Integer-Valued Polynomials on a Subset Original Research Article

LetRbe a Dedekind domain whose residue fields are finite, and letKbe the field of fractions ofR. WhenSis a (non-empty) subset ofKwe write Int(S) for the subring ofK[X] consisting of all polynomialsf(X) inK[X] such thatf(S)subset of or equal toR. We show that there exist fractional idealsJ0,J1, …,Jnand monic polynomialsf0,f1, …,fnsuch thatimagewhereVnis theK-space of polynomials of degree at mostninK[X]. This generalises classic results on Int(R).