Tag Archives: simple rings

Structure of Semisimple Rings

Posted on December 31, 2014 by limsup

It turns out there is a nice classification for semisimple rings. Theorem. Any semisimple ring R is a finite product: where each is a division ring and is the ring of n × n matrices with entries in D. Furthermore, the … Continue reading →

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Semisimple Rings and Modules

Posted on December 30, 2014 by limsup

After discussing simple modules, the next best thing is to look at semisimple modules, which are just direct sums of simple modules. Here’s a summary of the results we’ll prove: A module is semisimple iff it is a sum of simple … Continue reading →

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Introduction to Ring Theory (8)

Posted on October 31, 2012 by limsup

Matrix Rings In this post, we’ll be entering the matrix. Let R be a ring. The ring Mn×n(R) is the set of matrices whose entries are elements of R, where the addition and multiplication operations are given by the usual matrix addition … Continue reading →

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