Interval Rings
Commutative Algebra
2026-07-26 v1
Abstract
Interval rings comprise a class of one-dimensional integrally closed local integral domains which are overrings of a two-dimensional regular local ring. We construct them by intersecting carefully chosen valuation rings and prove that they have various nice properties. Our interest in these rings is that they represent a major stepping stone toward classifying all integrally closed overrings of a two-dimensional regular local ring.
Cite
@article{arxiv.2607.23823,
title = {Interval Rings},
author = {William Heinzer and K. Alan Loper and Bruce Olberding and Matthew Toeniskoetter},
journal= {arXiv preprint arXiv:2607.23823},
year = {2026}
}