# Sub-ideal of a Lie ring

From Groupprops

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 propertiesVIEW 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: subnormal subgroup

View other analogues of subnormal subgroup | View other analogues in Lie rings of subgroup properties (OR, View as a tabulated list)

## Definition

A subring of a Lie ring is a subring such that there exists an ascending chain of subrings:

such that each is an ideal in .