TL;DR
This paper introduces two new ideal closure operations in commutative rings related to root closure, analyzing their properties and demonstrating they are distinct, with implications for algebraic structure understanding.
Contribution
It defines and studies two novel root-related ideal closures, establishing their properties and differences from existing closures.
Findings
The two closures are distinct operations.
Properties of each closure are characterized.
Connections to Rees algebra are explored.
Abstract
We introduce two closure operations on ideals in commutative rings related to the ring operation of root closure. One closure is the result of iterating a root-like operation on ideals infinitely many times, and the other closure arises as a graded component of the root closure of the Rees algebra applied to an ideal. We study the properties of these closures and prove they are distinct operations.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Oxidative Organic Chemistry Reactions