SEMISIMPLE RINGS OF QUOTIENTS IN MORITA CONTEXTS

Let (R, (R)U(S), (S)V(R), S) be a Morita context with the trace ideals I in R and J in S, tau a Gabriel topology containing I on R-Mod, and tau' the corresponding Gabriel topology containing J on S-Mod. Necessa ry and sufficient conditions on tau and (R)U are given in order that t he ring of quotients S of S with respect to tau' be semisimple artinia n, simple artinian or a division ring respectively. Special cases incl ude earlier works.