On the core of ideals
| dc.creator | Huneke, Craig | |
| dc.creator | Trung, Ngo Viet | |
| dc.date | 2004-05-12 | |
| dc.date.accessioned | 2026-07-07T05:08:09Z | |
| dc.date.available | 2026-07-07T05:08:09Z | |
| dc.description | Our focus in this paper is in effective computation of the core core(I) of an ideal I which is defined to be the intersection of all minimal reductions of I. The first main result is a closed formula for the graded core(m) of the maximal graded ideal m of an arbitrary standard graded algebra A over a field k. This formula allows us to study basic properties of the graded core and to construct counter-examples to some open questions on the core of ideals in a local ring. For instance, we can show that in general, core(m \otimes E) \neq core(m)\otimes E, where E is a field extension of k. From this it follows that the equation core(I R') = core(I)R' does not hold for an arbitrary flat local homomorphism R \to R' of Cohen-Macaulay local rings. The second main result proves the formulae core(I)= (J^r:I^r)I = (J^r:I^r)J = J^{r+1}:I^r for any equimultiple ideal I in a Cohen-Macaulay ring R with with characteristic zero residue field, where J is a minimal reduction of I and r is its reduction number. This result has been obtained independently by Polini-Ulrich and Hyry-Smith in the one-dimensional case or when R is a Gorenstein ring. Moreover, we can prove that core(I) = IK, where K is the conductor of R in the blowing-up ring at I. | |
| dc.description | 20 pages, to appear in Compositio Math | |
| dc.identifier | https://arxiv.org/abs/math/0405213 | |
| dc.identifier | http://arxiv.org/abs/math/0405213 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71150 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A02 | |
| dc.title | On the core of ideals | |
| dc.type | text |