Wiktionary
semisimple
a. 1 (context mathematics of a module English) In which each submodule is a direct summand. 2 (context mathematics of an algebra or ring English) (rfdef lang=en topic=algebra) 3 (context mathematics of an operator or matrix English) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree. 4 (context mathematics of a Lie algebra English) Being a direct sum of simple Lie algebras. 5 (context mathematics of an algebraic group English) Being a linear algebraic group whose radical of the identity component is trivial.