On weak regular *-semigroups.
type: Item
instance of: scholarly article
title: On weak regular *-semigroups.
zbMATH Open document ID: 1061.20051
author: Yonghua Li
author: Haibin Kan
author: Bingjun Yu
publication date: 2004-10-01T00:00:00Z
review text: A semigroup \(S\) is called a weak regular *-semigroup if it has a unary operation * satisfying \[ xx^*x=x,\;(x^*)^*=x,\text{ and }(xx^*yy^*)^*=yy^*xx^*\text{ for all }x,y\text{ in }S. \] In this paper a type of partial algebra called a projective partial groupoid is defined. The inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular *-semigroup has a projective partial groupoid structure. Moreover, a weak regular *-product that connects a fundamental weak regular *-semigroup with a corresponding projective partial groupoid is introduced. Every weak regular *-product is a weak regular * -semigroup and any weak regular *-semigroup is constructed in this way.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 08A55
zbMATH DE Number: 2104916
zbMATH Keywords: regular *-semigroups
zbMATH Keywords: projective partial groupoids
zbMATH Keywords: idempotent-separating congruences
zbMATH Keywords: regular *-products
reviewed by: Peter M. Higgins
MaRDI profile type: Publication
full work available at URL: s10114-004-0355-x
OpenAlex ID: W1984729938
cites work: Q4126563
cites work: Q3941608
cites work: P-systems in regular semigroups
DOI: 10.1007/S10114-004-0355-X
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2104916