On Pseudo-valuation Domains whose Overrings are Going-down Domains
It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (for instance, a proper field extension) and M denotes the common maximal ideal of R and T, then each ring between R and T is a going-down domain if and only if the transcendence degree of T /M over R/M is at most 1. As a consequence, transcendence degree is used to characterize the pseudo-valuation domains all of whose overrings are going-down domains.
Houston Journal of Mathematics, Vol. 28, No. 1, 2002, 13-19.