Let R be a prime ring and n 〉 1 be a fixed positive integer. If g is a nonzero generalized derivation of R such that g（x）n = g（x） for all x ∈ R, then R is commutative except when R is a subring of the 2 × 2...Let R be a prime ring and n 〉 1 be a fixed positive integer. If g is a nonzero generalized derivation of R such that g（x）n = g（x） for all x ∈ R, then R is commutative except when R is a subring of the 2 × 2 matrix ring over a field. Moreover, we generalize the result to the case g（f（xi））n = g（f（xi）） for all xl,x2,...,xt ∈ R, where f（Xi） is a multilinear polynomial.展开更多
文摘Let R be a prime ring and n 〉 1 be a fixed positive integer. If g is a nonzero generalized derivation of R such that g（x）n = g（x） for all x ∈ R, then R is commutative except when R is a subring of the 2 × 2 matrix ring over a field. Moreover, we generalize the result to the case g（f（xi））n = g（f（xi）） for all xl,x2,...,xt ∈ R, where f（Xi） is a multilinear polynomial.
