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On the finiteness of associated primes of local cohomology modules. (English) Zbl 1190.13010
Summary: 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 M. P. Brodmann and A. Lashgari Faghani [Proc. Am. Math. Soc. 128, No. 10, 2851–2853 (2000; Zbl 0955.13007)] and independently of K. Khashyarmanesh and Sh. Salarian [Commun. Algebra 27, No. 12, 6191–6198 (1999; Zbl 0940.13013)].

##### MSC:
 13D45 Local cohomology and commutative rings
##### Keywords:
local cohomology; associated primes
Full Text:
##### References:
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