Prüfer domains of integer-valued polynomials

Abstract

Let D be an integral domain with quotient field K. The ring Int(D) ={f (x) ‖ f (D) ⊆ D} has been studied as a ring for more than forty years. A major topic of interest during that time has been the question of when the construction yields a Prüfer domain. The principal question has been resolved, but interesting generalizations are still being worked on. This is a survey paper that traces the history of study of integer-valued polynomial rings with a focus on when they are Prüfer domains.