On the structure of certain po-semigroups
type: Item
instance of: scholarly article
title: On the structure of certain po-semigroups
zbMATH Open document ID: 0759.22006
DOI: 10.1007/BF02574340
author: S. D. Hippisley-Cox
published in: Semigroup Forum
publication date: 1992-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/135144
review text: This article continues the work of \textit{A. M. Fourozanfar} and \textit{J. S. Pym} on the existence and structure of the minimal ideal in semigroups defined on partially ordered sets [ibid. 42, No. 2, 175-188 (1991; Zbl 0739.22003)]. The author calls a non-empty partially ordered set a complete semilattice if every non-empty subset has a supremum and every non-empty chain has an infimum. A semigroup on a partially ordered set is called a po-semigroup if its multiplication is non-decreasing (i.e., \(a\leq b\) and \(c\leq d\) always implies \(ac\leq bd\)). In analogy to the First Fundamental Theorem for compact semigroups with one-sidedly continuous multiplication the author shows that every po-semigroup \(S\) on a complete semilattice has minimal idempotents; from this fact he deduces in the usual way the existence and structure of the minimal ideal of \(S\).
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 35816
zbMATH Keywords: existence
zbMATH Keywords: structure
zbMATH Keywords: minimal ideal
zbMATH Keywords: partially ordered sets
zbMATH Keywords: complete semilattice
zbMATH Keywords: po-semigroup
zbMATH Keywords: minimal idempotents
reviewed by: Wolfgang A. F. Ruppert
MaRDI profile type: Publication
cites work: Q3995290
cites work: Q3848243
cites work: Q4692885
cites work: Compact right uppersemicontinuous semigroups of closed sets
cites work: Chain-complete posets and directed sets with applications
cites work: On Bounded po-Semigroups
description: scientific article; zbMATH DE number 35816