Factorization of rings of integer-valued rational functions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914860169691136 |
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| author | Liu, Baian |
| author_facet | Liu, Baian |
| contents | $\DeclareMathOperator{\Int}{Int}\DeclareMathOperator{\IntR}{Int{}^\text{R}}$For a domain $D$, the ring $\Int(D)$ of integer-valued polynomials over $D$ is atomic if $D$ satisfies the ascending chain condition on principal ideals. However, even for a discrete valuation domain $V$, the ring $\IntR(V)$ of integer-valued rational functions over $V$ is antimatter. We introduce a family of atomic rings of integer-valued rational functions and study various factorization properties on these rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01355 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Factorization of rings of integer-valued rational functions Liu, Baian Commutative Algebra $\DeclareMathOperator{\Int}{Int}\DeclareMathOperator{\IntR}{Int{}^\text{R}}$For a domain $D$, the ring $\Int(D)$ of integer-valued polynomials over $D$ is atomic if $D$ satisfies the ascending chain condition on principal ideals. However, even for a discrete valuation domain $V$, the ring $\IntR(V)$ of integer-valued rational functions over $V$ is antimatter. We introduce a family of atomic rings of integer-valued rational functions and study various factorization properties on these rings. |
| title | Factorization of rings of integer-valued rational functions |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2307.01355 |