\(\mathcal P\)-regular semigroups.
type: Item
instance of: scholarly article
title: \(\mathcal P\)-regular semigroups.
zbMATH Open document ID: 0664.20039
DOI: 10.1007/BF02573295
author: M. K. Sen
author: Miyuki Yamada
published in: Semigroup Forum
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134984
review text: Regular *-semigroups and orthodox semigroups have some common properties regarding the inverses of elements of these semigroups. These properties are in relation to the set of all projections, for regular *-semigroups, and in relation to the set of all idempotents, for orthodox semigroups. Let \(P\) denote the sets just specified, for these classes of semigroups. Then, the following is a key property that holds for both classes: let \(a'\) be an inverse of \(a\) and let \(b'\) be an inverse of \(b\) such that \(aa'\), \(a'a\), \(bb'\), \(b'b\) all belong to \(P\). Then \(b'a'\) is an inverse of \(ab\) and \(abb'a'\) and \(b'a'ab\) both belong to \(P\). This paper studies the properties of a class of semigroups giving a generalization of these shared properties of regular *-semigroups and orthodox semigroups.
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 4085917
zbMATH Keywords: orthodox semigroups
zbMATH Keywords: inverses of elements
zbMATH Keywords: projections
zbMATH Keywords: regular *-semigroups
zbMATH Keywords: idempotents
reviewed by: Miyuki Yamada
MaRDI profile type: Publication
cites work: Q3848243
cites work: Orthodox semigroups
cites work: Q4126563
cites work: Q3918310
cites work: Regular * semigroups
cites work: Q3934711
cites work: Q3941608
cites work: P-systems in regular semigroups
cites work: Q3792900
OpenAlex ID: W3080503698
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description: scientific article; zbMATH DE number 4085917