Definition
A subring of a Lie ring is termed a characteristic Lie subring or characteristic subring if it is invariant under all automorphisms of the Lie ring.
Relation with properties in related groupsRelation with other properties
Stronger properties
Property 
Meaning 
Proof of implication 
Proof of strictness (reverse implication failure) 
Intermediate notions


fully invariant Lie subring 
Lie subring that is invariant under all endomorphisms 


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fully invariant subgroup of additive group of a Lie ring 
subset of a Lie ring that is invariant under all endomorphisms of the additive group of the Lie ring 


Fully invariant Lie subring, Fully invariant ideal of a Lie ring, Lie subring invariant under any additive endomorphism satisfying a comultiplication conditionFULL LIST, MORE INFO

verbal Lie subring 
generated by a set of words using the Lie operations 


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marginal Lie subring 



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strictly characteristic Lie subring 



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injective endomorphisminvariant Lie subring 



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characteristic ideal of a Lie ring 
characteristic and also an ideal 


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characteristic derivationinvariant Lie subring 
characteristic and also a derivationinvariant Lie subring 


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Incomparable properties
Metaproperties