Semigroup algebras and Noetherian maximal orders: a survey.
type: Item
instance of: scholarly article
title: Semigroup algebras and Noetherian maximal orders: a survey.
zbMATH Open document ID: 1192.16027
author: Eric Jespers
published in: Acta Applicandae Mathematicae
publication date: 2009-12-09T00:00:00Z
review text: This is a survey of recent results on semigroup algebras \(K[S]\), of monoids \(S\) over a field \(K\), that are prime Noetherian maximal orders. First, a characterization of submonoids \(S\) of polycyclic-by-finite groups that lead to such algebras \(K[S]\) is presented. Then, certain classes of commutative maximal orders (or equivalently, integrally closed Noetherian domains) are discussed in terms of a finite presentation. Algebras related to the set theoretic solutions of the Yang-Baxter equation are then presented, which can be described as semigroup algebras of certain noncommutative monoids defined by quadratic relations, called monoids of \(I\)-type. Results concerning a generalization of the latter class to the so-called monoids of \(IG\)-type and their algebras are also discussed. An extensive bibliography is provided.
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 16S15
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16H10
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 5644665
zbMATH Keywords: semigroup algebras
zbMATH Keywords: Noetherian maximal orders
zbMATH Keywords: submonoids of polycyclic-by-finite groups
zbMATH Keywords: integrally closed Noetherian domains
zbMATH Keywords: finite presentations
zbMATH Keywords: monoids of \(I\)-type
reviewed by: Jan Okniński
MaRDI profile type: Publication
full work available at URL: s10440-008-9392-2
OpenAlex ID: W2082783267
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DOI: 10.1007/S10440-008-9392-2
description: scientific article; zbMATH DE number 5644665