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Associated primes and cofiniteness of local cohomology modules. (English) Zbl 1105.13016
Let $$\mathfrak{a}$$ be an ideal of a noetherian ring $$R$$. Given an $$R$$-module $$M$$, write $$H^i_{\mathfrak a}(M)$$ for the $$i$$th local cohomology module of $$M$$.
The authors generalize M. P. Brodmann and A. Lashgari Faghani’s result [Proc. Am. Math. Soc. 128, 2851–2853 (2000; Zbl 0955.13007)] by showing that the $$R$$-module $$\text{Hom}_R(R/\mathfrak{a},H^s_{\mathfrak a}(M))$$ is finitely generated provided $$s$$ is the first integer such that $$H^s_{\mathfrak a}(M)$$ is non-$$\mathfrak{a}$$-cofinite. Then, for a local noetherian ring $$(R,\mathfrak{m})$$, the last integer $$n$$ such that $$H^n_{\mathfrak a}(M)$$ is not $$\mathfrak{m}$$-cofinite is studied.

##### MSC:
 13D45 Local cohomology and commutative rings 13D25 Complexes (MSC2000) 13D05 Homological dimension and commutative rings
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##### References:
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