Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13F05

Retrieve articles in all journals with MSC: 13F05

Additional Information

Keywords: Krull domain, divisor class group, polynomial ring, symmetric algebra
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society