": 0.7142333984375}, {"start": 169.92, "end": 170.5, "word": " نحاول", 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ماقدر أقول موجود في A؟ ليس بالضرورة، يبقى مش موجود في A or ال A or ال R، A مش موجود فيه، هذا هو", "tokens": [1829, 3555, 4587, 7578, 20666, 1829, 4724, 39648, 3224, 45164, 25961, 2423, 316, 3714, 29245, 23328, 8978, 316, 293, 2423, 497, 3714, 29245, 23328, 8978, 497, 550, 2423, 316, 497, 19446, 28543, 2288, 5551, 39648, 3714, 29245, 23328, 8978, 316, 22807, 32239, 3794, 20666, 11242, 2288, 13063, 3660, 12399, 7251, 3555, 4587, 7578, 37893, 3714, 29245, 23328, 8978, 316, 420, 2423, 316, 420, 2423, 497, 12399, 316, 37893, 3714, 29245, 23328, 8978, 3224, 12399, 23758, 31439], "avg_logprob": -0.20008117037934142, "compression_ratio": 1.816326530612245, "no_speech_prob": 0.0, "words": [{"start": 195.71, "end": 196.25, "word": "يبقى", "probability": 0.908935546875}, {"start": 196.25, "end": 196.67, "word": " بالي", "probability": 0.624755859375}, {"start": 196.67, "end": 197.43, "word": " بقوله", "probability": 0.7591145833333334}, {"start": 197.43, "end": 197.87, "word": " لو", 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element", "probability": 0.87744140625}, {"start": 448.52, "end": 449.14, "word": " من", "probability": 0.99609375}, {"start": 449.14, "end": 449.62, "word": " A", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 16, "seek": 47844, "start": 450.04, "end": 478.44, "text": "R زائد له كبتل A هو عنصر موجود وين في ال factoring R modulo A الآن بناخد بعض الأمثلة على ذلك أول مثال على هذا الموضوع نفجر examples نملك واحد الـ Z", "tokens": [49, 30767, 16373, 3215, 46740, 9122, 3555, 2655, 1211, 316, 31439, 18871, 9381, 2288, 3714, 29245, 23328, 4032, 9957, 8978, 2423, 1186, 3662, 497, 1072, 13455, 316, 6024, 48506, 44945, 47283, 3215, 45030, 11242, 16247, 2304, 12984, 37977, 15844, 29910, 23275, 5551, 12610, 50113, 6027, 15844, 23758, 9673, 2407, 11242, 45367, 8717, 5172, 7435, 2288, 5110, 8717, 2304, 23275, 36764, 24401, 2423, 39184, 1176], "avg_logprob": -0.40697115384615384, "compression_ratio": 1.3352272727272727, "no_speech_prob": 0.0, "words": [{"start": 450.04, "end": 450.9, 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{"start": 458.04, "end": 459.06, "word": " modulo", "probability": 0.74267578125}, {"start": 459.06, "end": 459.52, "word": " A", "probability": 0.90283203125}, {"start": 459.52, "end": 460.44, "word": " الآن", "probability": 0.59649658203125}, {"start": 460.44, "end": 461.1, "word": " بناخد", "probability": 0.7899576822916666}, {"start": 461.1, "end": 461.68, "word": " بعض", "probability": 0.897705078125}, {"start": 461.68, "end": 463.3, "word": " الأمثلة", "probability": 0.9461669921875}, {"start": 463.3, "end": 463.78, "word": " على", "probability": 0.744140625}, {"start": 463.78, "end": 464.66, "word": " ذلك", "probability": 0.985595703125}, {"start": 464.66, "end": 465.12, "word": " أول", "probability": 0.796630859375}, {"start": 465.12, "end": 465.68, "word": " مثال", "probability": 0.913818359375}, {"start": 465.68, "end": 465.9, "word": " على", "probability": 0.84521484375}, {"start": 465.9, "end": 466.48, "word": " هذا", "probability": 0.947265625}, {"start": 466.48, "end": 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5551, 25513, 27884, 30767, 3215, 4032, 11933, 2655, 1863, 9957, 30767, 16373, 3215, 5551, 25513, 27884, 30767, 3215, 4032, 6055, 1211, 9307, 3660, 30767, 16373, 3215, 5551, 25513, 27884, 30767, 3215, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105, 479, 15104], "avg_logprob": -0.20537243803886518, "compression_ratio": 1.8208955223880596, "no_speech_prob": 0.0, "words": [{"start": 479.16, "end": 480.46, "word": "موديولو", "probability": 0.709228515625}, {"start": 480.46, "end": 481.44, "word": " أربعة", "probability": 0.7337239583333334}, {"start": 481.44, "end": 482.4, "word": " زد", "probability": 0.513427734375}, {"start": 482.4, "end": 484.84, "word": " عناصرها", "probability": 0.9169921875}, {"start": 484.84, "end": 485.54, "word": " ال", "probability": 0.66064453125}, {"start": 485.54, "end": 485.8, "word": " E", "probability": 0.4638671875}, {"start": 485.8, "end": 486.44, "word": " Zero", "probability": 0.277099609375}, {"start": 486.44, "end": 488.18, "word": " زائد", "probability": 0.8889973958333334}, {"start": 488.18, "end": 489.06, "word": " أربعة", "probability": 0.8963216145833334}, {"start": 489.06, "end": 489.6, "word": " زد", "probability": 0.9833984375}, {"start": 489.6, "end": 490.5, "word": " و", "probability": 0.779296875}, {"start": 490.5, "end": 491.36, "word": " واحد", "probability": 0.81103515625}, {"start": 491.36, "end": 492.1, "word": " زائد", "probability": 0.9892578125}, {"start": 492.1, "end": 492.84, "word": " أربعة", "probability": 0.9495442708333334}, {"start": 492.84, "end": 493.5, "word": " زد", "probability": 0.992431640625}, {"start": 493.5, "end": 494.36, "word": " و", "probability": 0.88720703125}, {"start": 494.36, "end": 495.5, "word": " إتنين", "probability": 0.81573486328125}, {"start": 495.5, "end": 496.4, "word": " زائد", "probability": 0.9853515625}, {"start": 496.4, "end": 497.16, "word": " أربعة", "probability": 0.9581705729166666}, {"start": 497.16, "end": 497.82, "word": " زد", "probability": 0.9931640625}, {"start": 497.82, "end": 498.48, "word": " و", "probability": 0.90234375}, {"start": 498.48, "end": 499.5, "word": " تلاتة", "probability": 0.8853759765625}, {"start": 499.5, "end": 500.44, "word": " زائد", "probability": 0.98681640625}, {"start": 500.44, "end": 501.28, "word": " أربعة", "probability": 0.955078125}, {"start": 501.28, "end": 502.24, "word": " زد", "probability": 0.99072265625}, {"start": 502.24, "end": 502.92, "word": " بالشكل", "probability": 0.9425455729166666}, {"start": 502.92, "end": 503.16, "word": " اللي", "probability": 0.966796875}, {"start": 503.16, "end": 503.66, "word": " عندنا", "probability": 0.95556640625}, {"start": 503.66, "end": 504.0, "word": " هنا", "probability": 0.63232421875}, {"start": 504.0, "end": 508.46, "word": " Factor", "probability": 0.5191650390625}], "temperature": 1.0}, {"id": 18, "seek": 53830, "start": 510.05, "end": 538.31, "text": "Ring is a factor ring because الأربعة Z is an ideal of the ring Z طب نحن أقنعكم مثال سابقا ان NZ is an ideal of Z", "tokens": [49, 278, 307, 257, 5952, 4875, 570, 16247, 25513, 27884, 1176, 307, 364, 7157, 295, 264, 4875, 1176, 23032, 3555, 8717, 5016, 1863, 5551, 4587, 1863, 3615, 24793, 50113, 6027, 8608, 16758, 4587, 995, 16472, 426, 57, 307, 364, 7157, 295, 1176], "avg_logprob": -0.37536336654840513, "compression_ratio": 1.1833333333333333, "no_speech_prob": 0.0, "words": [{"start": 510.05, "end": 510.95, "word": "Ring", "probability": 0.4556884765625}, {"start": 510.95, "end": 513.01, "word": " is", "probability": 0.55712890625}, {"start": 513.01, "end": 513.47, "word": " a", "probability": 0.86376953125}, {"start": 513.47, "end": 513.93, "word": " factor", "probability": 0.7353515625}, {"start": 513.93, "end": 514.61, "word": " ring", "probability": 0.79052734375}, {"start": 514.61, "end": 516.95, "word": " because", "probability": 0.7763671875}, {"start": 516.95, "end": 520.67, "word": " الأربعة", "probability": 0.7220052083333334}, {"start": 520.67, "end": 521.15, "word": " Z", 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28242, 3224, 6225, 3555, 9640, 3660, 18871, 7157, 8978, 2423, 4875, 16247, 3794, 32277, 1829, 13672, 1829, 31439, 2135, 710, 46599, 6027, 2655, 6027, 1829, 3714, 18513, 10943, 7157, 7251, 3555, 4587, 7578, 29538, 6225, 3555, 9640, 3660, 18871, 5952, 4875, 3714, 4117, 2407, 1863, 3660, 9154, 2135, 3714, 30544, 3660, 9154, 5551, 25513, 27884, 14739, 9381, 9640, 6024, 48506], "avg_logprob": -0.24023437957194718, "compression_ratio": 1.5572916666666667, "no_speech_prob": 0.0, "words": [{"start": 539.75, "end": 540.45, "word": "عدد", "probability": 0.759033203125}, {"start": 540.45, "end": 541.63, "word": " صحيح", "probability": 0.98486328125}, {"start": 541.63, "end": 542.21, "word": " موجب", "probability": 0.7181803385416666}, {"start": 542.21, "end": 542.97, "word": " in", "probability": 0.26025390625}, {"start": 542.97, "end": 543.61, "word": " positive", "probability": 0.912109375}, {"start": 543.61, "end": 544.27, "word": " integer", "probability": 0.90087890625}, {"start": 544.27, "end": 545.21, "word": " يبقى", "probability": 0.9407958984375}, {"start": 545.21, "end": 545.61, "word": " 2", "probability": 0.69140625}, {"start": 545.61, "end": 545.97, "word": " z", "probability": 0.156982421875}, {"start": 545.97, "end": 547.49, "word": " 3", "probability": 0.60595703125}, {"start": 547.49, "end": 548.11, "word": " z", "probability": 0.82275390625}, {"start": 548.11, "end": 548.67, "word": " 4", "probability": 0.76171875}, {"start": 548.67, "end": 549.07, "word": " z", "probability": 0.935546875}, {"start": 549.07, "end": 549.43, "word": " 5", "probability": 0.85400390625}, {"start": 549.43, "end": 549.87, "word": " z", "probability": 0.8994140625}, {"start": 549.87, "end": 550.25, "word": " 6", "probability": 0.93994140625}, {"start": 550.25, "end": 550.75, "word": " z", "probability": 0.96533203125}, {"start": 550.75, "end": 551.45, "word": " كله", "probability": 0.711181640625}, {"start": 551.45, "end": 551.83, "word": " عبارة", "probability": 0.99267578125}, {"start": 551.83, "end": 552.07, "word": " عن", "probability": 0.98974609375}, {"start": 552.07, "end": 552.49, "word": " ideal", "probability": 0.175537109375}, {"start": 552.49, "end": 552.75, "word": " في", "probability": 0.78369140625}, {"start": 552.75, "end": 552.81, "word": " ال", "probability": 0.9580078125}, {"start": 552.81, "end": 553.01, "word": " ring", "probability": 0.89794921875}, {"start": 553.01, "end": 553.71, "word": " الأساسي", "probability": 0.934326171875}, {"start": 553.71, "end": 553.87, "word": " اللي", "probability": 0.829345703125}, {"start": 553.87, "end": 554.07, "word": " هو", "probability": 0.47021484375}, {"start": 554.07, "end": 554.39, "word": " main", "probability": 0.7470703125}, {"start": 554.39, "end": 555.23, "word": " z", "probability": 0.5419921875}, {"start": 555.23, "end": 556.23, "word": " وبالتالي", "probability": 0.916796875}, {"start": 556.23, "end": 556.73, "word": " مادام", "probability": 0.6959635416666666}, {"start": 556.73, "end": 557.23, "word": " ideal", "probability": 0.6904296875}, {"start": 557.23, "end": 557.69, "word": " يبقى", "probability": 0.976806640625}, {"start": 557.69, "end": 558.09, "word": " هذه", "probability": 0.82421875}, {"start": 558.09, "end": 558.71, "word": " عبارة", "probability": 0.9962158203125}, {"start": 558.71, "end": 559.21, "word": " عن", "probability": 0.98876953125}, {"start": 559.21, "end": 560.01, "word": " factor", "probability": 0.771484375}, {"start": 560.01, "end": 560.53, "word": " ring", "probability": 0.8662109375}, {"start": 560.53, "end": 561.39, "word": " مكونة", "probability": 0.727099609375}, {"start": 561.39, "end": 561.55, "word": " من", "probability": 0.986328125}, {"start": 561.55, "end": 561.95, "word": " main", "probability": 0.57421875}, {"start": 561.95, "end": 563.11, "word": " مكونة", "probability": 0.8323567708333334}, {"start": 563.11, "end": 563.35, "word": " من", "probability": 0.99365234375}, {"start": 563.35, "end": 564.15, "word": " أربعة", "probability": 0.7649739583333334}, {"start": 564.15, "end": 565.07, "word": " أنصار", "probability": 0.84814453125}, {"start": 565.07, "end": 566.95, "word": " الآن", "probability": 0.676513671875}], "temperature": 1.0}, {"id": 20, "seek": 59494, "start": 567.32, "end": 594.94, "text": "بناء على هذا التعريف بدنا نعرف لك كيف أو نوريك كيف بتجمع هذه العناصر أوي بتضربيها مثلا Note that لاحظي لي ما يأتي الان لو بدي أجي أقول اتنين زائد أربعة زيه تمام؟ هذا عنصر بدي أجمع مع تلاتة زائد أربعة زيه", "tokens": [3555, 1863, 16606, 15844, 23758, 16712, 3615, 16572, 5172, 47525, 8315, 8717, 3615, 28480, 5296, 4117, 9122, 33911, 34051, 8717, 13063, 1829, 4117, 9122, 33911, 39894, 7435, 2304, 3615, 29538, 18863, 1863, 33546, 2288, 34051, 1829, 39894, 11242, 25513, 1829, 11296, 50113, 15040, 11633, 300, 20193, 5016, 19913, 1829, 32239, 19446, 7251, 10721, 31371, 2423, 7649, 45164, 4724, 16254, 5551, 7435, 1829, 5551, 39648, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 5551, 25513, 27884, 30767, 1829, 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1502.33, "word": " في", "probability": 0.9462890625}, {"start": 1502.33, "end": 1502.81, "word": " هذه", "probability": 0.953125}, {"start": 1502.81, "end": 1503.15, "word": " ال", "probability": 0.884765625}, {"start": 1503.15, "end": 1503.93, "word": " factor", "probability": 0.9189453125}, {"start": 1503.93, "end": 1504.67, "word": " ring", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 53, "seek": 153410, "start": 1505.52, "end": 1534.1, "text": "تمام يلجبجي بيقوله the factor ring اللي هو مين؟ M2 of Z modulo LI يساوي كل المصفوفات اللي على الشكل A وB وC وD", "tokens": [39237, 10943, 7251, 1211, 7435, 3555, 7435, 1829, 4724, 1829, 39648, 3224, 264, 5952, 4875, 13672, 1829, 31439, 3714, 9957, 22807, 376, 17, 295, 1176, 1072, 13455, 7169, 7251, 3794, 995, 45865, 28242, 9673, 9381, 5172, 38688, 9307, 13672, 1829, 15844, 25124, 28820, 316, 4032, 33, 4032, 34, 4032, 35], "avg_logprob": -0.27512253499498557, "compression_ratio": 1.176056338028169, "no_speech_prob": 0.0, "words": [{"start": 1505.52, "end": 1506.22, "word": "تمام", "probability": 0.6640625}, {"start": 1506.22, "end": 1508.28, "word": " يلجبجي", "probability": 0.62677001953125}, {"start": 1508.28, "end": 1509.1, "word": " بيقوله", "probability": 0.8192138671875}, {"start": 1509.1, "end": 1509.8, "word": " the", "probability": 0.2259521484375}, {"start": 1509.8, "end": 1512.18, "word": " factor", "probability": 0.8408203125}, {"start": 1512.18, "end": 1513.98, "word": " ring", "probability": 0.849609375}, {"start": 1513.98, "end": 1516.08, "word": " اللي", "probability": 0.925048828125}, {"start": 1516.08, "end": 1516.36, "word": " هو", "probability": 0.95947265625}, {"start": 1516.36, "end": 1517.24, "word": " مين؟", "probability": 0.7445475260416666}, {"start": 1517.24, "end": 1518.24, "word": " M2", "probability": 0.581787109375}, {"start": 1518.24, "end": 1518.74, "word": " of", "probability": 0.8095703125}, {"start": 1518.74, "end": 1519.26, "word": " Z", "probability": 0.85546875}, {"start": 1519.26, "end": 1521.0, "word": " modulo", "probability": 0.77294921875}, {"start": 1521.0, "end": 1522.34, "word": " LI", "probability": 0.5078125}, {"start": 1522.34, "end": 1523.8, "word": " يساوي", "probability": 0.8760986328125}, {"start": 1523.8, "end": 1525.14, "word": " كل", "probability": 0.88623046875}, {"start": 1525.14, "end": 1526.96, "word": " المصفوفات", "probability": 0.88447265625}, {"start": 1526.96, "end": 1527.62, "word": " اللي", "probability": 0.974853515625}, {"start": 1527.62, "end": 1527.92, "word": " على", "probability": 0.8310546875}, {"start": 1527.92, "end": 1528.66, "word": " الشكل", "probability": 0.95703125}, {"start": 1528.66, "end": 1529.32, "word": " A", "probability": 0.92138671875}, {"start": 1529.32, "end": 1531.2, "word": " وB", "probability": 0.807373046875}, {"start": 1531.2, "end": 1532.6, "word": " وC", "probability": 0.959716796875}, {"start": 1532.6, "end": 1534.1, "word": " وD", "probability": 0.986572265625}], "temperature": 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زائد", "probability": 0.83251953125}, {"start": 1538.39, "end": 1539.11, "word": " I", "probability": 0.87060546875}, {"start": 1539.11, "end": 1543.65, "word": " تمام؟", "probability": 0.55126953125}, {"start": 1543.65, "end": 1544.39, "word": " هذه", "probability": 0.7841796875}, {"start": 1544.39, "end": 1545.05, "word": " أنا", "probability": 0.74951171875}, {"start": 1545.05, "end": 1546.21, "word": " أزعم", "probability": 0.9256184895833334}, {"start": 1546.21, "end": 1547.51, "word": " أنها", "probability": 0.908203125}, {"start": 1547.51, "end": 1548.83, "word": " تساوي", "probability": 0.9757080078125}, {"start": 1548.83, "end": 1550.13, "word": " من", "probability": 0.98291015625}, {"start": 1550.13, "end": 1550.83, "word": " اللي", "probability": 0.91748046875}, {"start": 1550.83, "end": 1551.13, "word": " هي", "probability": 0.49658203125}, {"start": 1551.13, "end": 1551.91, "word": " تساوي", "probability": 0.982177734375}, {"start": 1551.91, "end": 1552.85, "word": " R1", 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"end": 1590.31, "text": "موجودة في الـ set 01 مرة ثانية نفسر نفسر الكلام اللي احنا قاليله ال M2Z modulo I أخذ element من ال ring هذي مين ما يكون يكون سميته ABCD زغط I مية المية", "tokens": [2304, 29245, 23328, 3660, 8978, 2423, 39184, 992, 23185, 3714, 25720, 38637, 7649, 10632, 8717, 36178, 2288, 8717, 36178, 2288, 2423, 28820, 10943, 13672, 1829, 1975, 5016, 8315, 12174, 6027, 26895, 3224, 2423, 376, 17, 57, 1072, 13455, 286, 5551, 9778, 8848, 4478, 9154, 2423, 4875, 8032, 8848, 1829, 3714, 9957, 19446, 7251, 30544, 7251, 30544, 8608, 2304, 36081, 3224, 22342, 35, 30767, 17082, 9566, 286, 3714, 10632, 9673, 10632], "avg_logprob": -0.2810299270589587, "compression_ratio": 1.3735632183908046, "no_speech_prob": 0.0, "words": [{"start": 1564.33, "end": 1565.47, "word": "موجودة", "probability": 0.91650390625}, {"start": 1565.47, "end": 1565.59, "word": " في", "probability": 0.94189453125}, {"start": 1565.59, "end": 1565.87, "word": " الـ", "probability": 0.57373046875}, {"start": 1565.87, "end": 1566.27, "word": " set", "probability": 0.284912109375}, {"start": 1566.27, "end": 1567.49, "word": " 01", "probability": 0.54345703125}, {"start": 1567.49, "end": 1574.07, "word": " مرة", "probability": 0.94873046875}, {"start": 1574.07, "end": 1574.43, "word": " ثانية", "probability": 0.83447265625}, {"start": 1574.43, "end": 1575.13, "word": " نفسر", "probability": 0.87841796875}, {"start": 1575.13, "end": 1577.17, "word": " نفسر", "probability": 0.84814453125}, {"start": 1577.17, "end": 1577.53, "word": " الكلام", "probability": 0.7854817708333334}, {"start": 1577.53, "end": 1577.63, "word": " اللي", "probability": 0.911376953125}, {"start": 1577.63, "end": 1577.77, "word": " احنا", "probability": 0.739990234375}, {"start": 1577.77, "end": 1578.43, "word": " قاليله", "probability": 0.7059326171875}, {"start": 1578.43, "end": 1579.33, "word": " ال", "probability": 0.76220703125}, {"start": 1579.33, "end": 1580.41, "word": " M2Z", "probability": 0.5867513020833334}, {"start": 1580.41, "end": 1581.19, "word": " modulo", "probability": 0.7685546875}, {"start": 1581.19, "end": 1581.67, "word": " I", "probability": 0.95361328125}, {"start": 1581.67, "end": 1582.57, "word": " أخذ", "probability": 0.8987630208333334}, {"start": 1582.57, "end": 1583.35, "word": " element", "probability": 0.60302734375}, {"start": 1583.35, "end": 1583.75, "word": " من", "probability": 0.994140625}, {"start": 1583.75, "end": 1583.97, "word": " ال", "probability": 0.9638671875}, {"start": 1583.97, "end": 1584.27, "word": " ring", "probability": 0.80224609375}, {"start": 1584.27, "end": 1584.77, "word": " هذي", "probability": 0.6839192708333334}, {"start": 1584.77, "end": 1585.13, "word": " مين", "probability": 0.7255859375}, {"start": 1585.13, "end": 1585.31, "word": " ما", "probability": 0.927734375}, {"start": 1585.31, "end": 1585.71, "word": " يكون", "probability": 0.846923828125}, {"start": 1585.71, "end": 1586.21, "word": " يكون", "probability": 0.96484375}, {"start": 1586.21, "end": 1587.31, "word": " سميته", "probability": 0.8297119140625}, {"start": 1587.31, "end": 1588.39, "word": " ABCD", "probability": 0.723388671875}, {"start": 1588.39, "end": 1588.97, "word": " زغط", "probability": 0.5107421875}, {"start": 1588.97, "end": 1589.33, "word": " I", "probability": 0.9716796875}, {"start": 1589.33, "end": 1589.81, "word": " مية", "probability": 0.772216796875}, {"start": 1589.81, "end": 1590.31, "word": " المية", "probability": 0.5284423828125}], "temperature": 1.0}, {"id": 56, "seek": 161636, "start": 1590.84, "end": 1616.36, "text": "بقوللي هذه تساوي عمليا ا ر واحد ا ر اتنين ا ر ثلاثة ا ر اربعة زي اد اعي مين الارات هدول بيقوللي ا ا يا اما صفر يا اما واحد غير هيك يبعتلك الله بيقوللي يا سلام قاللي اه هذا السؤال", "tokens": [3555, 39648, 20292, 29538, 6055, 3794, 995, 45865, 6225, 2304, 20292, 995, 1975, 12602, 36764, 24401, 1975, 12602, 1975, 2655, 1863, 9957, 1975, 12602, 38637, 1211, 5718, 104, 3660, 1975, 12602, 1975, 25513, 27884, 30767, 1829, 1975, 3215, 1975, 3615, 1829, 3714, 9957, 2423, 9640, 9307, 8032, 3215, 12610, 4724, 1829, 39648, 20292, 1975, 1975, 35186, 1975, 15042, 20328, 5172, 2288, 35186, 1975, 15042, 36764, 24401, 32771, 13546, 39896, 4117, 7251, 3555, 34268, 23275, 21984, 4724, 1829, 39648, 20292, 35186, 8608, 37440, 50239, 20292, 1975, 3224, 23758, 21136, 33604, 6027], "avg_logprob": -0.3112980625131628, "compression_ratio": 1.9444444444444444, "no_speech_prob": 0.0, "words": [{"start": 1590.84, "end": 1591.4, "word": "بقوللي", "probability": 0.5904134114583334}, {"start": 1591.4, "end": 1591.76, "word": " هذه", "probability": 0.830078125}, {"start": 1591.76, "end": 1592.5, "word": " تساوي", "probability": 0.9312744140625}, {"start": 1592.5, "end": 1593.58, "word": " عمليا", "probability": 0.77288818359375}, {"start": 1593.58, "end": 1593.88, "word": " ا", "probability": 0.25732421875}, {"start": 1593.88, "end": 1594.04, "word": " ر", "probability": 0.46484375}, {"start": 1594.04, "end": 1594.48, "word": " واحد", "probability": 0.89794921875}, {"start": 1594.48, "end": 1594.64, "word": " ا", "probability": 0.83154296875}, {"start": 1594.64, "end": 1594.78, "word": " ر", "probability": 0.966796875}, {"start": 1594.78, "end": 1595.16, "word": " اتنين", "probability": 0.8763427734375}, {"start": 1595.16, "end": 1595.34, "word": " ا", "probability": 0.958984375}, {"start": 1595.34, "end": 1595.44, "word": " ر", "probability": 0.9619140625}, {"start": 1595.44, "end": 1596.04, "word": " ثلاثة", "probability": 0.82607421875}, {"start": 1596.04, "end": 1596.12, "word": " ا", "probability": 0.95849609375}, {"start": 1596.12, "end": 1596.24, "word": " ر", "probability": 0.88720703125}, {"start": 1596.24, "end": 1596.74, "word": " اربعة", "probability": 0.7247721354166666}, {"start": 1596.74, "end": 1597.22, "word": " زي", "probability": 0.728515625}, {"start": 1597.22, "end": 1597.74, "word": " اد", "probability": 0.43988037109375}, {"start": 1597.74, "end": 1598.56, "word": " اعي", "probability": 0.5292561848958334}, {"start": 1598.56, "end": 1598.94, "word": " مين", "probability": 0.6583251953125}, {"start": 1598.94, "end": 1599.62, "word": " الارات", "probability": 0.620849609375}, {"start": 1599.62, "end": 1600.12, "word": " هدول", "probability": 0.8621419270833334}, {"start": 1600.12, "end": 1600.92, "word": " بيقوللي", "probability": 0.868408203125}, {"start": 1600.92, "end": 1601.4, "word": " ا", "probability": 0.54736328125}, {"start": 1601.4, "end": 1601.86, "word": " ا", "probability": 0.89599609375}, {"start": 1601.86, "end": 1602.24, "word": " يا", "probability": 0.467529296875}, {"start": 1602.24, "end": 1602.62, "word": " اما", "probability": 0.6650390625}, {"start": 1602.62, "end": 1603.5, "word": " صفر", "probability": 0.9562174479166666}, {"start": 1603.5, "end": 1604.34, "word": " يا", "probability": 0.91015625}, {"start": 1604.34, "end": 1604.92, "word": " اما", "probability": 0.946533203125}, {"start": 1604.92, "end": 1605.62, "word": " واحد", "probability": 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1651.27, "text": "اللي احنا بنحاول أن نجيب عليه حتى يكون الكلام هذا تبعناه صحيح طيب this is a true because هتقولي أي مصفوفة", "tokens": [6027, 20292, 1975, 5016, 8315, 44945, 5016, 995, 12610, 14739, 8717, 7435, 1829, 3555, 47356, 11331, 49975, 7251, 30544, 2423, 28820, 10943, 23758, 6055, 3555, 3615, 8315, 3224, 20328, 5016, 1829, 5016, 23032, 1829, 3555, 341, 307, 257, 2074, 570, 8032, 2655, 39648, 1829, 36632, 3714, 9381, 5172, 38688, 3660], "avg_logprob": -0.18305759511741937, "compression_ratio": 1.2835820895522387, "no_speech_prob": 0.0, "words": [{"start": 1622.43, "end": 1622.87, "word": "اللي", "probability": 0.885009765625}, {"start": 1622.87, "end": 1623.31, "word": " احنا", "probability": 0.8935546875}, {"start": 1623.31, "end": 1624.39, "word": " بنحاول", "probability": 0.9134521484375}, {"start": 1624.39, "end": 1624.79, "word": " أن", "probability": 0.477294921875}, {"start": 1624.79, "end": 1625.31, "word": " نجيب", "probability": 0.9793701171875}, {"start": 1625.31, 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اللي جريلك؟ ولا جرينا ولا حاجة، احنا مش هيرمشنا، بس احنا بنشتغل جبه، ماشتغلش real number لو بنتكلم في الأعداد الحقيقية وانت مجنون، عدد تخيلي بساوي عدد حقيقي", "tokens": [9566, 1829, 3555, 23758, 20449, 8315, 47395, 16472, 2423, 286, 47525, 11296, 6055, 3794, 995, 45865, 1975, 2655, 1863, 9957, 1975, 1829, 8592, 22807, 286, 47525, 3224, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 3714, 6027, 4117, 16472, 2655, 22807, 1975, 1829, 8592, 13672, 1829, 10874, 16572, 23275, 22807, 49429, 10874, 16572, 8315, 49429, 11331, 26108, 3660, 12399, 1975, 5016, 8315, 37893, 8032, 13546, 2304, 8592, 8315, 12399, 4724, 3794, 1975, 5016, 8315, 44945, 8592, 2655, 17082, 1211, 10874, 3555, 3224, 12399, 3714, 33599, 2655, 17082, 1211, 8592, 957, 1230, 45164, 4724, 29399, 4117, 19528, 8978, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 4032, 7649, 2655, 3714, 7435, 1863, 11536, 12399, 6225, 3215, 3215, 6055, 9778, 1829, 20292, 4724, 3794, 995, 45865, 6225, 3215, 3215, 11331, 38436, 38436], 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اتنين بنشتغل complex على جبر اتنين مع بعض مش أعداد حقيقية، بلغة الأعداد الحقيقية ده كلام مش صحيح لو جاء يقولوا لواحد خمسة يساوي صفر، يقولوا انت انجنت؟ خمسة يساوي صفر، يقولوا لأ ما انجنت، يعني كمال العقل، والحمد لله", "tokens": [3615, 23942, 28242, 36764, 24401, 5296, 9778, 9566, 10721, 47525, 8315, 8717, 17082, 1829, 11703, 2288, 6225, 26108, 1211, 8315, 1975, 5016, 8315, 44945, 8592, 2655, 17082, 1211, 8592, 8978, 957, 1230, 44945, 8592, 2655, 17082, 1211, 8978, 3997, 3714, 19913, 3555, 2407, 9566, 49429, 20193, 22807, 1975, 2655, 1863, 9957, 44945, 8592, 2655, 17082, 1211, 3997, 15844, 10874, 26890, 1975, 2655, 1863, 9957, 20449, 45030, 11242, 37893, 5551, 22488, 18513, 11331, 38436, 4587, 10632, 12399, 4724, 1211, 17082, 3660, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 11778, 3224, 28242, 10943, 37893, 20328, 5016, 1829, 5016, 45164, 10874, 16606, 7251, 39648, 14407, 5296, 14407, 24401, 16490, 2304, 3794, 3660, 7251, 3794, 995, 45865, 20328, 5172, 2288, 12399, 7251, 39648, 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"word": " لـ", "probability": 0.7236328125}, {"start": 2682.37, "end": 2682.85, "word": " principle", "probability": 0.2183837890625}, {"start": 2682.85, "end": 2683.53, "word": " ideal", "probability": 0.250244140625}, {"start": 2683.53, "end": 2684.27, "word": " generated", "probability": 0.740234375}, {"start": 2684.27, "end": 2684.87, "word": " by", "probability": 0.908203125}, {"start": 2684.87, "end": 2685.43, "word": " I", "probability": 0.65283203125}, {"start": 2685.43, "end": 2685.87, "word": " بسبب", "probability": 0.58984375}, {"start": 2685.87, "end": 2686.55, "word": " ساعة", "probability": 0.500244140625}, {"start": 2686.55, "end": 2687.65, "word": " من", "probability": 0.231201171875}, {"start": 2687.65, "end": 2688.89, "word": " عناصرها", "probability": 0.954345703125}, {"start": 2688.89, "end": 2690.41, "word": " Zero", "probability": 0.191650390625}, {"start": 2690.41, "end": 2692.17, "word": " زائد", "probability": 0.8297526041666666}, {"start": 2692.17, "end": 2693.05, "word": " اتنين", "probability": 0.900146484375}, {"start": 2693.05, "end": 2693.63, "word": " minus", "probability": 0.8095703125}, {"start": 2693.63, "end": 2694.09, "word": " ال", "probability": 0.54833984375}, {"start": 2694.09, "end": 2694.49, "word": " I", "probability": 0.8447265625}, {"start": 2694.49, "end": 2695.91, "word": " واحد", "probability": 0.7430419921875}, {"start": 2695.91, "end": 2696.63, "word": " زائد", "probability": 0.9837239583333334}, {"start": 2696.63, "end": 2697.33, "word": " اتنين", "probability": 0.9852294921875}, {"start": 2697.33, "end": 2697.93, "word": " minus", "probability": 0.98681640625}, {"start": 2697.93, "end": 2698.29, "word": " ال", "probability": 0.955078125}, {"start": 2698.29, "end": 2699.03, "word": " I", "probability": 0.98974609375}, {"start": 2699.03, "end": 2699.51, "word": " و", "probability": 0.7412109375}, {"start": 2699.51, "end": 2700.87, "word": " اتنين", "probability": 0.872802734375}, {"start": 2700.87, "end": 2703.33, "word": " زائد", "probability": 0.9677734375}, {"start": 2703.33, "end": 2703.83, "word": " لـ", "probability": 0.5216064453125}, {"start": 2703.83, "end": 2704.05, "word": " principle", "probability": 0.857421875}, {"start": 2704.05, "end": 2704.85, "word": " ideal", "probability": 0.87841796875}, {"start": 2704.85, "end": 2705.87, "word": " generated", "probability": 0.861328125}, {"start": 2705.87, "end": 2707.51, "word": " و", "probability": 0.60205078125}, {"start": 2707.51, "end": 2708.71, "word": " كذلك", "probability": 0.8917643229166666}, {"start": 2708.71, "end": 2710.09, "word": " التلاتة", "probability": 0.9278564453125}], "temperature": 1.0}, {"id": 96, "seek": 273494, "start": 2710.78, "end": 2734.94, "text": "الأربعة زائد ال principle ideal generated by اتنين minus ال I وأكا principle ideal والأربعة زائد ال principle ideal generated by اتنين minus ال I أنا أزعم هه زعمها مش كلامير مية المية لغاية ما نثبته انه مية المية", "tokens": [6027, 10721, 25513, 27884, 30767, 16373, 3215, 2423, 8665, 7157, 10833, 538, 1975, 2655, 1863, 9957, 3175, 2423, 286, 36725, 4117, 995, 8665, 7157, 16070, 10721, 25513, 27884, 30767, 16373, 3215, 2423, 8665, 7157, 10833, 538, 1975, 2655, 1863, 9957, 3175, 2423, 286, 41850, 5551, 11622, 25957, 8032, 3224, 30767, 25957, 11296, 37893, 28242, 10943, 13546, 3714, 10632, 9673, 10632, 5296, 17082, 995, 10632, 19446, 8717, 12984, 3555, 47395, 16472, 3224, 3714, 10632, 9673, 10632], "avg_logprob": -0.29132401472643804, "compression_ratio": 1.9620253164556962, "no_speech_prob": 0.0, "words": [{"start": 2710.78, "end": 2711.74, "word": "الأربعة", "probability": 0.614044189453125}, {"start": 2711.74, "end": 2711.74, "word": " زائد", "probability": 0.7306315104166666}, {"start": 2711.74, "end": 2711.74, "word": " ال", "probability": 0.254150390625}, {"start": 2711.74, "end": 2711.74, "word": " principle", "probability": 0.69677734375}, {"start": 2711.74, "end": 2712.48, "word": " ideal", "probability": 0.60107421875}, {"start": 2712.48, "end": 2713.14, "word": " generated", "probability": 0.72509765625}, {"start": 2713.14, "end": 2713.64, "word": " by", "probability": 0.92236328125}, {"start": 2713.64, "end": 2714.3, "word": " اتنين", "probability": 0.827392578125}, {"start": 2714.3, "end": 2714.9, "word": " minus", "probability": 0.70361328125}, {"start": 2714.9, "end": 2715.36, "word": " ال", "probability": 0.355712890625}, {"start": 2715.36, "end": 2715.76, "word": " I", "probability": 0.732421875}, {"start": 2715.76, "end": 2717.12, "word": " وأكا", "probability": 0.489501953125}, {"start": 2717.12, "end": 2717.74, "word": " principle", "probability": 0.85205078125}, {"start": 2717.74, "end": 2718.9, "word": " ideal", "probability": 0.88232421875}, {"start": 2718.9, "end": 2720.58, "word": " والأربعة", "probability": 0.8553466796875}, {"start": 2720.58, "end": 2721.64, "word": " زائد", "probability": 0.9747721354166666}, {"start": 2721.64, "end": 2722.14, "word": " ال", "probability": 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ماعنديش إلا العناصر الخمسة هدول فقط، لا غير، كويس؟ إحنا العملية اللي عندنا زي ما انت شايفها كلها عملية جامعة", "tokens": [28814, 1863, 18871, 33546, 2288, 8032, 3215, 12610, 4724, 3794, 18863, 1863, 33546, 2288, 13672, 1829, 6225, 42213, 8315, 11296, 13, 16490, 10859, 3215, 6024, 48506, 12399, 4724, 16254, 5551, 12984, 3555, 2655, 36145, 3224, 19446, 3615, 1863, 16254, 8592, 11933, 15040, 18863, 1863, 33546, 2288, 33962, 2304, 3794, 3660, 8032, 3215, 12610, 6156, 47432, 12399, 20193, 32771, 13546, 12399, 9122, 45865, 3794, 22807, 11933, 5016, 8315, 18863, 42213, 10632, 13672, 1829, 43242, 8315, 30767, 1829, 19446, 16472, 2655, 13412, 995, 33911, 11296, 28242, 11296, 6225, 42213, 10632, 10874, 10943, 27884], "avg_logprob": -0.24405571316247401, "compression_ratio": 1.811764705882353, "no_speech_prob": 0.0, "words": [{"start": 2735.49, "end": 2735.87, "word": "إن", "probability": 0.6856689453125}, {"start": 2735.87, "end": 2736.55, "word": " عناصر", "probability": 0.8732096354166666}, 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واحد زايدها تمام؟ لو جيت قولتلك خديلي خمسة في واحد زايد ال principle ideal generated by اتنين minus ال A يبقى هذا الكلام بده يساوي خمسة في واحد خمسة زايد ال principle ideal فالخمسة بيجي دي Zero", "tokens": [6027, 20292, 31439, 6055, 1211, 9307, 3660, 30767, 995, 25708, 5551, 25513, 27884, 286, 30767, 995, 25708, 11296, 7251, 3794, 995, 45865, 36764, 24401, 30767, 995, 25708, 11296, 46811, 10943, 22807, 45164, 10874, 36081, 12174, 12610, 2655, 23275, 16490, 3215, 1829, 20292, 16490, 2304, 3794, 3660, 8978, 36764, 24401, 30767, 995, 25708, 2423, 8665, 7157, 10833, 538, 1975, 2655, 1863, 9957, 3175, 2423, 316, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 8978, 36764, 24401, 16490, 2304, 3794, 3660, 30767, 995, 25708, 2423, 8665, 7157, 6156, 6027, 9778, 2304, 3794, 3660, 4724, 1829, 7435, 1829, 11778, 1829, 17182], "avg_logprob": -0.26748854523405025, "compression_ratio": 1.7799043062200957, "no_speech_prob": 0.0, "words": 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"probability": 0.97705078125}, {"start": 2806.07, "end": 2807.33, "word": " خمسة", "probability": 0.861083984375}, {"start": 2807.33, "end": 2808.11, "word": " زايد", "probability": 0.9845377604166666}, {"start": 2808.11, "end": 2808.31, "word": " ال", "probability": 0.9453125}, {"start": 2808.31, "end": 2808.97, "word": " principle", "probability": 0.9423828125}, {"start": 2808.97, "end": 2810.03, "word": " ideal", "probability": 0.6787109375}, {"start": 2810.03, "end": 2811.13, "word": " فالخمسة", "probability": 0.8318684895833334}, {"start": 2811.13, "end": 2811.43, "word": " بيجي", "probability": 0.59698486328125}, {"start": 2811.43, "end": 2811.87, "word": " دي", "probability": 0.485595703125}, {"start": 2811.87, "end": 2812.41, "word": " Zero", "probability": 0.18017578125}], "temperature": 1.0}, {"id": 100, "seek": 283819, "start": 2813.57, "end": 2838.19, "text": "يبقى هذا الكلام بده يساوي Zero زاد ال principle ideal generated by اللي هو ال principle ideal generated by I فبناء عليه، قداش ال order لهذا؟ خمسة وقد يكون أقل من خمسة صح ولا لأ؟", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 17182, 30767, 18513, 2423, 8665, 7157, 10833, 538, 13672, 1829, 31439, 2423, 8665, 7157, 10833, 538, 286, 6156, 3555, 1863, 16606, 47356, 12399, 12174, 3215, 33599, 2423, 1668, 46740, 15730, 22807, 16490, 2304, 3794, 3660, 4032, 28543, 7251, 30544, 5551, 4587, 1211, 9154, 16490, 2304, 3794, 3660, 20328, 5016, 49429, 5296, 10721, 22807], "avg_logprob": -0.29503676076145735, "compression_ratio": 1.4689265536723164, "no_speech_prob": 0.0, "words": [{"start": 2813.57, "end": 2814.25, "word": "يبقى", "probability": 0.8660888671875}, {"start": 2814.25, "end": 2814.65, "word": " هذا", "probability": 0.91943359375}, {"start": 2814.65, "end": 2815.43, "word": " الكلام", "probability": 0.9415690104166666}, {"start": 2815.43, "end": 2816.07, "word": " بده", "probability": 0.24652099609375}, {"start": 2816.07, "end": 2816.79, "word": " 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"word": " يكون", "probability": 0.969970703125}, {"start": 2835.01, "end": 2835.87, "word": " أقل", "probability": 0.9451497395833334}, {"start": 2835.87, "end": 2836.21, "word": " من", "probability": 0.9921875}, {"start": 2836.21, "end": 2837.19, "word": " خمسة", "probability": 0.988037109375}, {"start": 2837.19, "end": 2837.59, "word": " صح", "probability": 0.793212890625}, {"start": 2837.59, "end": 2837.81, "word": " ولا", "probability": 0.95068359375}, {"start": 2837.81, "end": 2838.19, "word": " لأ؟", "probability": 0.783203125}], "temperature": 1.0}, {"id": 101, "seek": 286807, "start": 2838.37, "end": 2868.07, "text": "يبقى ال order لل element اللي احنا بيقول أقل عدد صحيح بحطه أس لل element ليعطيني ال identity صح ولا لأ؟ هيك أخدناه في ال groups صح؟ يبقى هنا أنا أخدته أضرب اللي هو طلع مين طلع ال zero element يبقى ال order يا خمسة يا شغلة تانية طب بدي أشوف مين الشغلة التانية أليس هذا هو هذا؟ كدهش ال order لهذا؟", "tokens": [1829, 3555, 4587, 7578, 2423, 1668, 24976, 4478, 13672, 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2970.58, "end": 2970.82, "word": " ال", "probability": 0.93310546875}, {"start": 2970.82, "end": 2971.3, "word": " principle", "probability": 0.923828125}, {"start": 2971.3, "end": 2971.98, "word": " ideal", "probability": 0.853515625}, {"start": 2971.98, "end": 2972.88, "word": " generated", "probability": 0.92236328125}, {"start": 2972.88, "end": 2973.36, "word": " by", "probability": 0.9892578125}, {"start": 2973.36, "end": 2974.12, "word": " اتنين", "probability": 0.9774169921875}], "temperature": 1.0}, {"id": 106, "seek": 300417, "start": 2974.47, "end": 3004.17, "text": "-I بده يساوي 2-I يعني صار الواحد زي ال principle ideal generated بده يساوي 2-I هذا الكلام صحيح معناته ان الواحد موجود في ال principle ideal generated by 2-I", "tokens": [12, 40, 47525, 3224, 7251, 3794, 995, 45865, 568, 12, 40, 37495, 22653, 20328, 9640, 2423, 14407, 24401, 30767, 1829, 2423, 8665, 7157, 10833, 47525, 3224, 7251, 3794, 995, 45865, 568, 12, 40, 23758, 2423, 28820, 10943, 20328, 5016, 1829, 5016, 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{"start": 2996.29, "end": 2996.83, "word": " ان", "probability": 0.505859375}, {"start": 2996.83, "end": 2997.79, "word": " الواحد", "probability": 0.9881184895833334}, {"start": 2997.79, "end": 2998.49, "word": " موجود", "probability": 0.98388671875}, {"start": 2998.49, "end": 2998.67, "word": " في", "probability": 0.84033203125}, {"start": 2998.67, "end": 2998.87, "word": " ال", "probability": 0.935546875}, {"start": 2998.87, "end": 2999.47, "word": " principle", "probability": 0.9140625}, {"start": 2999.47, "end": 3000.41, "word": " ideal", "probability": 0.83056640625}, {"start": 3000.41, "end": 3001.73, "word": " generated", "probability": 0.88818359375}, {"start": 3001.73, "end": 3002.35, "word": " by", "probability": 0.68017578125}, {"start": 3002.35, "end": 3003.07, "word": " 2", "probability": 0.79443359375}, {"start": 3003.07, "end": 3004.17, "word": "-I", "probability": 0.889404296875}], "temperature": 1.0}, {"id": 107, "seek": 302833, "start": 3004.59, "end": 3028.33, "text": "طيب مدام واحد طب هذا عناصره element من ال ring الأصلية مضروف element من هنا صح ولا لا؟ يبقى هذا معناه إيش؟ معناته أن الواحد هذا بده يساوي element من ال ring الأصلية", "tokens": [9566, 1829, 3555, 3714, 3215, 10943, 36764, 24401, 23032, 3555, 23758, 18871, 33546, 2288, 3224, 4478, 9154, 2423, 4875, 16247, 36520, 10632, 3714, 11242, 32887, 5172, 4478, 9154, 34105, 20328, 5016, 49429, 20193, 22807, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 11933, 1829, 8592, 22807, 20449, 8315, 47395, 14739, 2423, 14407, 24401, 23758, 47525, 3224, 7251, 3794, 995, 45865, 4478, 9154, 2423, 4875, 16247, 36520, 10632], "avg_logprob": -0.18014705531737385, "compression_ratio": 1.7337662337662338, "no_speech_prob": 0.0, "words": [{"start": 3004.59, "end": 3006.43, "word": "طيب", "probability": 0.7206217447916666}, {"start": 3006.43, "end": 3006.97, "word": " مدام", "probability": 0.4615071614583333}, {"start": 3006.97, "end": 3007.73, "word": " واحد", "probability": 0.935546875}, {"start": 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{"start": 3016.01, "end": 3016.57, "word": " صح", "probability": 0.930419921875}, {"start": 3016.57, "end": 3016.79, "word": " ولا", "probability": 0.96484375}, {"start": 3016.79, "end": 3017.63, "word": " لا؟", "probability": 0.6185302734375}, {"start": 3017.63, "end": 3018.09, "word": " يبقى", "probability": 0.85595703125}, {"start": 3018.09, "end": 3018.57, "word": " هذا", "probability": 0.9599609375}, {"start": 3018.57, "end": 3019.33, "word": " معناه", "probability": 0.9768880208333334}, {"start": 3019.33, "end": 3020.27, "word": " إيش؟", "probability": 0.837890625}, {"start": 3020.27, "end": 3021.29, "word": " معناته", "probability": 0.9723307291666666}, {"start": 3021.29, "end": 3022.15, "word": " أن", "probability": 0.4443359375}, {"start": 3022.15, "end": 3023.23, "word": " الواحد", "probability": 0.9739583333333334}, {"start": 3023.23, "end": 3023.89, "word": " هذا", "probability": 0.91796875}, {"start": 3023.89, "end": 3024.81, "word": " بده", "probability": 0.853515625}, {"start": 3024.81, "end": 3025.39, "word": " يساوي", "probability": 0.9498291015625}, {"start": 3025.39, "end": 3026.23, "word": " element", "probability": 0.96240234375}, {"start": 3026.23, "end": 3026.55, "word": " من", "probability": 0.9970703125}, {"start": 3026.55, "end": 3026.77, "word": " ال", "probability": 0.990234375}, {"start": 3026.77, "end": 3027.09, "word": " ring", "probability": 0.98291015625}, {"start": 3027.09, "end": 3028.33, "word": " الأصلية", "probability": 0.9026692708333334}], "temperature": 1.0}, {"id": 108, "seek": 305774, "start": 3028.62, "end": 3057.74, "text": "مع الإثنين ناقص I في مين؟ في الـ A زائد بي R سجة الشعور الواحد موجود هنا صح؟ هذه من عناصرها ال principle هذه بدي أجيب element من R و أضربه في مين؟ في اللي هو ال element اللي عندنا هذا صح ولا لا؟", "tokens": [2304, 3615, 33688, 12984, 1863, 9957, 8717, 995, 4587, 9381, 286, 8978, 3714, 9957, 22807, 8978, 2423, 39184, 316, 30767, 16373, 3215, 4724, 1829, 497, 8608, 7435, 3660, 25124, 3615, 13063, 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"word": " هذه", "probability": 0.6962890625}, {"start": 3044.24, "end": 3044.58, "word": " من", "probability": 0.65673828125}, {"start": 3044.58, "end": 3045.86, "word": " عناصرها", "probability": 0.9881591796875}, {"start": 3045.86, "end": 3046.22, "word": " ال", "probability": 0.47265625}, {"start": 3046.22, "end": 3046.76, "word": " principle", "probability": 0.489990234375}, {"start": 3046.76, "end": 3047.14, "word": " هذه", "probability": 0.210693359375}, {"start": 3047.14, "end": 3047.44, "word": " بدي", "probability": 0.6597900390625}, {"start": 3047.44, "end": 3047.76, "word": " أجيب", "probability": 0.897216796875}, {"start": 3047.76, "end": 3048.58, "word": " element", "probability": 0.9423828125}, {"start": 3048.58, "end": 3049.18, "word": " من", "probability": 0.99462890625}, {"start": 3049.18, "end": 3049.88, "word": " R", "probability": 0.97607421875}, {"start": 3049.88, "end": 3050.54, "word": " و", "probability": 0.8115234375}, {"start": 3050.54, "end": 3051.48, "word": " أضربه", "probability": 0.949951171875}, {"start": 3051.48, "end": 3051.8, "word": " في", "probability": 0.97705078125}, {"start": 3051.8, "end": 3052.54, "word": " مين؟", "probability": 0.8767903645833334}, {"start": 3052.54, "end": 3052.96, "word": " في", "probability": 0.95068359375}, {"start": 3052.96, "end": 3053.56, "word": " اللي", "probability": 0.6866455078125}, {"start": 3053.56, "end": 3053.9, "word": " هو", "probability": 0.97412109375}, {"start": 3053.9, "end": 3054.44, "word": " ال", "probability": 0.93896484375}, {"start": 3054.44, "end": 3055.32, "word": " element", "probability": 0.90966796875}, {"start": 3055.32, "end": 3055.7, "word": " اللي", "probability": 0.9765625}, {"start": 3055.7, "end": 3056.36, "word": " عندنا", "probability": 0.968017578125}, {"start": 3056.36, "end": 3056.66, "word": " هذا", "probability": 0.921875}, {"start": 3056.66, "end": 3057.1, "word": " صح", "probability": 0.97021484375}, {"start": 3057.1, "end": 3057.32, "word": " ولا", 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9957, 22807, 5551, 25513, 27884, 363, 12174, 36150, 16490, 2304, 3794, 3660, 363, 16490, 2304, 3794, 3660, 13672, 1829, 31439, 363, 6055, 3794, 995, 45865, 2423, 14407, 24401, 7251, 3555, 4587, 7578, 2423, 363, 6055, 3794, 995, 45865, 9122, 3215, 3224, 8592, 22807, 9122, 3215, 3224, 8592, 22807, 36764, 24401, 15844, 16490, 2304, 3794, 3660, 23032, 3555, 13672, 1829, 31439, 2423, 363, 4032, 1975, 9957, 3714, 29245, 23328, 3660, 8032, 3215, 12610, 22807], "avg_logprob": -0.24864130123801853, "compression_ratio": 1.8465608465608465, "no_speech_prob": 0.0, "words": [{"start": 3171.44, "end": 3172.08, "word": "يبقى", "probability": 0.908447265625}, {"start": 3172.08, "end": 3172.98, "word": " أربعة", "probability": 0.7939453125}, {"start": 3172.98, "end": 3173.34, "word": " B", "probability": 0.172119140625}, {"start": 3173.34, "end": 3174.12, "word": " نقص", "probability": 0.8665364583333334}, {"start": 3174.12, "end": 3174.74, "word": " اتنين", "probability": 0.9322509765625}, {"start": 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3189.64, "end": 3190.82, "word": " يبقى", "probability": 0.9669189453125}, {"start": 3190.82, "end": 3191.02, "word": " ال", "probability": 0.9775390625}, {"start": 3191.02, "end": 3191.24, "word": " B", "probability": 0.595703125}, {"start": 3191.24, "end": 3191.8, "word": " تساوي", "probability": 0.9847412109375}, {"start": 3191.8, "end": 3192.94, "word": " كدهش؟", "probability": 0.62001953125}, {"start": 3192.94, "end": 3195.06, "word": " كدهش؟", "probability": 0.93701171875}, {"start": 3195.06, "end": 3195.58, "word": " واحد", "probability": 0.93798828125}, {"start": 3195.58, "end": 3195.96, "word": " على", "probability": 0.57177734375}, {"start": 3195.96, "end": 3197.2, "word": " خمسة", "probability": 0.9886474609375}, {"start": 3197.2, "end": 3197.42, "word": " طب", "probability": 0.700927734375}, {"start": 3197.42, "end": 3197.62, "word": " اللي", "probability": 0.739501953125}, {"start": 3197.62, "end": 3197.78, "word": " هو", "probability": 0.9150390625}, {"start": 3197.78, "end": 3197.96, "word": " ال", "probability": 0.98583984375}, {"start": 3197.96, "end": 3198.06, "word": " B", "probability": 0.9365234375}, {"start": 3198.06, "end": 3198.22, "word": " و", "probability": 0.65771484375}, {"start": 3198.22, "end": 3198.3, "word": " اين", "probability": 0.64990234375}, {"start": 3198.3, "end": 3198.8, "word": " موجودة", "probability": 0.878173828125}, {"start": 3198.8, "end": 3199.26, "word": " هدول؟", "probability": 0.5760498046875}], "temperature": 1.0}, {"id": 114, "seek": 322509, "start": 3199.79, "end": 3225.09, "text": "to z يبقى هذا does not belong to z يبقى ال order يساوي واحد كلام غلط مش صحيح انه قادني الى نتيجة خاطية يبقى ساعة ال order لواحد زي ال principle ideal generated لا يمكن ان يساوي الواحد هذا معناته", "tokens": [1353, 710, 7251, 3555, 4587, 7578, 23758, 775, 406, 5784, 281, 710, 7251, 3555, 4587, 7578, 2423, 1668, 7251, 3794, 995, 45865, 36764, 24401, 28242, 10943, 32771, 1211, 9566, 37893, 20328, 5016, 1829, 5016, 16472, 3224, 12174, 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"end": 3210.65, "word": " قادني", "probability": 0.707275390625}, {"start": 3210.65, "end": 3211.05, "word": " الى", "probability": 0.743408203125}, {"start": 3211.05, "end": 3211.83, "word": " نتيجة", "probability": 0.9925537109375}, {"start": 3211.83, "end": 3212.89, "word": " خاطية", "probability": 0.8834635416666666}, {"start": 3212.89, "end": 3214.17, "word": " يبقى", "probability": 0.971435546875}, {"start": 3214.17, "end": 3214.81, "word": " ساعة", "probability": 0.47412109375}, {"start": 3214.81, "end": 3215.67, "word": " ال", "probability": 0.92529296875}, {"start": 3215.67, "end": 3216.25, "word": " order", "probability": 0.96630859375}, {"start": 3216.25, "end": 3217.19, "word": " لواحد", "probability": 0.7911783854166666}, {"start": 3217.19, "end": 3217.71, "word": " زي", "probability": 0.894287109375}, {"start": 3217.71, "end": 3217.93, "word": " ال", "probability": 0.68310546875}, {"start": 3217.93, "end": 3218.51, "word": " principle", "probability": 0.83447265625}, {"start": 3218.51, "end": 3219.49, "word": " ideal", "probability": 0.60498046875}, {"start": 3219.49, "end": 3220.57, "word": " generated", "probability": 0.6845703125}, {"start": 3220.57, "end": 3221.01, "word": " لا", "probability": 0.6494140625}, {"start": 3221.01, "end": 3221.79, "word": " يمكن", "probability": 0.841064453125}, {"start": 3221.79, "end": 3222.15, "word": " ان", "probability": 0.69873046875}, {"start": 3222.15, "end": 3222.83, "word": " يساوي", "probability": 0.9801025390625}, {"start": 3222.83, "end": 3223.47, "word": " الواحد", "probability": 0.93701171875}, {"start": 3223.47, "end": 3224.21, "word": " هذا", "probability": 0.876953125}, {"start": 3224.21, "end": 3225.09, "word": " معناته", "probability": 0.984375}], "temperature": 1.0}, {"id": 115, "seek": 325447, "start": 3225.35, "end": 3254.47, "text": "إن ال order للواحد زي اتنين ناقص I بده يسوي خمسة وعدد العماصر هنا كتبناهم طلع خمسة إذا لا يمكن لهذا اللي يكون generator ومافيش غيرهم يبقى هنا therefore ولهذا اللي هو ال .. هذه مش واحد يا بنات هذه واحد", "tokens": [28814, 1863, 2423, 1668, 24976, 14407, 24401, 30767, 1829, 1975, 2655, 1863, 9957, 8717, 995, 4587, 9381, 286, 47525, 3224, 7251, 3794, 45865, 16490, 2304, 3794, 3660, 4032, 22488, 3215, 18863, 2304, 33546, 2288, 34105, 9122, 2655, 3555, 8315, 16095, 23032, 1211, 3615, 16490, 2304, 3794, 3660, 11933, 15730, 20193, 7251, 43020, 46740, 15730, 13672, 1829, 7251, 30544, 19265, 4032, 15042, 41185, 8592, 32771, 13546, 16095, 7251, 3555, 4587, 7578, 34105, 4412, 35525, 3224, 15730, 13672, 1829, 31439, 2423, 4386, 29538, 37893, 36764, 24401, 35186, 4724, 8315, 2655, 29538, 36764, 24401], "avg_logprob": -0.23165760594217674, "compression_ratio": 1.6372549019607843, "no_speech_prob": 0.0, "words": [{"start": 3225.35, "end": 3225.77, "word": "إن", "probability": 0.845458984375}, {"start": 3225.77, "end": 3226.03, "word": " ال", "probability": 0.8212890625}, {"start": 3226.03, "end": 3226.59, "word": " order", "probability": 0.783203125}, {"start": 3226.59, "end": 3227.55, "word": " للواحد", "probability": 0.647705078125}, {"start": 3227.55, "end": 3227.89, "word": " زي", "probability": 0.75830078125}, {"start": 3227.89, "end": 3228.63, "word": " اتنين", "probability": 0.83502197265625}, {"start": 3228.63, "end": 3229.47, "word": " ناقص", "probability": 0.8804931640625}, {"start": 3229.47, "end": 3229.91, "word": " I", "probability": 0.740234375}, {"start": 3229.91, "end": 3230.81, "word": " بده", "probability": 0.388916015625}, {"start": 3230.81, "end": 3231.27, "word": " يسوي", "probability": 0.79638671875}, {"start": 3231.27, "end": 3232.23, "word": " خمسة", "probability": 0.934814453125}, {"start": 3232.23, "end": 3233.21, "word": " وعدد", "probability": 0.8916015625}, {"start": 3233.21, "end": 3233.99, "word": " العماصر", "probability": 0.86297607421875}, {"start": 3233.99, "end": 3234.37, "word": " هنا", "probability": 0.85693359375}, {"start": 3234.37, "end": 3235.19, "word": " كتبناهم", "probability": 0.87587890625}, {"start": 3235.19, "end": 3235.55, "word": " طلع", "probability": 0.6671549479166666}, {"start": 3235.55, "end": 3236.09, "word": " خمسة", "probability": 0.950927734375}, {"start": 3236.09, "end": 3236.33, "word": " إذا", "probability": 0.9052734375}, {"start": 3236.33, "end": 3236.57, "word": " لا", "probability": 0.61669921875}, {"start": 3236.57, "end": 3237.05, "word": " يمكن", "probability": 0.942626953125}, {"start": 3237.05, "end": 3237.47, "word": " لهذا", "probability": 0.857666015625}, {"start": 3237.47, "end": 3237.71, "word": " اللي", "probability": 0.9130859375}, {"start": 3237.71, "end": 3238.25, "word": " يكون", "probability": 0.987548828125}, {"start": 3238.25, "end": 3239.51, "word": " generator", "probability": 0.763671875}, {"start": 3239.51, "end": 3240.45, "word": " ومافيش", "probability": 0.938232421875}, {"start": 3240.45, "end": 3241.17, "word": " غيرهم", "probability": 0.89697265625}, {"start": 3241.17, "end": 3242.43, "word": " يبقى", "probability": 0.9674072265625}, {"start": 3242.43, "end": 3242.95, "word": " هنا", "probability": 0.99072265625}, {"start": 3242.95, "end": 3244.31, "word": " therefore", "probability": 0.436767578125}, {"start": 3244.31, "end": 3247.73, "word": " ولهذا", "probability": 0.81103515625}, {"start": 3247.73, "end": 3249.03, "word": " اللي", "probability": 0.926513671875}, {"start": 3249.03, "end": 3249.49, "word": " هو", "probability": 0.9853515625}, {"start": 3249.49, "end": 3250.01, "word": " ال", "probability": 0.77099609375}, {"start": 3250.01, "end": 3252.51, "word": " ..", "probability": 0.398681640625}, {"start": 3252.51, "end": 3252.91, "word": " هذه", "probability": 0.358642578125}, {"start": 3252.91, "end": 3253.11, "word": " مش", "probability": 0.95751953125}, {"start": 3253.11, "end": 3253.33, "word": " واحد", "probability": 0.82861328125}, {"start": 3253.33, "end": 3253.47, "word": " يا", "probability": 0.53125}, {"start": 3253.47, "end": 3253.71, "word": " بنات", "probability": 0.76025390625}, {"start": 3253.71, "end": 3254.01, "word": " هذه", "probability": 0.51953125}, {"start": 3254.01, "end": 3254.47, "word": " واحد", "probability": 0.990234375}], "temperature": 1.0}, {"id": 116, "seek": 328444, "start": 3255.3, "end": 3284.44, "text": "هنا نوعا يبقى therefore الواحد زي ال principle ideal generated by اتنين minus ال I is a generator يبقى هدفه يعطينا ان ال order لمين لزد of I مدير ال principle ideal generated", "tokens": [3224, 8315, 8717, 45367, 995, 7251, 3555, 4587, 7578, 4412, 2423, 14407, 24401, 30767, 1829, 2423, 8665, 7157, 10833, 538, 1975, 2655, 1863, 9957, 3175, 2423, 286, 307, 257, 19265, 7251, 3555, 4587, 7578, 8032, 3215, 5172, 3224, 7251, 3615, 9566, 1829, 8315, 16472, 2423, 1668, 32767, 9957, 5296, 11622, 3215, 295, 286, 3714, 3215, 13546, 2423, 8665, 7157, 10833], "avg_logprob": -0.2761270569973305, "compression_ratio": 1.4654088050314464, "no_speech_prob": 0.0, "words": [{"start": 3255.3, "end": 3255.8, "word": "هنا", 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