On strongly \(\pi\)-regular ideals.
type: Item
instance of: scholarly article
title: On strongly \(\pi\)-regular ideals.
zbMATH Open document ID: 1077.16013
published in: Journal of Pure and Applied Algebra
publication date: 2005-02-23T00:00:00Z
review text: For an associative ring \(R\) with identity, the authors introduce the notion of strongly \(\pi\)-regular ideal as an ideal \(I\) of \(R\) with the property that for any \(x\in I\), there exist a natural number \(n\) and an element \(y\in I\) such that \(x^n=x^{n+1}y\). They show that every regular square matrix over a strongly \(\pi\)-regular ideal of a ring is unit-regular. This result allows them to prove that every regular square matrix over a strongly \(\pi\)-regular ideal of a ring admits a diagonal reduction. Also, for a strongly \(\pi\)-regular ideal \(I\) of \(R\) and a natural number \(n\), it is shown that \(R\) is isomorphic to some \(n\times n\) matrix ring if and only if \(R/I\) is isomorphic to some \(n\times n\) matrix ring.
reviewed by: Septimiu Crivei
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16D25
zbMATH DE Number: 2137305
zbMATH Keywords: strongly \(\pi\)-regular rings
zbMATH Keywords: diagonal reductions
zbMATH Keywords: strongly \(\pi\)-regular ideals
zbMATH Keywords: matrix rings
author: Huanyin Chen
author: Miao-Sen Chen
MaRDI profile type: Publication
full work available at URL: j.jpaa.2004.05.006
OpenAlex ID: W2084192020
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DOI: 10.1016/J.JPAA.2004.05.006
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description: scientific article; zbMATH DE number 2137305