The classical Morita Theorem for rings established the equivalence of three statements, involving categorical equivalences, isomorphisms between corners finite matrix rings, and bimodule homomorphisms. A fourth equivalent statement (established later) involves an isomorphism infinite rings. In our main result, we establish analogous statements graded homomorphisms,

Definition 1. Let A be a ring. A graded A-algebra is an A-algebra R which is also a graded ring in such a way that if r ∈ Rd then ar ∈ Rd for all a ∈ A. That is, Rd is an A-submodule of R for all d ≥ 0. Equivalently a graded A-algebra is a morphism of graded rings A −→ R where we grade A by setting A0 = A,An = 0 for n > 0. A morphism of graded A-algebras is a morphism of A-algebras which preser...

I was a graduate student at the Mas-sachusetts Institute of Technology. The rst three years of these studies were supported by an NSF Graduate Student Fellowship. My research there led to a Ph.D. thesis entitled \Noncommutative ruled surfaces." My thesis research describes certain classes of graded rings which arise as homogeneous coordinate rings of noncommutative quantizations of algebraicall...