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Introduction to Noncommutative Algebra

  • Matej Brešar

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxxvii
  2. Matej Brešar
    Pages 1-23
  3. Matej Brešar
    Pages 25-51
  4. Matej Brešar
    Pages 53-77
  5. Matej Brešar
    Pages 79-106
  6. Matej Brešar
    Pages 107-136
  7. Matej Brešar
    Pages 137-161
  8. Matej Brešar
    Pages 163-191
  9. Back Matter
    Pages 193-199

About this book

Introduction

Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients.

Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.

Keywords

Division Ring Module Noncommutative Rings and Algebras Polynomial Identity Prime Ring Primitive Ring Radical Rings of Quotients Semiprime Ring Simple Ring Structure of Rings and Algebras Tensor Product

Authors and affiliations

  • Matej Brešar
    • 1
  1. 1.University of LjubljanaLjubljanaSlovenia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-08693-4
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-08692-7
  • Online ISBN 978-3-319-08693-4
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site