Ample semigroups and Frobenius algebras.
type: Item
instance of: scholarly article
title: Ample semigroups and Frobenius algebras.
zbMATH Open document ID: 1336.20060
published in: Semigroup Forum
publication date: 2015-12-09T00:00:00Z
review text: Contracted semigroup algebras \(K_0[S]\) of ample semigroups \(S\) over a field \(K\) are considered. It is shown that, if \(K_0[S]\) is right self-injective then \(S\) must be a finite inverse semigroup. Hence, this algebra is also left self-injective and it is a Frobenius algebra. Recall that a semigroup is inverse if and only if it is ample and regular. The proof is based on showing that \(S\) has a finite ideal chain with factors that are weak Brandt semigroups with finitely many idempotents and next that every factor of this chain is actually a finite regular semigroup.
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 6518153
zbMATH Keywords: ample semigroups
zbMATH Keywords: semigroup algebras
zbMATH Keywords: right self-injective algebras
zbMATH Keywords: Frobenius algebras
zbMATH Keywords: finite inverse semigroups
author: Xiaojiang Guo
author: K. P. Shum
reviewed by: Jan Okniński
MaRDI profile type: Publication
full work available at URL: s00233-015-9726-0
OpenAlex ID: W578971616
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DOI: 10.1007/S00233-015-9726-0
description: scientific article; zbMATH DE number 6518153