Abstract
Let R be a prime ring of characteristic different from 2 with its Utumi quotient ring U and extended centroid C, be multilinear polynomial over C, which is not central valued on R. If d is a non-zero derivation of R and F is a non-zero generalized derivation of R such that
for all , then there exists such that F(x) = cx, for all and one of the following holds:
(1) is central valued on R;
(2) R satisfies s4, the standard identity of degree 4.
Keywords: