Ideal-large Lie subring

This article describes a Lie subring property: a property that can be evaluated for a subring of a Lie ring
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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: normality-large subgroup
View other analogues of normality-large subgroup | View other analogues in Lie rings of subgroup properties (OR, View as a tabulated list)

Definition

Let $L$ be a Lie ring. A subring $S$ of $L$ is termed an ideal-large Lie subring if, for any nonzero ideal $I$ of $L$, $S\cap I$ is also an ideal of $L$.

Facts

• Nilpotent implies center is ideal-large