Divisor class group descent for affine Krull domains
type: Item
instance of: scholarly article
title: Divisor class group descent for affine Krull domains
zbMATH Open document ID: 0549.13003
DOI: 10.1016/0021-8693(85)90150-4
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let K be a field, S a finitely generated Krull algebra over K, and R a Krull subalgebra of S. Let \(i: Cl(R)\to Cl(S)\) be the homomorphism of the divisor class groups induced by the inclusion. Is ker (i) finitely generated? It is shown in this paper that the answer is affirmative if \(char (K)=0\) or if K is algebraically closed in S. In particular if S is a ring of polynomials over K then Cl(R) is finitely generated. The paper also contains an example of a factorial ring S and its subring R with Cl(R) not finitely generated.
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 3875428
zbMATH Keywords: Galois descent
zbMATH Keywords: radical descent
zbMATH Keywords: finitely generated Krull algebra
zbMATH Keywords: divisor class groups
author: Bronisław Wajnryb
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90150-4
OpenAlex ID: W2021436726
cites work: Q5670698
cites work: Q3272926
cites work: Q3277840
cites work: The Class Group of Dedekind Domains
description: scientific article; zbMATH DE number 3875428