Complemented ideal of a Lie ring

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

Definition

Definition with symbols

Suppose $L$ is a Lie ring and $A$ is a subring of $L$. We say that $A$ is a complemented ideal of $L$ if there exists a subring $B$ of $L$ such that $A\cap B=0$ and $A+B=L$.

Relation with other properties

Stronger properties

• Direct factor of a Lie ring

Weaker properties

• Ideal of a Lie ring