Sub-ideal of a Lie ring

Definition
A subring $$S$$ of a Lie ring $$L$$ is a subring such that there exists an ascending chain of subrings:

$$S = S_0 \subseteq S_1 \subseteq S_2 \subseteq \dots \subseteq S_n = L$$

such that each $$S_i$$ is an ideal in $$L$$.

Stronger properties

 * Weaker than::Ideal of a Lie ring
 * Weaker than::2-sub-ideal of a Lie ring