Taghavi et al. in [TAGHAVI, A.|ROHI, H.|DARVISH, V.: Non-linear -Jordan derivations on von Neumann algebras, Linear Multilinear Algebra 64 (2016), 426{439] proved that the map : A ! A which satis es the following condition (A B) = (A) B + A (B) where A B = AB + BA for every A;B 2 A is an additive -derivation. In this short note, we prove that when A is a prime -algebras and : A ! A satis es the above condition, then is -additive. Moreover, if (iI) is self-adjoint then is derivation.
