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

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