On the associated primes of generalized local cohomology modules

Details On the associated primes of generalized local cohomology modules On the associated primes of generalized local cohomology modules

2005-10-13

arxiv.org/abs/math/0510274v1

Mathematics

Commutative Algebra

7 pages, to appear in Communications in Algebra

Scientific paper

Let $\fa$ be an ideal of a commutative Noetherian ring $R$ with identity and let $M$ and $N$ be two finitely generated $R$-modules. Let $t$ be a positive integer. It is shown that $\Ass_R(H_{\fa}^t(M,N))$ is contained in the union of the sets $\Ass_R(\Ext_R^i(M,H_{\fa}^{t-i}(N)))$, where $0\leq i\leq t$. As an immediate consequence, it follows that if either $H_{\fa}^i(N)$ is finitely generated for all $i

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