Central factor 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: central factor
View other analogues of central factor | View other analogues in Lie rings of subgroup properties (OR, View as a tabulated list)

Definition

A subring of a Lie ring is termed a central factor if it satisfies the following equivalent conditions:

  1. Every inner derivation of the whole Lie ring restricts to an inner derivation of the subring.
  2. The whole Lie ring is the sum of the subring and its centralizer.

Relation with other properties

Analogues in other algebraic structures

Stronger properties

Weaker properties