Vol. 18, No. 2, 1966

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Every abelian group is a class group

Luther Elic Claborn

Vol. 18 (1966), No. 2, 219–222

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.

Mathematical Subject Classification
Primary: 13.20
Secondary: 20.00
Received: 27 January 1965
Revised: 10 April 1965
Published: 1 August 1966
Luther Elic Claborn