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

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

## Definition

Suppose is a Lie ring and is a Lie subring of . We say that is **invariant under any derivation with partial divided Leibniz condition powers** if the following holds: for any positive integer and any derivation with divided Leibniz condition powers up to for given by , we have for all .

## 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 |