Partial ordering and congruences on LA-semigroups
type: Item
instance of: scholarly article
title: Partial ordering and congruences on LA-semigroups
zbMATH Open document ID: 0734.20028
author: N. E. Zubov
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1991-01-01T00:00:00Z
review text: A left almost semigroup (LA-semigroup, for short) is a groupoid satisfying the left invertive law \((ab)c=(cb)a\) and one of the equivalent weak associative laws \((ab)c=b(ca)\) or \((ab)c=b(ac)\). An LA-semigroup S is called inverse if for every \(a\in S\) there is \(a'\in S\) (an inverse of a) such that \((aa')a=a\) and \((a'a)a'=a'\). The present paper studies properties of compatible partial orderings and of congruences on inverse LA-semigroups. In particular, the greatest idempotent-separating congruence on an inverse LA-semigroup is described in detail.
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20N02
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 4214263
zbMATH Keywords: left almost semigroup
zbMATH Keywords: groupoid
zbMATH Keywords: left invertive law
zbMATH Keywords: weak associative laws
zbMATH Keywords: partial orderings
zbMATH Keywords: congruences
zbMATH Keywords: inverse LA-semigroups
reviewed by: Jaromír Duda
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4214263