On connectedness and indecomposibility of local cohomology modules

Details On connectedness and indecomposibility of local cohomology modules On connectedness and indecomposibility of local cohomology modules

2008-10-27

arxiv.org/abs/0810.4774v1

Mathematics

Commutative Algebra

Scientific paper

Let $I$ denote an ideal of a local Gorenstein ring $(R, \mathfrak m)$. Then we show that the local cohomology module $H^c_I(R), c = \height I,$ is indecomposable if and only if $V(I_d)$ is connected in codimension one. Here $I_d$ denotes the intersection of the highest dimensional primary components of $I.$ This is a partial extension of a result shown by Hochster and Huneke in the case $I$ the maximal ideal. Moreover there is an analysis of connectedness properties in relation to various aspects of local cohomology. Among others we show that the endomorphism ring of $H^c_I(R)$ is a local Noetherian ring if $\dim R/I = 1.$

Affiliated with

Also associated with

No associations

Rating

On connectedness and indecomposibility of local cohomology 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 On connectedness and indecomposibility of local cohomology modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On connectedness and indecomposibility of local cohomology modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-323773