Some remarkable congruences on completely regular semigroups
type: Item
instance of: scholarly article
title: Some remarkable congruences on completely regular semigroups
zbMATH Open document ID: 0934.20043
author: Mario Petrich
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-11-02T00:00:00Z
full work available at URL: CONT28-4.html
review text: A completely regular semigroup \(S\) is expressed as \((Y;S_\alpha)\) thereby indicating that \(S\) is a semilattice \(Y\) of completely simple semigroups \(S_\alpha\). For each pair \(\alpha,\beta\in Y\), \(\alpha>\beta\), let \(\kappa_{\alpha,\beta}\) be the congruence on \(S\) generated by the pairs \((a,b)\), \(a\in S_\alpha\), \(b\in S_\beta\), \(a>b\). It is shown that these congruences play a crucial role in finding conditions which ensure that the kernel relation \(K\) on the congruence lattice \(C(S)\) be a congruence. Further the author introduces a generalization of Rees congruences by involving two ideals of \(S\) and a congruence on \(S\). For a fixed congruence, this produces a lattice of congruences on \(S\) with several interesting properties.
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 1309888
zbMATH Keywords: completely regular semigroups
zbMATH Keywords: semilattices
zbMATH Keywords: completely simple semigroups
zbMATH Keywords: kernel relations
zbMATH Keywords: congruence lattices
zbMATH Keywords: Rees congruences
zbMATH Keywords: lattices of congruences
reviewed by: Jaromír Duda
MaRDI profile type: Publication
OpenAlex ID: W2000612363
cites work: The congruence lattice of a regular semigroup
cites work: Q4021416
cites work: Congruences on Completely Regular Semigroups
cites work: The kernel relation for a completely regular semigroup
cites work: Certain relations on the congruence lattice of a completely regular semigroup
DOI: 10.1216/RMJM/1181071726
description: scientific article; zbMATH DE number 1309888