Globalized pseudo-valuation domains of integer-valued polynomials on a subset

Abstract

Let D be a pseudo-valuation domain with associated valuation domain V and let E be a nonempty subset of V. We show that is a globalized pseudo-valuation domain if and only if is a Prüfer domain. In this case, is the associated Prüfer domain of is a globalized pseudo-valuation domain with associated Prüfer domain furthermore, every ring between and is a globalized pseudo-valuation domain. Also, in this case, we describe the unitary maximal ideals of and show that is a Bézout domain.