NILPOTENT VALUES OF GENERALIZED DERIVATION IN PRIME AND SEMIPRIME RINGS

Let I be a nonzero ideal of a prime ring R and m, n are positive integers. If R admits a generalized derivation F satisfying F(x)F-n(y)(m) - x(n)y(m) = 0 for any y, x is an element of I, then F(x) = ax for any x is an element of R and a(m+n) = 1, where a is an element of C, the extended centroid of R.