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On the associated primes of local cohomology modules. (English) Zbl 0940.13013
The main theorem of this paper is: Let \(I\) be an ideal of a Noetherian ring \(A\), and let \(M\) be a finitely generated \(A\)-module. For a positive integer \(n\), the following conditions are equivalent:
(i) \(H^i_I (M)\) is finitely generated for \(i=1, \dots,n-1;\)
(ii) there exists an unconditioned strong \(d\)-sequence of length \(n\) on \(M\) which is an \(I\)-filter regular sequence on \(M\). \((x_1, \dots, x_n\) is an unconditioned strong \(d\)-sequence on \(M\) if \(x_1^{i_1}, \dots, x_n^{i_n}\) is a \(d\)-sequence in any order for all positive integers \(i_j\).)
An application to associated primes of \(H^i_I(M)\) is given.

13D45 Local cohomology and commutative rings
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
Full Text: DOI
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