Lazard-divided Lie ideal

Definition
Suppose $$L$$ is a defining ingredient::Lazard-divided Lie ring. A subset $$S$$ of $$L$$ is termed a Lazard-divided Lie ideal in $$L$$ if $$S$$ is an ideal of $$L$$ and, for every prime number $$p$$, and any $$x_1,x_2,\dots,x_p \in L$$ such that at least one $$x_i$$ is in $$S$$, the result $$t_p(x_1,x_2,\dots,x_p)$$ is in $$S$$ (where $$t_p$$ denotes the Lazard division operation).

Weaker properties

 * Lazard-divided Lie subring