Simple Lie ring

This article defines a Lie ring property: a property that can be evaluated to true/false for any Lie ring.
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VIEW RELATED: Lie ring property implications | Lie ring property non-implications |Lie ring metaproperty satisfactions | Lie ring metaproperty dissatisfactions | Lie ring property satisfactions | Lie ring property dissatisfactions

ANALOGY: This is an analogue in Lie ring of a property encountered in group. Specifically, it is a Lie ring property analogous to the group property: simple group
View other analogues of simple group | View other analogues in Lie rings of group properties (OR, View as a tabulated list)

Definition

A Lie ring is said to be simple if it has no proper nonzero ideals. A related notion is that of simple Lie algebra. Note that while any simple Lie ring which is also a Lie algebra over a field must be a simple Lie algebra, there could be simple Lie algebras which are not simple as Lie rings. For instance, any one-dimensional Lie algebra over a field is simple as a Lie algebra, but not as a Lie ring.