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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Globalization of some local properties in Krull domains


Author: D. D. Anderson
Journal: Proc. Amer. Math. Soc. 85 (1982), 141-145
MSC: Primary 13F15; Secondary 13C12
MathSciNet review: 652428
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Abstract: Let $ R$ be a Krull domain. It is shown that a nonzero locally principal ideal is invertible. This is used to show that $ {\text{Cl}}(R)/{\text{Pic}}(R)$ is torsion if and only if $ {\text{Cl}}({R_M})$ is torsion for each maximal ideal $ M$ of $ R$. Here $ {\text{Cl}}(R)$ and $ {\text{Pic}}(R)$ denote the divisor class group and Picard group of $ R$, respectively.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0652428-1
PII: S 0002-9939(1982)0652428-1
Keywords: Krull domain, locally factorial, divisor class group
Article copyright: © Copyright 1982 American Mathematical Society



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