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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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