# semisimple

## EnglishEdit

### EtymologyEdit

### AdjectiveEdit

**semisimple** (*not comparable*)

- (mathematics, of a module) In which each submodule is a direct summand.
- (mathematics, of an algebra or ring) diagonalizable.
- (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.

## FrenchEdit

### Alternative formsEdit

### EtymologyEdit

### AdjectiveEdit

**semisimple** (*plural* **semisimples**)