Abstract
Let R be a noncommutative prime ring of characteristic different from 2, Qr be the right Martindale quotient ring of R and be the extended centroid of R. Suppose that
is a noncentral multilinear polynomial over C and
G are two generalized skew-derivations of R associated to the same automorphism α. If
for all
then one of the following holds:
There exist
and
such that
and
for all
There exists
such that F(x) = ax for all
and G = Id, the identity map.
There exist
such that F(x) = ax and G(x) = xb for all
with
and
is central valued on R.
2020 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors are thankful to the anonymous referees for their very carefully reading and giving constructive comments that lead to significant improvement in the readability of the paper.