Cancellative semigroup rings which are Azumaya algebras
type: Item
instance of: scholarly article
title: Cancellative semigroup rings which are Azumaya algebras
zbMATH Open document ID: 0658.20040
DOI: 10.1016/0021-8693(88)90108-1
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: A very satisfactory characterization of group rings which are Azumaya algebras has been obtained by \textit{F. DeMeyer} and \textit{G. Janusz} [Trans. Am. Math. Soc. 279, 389-395 (1983; Zbl 0525.16002)]. Let S be a cancellative semigroup, U(S) its group of units and G the two-sided group of fractions of S. The authors reduce the problem of characterizing semigroup rings K[S] which are Azumaya algebras to a problem about K[U(S)] and the tools used in this characterization are exactly the relations between K[U(S)], K[S] and K[G]. As a by-product of their results are obtained a new class of examples of Azumaya algebras that do not arise in a more trivial way.
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16U60
zbMATH DE Number: 4075406
zbMATH Keywords: Azumaya algebras
zbMATH Keywords: cancellative semigroup
zbMATH Keywords: group of units
zbMATH Keywords: group of fractions
zbMATH Keywords: semigroup rings
author: Jan Okniński
author: Fred Van Oystaeyen
reviewed by: L.V.Potemkin
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90108-1
OpenAlex ID: W2050648654
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description: scientific article; zbMATH DE number 4075406