Finitely generated 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 Lie ring $L$ is termed a finitely generated Lie ring if there is a finite subset $S$ of $L$ that is a generating set for $L$. Explicitly, this means that $S$ is not contained in any proper Lie subring of $L$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
finite Lie ring				|FULL LIST, MORE INFO
Lie ring whose additive group is finitely generated				|FULL LIST, MORE INFO