On the associated primes of generalized local cohomology modules
| dc.creator | Mafi, Amir | |
| dc.date | 2005-10-13 | |
| dc.date.accessioned | 2026-07-07T06:47:27Z | |
| dc.date.available | 2026-07-07T06:47:27Z | |
| dc.description | 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 $i<t$ or $\Supp_R(H_{\fa}^i(N))$ is finite for all $i<t$, then $\Ass_R(H_{\fa}^t(M,N))$ is finite. Also, we prove that if $d=\pd(M)$ and $n=\dim(N)$ are finite, then $H_{\fa}^{d+n}(M,N)$ is Artinian. In particular, $\Ass_R(H_{\fa}^{d+n}(M,N))$ is a finite set consisting of maximal ideals. | |
| dc.description | 7 pages, to appear in Communications in Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0510274 | |
| dc.identifier | http://arxiv.org/abs/math/0510274 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103654 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D45, 13E99 | |
| dc.title | On the associated primes of generalized local cohomology modules | |
| dc.type | text |