# Homomorph-containing subgroup of additive group of Lie ring is self-derivation-invariant and homomorph-containing

## Statement

Suppose is a Lie ring, and is a subgroup of the additive group of such that is a homomorph-containing subgroup of . Then, the following three conditions hold:

- is a Lie subring of .
- is a self-derivation-invariant Lie subring of .
- is a homomorph-containing Lie subring of .