The semigroup generated by certain operators on the congruence lattice of a Clifford semigroup
type: Item
instance of: scholarly article
title: The semigroup generated by certain operators on the congruence lattice of a Clifford semigroup
zbMATH Open document ID: 0766.20021
DOI: 10.1007/BF03025774
author: Mario Petrich
published in: Semigroup Forum
publication date: 1993-03-01T00:00:00Z
full work available at URL: https://eudml.org/doc/135196
review text: For any congruence relation \(\rho\) on a regular semigroup \(S\), let \(\rho K\) and \(\rho k\) be the greatest and the least congruences on \(S\) with the same kernel as \(\rho\), and, \(\rho T\) and \(\rho t\) the greatest and the least congruences on \(S\) with the same trace as \(\rho\). The semigroup generated by the set \(\Gamma=\{k,K,t,T\}\) of transformations of the congruence lattice of \(S\) is denoted by \(\Omega(S)\). The author finds a finitely presented semigroup \(\Omega=\langle\Gamma\mid\Sigma\rangle\) which has the following property: if \(S\) is any Clifford semigroup, then \(\Omega(S)\) is a homomorphic image of \(\Omega\). An example is given of a Clifford semigroup where \(\Omega\cong\Omega(S)\). The semigroup \(\Omega\) has 19 elements.
reviewed by: Francis Pastijn
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 126123
zbMATH Keywords: regular semigroup
zbMATH Keywords: kernel
zbMATH Keywords: congruences
zbMATH Keywords: trace
zbMATH Keywords: transformations
zbMATH Keywords: congruence lattice
zbMATH Keywords: finitely presented semigroup
zbMATH Keywords: Clifford semigroup
MaRDI profile type: Publication
cites work: Congruences on Regular Semigroups
cites work: Lattices of completely regular semigroup varieties
cites work: Q3337662
cites work: Congruences on strong semilattices of regular simple semigroups
cites work: Q4298982
cites work: A Network of Congruences on an Inverse Semigroup
cites work: Semigroups generated by certain operators on varieties of completely regular semigroups
description: scientific article; zbMATH DE number 126123