Finite Lie ring
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 finite Lie ring if its underlying set is a finite set, or equivalently, if its additive group is a finite group and thus a finite abelian group.
Relation with other properties
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| finitely generated Lie ring | |FULL LIST, MORE INFO | |||
| Lie ring whose additive group is finitely generated | |FULL LIST, MORE INFO |