Finite Fields And Galois Rings
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Finite Fields And Galois Rings
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Author : Zhe-Xian Wan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-09-13
Finite Fields And Galois Rings written by Zhe-Xian Wan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-13 with Mathematics categories.
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
Lectures On Finite Fields And Galois Rings
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Author : Zhe-Xian Wan
language : en
Publisher: World Scientific
Release Date : 2003
Lectures On Finite Fields And Galois Rings written by Zhe-Xian Wan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Finite Fields And Galois Rings
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Author : Wan Zhe-Xian
language : en
Publisher:
Release Date : 2011
Finite Fields And Galois Rings written by Wan Zhe-Xian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Galois Fields And Galois Rings Made Easy
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Author : Maurice Kibler
language : en
Publisher: Elsevier
Release Date : 2017-09-22
Galois Fields And Galois Rings Made Easy written by Maurice Kibler and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-22 with Mathematics categories.
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
Finite Commutative Rings And Their Applications
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Author : Gilberto Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite Commutative Rings And Their Applications written by Gilberto Bini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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 Rings With Identity
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Author : Bernard R. McDonald
language : en
Publisher:
Release Date : 1974
Finite Rings With Identity written by Bernard R. McDonald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Associative rings categories.
Fields And Rings
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Author : Irving Kaplansky
language : en
Publisher: University of Chicago Press
Release Date : 1972
Fields And Rings written by Irving Kaplansky and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
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
Groups Rings And Galois Theory
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Author : Victor P Snaith
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-09-29
Groups Rings And Galois Theory written by Victor P Snaith and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-29 with Mathematics categories.
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.
Fields And Galois Theory
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Author : John M. Howie
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-11
Fields And Galois Theory written by John M. Howie and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-11 with Mathematics categories.
A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews
Galois Theory And Cohomology Of Commutative Rings
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Author : Stephen Urban Chase
language : en
Publisher: American Mathematical Soc.
Release Date : 1969
Galois Theory And Cohomology Of Commutative Rings written by Stephen Urban Chase and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Commutative rings categories.