Lie ring whose additive group is finitely generated

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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 Lie ring L is termed a Lie ring whose additive group is finitely generated if the additive group of L is a finitely generated group, or equivalently, a finitely generated abelian group.

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
finitely generated abelian Lie ring |FULL LIST, MORE INFO
finitely generated nilpotent Lie ring |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finitely generated Lie ring