Rings with (x, y, z) - (z, y, x) in the right nucleus

Let R be a semiprime nonassociative ring satisfying (x, y, z) - (z, y, x) is an element of N-r then N-l = N-r where N-l and N-r are Lie ideals of R, the set {x is an element of N-r : (R, R, R)x= 0} = {x is an element of N-l : x(R, R, R) = 0} is an ideal of R, and it is contained in the nucleus. Further if [R, R]N-r subset of N-r and R is a prime ring with N-r not equal 0 then R is either associative or commutative.