# Fully invariant ideal of a Lie ring

This article describes a Lie subring property: a property that can be evaluated for a subring 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: fully invariant subgroup
View other analogues of fully invariant subgroup | View other analogues in Lie rings of subgroup properties (OR, View as a tabulated list)

## Definition

Suppose $L$ is a Lie ring and $S$ is a subring of $L$. We say that $S$ is a fully invariant ideal of $L$ if $S$ is an ideal of $L$ and $S$ is a fully invariant Lie subring of $L$, i.e., it is invariant under all the Lie ring endomorphisms of $L$.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
fully invariant derivation-invariant Lie subring fully invariant and derivation-invariant via derivation-invariant implies ideal |FULL LIST, MORE INFO
fully invariant subgroup of additive group of a Lie ring (via fully invariant derivation-invariant Lie subring) Fully invariant derivation-invariant Lie subring|FULL LIST, MORE INFO