# Baer Lie ring

## Contents

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.