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arXiv · 2510.03443

Note on the Krull dimension of rings of integer-valued polynomials

M. M. Chems-Eddin·B. Feryouch·A. Tamoussit
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Abstract

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 $D$

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M. M. Chems-Eddin, B. Feryouch, A. Tamoussit. 2025-10-03. Note on the Krull dimension of rings of integer-valued polynomials. https://doi.org/10.1007/s12215-025-01330-5

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