Classification of finite commutative semigroups for which the inverse monoid of local automorphisms is permutable.
type: Item
instance of: scholarly article
title: Classification of finite commutative semigroups for which the inverse monoid of local automorphisms is permutable.
zbMATH Open document ID: 1264.20066
author: V. D. Derech
published in: Ukrainian Mathematical Journal
publication date: 2013-01-23T00:00:00Z
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 of all local automorphisms of \(S\) is an inverse submonoid of the full symmetric inverse monoid on \(S\). The main result of this paper is the following Theorem. Let \(S\) be a commutative semigroup for which the inverse monoid of local automorphisms is permutable. Then \(S\) is either a linearly ordered semilattice, or a primitive semilattice, or an elementary Abelian \(p\)-group or a semigroup with zero multiplication or a nilpotent semigroup of a very special form.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 6128298
zbMATH Keywords: inverse semigroups
zbMATH Keywords: local automorphisms
zbMATH Keywords: permutable semigroups
zbMATH Keywords: finite commutative semigroups
zbMATH Keywords: congruences
MaRDI profile type: Publication
full work available at URL: s11253-012-0638-9
OpenAlex ID: W2021163240
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DOI: 10.1007/S11253-012-0638-9
description: scientific article; zbMATH DE number 6128298