An application of a theorem of Ash to finite covers.
type: Item
instance of: scholarly article
title: An application of a theorem of Ash to finite covers.
zbMATH Open document ID: 1073.20051
author: K. Auinger
author: Gracinda M. S. Gomes
author: Victoria Gould
author: Benjamin Steinberg
published in: Studia Logica
publication date: 2005-04-07T00:00:00Z
review text: The relation \(\widetilde R\) on a semigroup \(S\) is defined by \(a\widetilde Rb\) iff \(ea=a\Leftrightarrow eb=b\) for all \(e\in E(S)\). A semigroup \(S\) is called weakly left quasi-ample (wlqa), if for all \(a\in S\) the \(\widetilde R\)-class of \(a\) contains a unique idempotent \(a^+\) and the ample identity \(ae=(ae)^+a\) holds for all \(a\in S\), \(e\in E(S)\); \(S\) is weakly left ample (wla), if the idempotents of \(S\) commute and \(\widetilde R\) is a left congruence. The class of wlqa semigroups is a \((2,1)\)-quasivariety with binary semigroup operation and unary operation \(a\mapsto a^+\). This class contains the classes of groups, inverse, left ample and weakly left ample semigroups. It is shown that every finite wlqa semigroup has a finite proper wlqa cover and all wla semigroups have representations as \((2,1)\)-subalgebras of partial one-one transformations, where the unary operation maps a transformation \(\alpha\) to the identity map on the domain of \(\alpha\).
reviewed by: Jaak Henno
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 2153436
zbMATH Keywords: representations
zbMATH Keywords: weakly left quasi-ample semigroups
zbMATH Keywords: left ample semigroups
zbMATH Keywords: finite proper covers
zbMATH Keywords: quasivarieties
zbMATH Keywords: partial transformations
MaRDI profile type: Publication
full work available at URL: s11225-005-5057-6
OpenAlex ID: W2043257491
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DOI: 10.1007/S11225-005-5057-6
description: scientific article; zbMATH DE number 2153436