# Derivation-invariant direct factor

From Groupprops

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

View other analogues of characteristic direct factor | 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-invariant direct factor** if it is both derivation-invariant and a direct factor of the whole ring.