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كارشناسي ارشد

رياضي محض﴿جبر﴾

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1391

ده، 102ص.: مصور، جدول، نمودار

ص.ع. به فارسي و انگليسي

محمود بهبودي

عاطفه قرباني

24/8/91

منصور معتمدي، جواد اسدالهي

1396/09/21

كتابنامه

علوم رياضي

رياضي

ID6789

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

English abstract This thesis is based on an article by Gangyong Lee S Tariq Rizvi and CosminS Roman in 2010 We assume that R is a ring not necessarily commutative with unity and M is an unital right R module The concept of right Rickart rings Maeda 1960 or right p p rings Hattori 1960 has been extensivly studied inthe literature A ring R is called right Rickart if the right annihilator of anysingle element of R is generated by an idempotent as a right ideal A left Rickartring is defined similarly notion of Rickart rings is not left right symmetric Examples of right Rickart rings include domain von Neumann regular rings andright semi hereditary rings In particular the endomorphism ring of anLet S End M be the ring of R endomorphisms of M A right R module M isarbitrary direct sum of copies of a right hereditary ring is a right Rickart ring is generated by an idempotent of S equivalently r Ker M for everycalled a Rickart module if the right annihilator in M of any single element of S S It is easy to see that for M R the notion of a Rickart module coincideswith that of a right Rickart ring It is shown that every direct summand of aRickart module inherits the property Every Rickart module is K nonsingularand has the Summand Intersection Property SIP The class of rings R forwhich every right R module is Rickart is precisely that of the semisimpleArtinian ones while the class of rings R for which every free right R module is Rickart is precisely that of the right hereditary rings Examples andresults are provided to show that the concept of a Rickart module is distict fromthat of a Baer module While the endomorphism ring of a Rickart modules isshown to be always a right Rickart ring the converse does not hold true ingeneral Every Rickart module inherently satisfies a weak retractable property The notion of this weak retractability called k local retractability is preciselythe condition that is needed for the converse to hold in the result mentionedEnd M is a right Rickart ring and M is k local retractable In 1967 Smallabove In particular it is shown that M is a Rickart module if and only ifproved that a right Rickart ring with no infinite set of nonzero orthognalidempotents in its endomorphism ring is precisely a Baer module Analogous to

محمود بهبودي

عاطفه قرباني

منصور معتمدي، جواد اسدالهي