Strong Mori and Noetherian properties of integer-valued polynomial rings

Let D be a domain with quotient field K and let Int(D) be the ring of integer-valued polynomials {f K[X] f(D) D}. We give conditions on D so that the ring Int(D) is a Strong Mori domain. In particular, we give a complete characterization in the case that the conductor (D :D′) is nonzero, where D′ is the integral closure of D. We also show that when D is quasilocal with Int(D) ≠ D[X] or D is Noetherian, Int(D) is a Strong Mori domain if and only if Int(D) is Noetherian.