Direct factor 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 direct factor of $$L$$ if $$A$$ is an ideal of $$L$$ and there exists an ideal $$B$$ of $$L$$ such that $$A \cap B = 0$$ and $$A + B = L$$.

Weaker properties

 * Stronger than::Central factor of a Lie ring
 * Stronger than::Complemented ideal of a Lie ring
 * Stronger than::Ideal of a Lie ring