Finite Correspondence of Spectra in Noetherian Ring Extensions

Let R <-* S be an embedding of associative noetherian rings such that 5 is finitely generated as a right Ä-module. There is a correspondence from the prime spectrum of S to the prime spectrum of R obtained by associating to a given prime ideal P of S the prime ideals of R minimal over P n R . The prime and primitive ideal theories for several specific noncommutative noetherian rings, including group algebras, PI algebras, and enveloping algebras, depend on understanding instances of this correspondence. We prove that the correspondence has finite fibers for a class of noetherian ring extensions that unites these examples.