# Ideal property is not transitive for Lie rings

From Groupprops

This article gives the statement, and possibly proof, of a Lie subring property (i.e., ideal of a Lie ring)notsatisfying a Lie subring metaproperty (i.e., transitive Lie subring property).

View all Lie subring metaproperty dissatisfactions | View all Lie subring metaproperty satisfactions|Get help on looking up metaproperty (dis)satisfactions for Lie subring properties

Get more facts about ideal of a Lie ring|Get more facts about transitive Lie subring property|

ANALOGY: This is an analogue in Lie rings of a fact encountered in group. The old fact is: normality is not transitive.

View other analogues of normality is not transitive|View other analogues from group to Lie ring (OR, View as a tabulated list)

## Contents

## Statement

It is possible to have a Lie ring , an ideal of , and an ideal of , such that is *not* an ideal of .

## Related facts

### Related facts about Lie rings

- Derivation-invariant subring of ideal implies ideal
- Left transiter of ideal is derivation-invariant subring
- Derivation-invariance is transitive

### Analogues in other algebraic structures

- Normality is not transitive (for groups)