Prüfer domains of integer-valued polynomials and the two-generator property (Q2029250)

Let \(V\) be a valuation domain with field of fractions \(K\) and \(E\subseteq V\). It is shown in the paper that the ring \(\text{Int}(E,V):=\{f\in K[x]\ \vert\ f(E)\subseteq V\}\) is a Prüfer domain if and only if \(E\) is precompact or there exists a rank-one prime ideal \(P\) of \(V\) such that \(\text{Int}(E,V_P)\)is a Prufer domain. Several characterizations of domains such that \(\text{Int}(E,V)\) is a Prüfer domain are obtained as consequences of thie above result.