On P-Q ordered semigroups
type: Item
instance of: scholarly article
title: On P-Q ordered semigroups
zbMATH Open document ID: 0813.20069
DOI: 10.1007/BF01876340
author: V. Pereyra
published in: Periodica Mathematica Hungarica
publication date: 1995-04-02T00:00:00Z
review text: A partially ordered semigroup \(S\) is called P-ordered if for any \(a,b \in S\), \(ab \geq b\). The semigroup \(S\) is called Q-ordered if \(a \leq b\) implies \(a = b\) or \(b = ac\) for some \(c \in S\). These are the duals of N- M-ordered semigroups [in \textit{S. Y. Kwan} and \textit{K. P. Shum}, Semigroup Forum 19, 151-175 (1980; Zbl 0438.06010)]. The authors prove a number of results on P-Q-ordered semigroups. Theorem 1: Let \(S\) be a P-ordered semigroup. If \(S\) is regular, then \(S\) is a band. If \(S\) is an inverse semigroup, then \(S\) is a semilattice. Theorem 2: Let \(S\) be a P-Q-ordered semigroup in which every right principal ideal is completely prime, then \(S\) has no elements of finite order.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 698623
zbMATH Keywords: partially ordered semigroup
zbMATH Keywords: P-ordered semigroup
zbMATH Keywords: inverse semigroup
zbMATH Keywords: semilattice
zbMATH Keywords: P-Q-ordered semigroup
zbMATH Keywords: right principal ideal
reviewed by: Awad A. Iskander
MaRDI profile type: Publication
cites work: Q4126563
cites work: Lattices of order ideals on ordered semigroups
full work available at URL: https://doi.org/10.1007/bf01876340
OpenAlex ID: W1972911862
description: scientific article; zbMATH DE number 698623