Associated primes and cofiniteness of local cohomology modules
| dc.creator | Dibaei, Mohammad T. | |
| dc.creator | Yassemi, Siamak | |
| dc.date | 2004-05-26 | |
| dc.date | 2004-05-31 | |
| dc.date.accessioned | 2026-07-07T05:08:36Z | |
| dc.date.available | 2026-07-07T05:08:36Z | |
| dc.description | Let $\mathfrak{a}$ be an ideal of Noetherian ring $R$ and let $M$ be an $R$-module such that $\mathrm{Ext}^i_R(R/\mathfrak{a},M)$ is finite $R$-module for every $i$. If $s$ is the first integer such that the local cohomology module $\mathrm{H}^s_\mathfrak{a}(M)$ is non $\mathfrak{a}$-cofinite, then we show that $\mathrm{Hom}_{R}(R/\mathfrak{a}, \mathrm{H}^s_\mathfrak{a}(M))$ is finite. Specially, the set of associated primes of $\mathrm{H}^s_\mathfrak{a}(M)$ is finite. Next assume $(R,\mathfrak{m})$ is a local Noetherian ring and $M$ is a finitely generated module. We study the last integer $n$ such that the local cohomology module $\mathrm{H}^n_\mathfrak{a}(M)$ is not $\mathfrak{m}$-cofinite and show that $n$ just depends on the support of $M$. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405499 | |
| dc.identifier | http://arxiv.org/abs/math/0405499 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71331 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D45 | |
| dc.title | Associated primes and cofiniteness of local cohomology modules | |
| dc.type | text |