Lie subring invariant under any additive endomorphism satisfying a comultiplication condition

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This article describes a Lie subring property: a property that can be evaluated for a subring of a Lie ring
View a complete list of such properties
VIEW RELATED: Lie subring property implications | Lie subring property non-implications | Lie subring metaproperty satisfactions | Lie subring metaproperty dissatisfactions | Lie subring property satisfactions |Lie subring property dissatisfactions

Statement

Suppose L is a Lie ring and S is a Lie subring of L. We say that S is invariant under any additive endomorphism satisfying a comultiplication condition if, for any f:L \to L that is an additive endomorphism satisfying a comultiplication condition, we have f(S) \subseteq S.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
fully invariant subgroup of additive group of a Lie ring

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
fully invariant Lie subring
derivation-invariant Lie subring
characteristic subring of a Lie ring