Eventually regular Dubreil-Jacotin semigroups.
type: Item
instance of: scholarly article
title: Eventually regular Dubreil-Jacotin semigroups.
zbMATH Open document ID: 1072.20072
author: T. S. Blyth
author: Guilherme A. Pinto
published in: Semigroup Forum
publication date: 2005-02-25T00:00:00Z
review text: An ordered semigroup, as defined here, is one with an order with respect to which every translation is isotone. An ordered semigroup \(S\) is a Dubreil-Jacotin semigroup if and only if there is an ordered group \(G\) and an isotone epimorphism \(f\colon S\to G\) that is principal, in the sense that the pre-image of the negative cone of \(G\) is a principal down-set of \(S\). Finally, a semigroup is eventually regular if each element has a regular power. The purpose of the paper is to derive necessary and sufficient conditions for an ordered eventually regular semigroup \(S\) to be Dubreil-Jacotin; when this is the case \(S\) has a greatest idempotent.
reviewed by: Peter M. Higgins
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 2138813
zbMATH Keywords: ordered semigroups
zbMATH Keywords: eventually regular semigroups
zbMATH Keywords: Dubreil-Jacotin semigroups
zbMATH Keywords: idempotents
MaRDI profile type: Publication
full work available at URL: s00233-004-0136-y
OpenAlex ID: W2005832478
DOI: 10.1007/S00233-004-0136-Y
description: scientific article; zbMATH DE number 2138813