English

Closure-interior duality over complete local rings

Commutative Algebra 2021-04-26 v3

Abstract

We define a duality operation connecting closure operations, interior operations, and test ideals, and describe how the duality acts on common constructions such as trace, torsion, tight and integral closures, and divisible submodules. This generalizes the relationship between tight closure and tight interior given in [Epstein-Schwede 2014] and allows us to extend commonly used results on tight closure test ideals to operations such as those above.

Keywords

Cite

@article{arxiv.1909.05739,
  title  = {Closure-interior duality over complete local rings},
  author = {Neil Epstein and R. G. Rebecca},
  journal= {arXiv preprint arXiv:1909.05739},
  year   = {2021}
}

Comments

34 pages, to appear in Rocky Mountain Journal of Mathematics. Minor changes of phrasing

R2 v1 2026-06-23T11:13:37.924Z