Tag Archives: simple rings

Structure of Semisimple Rings

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

Posted in Notes | Tagged , , , | Leave a comment

Semisimple Rings and Modules

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

Posted in Notes | Tagged , , , | Leave a comment

Introduction to Ring Theory (8)

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

Posted in Notes | Tagged , , , , , , | Leave a comment