Finite Lie ring

From Groupprops

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