Finite Lie ring

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.

Weaker properties
{| class="sortable" border="1" ! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
 * Stronger than::finitely generated Lie ring || || || ||
 * Stronger than::Lie ring whose additive group is finitely generated || || || ||
 * Stronger than::Lie ring whose additive group is finitely generated || || || ||
 * Stronger than::Lie ring whose additive group is finitely generated || || || ||