Complemented ideal of a Lie ring

Definition with symbols
Suppose $$L$$ is a Lie ring and $$A$$ is a subring of $$L$$. We say that $$A$$ is a complemented ideal of $$L$$ if there exists a subring $$B$$ of $$L$$ such that $$A \cap B = 0$$ and $$A + B = L$$.

Stronger properties

 * Weaker than::Direct factor of a Lie ring

Weaker properties

 * Stronger than::Ideal of a Lie ring