The Schur group of a commutative ring
type: Item
instance of: scholarly article
title: The Schur group of a commutative ring
zbMATH Open document ID: 0555.13003
DOI: 10.1016/0022-4049(85)90034-9
author: Richard A. Mollin
author: Frank R. DeMeyer
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let R denote a commutative ring and B(R) the Brauer group of classes of Azumaya R-algebras as developed by \textit{M. Auslander} and \textit{O. Goldman} [Trans. Am. Math. Soc. 97(1960), 367-409 (1961; Zbl 0100.263)]. This paper introduces and gives basic facts about the Schur subgroup of B(R). An Azumaya R-algebra A represents a class in the Schur subgroup S(R) of B(R) when there is a finite group G and an R-algebra epimorphism \(f: RG\to A.\) If R is a commutative ring of positive characteristic, \(S(R)=0\). On the other hand, any finite abelian group is the Schur group of a commutative ring which is finitely generated as an algebra over the rational integers. Some standard facts about the Schur group of a field are generalized to commutative rings.
Mathematics Subject Classification ID: 14F22
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 3884279
zbMATH Keywords: Azumaya algebra
zbMATH Keywords: Schur subgroup of Brauer group
MaRDI profile type: Publication
full work available at URL: 0022-4049(85)90034-9
OpenAlex ID: W1997802253
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description: scientific article; zbMATH DE number 3884279