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.
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机译:设 A 为素数 (*) 代数,设 习 是 C {0, +/- 1} 的元素。我们证明映射 phi : A -> A 满足所有 A、B、C 的 phi (A 锭剂(习) B 锭剂(习) C) = phi (A) 锭剂(习) B 锭剂(习) C + A 锭剂(习) phi (B) 锭剂(习) C + A 锭剂(习) B 锭剂(习) phi (C) 对于所有 A、B、C 都是 A 的元素,当且仅当 phi 是加法 (*) 导数和 phi (习 A) = 习 所有 A 的元素 phi (A)。
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