Computing the core of ideals in arbitrary characteristic
| dc.creator | Fouli, Louiza | |
| dc.date | 2007-05-13 | |
| dc.date | 2007-10-10 | |
| dc.date.accessioned | 2026-07-07T08:35:15Z | |
| dc.date.available | 2026-07-07T08:35:15Z | |
| dc.description | 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. | |
| dc.description | 13 pages, revised. To appear in the Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/0705.1808 | |
| dc.identifier | http://arxiv.org/abs/0705.1808 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139690 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13-xx | |
| dc.title | Computing the core of ideals in arbitrary characteristic | |
| dc.type | text |