# Lie subring whose sum with any subring is a subring

This article describes a Lie subring property: a property that can be evaluated for a subring of a Lie ring
View a complete list of such properties
VIEW RELATED: Lie subring property implications | Lie subring property non-implications | Lie subring metaproperty satisfactions | Lie subring metaproperty dissatisfactions | Lie subring property satisfactions |Lie subring property dissatisfactions
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: permutable subgroup
View other analogues of permutable 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 Lie subring whose sum with any subring is a subring if, for any Lie subring $A$ of $L$, the subgroup $S + A$ is also a Lie subring of $L$.

## Metaproperties

A join of Lie subrings with this property also has this property.