Structure of a finite commutative inverse semigroup and a finite band for which the inverse monoid of local automorphisms is permutable.
type: Item
instance of: scholarly article
title: Structure of a finite commutative inverse semigroup and a finite band for which the inverse monoid of local automorphisms is permutable.
zbMATH Open document ID: 1261.20073
author: V. D. Derech
published in: Ukrainian Mathematical Journal
publication date: 2012-11-23T00:00:00Z
review text: A semigroup \(S\) is called permutable if any two congruences on \(S\) commute with respect to composition. A local automorphism of a semigroup \(S\) is an isomorphism between two subsemigroups of \(S\). The set \(PA(S)\) of all local automorphisms of \(S\) is an inverse submonoid of the full symmetric inverse monoid on \(S\). The main results of this paper are the following two theorems: Theorem 2. Let \(S\) be a commutative inverse semigroup. Then the semigroup \(PA(S)\) is permutable if and only if \(S\) is either a linearly ordered semilattice or a primitive semilattice or an elementary Abelian \(p\)-group. Theorem 3. Let \(S\) be a finite band. Then the semigroup \(PA(S)\) is permutable if and only if \(S\) is either a linearly ordered semilattice or a primitive semilattice or a semigroup of one-sided zeros.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 6110036
zbMATH Keywords: inverse semigroups
zbMATH Keywords: local automorphisms
zbMATH Keywords: permutable semigroups
zbMATH Keywords: congruences
zbMATH Keywords: linearly ordered semilattices
MaRDI profile type: Publication
full work available at URL: s11253-012-0586-4
OpenAlex ID: W2059399137
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cites work: Q3848243
cites work: Permutability of congruences on commutative semigroups
cites work: Classical finite transformation semigroups. An introduction.
DOI: 10.1007/S11253-012-0586-4
description: scientific article; zbMATH DE number 6110036