Self-derivation-invariant Lie subring

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Self-derivation-invariant Lie subring, all facts related to Self-derivation-invariant Lie subring) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

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

Definition

A Lie subring $A$ of a Lie ring $L$ is termed a self-derivation-invariant Lie subring if the following holds. Consider a map $d:A\to L$ that is a derivation from the Lie subring to the whole Lie ring viewed as a module over it. Then, $d(A)\subseteq A$.

Relation with other properties

Weaker properties

• Derivation-invariant Lie subring
• Ideal of a Lie ring

Facts

• Homomorph-containing subgroup of additive group of Lie ring is self-derivation-invariant and homomorph-containing