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∈ K[X]: f(E)⊆ D}. If R is an integral domain containing D , then we define Int_R(E,D):={f∈ R[X]: f(E)⊆ 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.