Completely (0-)simple semigroups and maximal quotient semigroups
type: Item
instance of: scholarly article
title: Completely (0-)simple semigroups and maximal quotient semigroups
zbMATH Open document ID: 0797.20054
author: Guangtian Song
published in: Southeast Asian Bulletin of Mathematics
publication date: 1994-04-12T00:00:00Z
review text: A semigroup \(S\) is called right (left) reductive if for \(s_ 1,s_ 2 \in S\) we have that \(s_ 1 t = s_ 2 t\) (\(ts_ 1 = ts_ 2\)) for all \(t \in S\) implies \(s_ 1 = s_ 2\). This is equivalent to saying that \(S\) has a maximal right (left) quotient semigroup. The author gives conditions for a completely 0-simple and a completely simple semigroup \(S\) to be right reductive in terms of the sandwich matrix \(P\) used in the matrix representation \(M^ 0[G;I,\Lambda;P]\) or \(M[G;I,\Lambda;P]\) of \(S\). In this case the maximal right quotient semigroup is described in either case as a certain column monomial matrix semigroup over \(G\).
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 548976
zbMATH Keywords: right reductive semigroup
zbMATH Keywords: Rees matrix semigroup
zbMATH Keywords: completely simple semigroup
zbMATH Keywords: sandwich matrix
zbMATH Keywords: matrix representation
zbMATH Keywords: maximal right quotient semigroup
zbMATH Keywords: column monomial matrix semigroup
reviewed by: Ulrich Knauer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 548976