Note on the Krull dimension of rings of integer-valued polynomials
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918189810581504 |
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| author | Chems-Eddin, M. M. Feryouch, B. Tamoussit, A. |
| author_facet | Chems-Eddin, M. M. Feryouch, B. Tamoussit, A. |
| contents | Let $D$ be an integral domain with quotient field $K,$ $E$ a subset of $K$ and $X$ an indeterminate over $K$. The set $\mathrm{Int}(E,D):=\{f\in K[X];\; f(E)\subseteq D\}$, of integer-valued polynomials on $E$ over $D$, is known to be an integral domain. The purpose of this note is to calculate the Krull dimension of $\mathrm{Int}(E,D)$ across various classes of integral domains $D$ and specific subsets $E$ of $D$. We further extend our study to the ring $\mathrm{Int}_B(E,D):=\{f\in B[X];\; f(E)\subseteq D\},$ where $B$ is an integral domain containing $D$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03443 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Note on the Krull dimension of rings of integer-valued polynomials Chems-Eddin, M. M. Feryouch, B. Tamoussit, A. Commutative Algebra Let $D$ be an integral domain with quotient field $K,$ $E$ a subset of $K$ and $X$ an indeterminate over $K$. The set $\mathrm{Int}(E,D):=\{f\in K[X];\; f(E)\subseteq D\}$, of integer-valued polynomials on $E$ over $D$, is known to be an integral domain. The purpose of this note is to calculate the Krull dimension of $\mathrm{Int}(E,D)$ across various classes of integral domains $D$ and specific subsets $E$ of $D$. We further extend our study to the ring $\mathrm{Int}_B(E,D):=\{f\in B[X];\; f(E)\subseteq D\},$ where $B$ is an integral domain containing $D$ |
| title | Note on the Krull dimension of rings of integer-valued polynomials |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2510.03443 |