Central ideal

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

Definition

Symbol-free definition

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

  1. It is a subgroup of the additive group and is contained in the center of the Lie ring.
  2. It is a subring and is contained in the center of the Lie ring.
  3. It is an ideal and is contained in the center of the Lie ring.

Relation with other properties

Weaker properties