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 Recent Papers
- One-dimensional monoid algebras and ascending chains of principal ideals
(with A. Bu, B. Li, and A. Zhao)
European Journal of Mathematics, Vol. 12 (2026) 57. - On the ascent of atomicity to monoid algebras
(with H. Rabinovitz)
Journal of Algebra, Vol. 663 (2025) 857–881. - On monoid algebras having every nonempty subset of \(\mathbb{N}_{\ge 2}\) as a length set
(with A. Geroldinger)
Mediterranean Journal of Mathematics, Vol. 22 (2025) 1–19. - Riemann zeta functions for Krull monoids
(with U. Krause)
Journal of Number Theory, Vol. 262 (2024) 134–160. - 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. - On the arithmetic of polynomial semidomains
(with H. Polo)
Forum Mathematicum, Vol. 35 (2023) 1179–1197.
Here is a relatively updated version of my full list of publications.