English

On the axioms for a unique factorization domain

Commutative Algebra 2025-07-09 v2

Abstract

With the growing evolution of the theory of non-unique factorization in integral domains and monoids, the study of several variations to the classical unique factorization domain (or UFD) property have become popular in the literature. Using one of these variations, the length-factorial property, it can be shown that part of the standard classical axioms used in the definition of a UFD is essentially superfluous.

Cite

@article{arxiv.2507.05188,
  title  = {On the axioms for a unique factorization domain},
  author = {Scott T. Chapman and Jim Coykendall},
  journal= {arXiv preprint arXiv:2507.05188},
  year   = {2025}
}

Comments

10 pages

R2 v1 2026-07-01T03:49:50.201Z