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

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 $${\mathrm{int}}_R(E,D):=\{\phi \in K(X);\phi (E)\subseteq D\}.$$ 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.

To appear in Archiv der Mathematik, DOI : 10.1007/s00013-024-02086-7