Semigroups with the ideal extension property
type: Item
instance of: scholarly article
title: Semigroups with the ideal extension property
zbMATH Open document ID: 1030.20038
DOI: 10.1016/S0021-8693(03)00313-2
published in: Journal of Algebra
publication date: 2003-09-25T00:00:00Z
review text: A semigroup \(S\) is said to have the ideal extension property if for each subsemigroup \(T\) of \(S\) and an ideal \(I\) of \(T\), there exists an ideal \(J\) of \(S\) such that \(J\cap T=I\). It is proved that \(S\) has this property if and only if \(S\) is a semilattice of ideal extensions of completely simple semigroups over torsion groups that satisfy three additional conditions involving the regular members of \(S\). Particular cases then give some crisp results: for instance a regular semigroup has the ideal extension property if and only if \(S\) is a completely regular semigroup each of whose maximum subgroups is a torsion group.
reviewed by: Peter M. Higgins
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M12
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 1985875
zbMATH Keywords: ideal extension property
zbMATH Keywords: semilattices of ideal extensions
zbMATH Keywords: completely simple semigroups
zbMATH Keywords: torsion groups
zbMATH Keywords: completely regular semigroups
zbMATH Keywords: maximal subgroups
author: Xiaojiang Guo
MaRDI profile type: Publication
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full work available at URL: s0021-8693(03)00313-2
OpenAlex ID: W2067146249
description: scientific article; zbMATH DE number 1985875