Minimal quasi-ideals in ternary semigroup
type: Item
instance of: scholarly article
title: Minimal quasi-ideals in ternary semigroup
zbMATH Open document ID: 0885.20041
author: V. N. Dixit
author: Sarita Dewan
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1997-11-26T00:00:00Z
review text: Assume the ternary semigroup \((T,[\cdots])\) without \(0\) has at least one ternary idempotent element. A non-empty subset \(Q\) of \(T\) is called a quasi-ideal iff \([TTQ]\cap\{[TQT]\cup[TTQTT]\}\cap[QTT]\subset Q\). All minimal quasi-ideals of a given semigroup are isomorphic. Moreover, every minimal quasi-ideal \(Q\) of \(T\) is a ternary subgroup of \(T\) and can be written in the form \(Q=[eTeTe]\), where \(e\) is the identity of \(Q\). If \(T\) has at least one minimal quasi-ideal, then the union of all minimal quasi-ideals of \(T\) is the kernel of \(T\) in the sense of \textit{F. M. Sioson} [Math. Jap. 10, 63-84 (1965; Zbl 0247.20085)].
Mathematics Subject Classification ID: 20N10
Mathematics Subject Classification ID: 20M12
Mathematics Subject Classification ID: 20N15
zbMATH DE Number: 1062340
zbMATH Keywords: ternary semigroups
zbMATH Keywords: minimal quasi-ideals
zbMATH Keywords: idempotents
reviewed by: Wiesław A. Dudek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1062340