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