Stable equivalence and rings whose modules are a direct sum of finitely generated modules

The representation theory of a ring Δ has been studied by examining the category of contravariant (additive) functors from the category of finitely generated left Δ-modules to the category of abelian groups. Closely connected with the representation theory of a ring is the study of stable equivalence, which is a relaxing of the notion of Morita equivalence. Here we relate two stably equivalent rings via their respective functor categories and examine left artinian rings with the property that every left Δ-module is a direct sum of finitely generated modules.