Nilpotent 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

Symbol-free definition

A Lie ring is termed a nilpotent Lie ring if it satisfies the following equivalent conditions:

1. Its upper central series stabilizes after a finite length at the whole Lie ring.
2. Its lower central series stabilizes after a finite length at the zero subring.
3. It has a central series.

Relation with other properties

Stronger properties

• Abelian Lie ring

Weaker properties

• Solvable Lie ring