LCS-Lazard 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-Lazard Lie ring is a Lie ring satisfying the following two properties:
- It is a 3-locally nilpotent Lie ring, i.e., any three elements of the Lie ring generate a nilpotent subring.
- Its 3-local lower central series powering threshold is .
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| abelian Lie ring | Lie bracket is trivial | |FULL LIST, MORE INFO | ||
| Baer Lie ring | uniquely 2-divisible and class at most two | |FULL LIST, MORE INFO | ||
| LCS-Baer Lie ring | |FULL LIST, MORE INFO | |||
| Lazard Lie ring | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| 3-locally nilpotent Lie ring |