论文标题
$ s $ closures的基本结果
Fundamental Results on $s$-Closures
论文作者
论文摘要
本文确定了$ s $ closures的基本属性，这是最近引入的封闭操作系列，涉及积极特征的理想。研究了分级环中均质理想的$ s $ pravile的行为，并给出了当$ s $ sy-s $ clublose the Ideals的标准可以准确地描述其紧密的封闭和理性的力量。对于较弱的$ $ $门子等于$ s $ clubersion，就建立了足够的条件。给出了Briancon-Skoda定理的概括，该概括比较了任何两个不同的$ s $ closures应用于相同理想的力量。
This paper establishes the fundamental properties of the $s$-closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the $s$-closure of homogeneous ideals in graded rings is studied, and criteria are given for when the $s$-closure of an ideal can be described exactly in terms of its tight closure and rational powers. Sufficient conditions are established for the weak $s$-closure to equal to the $s$-closure. A generalization of the Briancon-Skoda theorem is given which compares any two different $s$-closures applied to powers of the same ideal.
