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

 

Inert extensions of Krull domains


Authors: Douglas L. Costa and Jon L. Johnson
Journal: Proc. Amer. Math. Soc. 59 (1976), 189-194
MSC: Primary 13F05
MathSciNet review: 0412173
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Abstract: Let $ A \subseteq B$ be integral domains with $ B$ an inert extension of a Krull domain $ A$. Let $ \mathcal{P}(A)$ be the set of height one primes of $ A$, and let $ T = { \cap _{p \in \mathcal{P}(A)}}B \otimes {A_p}$. When each $ {B_p} = B \otimes {A_p}$ is a UFD, a necessary and sufficient condition for $ T$ to be a Krull domain is obtained. If $ T$ is a Krull domain and each $ {B_p}$ is a UFD, then the divisor class groups of $ A$ and $ T$ are isomorphic under the natural mapping.

These results are applied to $ A \subseteq B$ when $ B$ is a symmetric algebra over $ A$ and when $ B$ is locally a polynomial ring over $ A$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0412173-1
PII: S 0002-9939(1976)0412173-1
Keywords: Krull domain, divisor class group, polynomial ring, symmetric algebra
Article copyright: © Copyright 1976 American Mathematical Society