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 | |FULL LIST, MORE INFO | |||
| Lie ring of nilpotency class two | |FULL LIST, MORE INFO | |||
| nilpotent Lie ring | |FULL LIST, MORE INFO |