Ring Structure of Integer-Valued Rational Functions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910342255214592 |
|---|---|
| author | Liu, Baian |
| author_facet | Liu, Baian |
| contents | $\DeclareMathOperator{\IntR}{Int{}^\text{R}}$Integer-valued rational functions are a natural generalization of integer-valued polynomials. Given a domain $D$, the collection of all integer-valued rational functions over $D$ forms a ring extension $\IntR(D)$ of $D$. For a valuation domain $V$, we characterize when $\IntR(V)$ is a Prüfer domain and when $\IntR(V)$ is a Bézout domain. We also extend the classification of when $\IntR(D)$ is a Prüfer domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09935 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ring Structure of Integer-Valued Rational Functions Liu, Baian Commutative Algebra $\DeclareMathOperator{\IntR}{Int{}^\text{R}}$Integer-valued rational functions are a natural generalization of integer-valued polynomials. Given a domain $D$, the collection of all integer-valued rational functions over $D$ forms a ring extension $\IntR(D)$ of $D$. For a valuation domain $V$, we characterize when $\IntR(V)$ is a Prüfer domain and when $\IntR(V)$ is a Bézout domain. We also extend the classification of when $\IntR(D)$ is a Prüfer domain. |
| title | Ring Structure of Integer-Valued Rational Functions |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2208.09935 |