Nilpotent Lie cring

Definition
A nilpotent Lie cring is a Lie cring $$L$$ such that there exists a nonnegative integer $$c$$ with the property that for any elements $$x_1,x_2,\dots,x_{c+1} \in L$$ (with the elements possibly equal to each other), we have:

$$x_1 * (x_2 * (x_3 * ( \dots (x_c * x_{c+1}))\dots ) = 0$$