Semisimple Rings and Modules

The main result of this chapter is the Artin-Wedderburn theorem, which constructs the rings traditionally called semisimple Artinian. Wedderburn called a ring semisimple when it has no nonzero nilpotent ideal and considered in [1907] the particular case of finite-dimensional ring extensions of C. Artin [1927] showed that Wedderburn’s result depends only on the descending chain condition; this gave birth to noncommutative ring theory.