The minimum group congruence on certain eventually regular semigroups
type: Item
instance of: scholarly article
title: The minimum group congruence on certain eventually regular semigroups
zbMATH Open document ID: 0801.20046
author: V. Pereyra
published in: Southeast Asian Bulletin of Mathematics
publication date: 1994-12-01T00:00:00Z
review text: A semigroup \(S\) is called eventually regular if each element \(x \in S\) has a power which is regular. An eventually regular semigroup \(S\) is eventually orthodox if the set of idempotents \(E(S)\) of \(S\) forms a subsemigroup. Eventually conventional semigroups are a generalization of eventually orthodox semigroups having a slightly more complicated definition. The paper under review describes the minimum group congruence \(\sigma\) on an eventually conventional semigroup (and thus on an eventually orthodox semigroup) by \(\sigma = \{(a,b) \in S\times S\mid (\exists e \in E(S)) eae = ebe\}\) and thus generalizes known results for conventional semigroups. It should be noted that there is a relatively explicit description of the minimum group congruence on any \(E\)-inversive semigroup (which class is much more general than the class of eventually regular semigroups) [\textit{H. Mitsch}, J. Aust. Math. Soc., Ser. A 48, 66- 78 (1990; Zbl 0691.20050)]. It is, however, not clear whether the given description follows easily from the latter.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 493267
zbMATH Keywords: regular power
zbMATH Keywords: eventually regular semigroup
zbMATH Keywords: idempotents
zbMATH Keywords: eventually orthodox semigroups
zbMATH Keywords: minimum group congruence
zbMATH Keywords: eventually conventional semigroup
reviewed by: K. Auinger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 493267