Nilpotent semigroups and semigroup algebras
type: Item
instance of: scholarly article
title: Nilpotent semigroups and semigroup algebras
zbMATH Open document ID: 0818.16022
author: Eric Jespers
author: Jan Okniński
published in: Journal of Algebra
publication date: 1995-08-14T00:00:00Z
review text: First, the structure of nilpotent semigroups is discussed. If \(S\) is a completely 0-simple semigroup over a maximal group \(G\), then \(S\) is nilpotent if and only if \(G\) is nilpotent and \(S\) is an inverse semigroup. The main results on semigroup algebras are very interesting, but technical; they examine the prime homomorphic images of semigroup algebras \(K[S]\) of nilpotent semigroups. The classical ring of quotients of such a prime Goldie ring \(K[S]/ P\) actually comes from a prime homomorphic image of the group algebra \(K[G]\) of a nilpotent group. The prime radical of \(K[S]\) and the congruence it determines on \(S\) are studied. A full description is given for nilpotent semigroups of index 2; the prime ideals of these semigroups are completely prime. The last section of the paper contains many interesting examples that illustrate the uses of nilpotent semigroups and their semigroup algebras.
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 20F18
zbMATH DE Number: 701290
zbMATH Keywords: semigroup rings
zbMATH Keywords: nilpotent semigroups
zbMATH Keywords: completely 0-simple semigroups
zbMATH Keywords: inverse semigroups
zbMATH Keywords: semigroup algebras
zbMATH Keywords: prime homomorphic images
zbMATH Keywords: classical ring of quotients
zbMATH Keywords: prime Goldie rings
zbMATH Keywords: group algebras
zbMATH Keywords: prime radical
reviewed by: Mark L. Teply
MaRDI profile type: Publication
full work available at URL: jabr.1994.1322
OpenAlex ID: W2048063099
DOI: 10.1006/JABR.1994.1322
description: scientific article; zbMATH DE number 701290