Baer Lie ring

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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.