Lie subring invariant under any derivation with partial divided Leibniz condition powers

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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 Lie subring of L. We say that S is invariant under any derivation with partial divided Leibniz condition powers if the following holds: for any positive integer m and any derivation with divided Leibniz condition powers up to m for L given by d^{(1)}, d^{(2)}, \dots, d^{(m)}, we have d^{(i)}(S) \subseteq S for all i \in \{ 1,2,\dots,m\}.

Relation with other properties

Weaker properties

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