Derivation-faithful 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

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: automorphism-faithful subgroup
An alternative analogue of automorphism-faithful subgroup in Lie ring is: automorphism-faithful Lie subring
View other analogues of automorphism-faithful 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 derivation-faithful if every nonzero derivation of the whole Lie ring that sends the subring to itself restricts to a nonzero derivation of the subring.

Relation with other properties

Stronger properties

• Centralizer-free ideal: For full proof, refer: Centralizer-free ideal implies derivation-faithful