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 The section on Quasi-Galois rings presents new and unpublished results as well.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 (The Springer International Series in Engineering and Computer Science, 680)

Flamini, Flaminio

Bini, Gilberto

Reference

Springer

Finite Commutative Rings and Their Applications (The Springer International Series in Engineering and Computer Science)

<p>This Book Provides A Gentle Introduction To The Foundations Of Algebraic Geometry, Starting From Computational Topics (Ideals And Homogeneous Ideals, Zero Loci Of Ideals) Up To Increasingly Intrinsic And Abstract Arguments, Like ""Algebraic Varieties"", Whose Natural Continuation Is A More Advanced Course On The Theory Of Schemes, Vector Bundles And Sheaf-Cohomology. Valuable To The Students Studying In Algebraic Geometry And Geometry, A First Course In Algebraic Geometry And Algebraic Varieties Contains About 60 Solved Exercises To Help Students Deeply Understand The Theories Introduced In The Book. Proofs Of The Results Are Carried Out In All Details. Many Examples Are Discussed To Help The Student Understand Both The Theoretical Part And The Consequences And Possible Applications.</p>

First Course In Algebraic Geometry And Algebraic Varieties, A (Essential Textbooks In Mathematics)

Science & Math

Mathematics

WSPC (EUROPE)

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