# Characteristicity is transitive for Lie rings

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This article gives the statement, and possibly proof, of a Lie subring property (i.e., characteristic subring of a Lie ring) satisfying a Lie subring metaproperty (i.e., transitive Lie subring property)

View all Lie subring metaproperty satisfactions | View all Lie subring metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for Lie subring properties

Get more facts about characteristic subring of a Lie ring |Get facts that use property satisfaction of characteristic subring of a Lie ring | Get facts that use property satisfaction of characteristic subring of a Lie ring|Get more facts about transitive Lie subring property

ANALOGY: This is an analogue in Lie rings of a fact encountered in group. The old fact is: characteristicity is transitive.

Another analogue to the same fact, in the same new context, is: derivation-invariance is transitive

View other analogues of characteristicity is transitive|View other analogues from group to Lie ring (OR, View as a tabulated list)

## Statement

If are Lie rings such that is a characteristic subring of and is a characteristic subring of , then is a characteristic subring of .