پديد آورنده :
اماني جوآبادي، مهدي
عنوان :
مدول هايي كه حلقه ي درون ريختي شان منظم فون نيومان است
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
محمدرضا ودادي
استاد مشاور :
محمود بهبودي
توصيفگر ها :
مدول هاي درون منظم , اشتراك جمعوندها , مدول هاي ريكارت و هم ريكارت
استاد داور :
بيژن طائري، عاطفه قرباني
تاريخ ورود اطلاعات :
1395/08/03
چكيده انگليسي :
Modules whose endomorphism rings are Von Neumann regular Mehdi Amani Jouabadi m amani@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir Advisor Dr Mahmood Behboodi mbehboodi@cc iut ac ir 2000 MSC 16D10 16D70 16K99 16S50 Keywords Dual Rickart modules Division rings Endomorphism rings Rickart modules VonNeumann regular rings Abstract This M Sc thesis is based on the following paperGangyong Lee S Tariq Rizvi Cosmin Roman Modules Whose Endomorphism Rings are Von Neu mann Regular Communications in Algebra 41 11 4066 4088 2013 DOI 10 1080 00927872 2012 700979Throughout we assume that R is a ring with identity and modules M are unital rightR modules For a right R module M S EndR M denotes the endomorphism ring of M thus Mcan be viewed as a left S right R bimodule The study of the class of von Neumann regular rings has been a topic of wide interest Amongother factors the abundance of idempotent elements in such a ring makes this study interesting Itis well known that a ring R is von Neumann regular i Im a aR is a direct summand of RR forall a R and for all R homomorphisms a R R given by the left multiplication by a Abeliangroups whose endomorphism rings are von Neumann regular have been extensively investigated in theliterature Our focus of study in this paper is on modules whose endomorphism rings are von Neumannregular We call them endoregular modules We provide characterizations of endoregular modulesand investigate their properties Some classes of rings R are characterized in terms of endoregularR modules In fact the following general result also holds for modules Theorem Let M be a right R module and S EndR M Then S is regular i Ker andIm are direct summands of M Consequently S is a von Neumann regular ring i Ker and Im
استاد راهنما :
محمدرضا ودادي
استاد مشاور :
محمود بهبودي
استاد داور :
بيژن طائري، عاطفه قرباني
