A class of actions of inverse semigroups
type: Item
instance of: scholarly article
title: A class of actions of inverse semigroups
zbMATH Open document ID: 0839.20076
author: Mark V. Lawson
published in: Journal of Algebra
publication date: 1996-06-18T00:00:00Z
review text: The purpose of this paper is to use the theory of so-called ordered groupoids to give a unified account of some important constructions in inverse semigroup theory. The paper is the third of a trilogy written by the author on this theme, and does indeed draw upon results of one of its predecessors, both of which have appeared in the J. Algebra. The classical Munn representation of an inverse semigroup \(S\) is generalized to a so-called ordered representation of \(S\), the ingredients of which, \(\gamma\) a homomorphism from \(S\) into the inverse semigroup of all order isomorphisms between order ideals of a poset \(X\), and \(p\), an isotone surjection of \(X\) onto the set of all idempotents of \(S\), which together satisfy two axioms. Both the Wagner-Preston representation, and the effective actions of O'Carroll and McAlister are special cases. A one-to-one correspondence is established between ordered representations of an inverse semigroup \(S\) and special kinds of covers of \(S\). Applications include a full categorical account of the theory of idempotent pure congruences.
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 843880
zbMATH Keywords: ordered groupoids
zbMATH Keywords: inverse semigroups
zbMATH Keywords: Munn representation
zbMATH Keywords: ordered representation
zbMATH Keywords: idempotents
zbMATH Keywords: Wagner-Preston representation
zbMATH Keywords: covers
zbMATH Keywords: idempotent pure congruences
reviewed by: Peter M. Higgins
MaRDI profile type: Publication
full work available at URL: jabr.1996.0025
OpenAlex ID: W2042932698
DOI: 10.1006/JABR.1996.0025
description: scientific article; zbMATH DE number 843880