On continuous and adjoint morphisms between non-commutative prime spectra

Abstract

We study topological properties of the correspondence of prime spectra associated with a non-commutative 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.