12596

11524

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1396

نه،[104]ص.: مصور، جدول، نمودار

ص. ع. به فارسي و انگليسي

عاطفه قرباني

فريد بهرامي

واژه نامه

احمد حقاني، محمدرضا ودادي

1396/05/04

كتابنامه

علوم رياضي

رياضي

ID11524

Right SA Rings Akram Naghdi a naghdi@math iut ac ir 18 06 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Atefeh Ghorbani a ghorbani@cc iut ac ir Advisor Dr Farid Bahrami fbahrami@cc iut ac ir 2010 MSC Primary 16D25 16D70 45G05 Keywords Annihilator ideal Extermally disconnected space IN ring Quasi Baer ring SA ring Abstract This thesis is based on the article When is a Sum of Annihilator Ideals an Annihilator Ideal Written by G F Birkenmeier M Ghirati and A Taherifar Suppose R is a nonzero associative ringwith identity In this thesis we introduce and investigate the concept of a right SA ring We call R aright SA ring if for any ideals I and J of R there is an ideal K of R such that rR I rR J rR K Since rR X rR RX for all X r R R is a right SA ring if and only if for all X Y r R thereexists V r R such that rR X rR Y rR V A ring R is called a left quasi Baer Baer ring ifthe left annihilator of every ideal nonempty set of R is generated as a left ideal by an idempotent The quasi Baer Baer conditions are left right symmetric It is shown that R is a quasi Baer if andonly is Mn R is quasi Baer if and only if Tn R is a quasi Baer ring Also a ring R is called a leftIkeda Nakayama for short a left IN ring if the right annihilator of the intersection of any two leftideals is the sum of the right annihilators We say R is an IN ring if R is a left and a right IN ring It isshown that if a ring R is left self injective then R is a left IN ring We show that all quasi Baer henceall Baer rings and all left IN rings hence all left self injective rings are right SA rings Moreover We provede examples of right SA rings which are neither quasi Baer nor left IN rings Recall thatfor a ring R the set of right annihilator ideals of R partially ordered by inclusion forms a latticewith inf rR I rr J rR I rR J and sup rR I rr J rR lR rr I rR J for all ideals

عاطفه قرباني

فريد بهرامي

احمد حقاني، محمدرضا ودادي