# Lie ring of derivations

From Groupprops

## Definition

Let be a Lie ring. The **Lie ring of derivations** of , denoted , is defined as a Lie ring whose elements are the derivations of , where:

- The additive structure is given by pointwise addition. Thus, the zero of this ring is the zero derivation.
- The Lie bracket is given by the commutator. Thus, if are derivations, their Lie bracket is defined as:

.

In other words, .