摘要
Let R be a prime ring of characteristic different from 2, d and 9 two derivations of R at least one of which is nonzero, L a non-central Lie ideal of R, and a ∈ R. We prove that if a(d(u)u - ug(u)) = 0 for any u ∈ L, then either a = O, or R is an sa-ring, d(x) = [p, x], and g(x) = -d(x) for some p in the Martindale quotient ring of R.
Let R be a prime ring of characteristic different from 2, d and 9 two derivations of R at least one of which is nonzero, L a non-central Lie ideal of R, and a ∈ R. We prove that if a(d(u)u - ug(u)) = 0 for any u ∈ L, then either a = O, or R is an sa-ring, d(x) = [p, x], and g(x) = -d(x) for some p in the Martindale quotient ring of R.