On generalized derivations satisfying certain identities - Albaş, E. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
Let R be a prime ring with char R eq 2 and d be a generalized derivation on R. The goal of this study is to investigate the generalized derivation d satisfying any one of the following identities: (i) d[(x, y)] = [d(x), d(y)] for all x, y R; (ii) d[(x, y)] = [d(y), d(x)] for all x, y R; (iii)d([x, y]) = [d(x), d(y)] either d([x, y]) = [d(y), d(x)] for all x, y R.