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presents new and unpublished results as well.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.
This text is suitable for courses in commutative algebra, finite
commutative algebra, and coding theory. It is also suitable as a
supplementary text for courses in discrete mathematics, finite
fields, finite rings, etc.
General
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