摘要翻译：
我们在代数和复解析的背景下描述了理想的弱次积分闭包的一些基本事实。重点讨论了关于理想和模的积分闭包与理想的弱次积分闭包的结果之间的类比。首先，我们给出了Reid-Roberts-Singh准则的几何解释，当一个元素在子环上是弱次积分时。给出了理想的弱次积分闭包的新刻画。我们与理想的$I$环$a$一个理想的$I_>$相关联，它由$a$的所有元素组成，因此对于$I$的所有Rees估值$V$来说，$V(a)>V(I)$。理想的$i_>$在Whitney条件A和Thom条件$a_f$等分层理论的条件中起着重要的作用，并包含在$i$的每一个约简中。当一个元素处于理想的弱次积分闭包中时，我们给出了一个赋值准则。为此，我们为一对模引入了一种新的闭包操作，我们称之为相对闭包。
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英文标题：
《Weak subintegral closure of ideals》
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作者：
Terence Gaffney and Marie A. Vitulli
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Complex Variables        复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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英文摘要：
  We describe some basic facts about the weak subintegral closure of ideals in both the algebraic and complex-analytic settings. We focus on the analogy between results on the integral closure of ideals and modules and the weak subintegral closure of an ideal. We start by giving a geometric interpretation of the Reid-Roberts-Singh criterion for when an element is weakly subintegral over a subring. We give new characterizations of the weak subintegral closure of an ideal. We associate with an ideal $I$ of a ring $A$ an ideal $I_>$, which consists of all elements of $A$ such that $v(a)>v(I)$, for all Rees valuations $v$ of $I$. The ideal $I_>$ plays an important role in conditions from stratification theory such as Whitney's condition A and Thom's condition $A_f$ and is contained in every reduction of $I$. We close with a valuative criterion for when an element is in the weak subintegral closure of an ideal. For this, we introduce a new closure operation for a pair of modules, which we call relative closure.
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PDF链接：
https://arxiv.org/pdf/0708.3105