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 The section on Quasi-Galois rings presents new and unpublished results as well.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.
Finite Commutative Rings and Their Applications
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We want to start by recalling some elementary topics in ring theory; we basically focus on local rings, since Galois rings, the "main subject" of our work, are a particular class of such rings. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
basic irreducible polynomial, linear quaternary code, finite local rings, extraspecial group, regular polynomial, quaternary codes, commutative ring with identity, weight enumerator, formal duality, formal root, finite commutative rings, parity check polynomial, separable extension, cyclic codes, nonlinear codes, residue field, maximal ideal, primitive polynomial, splitting field, dual code, additive order, proper ideal Key Phrases - Capitalized Phrases (CAPs): (learn more)
Commutative Algebra, Finite Geometries New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We want to start by recalling some elementary topics in ring theory; we basically focus on local rings, since Galois rings, the "main subject" of our work, are a particular class of such rings. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
basic irreducible polynomial, linear quaternary code, finite local rings, extraspecial group, regular polynomial, quaternary codes, commutative ring with identity, weight enumerator, formal duality, formal root, finite commutative rings, parity check polynomial, separable extension, cyclic codes, nonlinear codes, residue field, maximal ideal, primitive polynomial, splitting field, dual code, additive order, proper ideal Key Phrases - Capitalized Phrases (CAPs): (learn more)
Commutative Algebra, Finite Geometries New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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