13161

12009

كارشناسي ارشد

رياضي محض

اصفهان:‌ دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

۱۳۹۶

هشت، [۷۳]ص.:‌ مصور

انگليسي به فارسي

1396/11/08

كتابنامه

علوم رياضي

رياضي

ID12009

Rings whose cyclics are C3 modules Azam Shirzad a shirzad@math iut ac ir 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Atefeh Ghorbani a ghorbani@cc iut ac ir Advisor Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir 2010 MSC 16D50 16E50 16L30 Keywords C3 module semiperfect ring ADS module right c ring right cc ring Abstract This M Sc thesis is based on the following paper Ibrahim Yasser Nguyen Xuan Hau Yousif Mohamed F and Zhou Yiqiang Rings whose cyclicsare C3 modules J Algebra Appl 15 8 1650152 18 2016 Troughout this review of thesis we assume that a ring R is associative with an identity and modulesare unital Let R be a ring An R module M is a C3 module if the sum of any two direct summandswith zero intersection is again a direct summand First it is shown that for n 1 every n generatedR module is a C3 module if and only if every cyclic Mn R module is a C3 module Then we concludethat a ring R is semisimple artinian if and only if every right R module is a C3 module if and only ifevery 3 generated right R module is a C3 module The following questions arise naturally Question 1 For which rings R is every cyclic right R module a C3 module Question 2 For which rings R is every 2 generated right R module a C3 module Here we carry out a study of the rings whose cyclics are C3 modules A ring R is called CC3 ringif every cyclic right R module is a C3 module It is shown that rings whose cyclics are SSP modules abelian exchange rings strongly regular rings and local rings are some importent examples of CC3 rings A ring R is called semiperfect if R J R is semisimple artinian and idempotents lift moduloJ R Two structure theorem are proved A semiperfect ring R is a right CC3 ring if and only ifR R1 R2 where R1 is semisimple artinian ring and R2 is a finite direct product of local rings Aright self injective regular ring is a right CC3 ring if and only if R is a direct product of a semisimple

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محمدرضا ودادي

احمد حقاني، بيژن طائري