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

 

Chain of prime ideals in formal power series rings


Authors: Ada Maria de S. Doering and Yves Lequain
Journal: Proc. Amer. Math. Soc. 88 (1983), 591-594
MSC: Primary 13A15; Secondary 13C15, 13F25, 13J10
MathSciNet review: 702281
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Abstract: Let $ R$ be a Noetherian domain and $ P$ a prime ideal of $ R$. Then $ {R_p}[[{X_1}, \ldots ,{X_n}]]$ has a maximal chain of prime ideals of length $ r$ if and only if $ R{[[{X_1}, \ldots ,{X_n}]]_{(P,{X_1}, \ldots ,{X_n})}}$ does, if and only if $ R{[[{X_1}, \ldots ,{X_n}]]_{(P,{X_1}, \ldots ,{X_n})}}$ does.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0702281-3
PII: S 0002-9939(1983)0702281-3
Keywords: Chain of prime ideals, formal power series ring, polynomial ring, localization
Article copyright: © Copyright 1983 American Mathematical Society