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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 global dimension of FBN rings with enough clans


Author: Robert F. Damiano
Journal: Proc. Amer. Math. Soc. 86 (1982), 25-28
MSC: Primary 16A60; Secondary 16A33
MathSciNet review: 663859
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Abstract: For an FBN ring $ R$, a classical set of prime ideals $ \left\{ {{P_1}, \ldots ,{P_n}} \right\}$ is one for which the semiprime ideal $ N = \cap _{i = 1}^n{P_i}$ satisfies the Artin-Rees property. A minimal classical set is called a clan. We say an FBN ring $ R$ has enough clans if each prime ideal $ P$ is an element of a clan. In this paper, we show that for such rings the Krull dimension is less than or equal to the global dimension.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0663859-8
PII: S 0002-9939(1982)0663859-8
Article copyright: © Copyright 1982 American Mathematical Society