Derivation-faithful ideal

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This page describes a Lie subring property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: derivation-faithful Lie subring and ideal of a Lie ring
View other Lie subring property conjunctions | view all properties of subrings in Lie rings
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 normal subgroup
View other analogues of automorphism-faithful normal 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 a derivation-faithful ideal if it is both an ideal and a derivation-faithful subring, i.e., any 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