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Chapter 9 Introducing Noncommutative Algebra

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Book Id: WPLBN0000673858
Format Type: PDF eBook
File Size: 350.50 KB
Reproduction Date: 2005

Title: Chapter 9 Introducing Noncommutative Algebra  
Language: English
Subject: Science., Mathematics, Logic
Publication Date:


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Chapter 9 Introducing Noncommutative Algebra. (n.d.). Chapter 9 Introducing Noncommutative Algebra. Retrieved from

Mathematics document containing theorems and formulas.

Excerpt: We will discuss noncommutative rings and their modules, concentrating on two fundamental results, the Wedderburn structure theorem and Maschke?s theorem. Further insight into the structure of rings will be provided by the Jacobson radical. 9.1 Semisimple Modules A vector space is the direct sum of one-dimensional subspaces (each subspace consists of scalar multiples of a basis vector). A one-dimensional space is simple in the sense that it does not have a nontrivial proper subspace. Thus any vector space is a direct sum of simple subspaces. We examine those modules which behave in a similar manner.


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