Linear semigroups with permutation properties
type: Item
instance of: scholarly article
title: Linear semigroups with permutation properties
zbMATH Open document ID: 0625.20054
DOI: 10.1007/BF02573117
author: Yechezkel Zalcstein
author: Max H. Garzon
published in: Semigroup Forum
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134881
review text: A semigroup S satisfies a permutation property if for some \(n\geq 2\) every product of n elements of S remains invariant under some nontrivial permutation of its factors. It is known that the semigroup algebra K[S] of a finitely generated semigroup satisfying a permutation property over a field K satisfies a polynomial identity whenever S is periodic [\textit{A. Restivo} and \textit{C. Reutenauer}, J. Algebra 89, 102-104 (1984; Zbl 0545.20051)], or S is cancellative [\textit{J. Okniński}, Commun. Algebra 15, 1667-1677 (1987; Zbl 0621.20040)]. In the note under review it is shown that the same holds if S is a regular linear finitely generated semigroup satisfying a permutation property and char K\(=0.\) Reviewer's note. 1. The hypothesis on the characteristic of K is superfluous. 2. In forthcoming papers by the reviewer the same is shown for the class of inverse semigroups and a counterexample is found in the class of regular semigroups.
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 4015019
zbMATH Keywords: permutation property
zbMATH Keywords: semigroup algebra
zbMATH Keywords: finitely generated semigroup
zbMATH Keywords: polynomial identity
zbMATH Keywords: inverse semigroups
zbMATH Keywords: regular semigroups
reviewed by: Jan Okniński
MaRDI profile type: Publication
cites work: Q4085956
cites work: On permutation properties in groups and semigroups
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cites work: On semigroup algebras satisfying polynomial identities
cites work: On the Burnside problem for semigroups
cites work: Finiteness Conditions for Matrix Semigroups
description: scientific article; zbMATH DE number 4015019