Galois Fields And Galois Rings Made Easy

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Author: Maurice Kibler
Publisher: Elsevier
ISBN: 0081023510
Size: 26.19 MB
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Galois Fields And Galois Rings Made Easy by Maurice Kibler


Original Title: Galois Fields And Galois Rings Made Easy

This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics. The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access. This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering). Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics. Contains numerous examples that accompany the text Includes an important chapter on mutually unbiased bases Helps physicists and theoretical chemists understand this area of mathematics

Lectures On Finite Fields And Galois Rings

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Author: Zhe-Xian Wan
Publisher: World Scientific
ISBN: 9789812385703
Size: 36.47 MB
Format: PDF, ePub
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Lectures On Finite Fields And Galois Rings by Zhe-Xian Wan


Original Title: Lectures On Finite Fields And Galois Rings

This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.

Fields And Galois Theory

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Author: John M. Howie
Publisher: Springer Science & Business Media
ISBN: 9781852339869
Size: 64.13 MB
Format: PDF, ePub
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Fields And Galois Theory by John M. Howie


Original Title: Fields And Galois Theory

This gentle introduction aimed at advanced undergraduates and beginning graduate students takes a modern, more "natural" approach to its subject, developing the theory at a gentle pace. Topics covered include rings and fields, integral domains and polynomials, field extensions and splitting fields, finite fields, and the Galois group. The book contains plenty of worked examples and exercises complete with full solutions.

Field And Galois Theory

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Author: Patrick Morandi
Publisher: Springer Science & Business Media
ISBN: 1461240409
Size: 73.31 MB
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Field And Galois Theory by Patrick Morandi


Original Title: Field And Galois Theory

In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.

Finite Commutative Rings And Their Applications

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Author: Gilberto Bini
Publisher: Springer Science & Business Media
ISBN: 1461509572
Size: 21.34 MB
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Finite Commutative Rings And Their Applications by Gilberto Bini


Original Title: Finite Commutative Rings And Their Applications

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 Fields And Galois Rings

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Author: Zhe-Xian Wan
Publisher: World Scientific Publishing Company
ISBN: 9813108223
Size: 25.89 MB
Format: PDF, ePub, Mobi
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Finite Fields And Galois Rings by Zhe-Xian Wan


Original Title: Finite Fields And Galois Rings

A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form. Errata(s) Errata

Field Extensions And Galois Theory

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Author: Julio R. Bastida
Publisher: Cambridge University Press
ISBN: 9780521302425
Size: 59.80 MB
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Field Extensions And Galois Theory by Julio R. Bastida


Original Title: Field Extensions And Galois Theory

This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.

Groups Rings And Galois Theory

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Author: Victor P Snaith
Publisher: World Scientific Publishing Company
ISBN: 9813102233
Size: 19.70 MB
Format: PDF, Kindle
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Groups Rings And Galois Theory by Victor P Snaith


Original Title: Groups Rings And Galois Theory

This book is ideally suited for a two-term undergraduate algebra course culminating in a discussion on Galois theory. It provides an introduction to group theory and ring theory en route. In addition, there is a chapter on groups — including applications to error-correcting codes and to solving Rubik's cube. The concise style of the book will facilitate student-instructor discussion, as will the selection of exercises with various levels of difficulty. For the second edition, two chapters on modules over principal ideal domains and Dedekind domains have been added, which are suitable for an advanced undergraduate reading course or a first-year graduate course.

Introduction To Abstract Algebra

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Author: Benjamin Fine
Publisher: JHU Press
ISBN: 1421411768
Size: 66.72 MB
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Introduction To Abstract Algebra by Benjamin Fine


Original Title: Introduction To Abstract Algebra

Presents a systematic approach to one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, this title begins with familiar topics such as rings, numbers, and groups before introducing more difficult concepts.

Fields And Rings

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Author: Irving Kaplansky
Publisher: University of Chicago Press
ISBN: 9780226424514
Size: 62.29 MB
Format: PDF, ePub
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Fields And Rings by Irving Kaplansky


Original Title: Fields And Rings

This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews

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