CS-Baer Lie ring

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


 * $$L$$ is a defining ingredient::Lie ring of nilpotency class two, i.e., the derived subring $$[L,L]$$ is contained in the center $$Z(L)$$.
 * There is a Lie subring $$K$$ of $$L$$ such that $$[L,L] \le K \le Z(L)$$ and such that every element of $$[L,L]$$ has a unique half in $$K$$. Note that since $$Z(L)$$ is an abelian Lie ring, any additive subgroup of $$Z(L)$$ gives a Lie subring contained in $$Z(L)$$.