English

Straight Domains are Locally Divided

Commutative Algebra 2023-07-13 v2

Abstract

We present a proof that all straight domains are locally divided\unicodex2014\unicode{x2014}thereby answering two open problems posed by Dobbs and Picavet, which appeared in the survey "Open Problems in Commutative Ring Theory" written by Cahen, Fontana, Frisch, and Glaz. In fact, we are able to prove a stronger result: a prime ideal of a domain is straight if and only if it is locally divided.

Cite

@article{arxiv.2305.01809,
  title  = {Straight Domains are Locally Divided},
  author = {Spencer Secord},
  journal= {arXiv preprint arXiv:2305.01809},
  year   = {2023}
}

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R2 v1 2026-06-28T10:24:02.038Z