Baer alternating loop ring

Definition
An alternating loop ring $$L$$ with multiplication $$*$$ is termed a Baer alternating loop ring if it satisfies the following two conditions:


 * 1) The subring generated by any two elements is a 2-Engel Lie ring: addition forms a group, and any triple product is zero.
 * 2) It is uniquely 2-divisible, i.e., the additive loop is powered over the prime 2.