# LCS-Baer Lie ring

This article defines a Lie ring property: a property that can be evaluated to true/false for any Lie ring.
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## Definition

A LCS-Baer Lie ring is a Lie ring that satisfies the following condition: it is a Lie ring of nilpotency class two and the additive group of its derived subring is uniquely 2-divisible, i.e., every element in the derived subring has a unique half.

This is a slight generalization of Baer Lie ring, where we require the whole Lie ring to be uniquely 2-divisible.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
abelian Lie ring |FULL LIST, MORE INFO
Baer Lie ring uniquely 2-divisible Lie ring of class at most two |FULL LIST, MORE INFO

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
CS-Baer Lie ring |FULL LIST, MORE INFO
Lie ring whose bracket is the double of a Lie bracket giving nilpotency class two CS-Baer Lie ring|FULL LIST, MORE INFO
Lie ring of nilpotency class two Lie ring arising as the double of a class two Lie cring, Lie ring arising as the skew of a class two near-Lie cring, Lie ring whose bracket is the double of a Lie bracket giving nilpotency class two|FULL LIST, MORE INFO
nilpotent Lie ring |FULL LIST, MORE INFO