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
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…
math.AC2023
Betti graphs and atomization of Puiseux monoids
Scott T. Chapman, Joshua Jang, Jason Mao +1
Let be a Puiseux monoid, that is, a monoid consisting of nonnegative rationals (under addition). A nonzero element of is called an atom if its only decomposition as a sum o…