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

 

Universally catenarian domains of $ D+M$ type


Authors: David F. Anderson, David E. Dobbs, Salah Kabbaj and S. B. Mulay
Journal: Proc. Amer. Math. Soc. 104 (1988), 378-384
MSC: Primary 13C15; Secondary 13G05
MathSciNet review: 962802
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Abstract: Let $ T$ be a domain of the form $ K + M$, where $ K$ is a field and $ M$ is a maximal ideal of $ T$. Let $ D$ be a subring of $ K$ and let $ R = D + M$. It is proved that if $ K$ is algebraic over $ D$ and both $ D$ and $ T$ are universally catenarian, then $ R$ is universally catenarian. The converse holds if $ K$ is the quotient field of $ D$. As a consequence, we construct for each $ n > 2$, an $ n$-dimensional universally catenarian domain which does not belong to any previously known class of universally catenarian domains.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0962802-7
PII: S 0002-9939(1988)0962802-7
Article copyright: © Copyright 1988 American Mathematical Society