Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A60, 16A33

Retrieve articles in all journals with MSC: 16A60, 16A33

Additional Information

PII: S 0002-9939(1982)0663859-8
Article copyright: © Copyright 1982 American Mathematical Society