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