On the axioms for a unique factorization domain

TL;DR

This paper investigates the axioms defining unique factorization domains (UFDs), showing that some classical axioms are unnecessary when considering the length-factorial property within the evolving theory of non-unique factorizations.

Contribution

It demonstrates that certain classical axioms for UFDs are redundant under the length-factorial property, contributing to the understanding of axiomatic foundations in non-unique factorization theory.

Findings

Some classical axioms are superfluous for UFDs with the length-factorial property

The study clarifies the axiomatic structure of UFDs in the context of non-unique factorizations

Advances the theoretical understanding of factorization properties in integral domains

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.