Invariance under any derivation with partial divided Leibniz condition powers is transitive

This article gives the statement, and possibly proof, of a Lie ring property (i.e., Lie subring invariant under any derivation with partial divided Leibniz condition powers) satisfying a Lie ring metaproperty (i.e., transitive Lie subring property)
View all Lie ring metaproperty satisfactions | View all Lie ring metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for Lie ring properties
Get more facts about Lie subring invariant under any derivation with partial divided Leibniz condition powers |Get facts that use property satisfaction of Lie subring invariant under any derivation with partial divided Leibniz condition powers | Get facts that use property satisfaction of Lie subring invariant under any derivation with partial divided Leibniz condition powers|Get more facts about transitive Lie subring property

Statement

Suppose $L$ is a Lie ring and $A,B$ are Lie subrings of $L$ with $A$ contained in $B$. Suppose $B$ is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in $L$. Similarly, suppose $A$ is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in $B$.

Then, $A$ is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in $L$.

Related facts

• Derivation-invariance is transitive