# Lie ring generated by abelian ideals

From Groupprops

This article defines a Lie ring property: a property that can be evaluated to true/false for any Lie ring.

View a complete list of properties of Lie ringsVIEW 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.