Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915761215242240 |
|---|---|
| author | Van Kien, Do Quy, Pham Hung |
| author_facet | Van Kien, Do Quy, Pham Hung |
| contents | Let $a,b$ be positive integers. In this note, we study the numerical semigroup $H=\left<a,a+1,b\right>$ 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 $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21819 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings Van Kien, Do Quy, Pham Hung Group Theory Commutative Algebra Number Theory 20M25, 11D07, 13A15, 13D40 Let $a,b$ be positive integers. In this note, we study the numerical semigroup $H=\left<a,a+1,b\right>$ 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 $R$. |
| title | Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings |
| topic | Group Theory Commutative Algebra Number Theory 20M25, 11D07, 13A15, 13D40 |
| url | https://arxiv.org/abs/2601.21819 |