Fundamental Results on $s$-Closures
Commutative Algebra
2020-04-29 v1
Abstract
This paper establishes the fundamental properties of the -closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the -closure of homogeneous ideals in graded rings is studied, and criteria are given for when the -closure of an ideal can be described exactly in terms of its tight closure and rational powers. Sufficient conditions are established for the weak -closure to equal to the -closure. A generalization of the Briancon-Skoda theorem is given which compares any two different -closures applied to powers of the same ideal.
Keywords
Cite
@article{arxiv.2004.13190,
title = {Fundamental Results on $s$-Closures},
author = {William D. Taylor},
journal= {arXiv preprint arXiv:2004.13190},
year = {2020}
}
Comments
10 pages