Research Interest
My research focuses on commutative algebra in connection to number theory and combinatorics. I am particularly interested in the ascent of algebraic, ideal-theoretic, and arithmetic properties to polynomial extensions, monoid and group algebras, and power semigroups. A central theme of my work is the study of non-unique factorization in commutative rings and monoids where the Fundamental Theorem of Arithmetic fails to hold. Most recently, I have been investigating analogues of classical number-theoretic problems within the framework of semirings, with a specific focus on simple semiring extensions and polynomial semirings.
Selected Publications
- Atomic semigroup rings and the ascending chain condition on principal ideals
(with B. Li)
Proceedings of the American Mathematical Society, Vol. 151 (2023) 2291-2302. - Length-factoriality in commutative monoids and integral domains
(with S. T. Chapman, J. Coykendall, and W. W. Smith)
Journal of Algebra, Vol. 578 (2021) 186-212. - On strongly primary monoids, with a focus on Puiseux monoids
(with A. Geroledinger and S. Tringali)
Journal of Algebra, Vol. 567 (2021) 310-345. - Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid
Linear Algebra and Its Applications, Vol. 604 (2020) 146-186. - Factorizations in upper triangular matrices over information semialgebras
(with N. R. Baeth)
Journal of Algebra, Vol. 562 (2020) 466-496. - On the atomicity of monoid algebras
(with J. Coykendall)
Journal of Algebra, Vol. 539 (2019) 138-151. - Increasing positive monoids of ordered fields are FF-monoids
Journal of Algebra, Vol. 518 (2019) 40-56. - Dyck paths and positroids from unit interval orders
(with A. Chavez) Journal of Combinatorial Theory Series A, Vol. 154 (2018) 507-532.
Here is a relatively updated version of my full list of publications.