Ring-theoretic properties of locally Mori domains and rings of the form Int(E, D)

An integral domain D is said to be locally Mori if any localization of D at a maximal ideal is a Mori domain. In this paper we are concerned with some ring-theoretic properties of locally Mori domains and their rings of integer-valued polynomials. First, we present some results on the transfer of the locally Mori property to flat overrings, Nagata ideal transforms, polynomial ring extensions and pullback constructions. Then, we investigate rings of integer-valued polynomials over (locally) Mori domains, and for an integral domain D, we give a necessary condition for Int(D) to be an MZ-Mori domain.