پديد آورنده :
حيدري، سجاد
عنوان :
مطالعه حلقه هاي تعويض پذير تماما دوري و تماما زنجيري
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
محمود بهبودي
واژه نامه :
به فارسي و انگليسي
استاد داور :
احمد حقاني، كامران ديواني آذر، محمدرضا ودادي
تاريخ ورود اطلاعات :
1395/07/05
كد ايرانداك :
ID904 دكتري
چكيده انگليسي :
Study of Completely Cyclic and Completely Serial Commutative Rings Sajad Heidari sajad heidari@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mahmood Behboodi mbehbood@cc iut ac ir Advisor Dr Amir Hashemi amir hashemi@cc iut ac ir 2010 MSC 13A18 13F30 16D70 13C99 Keywords Uniserial rings uniserial modules serial rings valuation rings serial modules completely cyclic module principal ideal ring AbstractIn this thesis we describe commutative rings whose proper ideals are direct sums of completely cyclicmodules In fact it is shown that every proper ideal of R is a direct sum of completely cyclic R modules if and only if R is a principal ideal ring or R is a local ring with maximal ideal M such that there is an index set and a set of elements x w R such that M Rx Rw with each Rw a simple R module and R Ann x a principal ideal ring Also we study commutativerings R whose maximal ideals are direct sums of completely cyclic modules It is shown that if everymaximal ideal of R is a direct sum of completely cyclic R modules then dim R 1 and either R is alocal ring such that every prime ideal of R is a direct sum of uniserial Noetherian R modules or R isa Noetherian ring and there exists a positive integer n such that every prime ideal of R is a direct sumof at most n completely cyclic modules Finally we characterize the structure of commutative rings Rfor which every proper ideal of R is serial It is shown that every proper ideal of a commutative ringR is serial if and only if either R is a serial ring or R is a local ring with maximal ideal M suchthat there is an index set a set of elements w R and a uniserial ideal U of R such that M U Rw with each Rw a simple R module
استاد راهنما :
محمود بهبودي
استاد داور :
احمد حقاني، كامران ديواني آذر، محمدرضا ودادي
