LCS-Baer Lie ring

Definition
A LCS-Baer Lie ring is a Lie ring that satisfies the following condition: it is a defining ingredient::Lie ring of nilpotency class two and the additive group of its defining ingredient::derived subring is uniquely 2-divisible, i.e., every element in the derived subring has a unique half.

This is a slight generalization of Baer Lie ring, where we require the whole Lie ring to be uniquely 2-divisible.