Fully invariant derivation-invariant Lie subring

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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

Definition

Suppose L is a Lie ring and S is a subring of L. We say that S is a fully invariant derivation-invariant Lie subring of L if S is a fully invariant Lie subring and is also a derivation-invariant Lie subring of L.

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 Fully invariant subgroup of additive group of Lie ring is derivation-invariant and fully invariant |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
fully invariant ideal of a Lie ring |FULL LIST, MORE INFO
fully invariant Lie subring Fully invariant ideal of a Lie ring|FULL LIST, MORE INFO
derivation-invariant Lie subring |FULL LIST, MORE INFO