Baer Malcev ring

Definition
A Baer Malcev ring is a Malcev ring $$M$$ with muliplication $$*$$satisfying the following two conditions:


 * 1) The subring generated by any subset of size at most two has nilpotency class at most two, i.e., $$(x * y) * z = x * (y * z) = 0$$ for all $$x,y,z$$ living in a subring generated by a subset of size at mots two.
 * 2) The additive group is uniquely 2-divisible, i.e., it is powered over the prime 2.