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The Local Class Group of a Krull Domain

Published online by Cambridge University Press:  20 November 2018

A. Bouvier
A. Bouvier*
Affiliation:
Department de Mathématiques, Université Claude Bernard Lyon 143, Boulevard du 11 Novembre 1918 69621 Villeurbanne, France
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Abstract

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The local class group of a Krull domain A is the quotient group G(A) = CI(A)/Pic(A). A Krull domain A is locally factorial if and only if G(A) = 0. In this paper, we characterize the Krull domains for which G(A) is a torsion group. We evaluate the local class group of several examples and finally, we explain why every abelian group is the local class group of a Krull domain.

Keywords

13F0513F1514J05Krull domainlocally factorialdivisor class groupPicard group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 1 , 01 March 1983 , pp. 13 - 19
Copyright
Copyright © Canadian Mathematical Society 1983

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