The ring of integer-valued polynomials of a Dedekind domain

Gilmer, Robert; Heinzer, William; Lantz, David; Smith, William

doi:10.1090/S0002-9939-1990-1009989-7

The ring of integer-valued polynomials of a Dedekind domain
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by Robert Gilmer, William Heinzer, David Lantz and William Smith

Proc. Amer. Math. Soc. 108 (1990), 673-681

DOI: https://doi.org/10.1090/S0002-9939-1990-1009989-7

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Abstract:

Let $D$ be a Dedekind domain and $R = Int(D)$ be the ring of integer-valued polynomials of $D$. We relate the ideal class groups of $D$ and $R$. In particular we prove that, if $D = \mathbb {Z}$ is the ring of rational integers, then the ideal class group of $R$ is a free abelian group on a countably infinite basis.

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