Verbal 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
ANALOGY: This is an analogue in Lie ring of a property encountered in group. Specifically, it is a Lie subring property analogous to the subgroup property: verbal subgroup
View other analogues of verbal subgroup | View other analogues in Lie rings of subgroup properties (OR, View as a tabulated list)

Definition

A subring of a Lie ring is termed a verbal Lie subring if there is a collection of words involving the Lie ring operations such that the subring is generated by all elements of the Lie ring obtained by substituting elements of the Lie ring into these words.

Relation with other properties

Weaker properties

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