封闭件的缩径和特殊部件
Reductions and special parts of closures
摘要：
我们提供了一个公理化的框架，用于处理交换代数中理想和子模上的各种闭包运算，包括闭包的简化、独立、扩展和特殊部分等概念。这个框架适用于紧闭包、Frobenius闭包和整闭包。应用程序的演变和特殊的Briançon-Skoda定理。
英文摘要：
We provide an axiomatic framework for working with a wide variety of closure operations on ideals and submodules in commutative algebra, including notions of reduction, independence, spread, and special parts of closures. This framework is applied to tight, Frobenius, and integral closures. Applications are given to evolutions and special Briançon-Skoda theorems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
