3 papers
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
On three families of dense Puiseux monoids
Scott. T. Chapman, Felix Gotti, Marly Gotti +1
A positive monoid is a submonoid of the nonnegative cone of a linearly ordered abelian group. The positive monoids of rank are called Puiseux monoids, and their atomicity, arit…
math.AC2025
Betti elements and full atomic support in rings and monoids
Scott T. Chapman, Pedro GarcÃa-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…