Proper two-sided restriction semigroups and partial actions.
type: Item
instance of: scholarly article
title: Proper two-sided restriction semigroups and partial actions.
zbMATH Open document ID: 1258.20047
author: Claire Cornock
author: Victoria Gould
published in: Journal of Pure and Applied Algebra
publication date: 2012-06-08T00:00:00Z
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 6043597
zbMATH Keywords: proper restriction semigroups
zbMATH Keywords: partial actions of monoids
reviewed by: Grigori I. Zhitomirski
MaRDI profile type: Publication
full work available at URL: j.jpaa.2011.10.015
OpenAlex ID: W2109816124
cites work: Extensions and covers for semigroups whose idempotents form a left regular band.
cites work: Q3411949
cites work: Restriction categories. I: Categories of partial maps
cites work: Right PP monoids with central idempotents
cites work: A CLASS OF RIGHT PP MONOIDS
cites work: PROPER COVERS OF AMPLE MONOIDS
cites work: THE FREE AMPLE MONOID
cites work: PROPER WEAKLY LEFT AMPLE SEMIGROUPS
cites work: Graph expansions of unipotent monoids
cites work: Q5393094
cites work: Q4846425
cites work: An invitation to \(C\)-semigroups
cites work: A common framework for restriction semigroups and regular \(*\)-semigroups.
cites work: THE STRUCTURE OF TYPE A SEMIGROUPS
cites work: Groups, Semilattices and Inverse Semigroups
cites work: Groups, Semilattices and Inverse Semigroups. II
cites work: Guarded and banded semigroups.
cites work: A Note onE-Unitary Inverse Semigroups
cites work: Embedding theorems for proper inverse semigroups
cites work: A REPRESENTATION OF E-UNITARY INVERSE SEMIGROUPS
cites work: Q5597568
cites work: Relation algebras and function semigroups
DOI: 10.1016/J.JPAA.2011.10.015
review text: An algebra \((S,\cdot,+,*)\) of type \((2,1,1)\) is called a (two-sided) restriction semigroup if \((S,\cdot )\) is a semigroup, \((S,\cdot,+)\) satisfies the identities \(x^+x=x\), \(x^+y^+=y^+x^+\), \((x^+y^+)^+=x^+y^+\), \(xy^+=(xy)^+x\), \((S,\cdot,*)\) satisfies the dual identities, and \((x^+)^*=x^+\), \((x^*)^+=x^*\).NEWLINENEWLINE The structure of restriction semigroups is studied. Using both sides actions of a monoid on a semilattice, a proper restriction semigroup is constructed. To obtain the full class of proper restriction semigroups, partial actions of monoids are used. Thus the main result is a structure theorem for proper restriction semigroups.NEWLINENEWLINE Reviewer's comment: The topic of the paper under review is close to that of a paper by \textit{M. B. Szendrei}, [Int. J. Algebra Comput. 22, No. 3, 1250024 (2012; Zbl 1258.20048)].
description: scientific article; zbMATH DE number 6043597