Subring of a multiplicative Lie ring

Definition
Suppose $$L$$ is a multiplicative Lie ring. A subset $$S$$ of $$L$$ is termed a subring of $$L$$ if both the following conditions hold:


 * $$S$$ is a subgroup of the underlying group of $$L$$.
 * $$S$$ is closed under the bracket operation: $$\{x,y \} \in S$$ for all $$x,y \in S$$.