CORE AND RESIDUAL INTERSECTIONS OF IDEALS
CORE AND RESIDUAL INTERSECTIONS OF IDEALS
复制标题
理想的核心和剩余交叉点
DOI：
10.1090/s0002-9947-02-02908-2
复制
发表时间：
2002
影响因子：
1.3
通讯作者：
B. Ulrich
中科院分区：
文献类型：
--
作者：
A. Corso;C. Polini;B. Ulrich
D. Rees和J. Sally将r -理想I的核心定义为I的所有（最小）约简的交叉点。然而，用附加在理想上的数据来明确表征它并不容易。直到最近，已知封闭公式的唯一情况是二维正则局部环上的积分封闭理想公式，这是由C. Huneke和I. Swanson提出的。本文的主要结果明确地描述了任意局部Cohen-Macaulay环上一类具有良好剩余性质的理想的核心。我们还发现，为了得到核心，需要相交的最小化简数有一个明确的界限。
D. Rees and J. Sally defined the core of an R-ideal I as the in- tersection of all (minimal) reductions of I. However, it is not easy to give an explicit characterization of it in terms of data attached to the ideal. Until recently, the only case in which a closed formula was known is the one of inte- grally closed ideals in a two-dimensional regular local ring, due to C. Huneke and I. Swanson. The main result of this paper explicitly describes the core of a broad class of ideals with good residual properties in an arbitrary local Cohen-Macaulay ring. We also find sharp bounds on the number of minimal reductions that one needs to intersect to get the core.