On quasi-valuation domains (Q2709726)

Let \(D\) be an integral domain with quotient field \(K.\) \(D\) is called a quasi-valuation domain (QVD) if for each overring \(R \neq D\) of \(D\) which has a unique maximal ideal \(m_{R},\) we have \(\{x \in K \mid xR \subseteq D \}=m_{R}\). In this paper the author gives several characterizations of a QVD. In particular it is shown that a quasi-local domain \(D\) is a QVD if and only if each overring of \(D\) is a pseudo-valuation domain.