Semigroup algebras of finite ample semigroups.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1248.20062
DOI: 10.1017/S0308210510000715
author: Xiaojiang Guo
author: Lin Chen
publication date: 2012-05-06T00:00:00Z
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 16N20
zbMATH DE Number: 6031031
zbMATH Keywords: finite ample semigroups
zbMATH Keywords: inverse semigroups
zbMATH Keywords: semigroup rings
zbMATH Keywords: Jacobson radical
zbMATH Keywords: generalized Green relations
zbMATH Keywords: idempotents
MaRDI profile type: Publication
title: Semigroup algebras of finite ample semigroups.
published in: Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
review text: Let \(\mathcal R^*\) and \(\mathcal L^*\) denote the generalized Green relations on a semigroup \(S\). Then \(S\) is called an ample semigroup if the set \(E(S)\) of idempotents of \(S\) forms a semilattice, the \(\mathcal R^*\)-class and the \(\mathcal L^*\)-class of every element \(a\in S\) contain exactly one idempotent, denoted by \(a^+\) and \(a^*\), respectively, and \(ae=(ae)^+a\), \(ea=a(ea)^*\). In particular, the class of inverse semigroups coincides with the class of regular ample semigroups. A generalized triangular matrix representation is found for a finite ample semigroup \(S\). A description of the Jacobson radical of the semigroup ring \(A[S]\) over a commutative unital ring \(A\) is derived.
reviewed by: Jan Okniński
description: scientific article; zbMATH DE number 6031031