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

2025/10/03 by Chems-Eddin, M. M., Feryouch, B., Tamoussit, A.
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.03443

Abstract

Let D be an integral domain with quotient field K, E a subset of K and X an indeterminate over K. The set Int(E,D):=\f∈ K[X]; f(E)⊆ 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 Int(E,D) across various classes of integral domains D and specific subsets E of D. We further extend our study to the ring Int_B(E,D):=\f∈ B[X]; f(E)⊆ D\, where B is an integral domain containing D

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