Sub-ideal of a Lie ring

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

S = S_0 \subseteq S_1 \subseteq S_2 \subseteq \dots \subseteq S_n = L

such that each S_i is an ideal in L.

Relation with other properties

Stronger properties