Lie ring whose additive group is finitely generated
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 is termed a Lie ring whose additive group is finitely generated if the additive group of 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 |