Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings
Abstract
Let $a,b$ be positive integers. In this note, we study the numerical semigroup $H=\left$ and and the associated numerical semigroup ring $R=k[[H]]$. Under the certain conditions, we provide explicit formulas for the Frobenius number of $H$ and for the first Hilbert coefficient of $R$.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Algebraic Geometry and Number Theory
Rings
Modules
and Algebras
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 29 January 2026
- Document type
- Preprint