A note on locally inverse semigroup algebras.
type: Item
instance of: scholarly article
title: A note on locally inverse semigroup algebras.
zbMATH Open document ID: 1145.20035
DOI: 10.1155/2008/576061
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-08-19T00:00:00Z
full work available at URL: https://eudml.org/doc/54490
review text: Summary: Let \(R\) be a commutative ring and \(S\) a finite locally inverse semigroup. It is proved that the semigroup algebra \(R[S]\) is isomorphic to the direct product of Munn algebras \(\mathcal M(R[G_J],m_J,n_J;P_J)\) with \(J\in S/\mathcal J\), where \(m_J\) is the number of \(\mathcal R\)-classes in \(J\), \(n_J\) the number of \(\mathcal L\)-classes in \(J\), and \(G_J\) a maximum subgroup of \(J\). As applications, we obtain sufficient and necessary conditions for the semigroup algebra of a finite locally inverse semigroup to be semisimple.
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 5313282
zbMATH Keywords: finite locally inverse semigroups
zbMATH Keywords: semisimple semigroup algebras
zbMATH Keywords: direct products of Munn algebras
Wikidata QID: Q58644796
author: Xiaojiang Guo
MaRDI profile type: Publication
OpenAlex ID: W2056167056
cites work: Q3848243
cites work: Möbius functions and semigroup representation theory.
cites work: The natural partial order on a regular semigroup
cites work: Structure of regular semigroups. I
DBLP publication ID: journals/ijmmsc/Guo08
description: scientific article; zbMATH DE number 5313282