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
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 rings of the subgroup property:
View other analogues of normality | View other analogues in Lie rings of subgroup properties

Definition

A subset $B$ of a Lie ring $A$ is termed an ideal in $A$ if $B$ is additively a subgroup and $[x,y]\in B$ whenever $x\in B$ and $y\in A$.