Associated primes of local cohomology modules of weakly Laskerian modules

Details Associated primes of local cohomology modules of weakly Laskerian modules Associated primes of local cohomology modules of weakly Laskerian modules

2005-02-03

arxiv.org/abs/math/0502074v1

Mathematics

Commutative Algebra

11 pages, to appear in Communications in Algebra

Scientific paper

The notion of weakly Laskerian modules was introduced recently by the authors. Let $R$ be a commutative Noetherian ring with identity, $\fa$ an ideal of $R$, and $M$ a weakly Laskerian module. It is shown that if $\fa$ is principal, then the set of associated primes of the local cohomology module $H_{\fa}^i(M)$ is finite for all $i\geq 0$. We also prove that when $R$ is local, then $\Ass_R(H_{\fa}^i(M))$ is finite for all $i\geq 0$ in the following cases: (1) $\dim R\leq 3$, (2) $\dim R/\fa\leq 1$, (3) $M$ is Cohen-Macaulay and for any ideal $\fb$, with $l=\grade(\fb,M)$, $\Hom_R(R/\fb,H_{\fb}^{l+1}(M))$ is weakly Laskerian.

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