ON η- GENERALIZED DERIVATIONS IN RINGS WITH JORDAN INVOLUTION

Let K be a ring. An additive map u degrees degrees -> u is called Jordan involution on K if (u degrees)degrees degrees ) degrees = u and (uv+vu)degrees degrees = u degrees v degrees+v degrees u degrees degrees v degrees +v degrees u degrees for all u, v EK . If e is a (non-zero) r/-generalized derivation on K associated with a derivation ohm on K , then it is shown that e(u) = gamma u for all u E K such that gamma E Xi and gamma 2 2 = 1, whenever e possesses [e(u), e(u degrees)] degrees )] = [u, u degrees] degrees ] for all u EK .