Abstract
Let R be a semiprime ring with extended centroid C and with maximal left ring of quotients . An additive map
is called a Jordan triple derivation if
for all
. In 1957, Herstein proved that a Jordan triple derivation, which is also a Jordan derivation, of a noncommutative prime ring of characteristic 2, must be a derivation. In 1989, Brešar proved that any Jordan triple derivation of a 2-torsion free semiprime ring is a derivation. In the article, we give a complete characterization of Jordan triple derivations of arbitrary semiprime rings. To get such a characterization we first show that, in some sense, an additive map
satisfying
for all
can be realized as a centralizer with only an exceptional case that
and R is commutative.
Acknowledgements
The authors are grateful to the referee for carefully reading the manuscript.