English

A guide to closure operations in commutative algebra

Commutative Algebra 2015-12-11 v3

Abstract

This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part. The survey is broad enough to encompass the radical, tight closure, integral closure, basically full closure, saturation with respect to a fixed ideal, and the v-operation, among others.

Keywords

Cite

@article{arxiv.1106.1119,
  title  = {A guide to closure operations in commutative algebra},
  author = {Neil Epstein},
  journal= {arXiv preprint arXiv:1106.1119},
  year   = {2015}
}

Comments

32 pages; minor changes to section 4; to appear in the volume "Progress in Commutative Algebra" (Sean Sather-Wagstaff, Christopher Francisco, Lee Klingler, and Janet Vassilev, eds.), de Gruyter publ

R2 v1 2026-06-21T18:18:27.373Z