3-locally nilpotent Lie ring

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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 L is termed a 3-locally nilpotent Lie ring if the subring of L generated by any subset of L 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 LCS-Lazard 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 LCS-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