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arXiv · 2507.05188

On the axioms for a unique factorization domain

Scott T. Chapman·Jim Coykendall
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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.

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Scott T. Chapman, Jim Coykendall. 2025-07-07. On the axioms for a unique factorization domain. https://arxiv.org/abs/2507.05188

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