Definition:Lie Algebra

Definition
Let $\left({A_R, \oplus}\right)$ be an algebra over a ring.

Then $\left({A_R, \oplus}\right)$ is a Lie algebra :


 * $\forall a \in A_R: a^2 = 0$


 * $\forall a, b, c \in A_R: a \left({b c}\right) + b \left({c a}\right) + c \left({a b}\right) = 0$