Artinianness of local cohomology modules of ZD-modules
| dc.creator | Divaani-Aazar, Kamran | |
| dc.creator | Esmkhani, Mohammad Ali | |
| dc.date | 2004-12-30 | |
| dc.date.accessioned | 2026-07-07T05:15:42Z | |
| dc.date.available | 2026-07-07T05:15:42Z | |
| dc.description | This paper centers around Artinianness of the local cohomology of $ZD$-modules. Let $\fa$ be an ideal of a commutative Noetherian ring $R$. The notion of $\fa$-relative Goldie dimension of an $R$-module $M$, as a generalization of that of Goldie dimension is presented. Let $M$ be a $ZD$-module such that $\fa$-relative Goldie dimension of any quotient of $M$ is finite. It is shown that if $\dim R/\fa=0$, then the local cohomology modules $H^i_{\fa}(M)$ are Artinian. Also, it is proved that if $d=\dim M$ is finite, then $H^d_{\fa}(M)$ is Artinian, for any ideal $\fa$ of $R$ . These results extend the previously known results concerning Artinianness of local cohomology of finitely generated modules. | |
| dc.description | 8 pages, to appear in Communications in Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0412541 | |
| dc.identifier | http://arxiv.org/abs/math/0412541 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73722 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D45, 13E10 | |
| dc.title | Artinianness of local cohomology modules of ZD-modules | |
| dc.type | text |