Interpolation domains

Call a domain D with quotient field K an interpolation domain if, for each choice of distinct arguments a(1),...,a(n) and arbitrary values c(1),...,c(n), in D, there exists an integer-valued polynomial f (that is, f is an element of K[X] with f(D) subset of or equal to (D)), such that f(a(i)) = c(i) for 1 less than or equal to i less than or equal to n. We characterize completely the interpolatian domains if D is Noetherian or a Prufer domain. In the first case, we show that D is an interpolation domain if and only if it is one-dimensional locally unibranched with finite residue fields, in the second one, if and only if the ring Int(D) = {f is an element of K[X]\f(D) subset of or equal to D} of integer-valued polynomials is itself a Prufer domain. We also show that an interpolation domain must satisfy a double-boundedness condition, and thereby simplify a recent characterization of the domains D such that Int(D) is a Prufer domain. (C) 2000 Academic Press.