Ring theory | Module theory

Semisimple module

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. (Wikipedia).

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Free ebook http://tinyurl.com/EngMathYT An example on how to integrate using partial fractions.

From playlist A second course in university calculus.

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Related pages

Injective module | Semiprimitive ring | Semisimple algebra | Vector space | Division ring | Subring | Direct sum of modules | Homological algebra | Kasch ring | Maschke's theorem | Artinian ring | Jacobson radical | Indecomposable module | Finite group | Direct product | Matrix ring | Projective module | Group ring | Socle (mathematics) | Characteristic (algebra) | Mathematics | Von Neumann regular ring | Field (mathematics) | Ring homomorphism | Simple module | Noetherian ring | Reduced ring | Ring (mathematics) | Endomorphism ring | Radical of a module | Direct sum | Weyl algebra | Abstract algebra | Semisimple representation | Domain (ring theory) | Finitely generated module | Endomorphism | Abelian group | Module (mathematics)