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

초록

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

키워드