Derivation of a Lazard-divided Lie ring

Definition
Suppose $$L$$ is a Lazard-divided Lie ring. A set map $$d: L \to L$$is termed a derivation of $$L$$ if it satisfies the following conditions:


 * $$d$$ is a derivation of $$L$$
 * For any prime number $$p$$, we have the following, where $$t_p$$ denotes the Lazard division operation:

$$d(t_p(x_1,x_2,\dots,x_p)) = \sum_{i=1}^p t_p(x_1,x_2,\dots,x_{i-1},dx_i,x_{i+1},\dots,x_p)$$

Related notions

 * Derivation of a Lie ring
 * Derivation of a non-associative ring
 * Derivation with divided powers
 * Derivation with divided powers of a Lazard-divided Lie ring