Finite Commutative Rings and Their Applications

  • Gilberto Bini
  • Flaminio Flamini

Table of contents

  1. Front Matter
    Pages i-x
  2. Gilberto Bini, Flaminio Flamini
    Pages 1-27
  3. Gilberto Bini, Flaminio Flamini
    Pages 29-38
  4. Gilberto Bini, Flaminio Flamini
    Pages 39-60
  5. Gilberto Bini, Flaminio Flamini
    Pages 61-69
  6. Gilberto Bini, Flaminio Flamini
    Pages 71-80
  7. Gilberto Bini, Flaminio Flamini
    Pages 81-119
  8. Gilberto Bini, Flaminio Flamini
    Pages 121-143
  9. Gilberto Bini, Flaminio Flamini
    Pages 145-165
  10. Back Matter
    Pages 167-176

About this book

Introduction

Foreword by Dieter Jungnickel
Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory.

The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory.

Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

Keywords

algebra coding theory communication finite field information

Authors and affiliations

  • Gilberto Bini
    • 1
  • Flaminio Flamini
    • 2
  1. 1.University of MichiganUSA
  2. 2.Universita degli Studi Roma TreItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-0957-8
  • Copyright Information Kluwer Academic Publishers 2002
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-5323-2
  • Online ISBN 978-1-4615-0957-8
  • Series Print ISSN 0893-3405
  • About this book