SEMISIMPLE QUOTIENT-RINGS AND MORITA CONTEXT

Let (U, V; I, J) be a Morita context with the trace ideals I and J, ta u a Gabriel topology containing I on R-Mod, and tau' the corresponding Gabriel topology containing J on S-Mod. If tau - d((R)U) < infinity, and R is semisimple, simple respectively, then S is semisimple, simple respectively, moreover they are Morita equivalent, where R, S are the rings of quotients of R with respect to tau, resp., and of quotients of S with respect to tau'.