Artinianness of local cohomology modules of ZD-modules
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- December 2004
- DOI:
- arXiv:
- arXiv:math/0412541
- Bibcode:
- 2004math.....12541D
- Keywords:
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- Commutative Algebra;
- 13D45;
- 13E10
- E-Print:
- 8 pages, to appear in Communications in Algebra