# Derivation-invariant subring of ideal implies ideal

From Groupprops

ANALOGY: This is an analogue in Lie rings of a fact encountered in group. The old fact is: characteristic of normal implies normal.

View other analogues of characteristic of normal implies normal|View other analogues from group to Lie ring (OR, View as a tabulated list)

## Statement

Suppose is a Lie ring, is an ideal of , and is a derivation-invariant subring of . Then, is also an ideal of .

## Related facts

### Analogues

- Characteristic of normal implies normal: A characteristic subgroup of a normal subgroup is normal. Here, characteristic subgroup plays the role analogous to derivation-invariant subring, and normal subgroup plays a role analogous to ideal.