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Associated primes of local cohomology modules

Authors: Kamran Divaani-Aazar and Amir Mafi
Journal: Proc. Amer. Math. Soc. 133 (2005), 655-660
MSC (2000): Primary 13D45, 13E99
Published electronically: October 7, 2004
MathSciNet review: 2113911
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Abstract: Let $\mathfrak{a}$ be an ideal of a commutative Noetherian ring $R$ and $M$ a finitely generated $R$-module. Let $t$ be a natural integer. It is shown that there is a finite subset $X$ of $\operatorname{Spec}R$, such that $\operatorname{Ass}_R(H_{\mathfrak{a}}^t(M))$ is contained in $X$ union with the union of the sets $\operatorname{Ass}_R(\operatorname{Ext} _R^j(R/\mathfrak{a},H_{\mathfrak{a}}^i(M)))$, where $0\leq i<t$ and $0\leq j\leq t^2+1$. As an immediate consequence, we deduce that the first non- $\mathfrak{a}$-cofinite local cohomology module of $M$ with respect to $\mathfrak{a}$ has only finitely many associated prime ideals.

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Kamran Divaani-Aazar
Affiliation: Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran — and — Institute for Studies in Theoretical Physics and Mathematics, P. O. Box 19395-5746, Tehran, Iran

Amir Mafi
Affiliation: Institute of Mathematics, University for Teacher Education, 599 Taleghani Avenue, Tehran 15614, Iran

Keywords: Local cohomology, associated prime ideals, cofiniteness, weakly Laskerian modules, spectral sequences
Received by editor(s): October 16, 2003
Published electronically: October 7, 2004
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2004 American Mathematical Society

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