Finite Commutative Rings and Their Applications
By: by Gilberto Bini, Flaminio Flamini
Contributors: Flamini, Flaminio
Series: The Springer International Series in Engineering and Computer Science -- 680; International series in engineering and computer science -- 680.
Publisher: Springer US
Published: 2002
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] /
Number of pages: 176
ISBN-13: 9781461353232; 9781461509578
Subjects: Computer engineering; Computational complexity; Coding theory; Engineering
Description: 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 The section on Quasi-Galois rings presents new and unpublished results as well.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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