# Fully invariant derivation-invariant Lie subring

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