On weakly commutative ordered semigroups
type: Item
instance of: scholarly article
title: On weakly commutative ordered semigroups
zbMATH Open document ID: 0890.06010
author: Niovi Kehayopulu
author: Michael Tsingelis
published in: Semigroup Forum
publication date: 1998-06-29T00:00:00Z
review text: A partially ordered semigroup \((S, \cdot, \leq)\) is ``weakly commutative'' if for all \(a,b \in S\) there exist \(x\in S\) and a nonnegative integer \(n\) such that \((ab)^n \leq bxa\). It is ``archimedean'' if for all \(a,b\in S\) there exist \(x,y\in S\) and \(m\) such that \(a^m\leq xby\). It was shown by \textit{N. Kehayopulu}, \textit{P. Kiriakuli}, \textit{S. Hanumantha Rao} and \textit{P. Lakshimi} [Semigroup Forum 41, 373-376 (1990; Zbl 0708.06011)] that if \((S,\cdot,\leq)\) is a ``weakly commutative'' partially ordered semigroup with greatest element, then \((S,\cdot,\leq)\) is a semilattice of ``archimedian'' semigroups. In the paper under review the analogous result is proved for ``weakly commutative'' semigroups \((S, \cdot, \leq)\) without greatest element by use of the same semilattice congruence. Again, by a counterexample it is shown that the decomposition is not unique. It is unique if only complete semilattice congruences are considered (see the review above).
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 1106578
zbMATH Keywords: weakly commutative
zbMATH Keywords: archimedean
zbMATH Keywords: semilattice of ordered semigroups
zbMATH Keywords: partially ordered semigroup
zbMATH Keywords: semilattice congruence
zbMATH Keywords: decomposition
reviewed by: H. Mitsch
MaRDI profile type: Publication
full work available at URL: s00233-002-7002-6
OpenAlex ID: W2127631034
DOI: 10.1007/S00233-002-7002-6
description: scientific article; zbMATH DE number 1106578