14464

1359 دكتري

دكتري

رياضي

اصفهان : دانشگاه صنعتي اصفهان

1396

[سيزده]، 97ص.

حسين خبازيان، يانگ لي

محمود بهبودي

انگليسي به فارسي ; فارسي به انگليسي

جواد اسداللهي، شكراله سالاريان، محمدرضا ودادي

1398/01/17

كتابنامه

علوم رياضي

رياضي

1398/01/19

ID1359 دكتري

The Generalizations of Commutativity and Reducibility of Rings Mehdi Kheradmand m kheradmand@math iut ac ir September 11 2017 Doctor of Philosophy in Mathematics Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranFirst Supervisor Dr Hossein Khabazian khabaz@cc iut ac irSecond Supervisor Prof Yang Lee ylee@pusan ac krAdvisor Dr Mahmood Behboodi mbehbood@cc iut ac ir2000 MSC 16N40 16S70 16U80Keywords nil reflexive ring reflexive nilpotent property RNP nil ideal matrix ring polynomial ring powerseries ring right quotient ring Abstract Mason introduced the reflexive property for ideals We in this thesis consider the reflexive ring property on nilideals introducing the concept of a nil reflexive ring as a generalization of the reflexive ring property We willcall a ring R nil reflexive if IJ 0 implies JI 0 for nil ideals I J of R The polynomial and the powerseries rings over a right Noetherian ring or an NI ring R are shown to be nil reflexive if aRb 2 0 impliesaRb 0 for all a b N R We further investigate the structure of nil reflexive rings related to varioussorts of ring extensions Afterwards we restrict the reflexivity to nilpotent elements and a ring will be said to beRNP if it satisfies this restriction The structure of RNP rings is studied in relation to the near concepts and ringextensions which have roles in ring theory

حسين خبازيان، يانگ لي

محمود بهبودي

جواد اسداللهي، شكراله سالاريان، محمدرضا ودادي