  We study topological properties of the correspondence of prime spectra
associated to a noncommutative ring homomorphism R -> S. Our main result
provides criteria for the adjointness of certain functors between the
categories of Zariski closed subsets of Spec(R) and Spec(S); these functors
arise naturally from restriction and extension of scalars. When R and S are
left noetherian, adjointness occurs only for centralizing and ``nearly
centralizing'' homomorphisms.
