Brauer groups and class groups for Krull domains: a \(K\)-theoretic approach
type: Item
instance of: scholarly article
title: Brauer groups and class groups for Krull domains: a \(K\)-theoretic approach
zbMATH Open document ID: 0564.13008
DOI: 10.1016/0022-4049(84)90007-0
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: In this paper we prove that the exact sequence \[ 0\rightarrow\text{Pic}(R)\rightarrow \text{Cl}(R)\rightarrow \text{Bcl}(R)\rightarrow (R)\rightarrow \beta (R) \] defined by \textit{B. Auslander} [J. Algebra 4, 220--273 (1966; Zbl 0144.03401)], \textit{M. Orzech} [in: Brauer groups in ring theory and algebraic geometry, Proc., Antwerp 1981, Lect. Notes Math. 917, 66--90 (1982; Zbl 0492.13003)], and \textit{H. Lee} and \textit{M. Orzech} [Can. J. Math. 34, 996--1010 (1982; Zbl 0502.13004)] for a Krull domain \(R\) may be recovered as the \((K_ 0\), \(K_ 1)\)-exact sequence for some suitable category with product \(C(R)\).
Mathematics Subject Classification ID: 13D15
Mathematics Subject Classification ID: 14F22
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 19D50
zbMATH DE Number: 3899040
zbMATH Keywords: algebraic K-theory
zbMATH Keywords: Brauer groups
zbMATH Keywords: class groups
zbMATH Keywords: Krull domains
author: Alain Verschoren
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90007-0
OpenAlex ID: W1974581150
cites work: The Brauer group of a ringed space
cites work: Maximal Orders
cites work: Q5562621
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cites work: Brauer Groups, Class Groups and Maximal Orders for a Krull Scheme
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description: scientific article; zbMATH DE number 3899040