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