Inner automorphism of a Lie ring

Definition
Suppose $$L$$ is a Lie ring. We call an automorphism $$\sigma$$ of $$L$$ a basic inner automorphism of $$L$$ if $$\sigma = \exp(d)$$ where $$d$$ is an defining ingredient::inner derivation of $$L$$ (i.e., the adjoint action by some element) that is also an defining ingredient::exponentiable derivation.

We call an automorphism of $$L$$ an inner automorphism if it can be expressed as a product of basic inner automorphisms. Note that the inverse of a basic inner automorphism is basic inner, so we see that the inner automorphisms are precisely the automorphisms in the subgroup generated by the basic inner automorphisms.