3-locally nilpotent 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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ANALOGY: This is an analogue in Lie ring of a property encountered in group. Specifically, it is a Lie ring property analogous to the group property: 3-locally nilpotent group
View other analogues of 3-locally nilpotent group | View other analogues in Lie rings of group properties (OR, View as a tabulated list)
Definition
A Lie ring is termed a 3-locally nilpotent Lie ring if the subring of generated by any subset of of size at most three is a nilpotent Lie ring.
If there is a common bound on the nilpotency class for all such subrings, then the smallest common bound is termed the 3-local nilpotency class.
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 | |||
| Lie ring of nilpotency class two | |FULL LIST, MORE INFO | |||
| nilpotent Lie ring | |FULL LIST, MORE INFO | |||
| LCS-Lazard Lie ring | |FULL LIST, MORE INFO | |||
| Lazard Lie ring | |FULL LIST, MORE INFO | |||
| locally nilpotent Lie ring | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Engel Lie ring | |FULL LIST, MORE INFO |