Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2023; 60(6): 1463-1475

Online first article November 17, 2023      Printed November 30, 2023

https://doi.org/10.4134/BKMS.b220573

Copyright © The Korean Mathematical Society.

On a generalization of unit regular rings

Tahire Ozen

G\"olk\"oy Kamp\"us\"u

Abstract

In this paper, we introduce a class of rings generalizing unit regular rings and being a subclass of semipotent rings, which is called idempotent unit regular. We call a ring $R$ an idempotent unit regular ring if for all $r\in R-J(R)$, there exist a non-zero idempotent $e$ and a unit element $u$ in $R$ such that $er=eu$, where this condition is left and right symmetric. Thus, we have also that there exist a non-zero idempotent $e$ and a unit $u$ such that $ere=eue$ for all $r\in R-J(R)$. Various basic characterizations and properties of this class of rings are proved and it is given the relationships between this class of rings and some well-known classes of rings such as semiperfect, clean, exchange and semipotent. Moreover, we obtain some results about when the endomorphism ring of a module in a class of left $R$-modules $X$ is idempotent unit regular.

Keywords: Jacobson radical, unit regular ring, idempotent element, clean ring

MSC numbers: Primary 16E50, 16U40, 16N20

Stats or Metrics

Share this article on :

Related articles in BKMS

more +