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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
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
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 advanced, cramer's rule, determinants, matrix rings, ring theory, rings, simple rings
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