Abstract
Let R be a prime ring with extended centroid C and with maximal left ring of quotients . An additive map
is called a weak Jordan derivation if
for all
. Applying the theory of functional identities and dealing with the low dimensional cases, we give a complete characterization of weak Jordan derivations of prime rings. Moreover, we generalize Brešar's theorem concerning additive maps
satisfying
for all
.
Acknowledgements
The author thanks Professor Tsiu-Kwen Lee for useful suggestions, and also thanks the referee for carefully reading the manuscript and for giving helpful comments.
Disclosure statement
No potential conflict of interest was reported by the author.