Semisimple Module
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 which 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 semisimpl...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 which 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 direct products of matrix rings.
