Derivation-invariant subring of ideal implies ideal

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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