Semisimple Lie ring

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 defining ingredient::abelian ideal.
 * 2) It has no nonzero defining ingredient::nilpotent ideal.
 * 3) It has no nonzero defining ingredient::solvable ideal.
 * 4) Its defining ingredient::Fitting ideal is zero.
 * 5) Its radical is zero.

Stronger properties

 * Weaker than::Simple non-abelian Lie ring