Derivation-invariant subring of ideal implies ideal

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 $L$ is a Lie ring, $A$ is an ideal of $L$, and $B$ is a derivation-invariant subring of $A$. Then, $B$ is also an ideal of $L$.

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.