# Homomorphism of Lie rings

From Groupprops

## Definition

Suppose and are Lie rings. A **homomorphism of Lie rings** is a map such that:

- is a homomorphism of groups with respect to the additive group structures of and .
- , i.e., commutes with the Lie bracket.

In other words, a homomorphism of Lie rings is a homomorphism in the variety of Lie rings.