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arXiv · 2412.07931

On the Krull dimension of rings of integer-valued rational functions

Mohamed Mahmoud Chems-Eddin·Badr Feryouch·Hakima Mouanis·Ali Tamoussit
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Abstract

Let $D$ be an integral domain with quotient field $K$ and $E$ a subset of $K$. The \textit{ring of integer-valued rational functions on} $E$ is defined as $$\mathrm{int}_R(E,D):=\lbrace \varphi \in K(X);\; \varphi(E)\subseteq D\rbrace.$$ The main goal of this paper is to investigate the Krull dimension of the ring $\mathrm{int}_R(E,D).$ Particularly, we are interested in domains that are either Jaffard or PVDs. Interesting results are established with some illustrating examples.

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Mohamed Mahmoud Chems-Eddin, Badr Feryouch, Hakima Mouanis, Ali Tamoussit. 2024-12-10. On the Krull dimension of rings of integer-valued rational functions. https://arxiv.org/abs/2412.07931

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