# Characteristic derivation-invariant Lie subring

From Groupprops

This page describes a Lie subring property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subring of a Lie ring and derivation-invariant Lie subring

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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: characteristic subgroup

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## Definition

A subring of a Lie ring is termed a **characteristic derivation-invariant Lie subring** if it is both a characteristic subring (i.e., it is invariant under all automorphisms of the Lie ring) and a derivation-invariant Lie subring (i.e., it is invariant under all derivations of the Lie ring).