Baer alternating loop ring

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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.