(1,1)-bi-Engel Lie ring

Definition
A Lie ring $$L$$ is termed a (1,1)-bi-Engel Lie ring if it satisfies the following:

$$u,x],[u,y = 0 \ \forall \ u,x,y \in L$$

For more, see bi-Engel Lie ring.

Facts

 * (1,1)-bi-Engel and 2-torsion-free implies metabelian