Exponentiable derivation

Definition
Suppose $$R$$ is a non-associative ring and $$d$$ is a derivation on $$R$$. We say that $$d$$ is an exponentiable derivation if it satisfies the following three conditions:


 * 1) $$d$$ is locally nilpotent, i.e., for every $$x \in R$$, there exists a natural number $$n$$, possibly dependent upon $$x$$, such that $$d^n(x) = 0$$.
 * 2) $$d$$ is an infinitely powered endomorphism of the additive structure of $$R$$, i.e., for all natural numbers $$n$$, $$d^n(R)$$ is powered for all primes less than or equal to $$n$$.
 * 3) The exponential of $$d$$, which can be defined because of (1) and (2), is an automorphism of $$R$$.

Facts

 * Exponential of derivation is automorphism under suitable nilpotency assumptions