A note on weakly clean rings.
type: Item
instance of: scholarly article
title: A note on weakly clean rings.
zbMATH Open document ID: 1232.16022
published in: Acta Mathematica Hungarica
publication date: 2011-12-19T00:00:00Z
review text: Let \(R\) be an associative ring. An element \(x\in R\) is called weakly clean if \(x\) is the sum of a unit element and an idempotent of \(R\). A ring is weakly clean if every element of it is weakly clean. As the main theorem the authors prove that a ring \(R\) is weakly clean if and only if for any \(x\in R\) there is an idempotent \(e\in R\) such that \(e\in xR\) and either \(1-e\in(1-x)R\) or \(1-e\in(1+x)R\). Two characterizations of unit regular rings are given in Theorems 2.2 and 2.3.
reviewed by: Dinh Van Huynh
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16E50
zbMATH DE Number: 5990622
zbMATH Keywords: weakly clean rings
zbMATH Keywords: unit regular elements
zbMATH Keywords: idempotents
zbMATH Keywords: unit regular rings
zbMATH Keywords: sums of units
author: Angelina Y. M. Chin
author: Kiat Tat Qua
MaRDI profile type: Publication
full work available at URL: s10474-011-0100-8
OpenAlex ID: W1970041129
cites work: Weakly clean rings and almost clean rings
cites work: A CHARACTERIZATION OF UNIT REGULAR RINGS
cites work: Lifting Idempotents and Exchange Rings
DOI: 10.1007/S10474-011-0100-8
description: scientific article; zbMATH DE number 5990622