Mathematics – Commutative Algebra
Scientific paper
2011-08-22
Mathematics
Commutative Algebra
8 pages
Scientific paper
In this article, we prove that if $R\to S$ is a homomorphism of Noetherian rings that splits, then for every $i\geq 0$ and ideal $I\subset R$, $\Ass_R H^i_I(R)$ is finite when $\Ass_S H^i_{IS}(S)$ is finite. In addition, if $S$ is a Cohen-Macaulay ring that is finitely generated as an $R$-module, such that all the Bass numbers of $H^i_{IS}(S)$, as an $S$-module, are finite, then all the Bass numbers of $H^i_{I}(R)$, as an $R$-module, are finite. Moreover, we show these results for a larger class a functors introduced by Lyubeznik. As a consequence, we exhibit a Gorenstein $F$-regular UFD of positive characteristic that is not a direct summand, not even a pure subring, of any regular ring.
No associations
LandOfFree
Local cohomology properties of direct summands 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 Local cohomology properties of direct summands, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local cohomology properties of direct summands will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-66503