On the weak regularity of semigroup rings
type: Item
instance of: scholarly article
title: On the weak regularity of semigroup rings
zbMATH Open document ID: 0815.16010
DOI: 10.1007/BF02573665
published in: Semigroup Forum
publication date: 1995-07-03T00:00:00Z
full work available at URL: https://eudml.org/doc/135307
review text: A ring \(R\) is said to be weakly regular iff, for every \(a \in R\), there exists \(x \in R^ 1 aR^ 1\) such that \(a = xa\). The aim of the paper is to investigate weakly regular semigroup rings. So far there is only one known result in this direction: Vanaja (1970) and Fisher (1974) described weakly regular group rings (this description may be obtained from the well known description of regular group rings by changing ``regular'' for ``weakly regular''). The author obtains many results giving sufficient conditions for some semigroup rings to be weakly regular. The full description of weakly regular semigroup rings \(R[S]\) is given only for a locally finite inverse semigroup \(S\), and for \(S\) a generalized Brandt semigroup (i.e. an orthodox completely 0-simple semigroup).
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 549059
zbMATH Keywords: weakly regular semigroup rings
zbMATH Keywords: weakly regular group rings
zbMATH Keywords: locally finite inverse semigroup
zbMATH Keywords: generalized Brandt semigroup
author: Fang Li
reviewed by: Josif S. Ponizovskii
MaRDI profile type: Publication
cites work: Q3848243
cites work: Q4126563
cites work: Regularity of Semilattice Sums of Rings
cites work: Q3337662
cites work: Semigroup rings
cites work: Regularity of Semigroup Rings
cites work: Q3474796
cites work: Q5597570
description: scientific article; zbMATH DE number 549059