ON GENERALIZED DERIVATIONS SATISFYING CERTAIN IDENTITIES

Let R be a prime ring with char R not equal 2 and let d be a generalized derivation on R. We study the generalized derivation d satisfying any of the following identities: (i) d[(x, y)] = [d(x), d(y)] for all x, y is an element of R; (ii) d[(x, y)] = [d(y), d(x)] for all x, y is an element of R; (iii) either d([x, y]) = [d(x), d(y)] or d([x, y]) = [d(y), d(x)] for all x, y is an element of R.