Abstract
Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f(x (1), . . . , x (n) ) a multilinear polynomial over C, rho a nonzero right ideal of R and m > 1 a fixed integer such that
([d(f(r(1), ..., r(n))), f(r(1), ..., r(n))])(m) = [d(f((r(1), ..., r(n))), f(r(1), ..., r(n))]
for all r (1), . . . , r (n) a rho. Then either [f(x (1),aEuro broken vertical bar,x (n) ),x (n+1)]x (n+2) is an identity for rho or d(rho)rho = 0.