Baer Lie ring

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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a Lie ring property: a property that can be evaluated to true/false for any Lie ring.
View a complete list of properties of Lie rings
VIEW RELATED: Lie ring property implications | Lie ring property non-implications |Lie ring metaproperty satisfactions | Lie ring metaproperty dissatisfactions | Lie ring property satisfactions | Lie ring property dissatisfactions

Definition

A Baer Lie ring is a Lie ring L satisfying the following two conditions:

  1. L is a nilpotent Lie ring and has nilpotency class at most two. In other words, L/Z(L) is an abelian Lie ring, where Z(L) is the center of L.
  2. The additive group of L is powered over the prime 2. In other words, L is uniquely 2-divisible, i.e., for every a \in L, there is a unique element b \in L such that 2b = a, where 2b means b + b.

A Baer Lie ring is a Lie ring that can participate as the Lie ring side of a Baer correspondence.