Remarks on canonical quasi-ideals in semigroups
type: Item
instance of: scholarly article
title: Remarks on canonical quasi-ideals in semigroups
zbMATH Open document ID: 0675.20051
author: Otto Steinfeld
author: Tran Thanh Thang
published in: Beiträge zur Algebra und Geometrie
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138396
review text: A canonical quasi-ideal in a semigroup is defined as a non-zero intersection of a 0-minimal right ideal and a 0-minimal left ideal. The paper extends results on 0-minimal quasi-ideals of semiprime semigroups to canonical quasi-ideals of arbitrary semigroups. (In a semiprime semigroup every 0-minimal quasi-ideal is canonical.) It is proved e.g. that a semigroup has a completely 0-simple ideal iff it has an idempotent canonical quasi-ideal, and then primitive regular semigroups are characterized by using idempotent canonical quasi-ideals.
Mathematics Subject Classification ID: 20M12
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 4105243
zbMATH Keywords: 0-minimal quasi-ideals
zbMATH Keywords: semiprime semigroups
zbMATH Keywords: canonical quasi-ideals
zbMATH Keywords: completely 0-simple ideal
zbMATH Keywords: primitive regular semigroups
zbMATH Keywords: idempotent canonical quasi-ideals
reviewed by: L. Márki
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4105243