Finite Commutative Rings and Their Applications / Edition 1

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Overview

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 The section on Quasi-Galois rings presents new and unpublished results as well.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.

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Editorial Reviews

From The Critics
This introductory reference treats theoretical and practical aspects of finite commutative ring theory as applied to information and communication theory. It will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book focuses on Galois and quasi-Galois rings, and provides an approach to the study of the purely algebraic structure and properties of finite commutative rings as well as to their applications to coding theory, through explanatory examples rather than abstract presentation. The section on quasi-Galois rings presents new and unpublished results. Some applications of finite rings, in particular Galois rings, to coding theory are introduced, using an algebraic and geometric theoretical background. Bini is affiliated with the University of Michigan. Flamini is affiliated with Universita degli Studi Roma Tre, Italy. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Foreword. Preface. 1. Fundamental Notions in Ring Theory. 2. Finite Field Structure. 3. Finite Commutative Rings. Regular Polynomials. 4. Separable Extensions of Finite Fields and Finite Rings. 5. Galois Theory for Local Rings. 6. Galois and Quasi-Galois Rings: Structure and Properties. 7. Basic Notions of Codes Over Finite Fields. 8. Basic Notions on Codes over Galois Rings. Bibliography. Index.
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