A Note on Skew Derivations in Prime Rings
نویسندگان
چکیده
Let m,n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : R −→ R be a skew derivation of R and E(x) = D(xm+n+r)−D(xm)xn+r − xmD(xn)xr − xm+nD(xr). We prove that if E(x) = 0 for all x ∈ L, then D is a usual derivation of R or R satisfies s4(x1, . . . , x4), the standard identity of degree 4.
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