Exchange rings satisfying the related comparability
type: Item
instance of: scholarly article
title: Exchange rings satisfying the related comparability
zbMATH Open document ID: 1030.16005
author: Huanyin Chen
author: Fu-an Li
published in: Collectanea Mathematica
publication date: 2003-06-30T00:00:00Z
full work available at URL: https://eudml.org/doc/42891
review text: An exchange ring \(R\) is said to satisfy the related comparability, provided that for any idempotents \(e,f\in R\) with \(e=1+ab\) and \(f=1+ba\) for some \(a\in(1-e)R(1-f)\) and \(b\in(1-f)R(1-e)\), there exists a central idempotent \(u\in R\) such that \(ueR\lesssim^\oplus ufR\) and \((1-u)fR\lesssim^\oplus(1-u)eR\). It is shown that an exchange ring \(R\) satisfies the related comparability if and only if for any regular \(x\in R\), there exist a related unit \(w\in R\) and a group \(G\) in \(R\) such that \(wx\in G\). In addition, we investigate the uniqueness of related units for generalized inverses in exchange rings.
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 16U60
zbMATH DE Number: 1943352
zbMATH Keywords: exchange rings
zbMATH Keywords: related comparability
zbMATH Keywords: central idempotents
zbMATH Keywords: related units
zbMATH Keywords: generalized inverses
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1943352