Associative Algebras

  • Richard S. Pierce

Part of the Graduate Texts in Mathematics book series (GTM, volume 88)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Richard S. Pierce
    Pages 1-20
  3. Richard S. Pierce
    Pages 21-39
  4. Richard S. Pierce
    Pages 40-54
  5. Richard S. Pierce
    Pages 55-71
  6. Richard S. Pierce
    Pages 72-87
  7. Richard S. Pierce
    Pages 88-107
  8. Richard S. Pierce
    Pages 108-125
  9. Richard S. Pierce
    Pages 126-156
  10. Richard S. Pierce
    Pages 157-178
  11. Richard S. Pierce
    Pages 179-195
  12. Richard S. Pierce
    Pages 196-217
  13. Richard S. Pierce
    Pages 218-233
  14. Richard S. Pierce
    Pages 234-249
  15. Richard S. Pierce
    Pages 250-275
  16. Richard S. Pierce
    Pages 276-293
  17. Richard S. Pierce
    Pages 294-313
  18. Richard S. Pierce
    Pages 314-341
  19. Richard S. Pierce
    Pages 342-365
  20. Richard S. Pierce
    Pages 366-394

About this book

Introduction

For many people there is life after 40; for some mathematicians there is algebra after Galois theory. The objective ofthis book is to prove the latter thesis. It is written primarily for students who have assimilated substantial portions of a standard first year graduate algebra textbook, and who have enjoyed the experience. The material that is presented here should not be fatal if it is swallowed by persons who are not members of that group. The objects of our attention in this book are associative algebras, mostly the ones that are finite dimensional over a field. This subject is ideal for a textbook that will lead graduate students into a specialized field of research. The major theorems on associative algebras inc1ude some of the most splendid results of the great heros of algebra: Wedderbum, Artin, Noether, Hasse, Brauer, Albert, Jacobson, and many others. The process of refine­ ment and c1arification has brought the proof of the gems in this subject to a level that can be appreciated by students with only modest background. The subject is almost unique in the wide range of contacts that it makes with other parts of mathematics. The study of associative algebras con­ tributes to and draws from such topics as group theory, commutative ring theory, field theory, algebraic number theory, algebraic geometry, homo­ logical algebra, and category theory. It even has some ties with parts of applied mathematics.

Keywords

Algebras Assoziative Algebra Category theory Cohomology Group theory Lattice algebra homomorphism ring theory

Authors and affiliations

  • Richard S. Pierce
    • 1
  1. 1.University of ArizonaTucsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-0163-0
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-0165-4
  • Online ISBN 978-1-4757-0163-0
  • Series Print ISSN 0072-5285
  • About this book