12232

11205

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

نه، [96]ص.: مصور.

ص. ع. به فارسي و انگليسي

واژه نامه

1395/12/04

كتابنامه

علوم رياضي

رياضي

ID11205

On Weak Dual Rickart Modules and Dual Baer Modules zadeh Mehregan A a mehregan@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Atefeh Ghorbani a ghorbani@cc iut ac ir Advisor Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir 2000 MSC 16D10 16D70 16S50 16D80 Keywords Dual Rickart modules Dual Baer modules Endomorphism rings Semipotent ringsand modules Weak dual Rickart modules Abstract This M Sc thesis is based on the following paperTribak Rachid On weak dual Rickart modules and dual Baer modules Comm Algebra 43 8 3190 3206 2015 Recall a module M is said to be d Rickart if for every endomorphism of M Im is a direct summandof M also a module M is called retractable if for every nonzero submodule N M there exists anonzero endomorphism of M such that Im N It was shown that if M is a retractable d Rickartmodule then every nonzero submodule contains a nonzero direct summand of M We introduce thenotion of Wd Rickart modules i e modules M such that for every nonzero endomorphism of M Im contains a nonzero direct summand of M We study some basic properties of Wd Rickart modules We show that any direct summands of a Wd Rickart module inherits the property while direct sumsof Wd Rickart modules do not Some conditions under which a direct sum of Wd Rickart modules isWd Rickart are provided We show that RR is Wd Rickart if and only if for every nonzero elementa R there is a nonzero element x R with x xax The class of rings R for which every rightR module is Wd Rickart is shown to be precisely that of right semi artinian right V rings providingsome examples showing that a Wd Rickart module need not be d Rickart Remind that a module Mis said to be dual Baer if for every N M there exists an idempotent e S EndR M such thatD N eS where D N S Im N It is natural to try to relate Wd Rickart modules tothe notion of dual Baer modules It is clear that every dual Baer module is Wd Rickart We extend

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