Axioms for function semigroups with agreement quasi-order.
type: Item
instance of: scholarly article
title: Axioms for function semigroups with agreement quasi-order.
zbMATH Open document ID: 1238.20071
published in: Algebra Universalis
publication date: 2011-11-23T00:00:00Z
review text: The agreement quasi-order \(\preccurlyeq\) on pairs of partial transformations on a set \(X\) is defined by \((f,g)\preccurlyeq(h,k)\) if whenever \(f\) and \(g\) are defined and agree, so do \(h\) and \(k\). The paper axiomatizes function semigroups (and monoids) \(S\) with this quasi-order through a list of six axioms on the order ideals generated by pairs \((s,t)\) in \(S\times S\) under this quasi-order. Finite axiomizations are obtained for groups and for inverse semigroups of injective functions equipped with the quasi order of fixed set inclusion.
reviewed by: Peter M. Higgins
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 20A05
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 5977544
zbMATH Keywords: quasi-orders
zbMATH Keywords: transformation semigroups
zbMATH Keywords: axioms
zbMATH Keywords: partial transformations
zbMATH Keywords: order ideals
author: T. E. Stokes
MaRDI profile type: Publication
full work available at URL: s00012-011-0152-1
OpenAlex ID: W1988280807
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DOI: 10.1007/S00012-011-0152-1
description: scientific article; zbMATH DE number 5977544