On the Equality of Triple Derivations and Derivations of Lie Algebras

چکیده مقاله

Let L be a Lie algebra over a commutative ring with identity. In the present paper under some mild conditions on L, it is proved that every triple derivation of L is a derivation. In particular, we show that in perfect Lie algebras and free Lie algebras every triple derivation is a derivation. Finally we apply our results to show that every triple derivation of the Lie algebra of block upper triangular matrices is a derivation.