On ordered quasi-Gamma-ideals of regular ordered Gamma-semigroups.
type: Item
instance of: scholarly article
title: On ordered quasi-Gamma-ideals of regular ordered Gamma-semigroups.
zbMATH Open document ID: 1329.06017
DOI: 10.1155/2013/565848
author: Abul Basar
author: M. Y. Abbasi
published in: Algebra
publication date: 2015-12-11T00:00:00Z
review text: Summary: We introduce the notion of ordered quasi-\(\Gamma\)-ideals of regular ordered \(\Gamma\)-semigroups and study the basic properties of ordered quasi-\(\Gamma\)-ideals of ordered \(\Gamma\)-semigroups. We also characterize regular ordered \(\Gamma\)-semigroups in terms of their ordered quasi-\(\Gamma\)-ideals, ordered right \(\Gamma\)-ideals, and left \(\Gamma\)-ideals. Finally, we have shown that (i) a partially ordered \(\Gamma\)-semigroup \(S\) is regular if and only if for every ordered bi-\(\Gamma\)-ideal \(B\), every ordered \(\Gamma\)-ideal \(I\), and every ordered quasi-\(\Gamma\)-ideal \(Q\), we have \(B\cap I\cap Q\subseteq(B\Gamma I\Gamma Q]\) and (ii) a partially ordered \(\Gamma\)-semigroup \(S\) is regular if and only if for every ordered quasi-\(\Gamma\)-ideal \(Q\), every ordered left \(\Gamma\)-ideal \(L\), and every ordered right-\(\Gamma\)-ideal \(R\), we have that \(R\cap Q\cap L\subseteq(R\Gamma Q\Gamma L]\).
Mathematics Subject Classification ID: 06F99
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 6519789
zbMATH Keywords: regular ordered \(\Gamma\)-semigroups
zbMATH Keywords: ordered quasi-\(\Gamma\)-ideals
zbMATH Keywords: ordered right \(\Gamma\)-ideals
zbMATH Keywords: partially ordered \(\Gamma\)-semigroups
Wikidata QID: Q58919917
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/565848
OpenAlex ID: W2023259942
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description: scientific article; zbMATH DE number 6519789