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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.

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