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The distribution of prime ideals of a Dedekind domain

Published online by Cambridge University Press:  17 April 2009

Anne P. Grams
Anne P. Grams
Affiliation:
Department of Mathematics, University of Tennessee at Nashville, Nashville, Tennessee, USA.
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Abstract

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Let G be an abelian group, and let S be a subset of G. Necessary and sufficient conditions on G and S are given in order that there should exist a Dedekind domain D with class group G with the property that S is the set of classes that contain maximal ideals of D. If G is a torsion group, then S is the set of classes containing the maximal ideals of D if and only if S generates G. These results are used to determine necessary and sufficient conditions on a family {Hλ} of subgroups of G in order that there should exist a Dedekind domain D with class group G such that {G/Hλ} is the family of class groups of the set of overrings of D. Several applications are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 429 - 441
Copyright
Copyright © Australian Mathematical Society 1974

References

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