Abstract
Let
be a prime ring,
the right Martindale quotient ring of
and
the extended centroid of
.
In this paper, we discuss the relationship between the structure of prime rings and the behavior of skew derivations on multilinear polynomials. More precisely, we investigate the
-potent commutators of skew derivations involving multilinear polynomials, i.e.,
where
,
is a non-central multilinear polynomial over
and δ is a skew derivation of