GRADED MORITA THEORY FOR INFINITE GROUPS

Having shown that not all graded rings are graded equivalent (via clas sical Morita theory) to a skew group ring, we extend classical Morita theory, which is based on rings with identity, to a generalized graded Morita theory for rings with local units. This enables us to give nec essary and sufficient conditions for graded Morita equivalence between two rings graded by a group. We show that the strongly graded propert y is a graded Morita invariant and we show that a graded ring is grade d Morita equivalent to a skew group ring (namely, (R#G)G) if and only if it is strongly graded. These results extend the classical Cohen-Mo ntgomery duality theory to rings graded by infinite groups. The fundam ental tools include rings with local units and the results of Boisen. (C) 1994 Academic Press, Inc.