# Self-derivation-invariant Lie subring

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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 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

## Definition

A Lie subring of a Lie ring is termed a **self-derivation-invariant Lie subring** if the following holds. Consider a map that is a derivation from the Lie subring to the whole Lie ring viewed as a module over it. Then, .