semisimple

adjective9

1. •
   In any of several technical senses, decomposable into sub-objects that have a simple structure.
2. •
   Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
3. •
   In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
4. •
   Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
5. •
   For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
6. •
   Being a direct sum of simple Lie algebras.
7. •
   Being a direct sum of simple representations (also known as irreducible representations).
8. •
   Being a linear algebraic group whose radical of the identity component is trivial.
9. •
   (nonstandard) Semiprimitive: having trivial Jacobson radical.