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Semisimple Rings and Modules

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Part of the Graduate Texts in Mathematics book series (GTM,volume 242)

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.

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(2007). Semisimple Rings and Modules. In: Abstract Algebra. Graduate Texts in Mathematics, vol 242. Springer, New York, NY. https://doi.org/10.1007/978-0-387-71568-1_9

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