Abelian multiplicative Lie ring

Definition
A multiplicative Lie ring $$L$$ is termed abelian if its bracket operation is trivial, i.e., $$\{ x, y \} = 1$$ for all $$x,y \in L$$.

Note that the term abelian here does not mean that the underlying group is an abelian group. The condition that the underlying group is an abelian group makes the multiplicative Lie ring a Lie ring in the ordinary sense. The condition that the underlying group is an abelian group and the Lie bracket is trivial makes the multiplicative Lie ring an abelian Lie ring.