A network of congruences on an ample semigroup
type: Item
instance of: scholarly article
title: A network of congruences on an ample semigroup
zbMATH Open document ID: 1487.20022
author: Abdulsalam El-Qallali
published in: Semigroup Forum
publication date: 2021-06-09T00:00:00Z
review text: In this paper, a network of congrunces on an ample semigroup is discussed. Ample semigroups are generalisations of inverse semigroups using generalised Green's relations: \(\mathcal{L}^*\) and \(\mathcal{R}^*\). The author discusses cancellative congruences, the semilattice congruences, the semilattice of cancellative monoids congruences, the strongly \(E\)-reflexive congruences and the \(E\)-unitary congruences on ample semigroups. The concept of \(P\)-congruence on an ample semigroup is introduced and the minimum admissible congruence is characterised for some special conditions based on a \(P\)-congruence. Also, some particular minimum admissible congruences on an ample semigroup are recognized and this is used to study a network of certain minimum admissible congruences on the semigroup.
reviewed by: P. A. Azeef Muhammed
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 7357023
zbMATH Keywords: ample semigroup
zbMATH Keywords: admissible congruences
zbMATH Keywords: trace
zbMATH Keywords: kernel
MaRDI profile type: Publication
full work available at URL: s00233-021-10168-z
OpenAlex ID: W3138769171
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DOI: 10.1007/S00233-021-10168-Z
description: scientific article; zbMATH DE number 7357023