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The study analyses unique factorisation domain axioms, revealing some are unnecessary for the length-factorial property.
With the growing evolution of the theory of nonunique factorisation in integral domains and monoids, the study of several variations to the classical unique factorisation domain (or UFD) property has 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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Chapman et al. (2026) studied this question.
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