Congruences on an inverse Bruck-Reilly monoid. I: Non-group congruences
type: Item
instance of: scholarly article
title: Congruences on an inverse Bruck-Reilly monoid. I: Non-group congruences
zbMATH Open document ID: 0818.20076
DOI: 10.1007/BF02573425
author: Stuart A. Rankin
published in: Semigroup Forum
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/135082
review text: Let \(T\) be an inverse monoid with group of units \(G\) and let \(\alpha: T\to G\) be a homomorphism. The Bruck-Reilly extension \(S= \text{BR} (T, \alpha)\) is again an inverse monoid. Congruences \(\rho\) on \(S\) divide naturally into group congruences (for which \(S/\rho\) is a group) and nongroup congruences. The author gives a description of the nongroup congruences on \(\text{BR} (T, \alpha)\), the key elements in the description being ``crossover \(\alpha\)-congruences'' on \(T\). A congruence \(\rho\) is called an \(\alpha\)-congruence if (\(\forall x,y\in S\)) \(x\rho y\Rightarrow x\alpha \rho y\alpha\). It is a crossover \(\alpha\)-congruence if in addition there exists a proper ideal \(I\) of \(T\) such that \(\rho\) saturates \(I\) and (\(\forall x,y\in I\)) \(x\rho y\Leftrightarrow x\alpha\rho y\alpha\).
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 7885
zbMATH Keywords: inverse monoids
zbMATH Keywords: group of units
zbMATH Keywords: Bruck-Reilly extensions
zbMATH Keywords: group congruences
zbMATH Keywords: nongroup congruences
MaRDI profile type: Publication
cites work: Q5515384
cites work: Q4126563
cites work: Regular ω-semigroups
cites work: On simple inverse semigroups
cites work: Congruences on a bisimple ω-semigroup
cites work: Congruences on simple ω-semigroups
cites work: Q3337662
cites work: Harmonic inverse semigroups
cites work: Bisimple ω-Semigroups
OpenAlex ID: W1974557328
description: scientific article; zbMATH DE number 7885