Complete Lie ring

This article defines a Lie ring property: a property that can be evaluated to true/false for any Lie ring.
View a complete list of properties of Lie rings
VIEW RELATED: Lie ring property implications | Lie ring property non-implications |Lie ring metaproperty satisfactions | Lie ring metaproperty dissatisfactions | Lie ring property satisfactions | Lie ring property dissatisfactions

ANALOGY: This is an analogue in Lie ring of a property encountered in group. Specifically, it is a Lie ring property analogous to the group property: complete group
View other analogues of complete group | View other analogues in Lie rings of group properties (OR, View as a tabulated list)

Definition

A Lie ring is termed complete if it is centerless and every derivation of it is inner. Equivalently a Lie ring is termed complete if the natural map from it to its Lie ring of derivations, is an isomorphism.