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

 

On the finiteness of associated primes of local cohomology modules


Author: Pham Hung Quy
Journal: Proc. Amer. Math. Soc. 138 (2010), 1965-1968
MSC (2010): Primary 13D45, 13E99
Published electronically: February 12, 2010
MathSciNet review: 2596030
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Abstract: Let $ R$ be a Noetherian ring, $ \mathfrak{a}$ be an ideal of $ R$ and $ M$ be a finitely generated $ R$-module. The aim of this paper is to show that if $ t$ is the least integer such that neither $ H^t_{\mathfrak{a}}(M)$ nor $ {supp}(H^t_{\mathfrak{a}}(M))$ is non-finite, then $ H^t_{\mathfrak{a}}(M)$ has finitely many associated primes. This combines the main results of Brodmann and Faghani and independently of Khashyarmanesh and Salarian.


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Additional Information

Pham Hung Quy
Affiliation: Department of Mathematics, FPT University (Dai Hoc FPT), 15B Pham Hung Street, Ha Noi, Vietnam
Email: phamhungquy@gmail.com, quyph@fpt.edu.vn

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10235-4
PII: S 0002-9939(10)10235-4
Keywords: Local cohomology, associated primes.
Received by editor(s): March 23, 2009
Received by editor(s) in revised form: October 1, 2009
Published electronically: February 12, 2010
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.