Back Halbeinfacher Modul German Módulo semisimple Spanish مدول نیم-ساده Persian Puoliyksinkertainen moduli Finnish Module semi-simple French מודול פשוט למחצה HE 半単純加群 Japanese 반단순 가군 Korean Полупростой модуль Russian Halvenkel modul Swedish
In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring that is a semisimple module over itself is known as an Artinian semisimple ring. Some important rings, such as group rings of finite groups over fields of characteristic zero, are semisimple rings. An Artinian ring is initially understood via its largest semisimple quotient. The structure of Artinian semisimple rings is well understood by the Artin–Wedderburn theorem, which exhibits these rings as finite direct products of matrix rings.
For a group-theory analog of the same notion, see Semisimple representation.