Integral Closedness of Complete-Intersection Ideals
Integral Closedness of Complete-Intersection Ideals
复制标题
完全相交理想的整体封闭性
DOI：
10.1016/0021-8693(87)90128-1
复制
发表时间：
1987
影响因子：
0.9
通讯作者：
S. Goto
中科院分区：
文献类型：
--
作者：
S. Goto
本文的目的是给出Noether环中某些整闭理想的结构定理。设A是Noether环，I是A的理想.则称A的一个元素x在Z上是积分的，如果x满足方程x”+ c，x”-'+.+在A中Ci = 0，其中Ci E I '。Z的积分闭包I定义为A中在Z上积分的元素的集合，如果f= I，则理想Z称为积分闭的。设uA（Z）（resp. ht，I）表示Z（resp.的高度）。设Min，A/Z是I的极小素因子集。本文研究了当A的理想Z使得uA（Z）= ht，Z为整闭时的问题，得到了如下结果：
The aim of this paper is to give some structure theorem of certain integrally closed ideals in Noetherian rings. Let A be a Noetherian ring and I an ideal of A. Then an element x of A is said to be integral over Z if x satisfies an equation x”+ c, x”-’+...+ c,= 0 in A with ci E I’. The integral closure I of Z is by definition the set of elements in A which are integral over Z and the ideal Z is called integrally closed if f= I. Let uA (Z)(resp. ht, I) denote the smallest number of elements in systems of generators for Z (resp. the height of I). Let Min, A/Z be the set of minimal prime divisors of I. In this paper we shall study the problem when the ideals Z of A such that uA (Z)= ht, Z are integrally closed and our result is stated as follows: