A quadratic differential identity with skew derivations

Let R be a prime ring of characteristic different from 2, with right Martindale quotient ring Qr and extended centroid C, and let f(x1,...,xn) be a multilinear polynomial over C, not central valued on R. Suppose that F and G are skew derivations of R, associated with the automorphism α, such that F(f(r1,...,rn))G(f(r1,...,rn)) + G(f(r1,...,rn))F(f(r1,...,rn)) = 0 for all r1,...,rn ∈ R. Then either F = 0 or G = 0. © 2018 Taylor & Francis.