Algebraic Structures

  • George R. Kempf

Table of contents

  1. Front Matter
    Pages I-IX
  2. George R. Kempf
    Pages 1-12
  3. George R. Kempf
    Pages 13-24
  4. George R. Kempf
    Pages 25-34
  5. George R. Kempf
    Pages 35-41
  6. George R. Kempf
    Pages 42-52
  7. George R. Kempf
    Pages 53-64
  8. George R. Kempf
    Pages 65-77
  9. George R. Kempf
    Pages 78-83
  10. George R. Kempf
    Pages 84-94
  11. George R. Kempf
    Pages 95-105
  12. George R. Kempf
    Pages 106-114
  13. George R. Kempf
    Pages 115-120
  14. George R. Kempf
    Pages 121-127
  15. George R. Kempf
    Pages 128-130
  16. George R. Kempf
    Pages 131-135
  17. George R. Kempf
    Pages 136-138
  18. George R. Kempf
    Pages 139-140
  19. George R. Kempf
    Pages 141-143
  20. George R. Kempf
    Pages 144-149

About this book

Introduction

The laws of composition include addition and multiplication of numbers or func­ tions. These are the basic operations of algebra. One can generalize these operations to groups where there is just one law. The theory of this book was started in 1800 by Gauss, when he solved the 2000 year-old Greek problem about constructing regular n-gons by ruler and compass. The theory was further developed by Abel and Galois. After years of development the theory was put in the present form by E. Noether and E. Artin in 1930. At that time it was called modern algebra and concentrated on the abstract exposition of the theory. Nowadays there are too many examples to go into their details. I think the student should study the proofs of the theorems and not spend time looking for solutions to tricky exercises. The exercises are designed to clarify the theory. In algebra there are four basic structures; groups, rings, fields and modules. We present the theory of these basic structures. Hopefully this will give a good introduc­ tion to modern algebra. I have assumed as background that the reader has learned linear algebra over the real numbers but this is not necessary.

Keywords

Algebra Algebraic structure Field Theory Group Theory algebra Logic Modern Linear Algebra Modules

Authors and affiliations

  • George R. Kempf
    • 1
  1. 1.Department of MathematicsJohns Hopkins UniversityBaltimoreUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-80278-1
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 1995
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-528-06583-6
  • Online ISBN 978-3-322-80278-1
  • About this book