Nonlinear lie-type derivations on full matrix algebras

Let R be a 2-torsion free commutative ring with identity and M_n(R) (n ≥ 2) be the full matrix algebra over R. In this note, we prove that every nonlinear Lie triple derivation on M_n(R) is of the standard form, i. e. it can be expressed as a sum of an inner derivation, an additive induced derivation and a functional annihilating all second commutators of M_n(R). A open conjecture about Lie n-derivations is posed at the end of this note.