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arXiv · 2607.23823

Interval Rings

William Heinzer·K. Alan Loper·Bruce Olberding·Matthew Toeniskoetter
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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.

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William Heinzer, K. Alan Loper, Bruce Olberding, Matthew Toeniskoetter. 2026-07-26. Interval Rings. https://arxiv.org/abs/2607.23823

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