Ring Theoretic Properties of Matrix Rings

K. Morita has shown that, given two rings R and S, there is an isomorphism between the category of left R-modules and the category of left S-modules if and only if there exists an R-S bimodule U such that(1) U is a progenerator in the category of left R-modules, and(2) S ≅ (EndR U)opp as rings.