Fundamental results on s-closures

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Taylor, William D.¹ 

[1] Tennessee State Univ, Dept Math Sci, 3500 John A Merritt Dr, Nashville, TN 37209 USA

关键词: Commutative algebra;    Positive characteristic;    Closure operations;    s-closures;   

DOI  :  10.1016/j.jpaa.2020.106565

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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