Baer Malcev ring

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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.