Ideal of a multiplicative Lie ring

Definition
Suppose $$L$$ is a multiplicative Lie ring. A subset $$I$$ of $$L$$ is termed an ideal of $$L$$ if it satisfies 'both the following two conditions:


 * $$I$$ is a normal subgroup of the underlying group of $$L$$.
 * $$\{ x,y \} \in I$$ for all $$x \in I, y \in L$$.