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

The catenarian property of power series rings over a Prüfer domain


Author: J. T. Arnold
Journal: Proc. Amer. Math. Soc. 94 (1985), 577-580
MSC: Primary 13C15; Secondary 13F05, 13F25
MathSciNet review: 792263
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Abstract: Let $ D$ be a Prüfer domain that has the SFT-property. It is shown that the power series ring $ D[[x]]$ is catenarian. If $ n > 1$ and dim $ D > 1$ then the ring $ D[[{x_1}, \ldots ,{x_n}]]$ is not catenarian.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0792263-X
PII: S 0002-9939(1985)0792263-X
Keywords: Catenary ring, power series ring, Prüfer domain, prime ideal, rank
Article copyright: © Copyright 1985 American Mathematical Society