ABSTRACT
Let R be a prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R, F and G non-zero generalized derivations of R and a multilinear polynomial over C. Suppose that
is not central valued on R, and R does not embed in
, the algebra of
matrices over a field K. We describe all possible forms of F and G in the case
for any
.
Keywords:
Acknowledgments
The authors are really grateful to the referee's careful reading and valuable comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).