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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
DOI: https://doi.org/10.1090/S0002-9939-1976-0412173-1
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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Keywords: Krull domain, divisor class group, polynomial ring, symmetric algebra
Article copyright: © Copyright 1976 American Mathematical Society