Lie ring generated by abelian ideals

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: group generated by abelian normal subgroups
View other analogues of group generated by abelian normal subgroups | View other analogues in Lie rings of group properties (OR, View as a tabulated list)

Definition

A Lie ring is termed a Lie ring generated by abelian ideals if it is generated as a Lie ring by its abelian ideals.