Derived series of a Lie ring

Definition
Let $$L$$ be a Lie ring. The derived series of $$L$$ is defined as follows:

L^{(0)} = L</math.

and:

$$L^{(n + 1)} = [L^{(n)},L^{(n)}]$$

In other words, each member of the derived series is obtained as the derived subring of the previous member.