On Pseudo-valuation Domains whose Overrings are Going-down Domains

Document Type

Article

Publication Date

2002

Abstract

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.

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