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Graduate Texts In Mathematics 144:noncommutative Algebra by Benson Farb, R. Keith Dennis (auth.) is a nonfiction available to read on EtoBox.
What is Graduate Texts In Mathematics 144:noncommutative Algebra about?
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 glob
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It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Benson Farb, R. Keith Dennis (auth.)
- Publisher
- Springer-Verlag New York
- Published
- 1993
- Language
- EN
- ISBN
- 9780387940571
- Category
- nonfiction
- Subjects
- Mathematics, Stem