LCS-Lazard 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.
View a complete list of properties of Lie rings
VIEW RELATED: Lie ring property implications | Lie ring property non-implications |Lie ring metaproperty satisfactions | Lie ring metaproperty dissatisfactions | Lie ring property satisfactions | Lie ring property dissatisfactions

Definition

A LCS-Lazard Lie ring is a Lie ring L satisfying the following two properties:

  1. It is a 3-locally nilpotent Lie ring, i.e., any three elements of the Lie ring generate a nilpotent subring.
  2. Its 3-local lower central series powering threshold is \infty.

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