THE SKOLEM PROPERTY IN RINGS OF INTEGER-VALUED POLYNOMIALS

Let D be an integral domain with quotient field K and E subset of or e qual to D. We investigate the relationship between the Skolem and comp letely integrally closed properties in the ring of integer-valued poly nomials Int(E, D) = {f(X) \ f(X) is an element of K[X] and f(a) is an element of D for every a is an element of E}. Among other things, we s how for the case D = Z and /E/ = infinity that the following are equiv alent: (1) Int(E,Z) is strongly Skolem, (2) Int(E,Z)is completely inte grally closed, and (3) Int(E,Z) = Int(E\{a}, Z) for every a is an elem ent of E.