# Verbal Lie subring

From Groupprops

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 propertiesVIEW 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 |