Vol. 15, No. 3, 1965

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Dedekind domains: Overrings and semi-prime elements

Luther Elic Claborn

Vol. 15 (1965), No. 3, 799–804

This paper develops two themes: (1) the relation of the class group of a Dedekind domain A to that of an overring B and (2) the question of finding a nonzero, nonunit element x of a Dedekind domain A such that A∕xA is regular. We obtain complete results in answer to the first question, giving a corollary concerning the realization of certain groups as class groups. We give various sufficient conditions in answer to the second question; some in terms of the class group, others concerning Dedekind domains which often arise in practice.

Mathematical Subject Classification
Primary: 13.20
Secondary: 13.80
Received: 27 August 1964
Published: 1 September 1965
Luther Elic Claborn