Divisor class group descent for affine Krull domains
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.
scientific article; zbMATH DE number 3875428