# Ring of differential operators on a Lie ring

Suppose $L$ is a Lie ring, and $\operatorname{Der}(L)$ is the Lie ring of derivations of $L$. The ring of differential operators of $L$ is the collection of all maps from $L$ to $L$ that can be expressed as sums and differences of the identity map and composites of derivations. This is a unital ring where: