Baer Lie ring

Definition
A Baer Lie ring is a Lie ring $$L$$ satisfying the following two conditions:


 * 1) $$L$$ is a nilpotent Lie ring and has nilpotency class at most two. In other words, $$L/Z(L)$$ is an abelian Lie ring, where $$Z(L)$$ is the center of $$L$$.
 * 2) The additive group of $$L$$ is powered over the prime 2. In other words, $$L$$ is uniquely 2-divisible, i.e., for every $$a \in L$$, there is a unique element $$b \in L$$ such that $$2b = a$$, where $$2b$$ means $$b + b$$.

A Baer Lie ring is a Lie ring that can participate as the Lie ring side of a Baer correspondence.