Artinianness of local cohomology modules of ZD-modules

Details Artinianness of local cohomology modules of ZD-modules Artinianness of local cohomology modules of ZD-modules

2004-12-30

arxiv.org/abs/math/0412541v1

Mathematics

Commutative Algebra

8 pages, to appear in Communications in Algebra

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Artinianness of local cohomology modules of ZD-modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Artinianness of local cohomology modules of ZD-modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Artinianness of local cohomology modules of ZD-modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-45734