Noncommutative Algebra /
This book is an introduction to the theory of noncommutative algebra. The core of the book is suitable for a one-semester course for graduate students. The approach, which is more homological than ring-theoretic, clarifies the subject and its relation to other important areas of mathematics, includi...
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1993.
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| Series: | Graduate texts in mathematics ;
144. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | This book is an introduction to the theory of noncommutative algebra. The core of the book is suitable for a one-semester course for graduate students. The approach, which is more homological than ring-theoretic, clarifies the subject and its relation to other important areas of mathematics, including K-theory, homological algebra, and representation theory. The main part of the book begins with a brief review of background material; the first chapter covers the basics of semisimple modules and rings, including the Wedderburn structure theorem; chapter two discusses the Jacobson radical, giving several different views; chapter three develops the theory of central simple algebras, including proofs of the Skolem-Noether and Double Centralizer theorems, with two famous theorems of Wedderburn and Frobenius given as applications; and chapter four is an introduction to the Brauer group and its relation to cohomology. The remaining chapters introduce several special topics: the notion of primitive ring is developed along lines parallel to that of simple rings; the representation theory of finite groups is combined with the Wedderburn Structure Theorem to prove Burnside's Theorem; the global dimension of a ring is studied using Kaplansky's elementary point of view; and the Brauer group of a commutative ring is introduced. Problems throughout the book provide concrete examples, applications and amplifications of the text; a set of supplementary problems explores further topics and can serve as starting points for student projects. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xiv, 226 pages) |
| ISBN: | 9781461208891 (electronic bk.) 1461208890 (electronic bk.) |
| ISSN: | 0072-5285 ; |