Nilpotent Lie ring

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.

Stronger properties

 * Weaker than::Abelian Lie ring

Weaker properties

 * Stronger than::Solvable Lie ring