Semisimple Definition

(mathematics, of a module) In which each submodule is a direct summand.

(mathematics, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.

(mathematics, of a Lie algebra) Being a direct sum of simple Lie algebras.

(mathematics, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial.