Weakly Semicommutative Rings and Strongly Regular Rings

• Journal title : Kyungpook mathematical journal
• Volume 54, Issue 1,  2014, pp.65-72
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2014.54.1.65
Title & Authors
Weakly Semicommutative Rings and Strongly Regular Rings
Wang, Long; Wei, Junchao;

Abstract
A ring R is called weakly semicommutative ring if for any a, $\small{b{\in}R^*}$ = R\{0} with ab = 0, there exists $\small{n{\geq}1}$ such that either an $\small{a^n{\neq}0}$ and $\small{a^nRb=0}$ or $\small{b^n{\neq}0}$ and $\small{aRb^n=0}$. In this paper, many properties of weakly semicommutative rings are introduced, some known results are extended. Especially, we show that a ring R is a strongly regular ring if and only if R is a left SF-ring and weakly semicommutative ring.
Keywords
weakly semicommutative rings;SF-rings;strongly regular rings;semicommutative rings;Abelian rings;
Language
English
Cited by
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