The ring of integer-valued polynomials of a Dedekind domain

Abstract

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