Lie subring whose sum with any subring is a subring

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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.

Relation with other properties

Stronger properties

Metaproperties

Template:Join-closed Lie subring property

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