Let A be a prime (*)-algebra and let xi is an element of C {0, +/- 1}. We prove that a mapping phi : A -> A satisfies phi (A lozenge(xi) B lozenge(xi) C) = phi (A) lozenge(xi) B lozenge(xi) C + A lozenge(xi) phi (B) lozenge(xi) C + A lozenge(xi) B lozenge(xi) phi (C) for all A, B, C is an element of A if and only if phi is an additive (*)-derivation and phi (xi A) = xi phi (A) for all A is an element of A.
展开▼
