Every abelian group is a class group

Abstract

Let T be the set of minimal primes of a Krull domain A. If S is a subset of T, we form B = ∩ AP for P ∈ S and study the relation of the class group of B to that of A. We find that the class group of B is always a homomorphic image of that of A. We use this type of construction to obtain a Krull domain with specified class group and then alter such a Krull domain to obtain a Dedekind domain with the same class group. © 1966 by Pacific Journal of Mathematics.