پديد آورنده :
دهقاني، نجمه
عنوان :
مطالعه ي رده ي مدول هاي جمع شدني و زيررده هاي معيني از آن ها با كاربرد در نظريه ي حلقه ها
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
محمدرضا ودادي
استاد مشاور :
عاطفه قرباني
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
مدول نيم اول , مدول اول , مدول به هم فشردني ضعيف , كلاس توسيعي , حلقه ي نيم آرتيني , حلقه ي نيم آرتيني منفرد , حلقه نيم موضعي , هم ارزي موريتا
تاريخ نمايه سازي :
1394/09/24
استاد داور :
احمد حقاني، احمد موسوي، محمود بهبودي
كد ايرانداك :
ID811 دكتري
چكيده انگليسي :
Study of the class of retractable modules and its certain subclasses with application to ring theory Najmeh Dehghani n dehghani@math iut ac ir June 16 2015 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir Advisor Dr Atefeh Ghorbani a ghorbani@cc iut ac irDepartment of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranAbstractLet R be a ring We carry out a study of the widely used and important subclasses ofthe class of retractable R modules namely weakly compressible R modules An R moduleM is called retractable weakly compressible if HomR M N 0 HomR M N N 0 forany 0 N MR Weakly compressible R modules are semiprime i e M Cog N forany 0 N ess MR It is routine to see that R is a semiprime ring if and only if RR isweakly compressible if and only if RR is semiprime Generally in any module generalizationsof the concepts of prime and semiprime rings the question when are semiprime modulessubdirect product of primes is naturally appeared and studied in the literature In thisthesis for many rings R we characterize weakly compressible and semiprime R modules byshowing that if R is a prime ring over which cyclic modules have nite uniform dimensionsand singular modules have nonzero socles then i MR is weakly compressible if and onlyif M Cog Soc M R and M Soc M Cog R ii MR is semiprime if and only ifM Cog Soc M R Also it is shown that for a class of rings R containing commutativerings weakly compressible R modules are subdirect product of prime modules and theconverse holds precisely when the class of weakly compressible modules is enveloping formod R or equivalently every semiprime module is weakly compressible Semi Artinian ringsR are shown to have the latter property and the converse is true when R is strongly regular Duo Noetherian rings over which weakly compressible modules form an enveloping class areshown to have a nite number of maximal ideals Finally we prove that for many rings R including duo rings weakly compressible R modules are precisely subdirect products of primeR modules if and only if dim R 0 and R N R is a semi Artinian ring if and only if everyclassical semiprime module is semiprime Key Words Classical prime module classical semiprime module enveloping class Krulldimension prime modules semilocal ring semiprime module singular semi Artinian ring 1
استاد راهنما :
محمدرضا ودادي
استاد مشاور :
عاطفه قرباني
استاد داور :
احمد حقاني، احمد موسوي، محمود بهبودي
