ABSTRACT
Let be a unital prime
-ring containing a nontrivial symmetric idempotent. For
, the 3-skew commutator is defined by
. Let
be a surjective map. It is shown that
satisfies
for all
if and only if there exists
with
such that
for all
. Where I is the unit of
and
is the symmetric center of
. This result then is applied to some operator algebras.
Communicated by Igor Klep
Acknowledgments
The authors wish to give their thanks to the referees for their helpful comments and suggestions that make much improvement of the paper.