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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
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[1] M. P. Brodmann and A. Lashgari Faghani, A finiteness result for associated primes of local cohomology modules, Proc. Amer. Math. Soc. 128 (2000), no. 10, 2851 – 2853. · Zbl 0955.13007
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