Semisimple 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: Fitting-free group
View other analogues of Fitting-free group | View other analogues in Lie rings of group properties (OR, View as a tabulated list)

Definition

A Lie ring is termed a semisimple Lie ring or Fitting-free Lie ring if it satisfies the following equivalent conditions:

1. It has no nonzero abelian ideal.
2. It has no nonzero nilpotent ideal.
3. It has no nonzero solvable ideal.
4. Its Fitting ideal is zero.
5. Its radical is zero.

Relation with other properties

Stronger properties

• Simple non-abelian Lie ring