Relatively congruence-free regular semigroups.
type: Item
instance of: scholarly article
title: Relatively congruence-free regular semigroups.
zbMATH Open document ID: 1314.20049
author: Peter R. Jones
published in: Semigroup Forum
publication date: 2015-01-09T00:00:00Z
full work available at URL: https://epublications.marquette.edu/cgi/viewcontent.cgi
review text: Let \(\tau\) be an equivalence relation on a semigroup \(S\). According to \textit{H. Yu} et al. [Semigroup Forum 84, No. 2, 308-322 (2012; Zbl 1257.20057)], \(S\) is called \(\tau\)-congruence-free if any congruence \(\rho\) on \(S\) is either disjoint from \(\tau\) or contains \(\tau\). Let \(\tau\) be one of Green's relations: \(\mathcal J\), \(\mathcal L\), \(\mathcal R\). In these cases, \(\tau\)-congruence-free regular semigroups are characterized, modulo congruence-free regular semigroups. If \(S\) is a completely semisimple semigroup, a complete characterization is obtained for the mentioned values of \(\tau\) and also for the case \(\tau=\mathcal H\).
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 6385106
zbMATH Keywords: relatively congruence-free semigroups
zbMATH Keywords: Green relations
zbMATH Keywords: regular semigroups
zbMATH Keywords: completely semisimple semigroups
zbMATH Keywords: congruences
reviewed by: Grigori I. Zhitomirski
MaRDI profile type: Publication
OpenAlex ID: W2005340363
cites work: Classification of some \(\tau\)-congruence-free completely regular semigroups.
cites work: Q3848243
cites work: Q4846425
cites work: Certain fundamental congruences on a regular semigroup
cites work: Q3231197
DOI: 10.1007/S00233-014-9575-2
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description: scientific article; zbMATH DE number 6385106