12852

11758

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1396

هشت، [66]ص.: مصور

ص.ع. به فارسي و انگليسي

واژه نامه انگليسي به فارسي

1396/07/15

كتابنامه

علوم رياضي

رياضي

ID11758

Fine rings A new class of simple rings Maryam Azarian m azarian@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mahmood Behboodi mbehboodi@cc iut ac ir Advisor Dr MohammadReza Vedadi mrvedadi@cc iut ac ir 2010 MSC 12E15 15B33 15B36 16E50 16N40 16U60 Keywords Units nilpotents matrix rings artinian rings simple rings clean rings ne rings UU rings AbstractThis M Sc thesis is based on the following paper C lug reanu G and Lam T Y ne rings a new class of simple rings J Algebra Appl 1650173 18 2016 9 The work in this thesis is prompted by the idea of looking at the three sets U R idem R andnil R in any unital ring R which denote respectively the unit group the set of idempotents andthe set of nilpotent elements in R In the last four decades an additive theory has emerged in thestudy of these three interesting sets In 2 Nicholson de ned a ring element a R to be clean if itcan be written in the form e u where e idem R and u U R If every a R is clean R is saidto be a clean ring Prompted by this Diesl 3 de ned a ring element b R to be nil clean if b e tfor some e idem R and t nil R If every b R is nil clean R is said to be a nil clean ring Itis easy to see that nil clean rings are always clean 3 Proposition 3 4 though in general clean ringsneed not be nil clean Guided by the de nitions in the last paragraph we investigate in this work thethird and last possible way of adding a pair of elements from two of the three sets U R idem R and nil R above Thus we de ne a nonzero ring element a R to be ne if a u t for someu U R and some t nil R The intuitive idea behind a R 0 being ne is that a is invertiblemodulo a nilpotent element Any equation of the form a u t will be called a ne decompositionof a R 0 and we will write R for the set of ne elements in R 0 The reason for stipulatingthat 0 R is that if there exists an equation 0 u t where u U R and t nil R then u t

محمود بهبودي

محمدرضا ودادي

عاطفه قرباني، بيژن طائري