Semisimple module

Summary

A semisimple module is a module that is a direct sum of simple modules. Equivalently, every submodule of it has a complement, so the module splits as cleanly as a vector space. Semisimple modules are the modules for which linear algebra works best. The rings all of whose modules are semisimple are described completely by the Artin–Wedderburn theorem. By Maschke's theorem, every representation of a finite group over a field of characteristic zero is semisimple.