semisimple

Meanings

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. Semiprimitive: having trivial Jacobson radical.
6. For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
7. Being a direct sum of simple Lie algebras.
8. Being a direct sum of simple representations (also known as irreducible representations).
9. Being a linear algebraic group whose radical of the identity component is trivial.

Etymology

From semi- + simple.