# Fully invariant derivation-invariant 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

## Contents

## Definition

Suppose is a Lie ring and is a subring of . We say that is a **fully invariant derivation-invariant Lie subring** of if is a fully invariant Lie subring and is also a derivation-invariant Lie subring of .

## 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 |
---|---|---|---|---|

fully invariant ideal of a Lie ring | |FULL LIST, MORE INFO | |||

fully invariant Lie subring | Fully invariant ideal of a Lie ring|FULL LIST, MORE INFO | |||

derivation-invariant Lie subring | |FULL LIST, MORE INFO |