Cocentral Lie subring

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

Definition

A subring $A$ of a Lie ring $L$ is termed a cocentral Lie subring if $A+Z(L)=L$, where $Z(L)$ is the center of $L$.

Relation with other properties

Weaker properties

• Central factor of a Lie ring
• Ideal of a Lie ring