Year: 2010
Author: Weixing Chen, Shuying Cui
Communications in Mathematical Research , Vol. 26 (2010), Iss. 4 : pp. 313–320
Abstract
A general ring means an associative ring with or without identity. An idempotent $e$ in a general ring $I$ is called left (right) semicentral if for every $x ∈ I$, $xe = exe (ex = exe)$. And $I$ is called semiabelian if every idempotent in $I$ is left or right semicentral. It is proved that a semiabelian general ring $I$ is $π$-regular if and only if the set $N(I)$ of nilpotent elements in $I$ is an ideal of $I$ and $I/N(I)$ is regular. It follows that if $I$ is a semiabelian general ring and $K$ is an ideal of $I$, then $I$ is $π$-regular if and only if both $K$ and $I/K$ are $π$-regular. Based on this we prove that every semiabelian GVNL-ring is an SGVNL-ring. These generalize several known results on the relevant subject. Furthermore, we give a characterization of a semiabelian GVNL-ring.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-CMR-19128
Communications in Mathematical Research , Vol. 26 (2010), Iss. 4 : pp. 313–320
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: semiabelian ring $π$-regular ring GVNL-ring exchange ring.