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math.AC2025
On the axioms for a unique factorization domain
Scott T. Chapman, Jim Coykendall
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 (…
math.AC2025
Betti elements and full atomic support in rings and monoids
Scott T. Chapman, Pedro García-Sánchez, Christopher O'Neill +1
Several papers in the recent literature have studied factorization properties of affine monoids using the monoid's Betti elements. In this paper, we extend this study to more gener…