On unit-regular ideals.
type: Item
instance of: scholarly article
title: On unit-regular ideals.
zbMATH Open document ID: 1049.16009
author: Huanyin Chen
author: Miao-Sen Chen
published in: The New York Journal of Mathematics
publication date: 2004-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/123847
full work available at URL: 9-15nf.htm
review text: The authors introduce the notion of unit-regular ideal in a unital ring. This generalizes the notion of a unit-regular ring. They give a necessary and sufficient condition for a regular ideal \(I\) of a unital ring \(R\) to be unit-regular in terms of elements of \(I\). They prove that every square matrix over a unit-regular ideal of a unital ring is a product of an idempotent matrix and an invertible matrix. They also prove that every square matrix over a unit-regular ideal of a unital ring admits a diagonal reduction. Finally, they prove that a regular ideal \(I\) of a unital ring \(R\) is unit-regular if and only if the pseudo-similarity via \(I\) implies similarity.
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 2028909
zbMATH Keywords: unit-regular ideals
zbMATH Keywords: diagonal reductions
zbMATH Keywords: pseudo-similarities
zbMATH Keywords: idempotent matrices
reviewed by: Veereshwar A. Hiremath
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2028909