科研之友
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摘要
Let R be a prime ring, H a generalized derivation of R, L a noncentral Lie ideal of R, and 0 not equal a is an element of R. Suppose that au(s) (H(u))(n)u(t) = 0 for all u is an element of L, where s, t >= 0 and n > 0 are fixed integers. If s = 0, then H(x) = bx for all x is an element of R, where b is an element of U, the right Utumi quotient ring of R, with ab = 0 unless R satisfies s(4), the standard identity in four variables. If s > 0, then H = 0 unless R satisfies s(4).
