# Baer Lie ring

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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 ringsVIEW 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 satisfying the following two conditions:

- is a nilpotent Lie ring and has nilpotency class at most two. In other words, is an abelian Lie ring, where is the center of .
- The additive group of is powered over the prime 2. In other words, is uniquely 2-divisible, i.e., for every , there is a unique element such that , where means .

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