The conditionsInt(R) ⊆ RS[X] andInt(RS) = Int(R)S for integer-valued polynomials

AbstractLetR be an integral domain with quotient fieldK and letInt(R) = {f ε K[X]|f(R) ⊆ R}. In this note we determine whenInt(R) = R[X] for an arbitrary integral domainR. More generally we determine whenInt(R) ⊆ RS[X] for a multiplicative subsetS ofR. In the case thatR is an almost Dedekind domain with finite residue fields we also determine whenInt(RS) = Int(R)S for each multiplicative subsetS ofR, and show that if this holds then finitely generated ideals ofInt(R) can be generated by two elements