Central factor of a Lie ring

Definition
A subring of a Lie ring is termed a central factor if it satisfies the following equivalent conditions:


 * 1) Every defining ingredient::inner derivation of the whole Lie ring restricts to an inner derivation of the subring.
 * 2) The whole Lie ring is the sum of the subring and its centralizer.

Analogues in other algebraic structures

 * Central factor in groups.

Stronger properties

 * Weaker than::Direct factor of a Lie ring
 * Weaker than::Central Lie subring
 * Weaker than::Cocentral Lie subring

Weaker properties

 * Stronger than::Ideal of a Lie ring