پديد آورنده :
صفاري، زهرا
عنوان :
خاصيت انعكاسي حلقه ها
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض﴿جبر﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي وو انگليسي
استاد راهنما :
عاطفه قرباني
استاد مشاور :
محمدرضا ودادي
توصيفگر ها :
حلقه ي ماتريس , حلقه ي چند جمله اي , حلقه ي انعكاسي , حلقه ي انعكاسي خود توان راست ﴿چپ﴾ , حلقه ي به طور اصلي شبه بئر راست , حلقه ي كسرهاي راست , حلقه ي نيم اول
تاريخ نمايه سازي :
10/4/93
استاد داور :
حسين خبازيان، محمود بهبودي
چكيده انگليسي :
Reflexive Property of Rings Zahra Saffari z saffari@math iut ac ir Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Atefeh Ghorbani a ghorbani@cc iut ac irAdvisor Mr MohammadReza Vedadi mrvedadi@cc iut ac ir2000 MSC 16S99 16U80Keywords Matrix ring Polynomail ring Reflexive ring Right idempotent reflexive ring Rightprincipally quasi Baer ring Right quotient ring Semiprime ring AbstractThis thesis is based on the article Reflexive Property of Rings written by T K Kwak and Y Lee Already the reflexive property for ideals introduced by Mason and then this concept wasgeneralized by Kim and Baik Suppose R is a unitary ring R is called reflexive if aRb 0implies bRa 0 for a b R Note that every semiprime ring is reflexive and also for an ideal Iof a fully idempotent ring R i e I 2 I for every ideal I R I is reflexive ring For a nonemptysubset X of a ring R we write rR X c R Xc 0 which is called the right annihilatorof X in R The left annihilator is defined similarly and denoted by lR x Let R be a ring thenR is reflexive if and only if for each a R rR aR lR Ra if and only if ARB 0 impliesBRA 0 for any nonempty subsets A B of R if and only if IJ 0 implies JI 0 for all right or left 2 sided ideals I J of R Then we give examples that the class of reflexive rings arenot closed under homomorphic images and subrings A ring R called right idempotent reflexiveif aRe 0 implies eRa 0 for any a e2 e R Left idempotent reflexive ring is definedsimilarly If a ring is both left and right idempotent reflexive then the ring is called an idempotentreflexive ring Note that every reflexive ring is an idempotent reflexive ring Let R be a ringthen R is right idempotent reflexive if and only if for e2 e R lR Re rR eR if and onlyif for any nonempty subset A and nonempty subset E of idempotents in R ARE 0 implies
استاد راهنما :
عاطفه قرباني
استاد مشاور :
محمدرضا ودادي
استاد داور :
حسين خبازيان، محمود بهبودي
