Extension Fields and Integer-Valued Polynomials Original Research Article

LetAbe a Dedekind domain with finite residue fields,Kitʹs quotient field,La finite separable extension ofK, andBthe integral closure ofAinL. The rings of integer-valued polynomials onAandBare known to be Prüfer domains and will be denoted by Int(A) and Int(B), respectively. We will present some connections between the localizations of each of these rings (Theorem2 andCorollary4) and in particular we answer the question when Int(A) is a subset of Int(B).