different between submodule vs semisimple

English

Etymology

sub- +? module

Noun

submodule (plural submodules)

1. A module making up part of a larger module.

   The first-year English Literature module consists of three submodules.

2. (algebra) A module contained in a larger module, both over the same ring, such that the ring multiplication in the former is a restriction of that in the latter.

English

Etymology

semi- +? simple

Adjective

semisimple (not comparable)

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

French

Alternative forms

• semi-simple

Etymology

semi- +? simple

Adjective

semisimple (plural semisimples)

1. (mathematics) semisimple