# Centralizer-free ideal

From Groupprops

This page describes a Lie subring property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: centralizer-free 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: centralizer-free normal subgroup

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## Definition

A subring of a Lie ring is termed a **centralizer-free ideal** if it is both centralizer-free as a subring (in other words, its centralizer in the whole Lie ring is the zero Lie ring) and is an ideal of the Lie ring.