Valuation rings and the (catenary) chain conjectures

AbstractFor a Noetherian domain R (altitude R < ∞) with quotient field F, an overring I(R) of R is defined as the intersection of a certain family of valuation rings in F which contain R. I(R) is characterized in several ways, and it is shown that I(R) has many properties which are analogous to properties of the integral closure of R. Then it is shown that further knowledge of I(R) should help to settle some of the conjectures concerning maximal chains of prime ideals in a Noetherian domain