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Details van artikel 23 van 28 gevonden artikelen
| Titel: |
The Leading Ideal of a Complete Intersection of Height Two in a 2-Dimensional Regular Local Ring |
| Auteur: |
Goto, Shiro Heinzer, William Kim, Mee-Kyoung |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 36 (2008) nr. 5 pagina's 1901-1910 |
| Jaar: |
2008-05 |
| Inhoud: |
Let (S,) be a 2-dimensional regular local ring and let I = (f, g) be an ideal in S generated by a regular sequence f, g of length two. Let I* be the leading ideal of I in the associated graded ring gr(S), and set R = S/I and = /I. In Goto et al. (2007), we prove that if μG(I*) = n, then I* contains a homogeneous system {ξi}1≤i≤n of generators such that deg ξi + 2 ≤ deg ξi+1 for 2 ≤ i ≤ n - 1, and htG(ξ1, ξ2,…, ξn-1) = 1, and we describe precisely the Hilbert series H(gr(R), λ) in terms of the degrees ci of the ξi and the integers di, where di is the degree of Di = GCD(ξ1,…, ξi). To the complete intersection ideal I = (f, g)S we associate a positive integer n with 2 ≤ n ≤ c1 + 1, an ascending sequence of positive integers (c1, c2,…, cn), and a descending sequence of integers (d1 = c1, d2,…, dn = 0) such that ci+1 - ci > di-1 - di > 0 for each i with 2 ≤ i ≤ n - 1. We establish here that this necessary condition is also sufficient for there to exist a complete intersection ideal I = (f, g) whose leading ideal has these invariants. We give several examples to illustrate our theorems. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 23 van 28 gevonden artikelen
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