The closed socle of a relative Azumaya algebra
type: Item
instance of: scholarly article
title: The closed socle of a relative Azumaya algebra
zbMATH Open document ID: 0531.16002
DOI: 10.1016/0022-4049(84)90090-2
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: In [Lect. Notes Math. 917, 260-278 (1982; Zbl 0484.16002)], the author introduced the notion of a relative Azumaya algebra with respect to an idempotent kernel functor and applied it to the study of the Brauer group of a quasi-affine scheme. In this paper, the notion of closed socle of an Azumaya algebra introduced by \textit{D. E. Haile} [J. Algebra 51, 97-106 (1978; Zbl 0375.16004)] (see also [\textit{F. R. DeMeyer}, Proc. Am. Math. Soc. 78, 299-303 (1980; Zbl 0435.13001)]) is extended to relative Azumaya algebras. The notion is Brauer invariant (in the relative sense) and yields information about the splitting of relative Azumaya algebras. Some geometrical applications are given.
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 14F22
zbMATH DE Number: 3842066
zbMATH Keywords: Brauer group of quasi-affine scheme
zbMATH Keywords: idempotent kernel functor
zbMATH Keywords: closed socle
zbMATH Keywords: relative Azumaya algebras
author: Alain Verschoren
reviewed by: M.-A. Knus
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90090-2
OpenAlex ID: W1980122203
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description: scientific article; zbMATH DE number 3842066