Computing the core of ideals in arbitrary characteristic

Details Computing the core of ideals in arbitrary characteristic Computing the core of ideals in arbitrary characteristic

2007-05-13

arxiv.org/abs/0705.1808v2

Mathematics

Commutative Algebra

13 pages, revised. To appear in the Journal of Algebra

Scientific paper

Let $R$ be a local Gorenstein ring with infinite residue field of arbitrary characteristic. Let $I$ be an $R$--ideal with $g=\height I >0$, analytic spread $\ell$, and let $J$ be a minimal reduction of $I$. We further assume that $I$ satisfies $G_{\ell}$ and ${\depth} R/I^j \geq \dim R/I -j+1$ for $1 \leq j \leq \ell-g$. The question we are interested in is whether $\core{I}=J^{n+1}:\ds \sum_{b \in I} (J,b)^n$ for $n \gg 0$. In the case of analytic spread one Polini and Ulrich show that this is true with even weaker assumptions (\cite[Theorem 3.4]{PU}). We give a negative answer to this question for higher analytic spreads and suggest a formula for the core of such ideals.

Affiliated with

Also associated with

No associations

Rating

Computing the core of ideals in arbitrary characteristic 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 Computing the core of ideals in arbitrary characteristic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computing the core of ideals in arbitrary characteristic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-457910