Various properties of a general class of integer-valued polynomials

In this paper, we study various properties for some classes of domains that are generalizations of integer-valued polynomial rings. For D an integral domain with quotient field K and E a subset of K, one defines as usual Int (E, D) := {f is an element of K[X] : f(E) subset of D}. If R is an integral domain containing D, then we define Int(R) (E, D) := {f is an element of R[X] : f(E) subset of D}, which is called the ring of D-valued R-polynomials over E. Among other things, we investigate various properties and facts around the rings Int(R) (E, D), such as localization, (faithful) flatness, Krull dimension and some other transfer properties.