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Galois fields and Galois rings made easy

Kibler, Maurice R.

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Galois fields and Galois rings made easy

Record Type:	Electronic resources : Monograph/item
Title/Author:	Galois fields and Galois rings made easy/ Maurice Kibler.
Author:	Kibler, Maurice R.
Published:	Amsterdam :Elsevier, : 2017.,
Description:	1 online resource.
Notes:	The Structures of Ring and Field Galois Fields Galois Rings Mutually Unbiased Bases Appendix on Number Theory and Group Theory.
[NT 15003449]:	Front Cover; Dedication ; Galois Fields and Galois Rings Made Easy; Copyright ; Contents; Acknowledgments; Preface; List of Mathematical Symbols; Sets; Numbers; Matrices; Groups; Rings; Fields; 1. The Structures of Ring and Field; 1.1. Rings; 1.2. Fields; 2. Galois Fields; 2.1. Generalities; 2.2. Extension of a field: a typical example; 2.3. Extension of a field: the general case; 2.4. Sub-field of a Galois field; 2.5. Factorizations; 2.6. The application trace for a Galois field; 2.7. Bases of a Galois field; 2.8. Characters of a Galois field; 2.9. Gaussian sums over Galois fields.
[NT 15003449]:	3. Galois Rings3.1. Generalities; 3.2. Construction of a Galois ring; 3.3. Examples and counter-examples of Galois rings; 3.4. The application trace for a Galois ring; 3.5. Characters of a Galois ring; 3.6. Gaussian sums over Galois rings; 4. Mutually Unbiased Bases; 4.1. Generalities; 4.2. Quantum angular momentum bases; 4.3. SU(2) approach to mutually unbiased bases; 4.4. Galois field approach to mutually unbiased bases; 4.5. Galois ring approach to mutually unbiased bases; 5. Appendix on Number Theory and Group Theory; 5.1. Elements of number theory; 5.2. Elements of group theory.
Subject:	Galois theory. -
Online resource:	https://www.sciencedirect.com/science/book/9781785482359
ISBN:	9780081023518 (electronic bk.)

Galois fields and Galois rings made easy
Kibler, Maurice R.

Galois fields and Galois rings made easy[electronic resource] /Maurice Kibler. - Amsterdam :Elsevier,2017. - 1 online resource.

The Structures of Ring and Field Galois Fields Galois Rings Mutually Unbiased Bases Appendix on Number Theory and Group Theory.

Includes bibliographical references and index.

Front Cover; Dedication ; Galois Fields and Galois Rings Made Easy; Copyright ; Contents; Acknowledgments; Preface; List of Mathematical Symbols; Sets; Numbers; Matrices; Groups; Rings; Fields; 1. The Structures of Ring and Field; 1.1. Rings; 1.2. Fields; 2. Galois Fields; 2.1. Generalities; 2.2. Extension of a field: a typical example; 2.3. Extension of a field: the general case; 2.4. Sub-field of a Galois field; 2.5. Factorizations; 2.6. The application trace for a Galois field; 2.7. Bases of a Galois field; 2.8. Characters of a Galois field; 2.9. Gaussian sums over Galois fields.

AnnotationPresents physicists and theoretical chemists with discussions from the field of mathematics. The bodies and Galois rings are an important field of pure mathematics. In recent years, they have proven to be very useful in theoretical physics, especially in the field of the theory of quantum information. Unfortunately, the literature on body and Galois rings is primarily made for mathematicians and is difficult to access for physicists, hence the need for this timely book.

ISBN: 9780081023518 (electronic bk.)Subjects--Topical Terms:

523821
Galois theory.
Index Terms--Genre/Form:

542853
Electronic books.

LC Class. No.: QA214

Dewey Class. No.: 512.32

Galois fields and Galois rings made easy
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100 1 $a Kibler, Maurice R. $3 3508451
245 1 0 $a Galois fields and Galois rings made easy $h [electronic resource] / $c Maurice Kibler.
260 $a Amsterdam : $b Elsevier, $c 2017.
300 $a 1 online resource.
500 $a The Structures of Ring and Field Galois Fields Galois Rings Mutually Unbiased Bases Appendix on Number Theory and Group Theory.
504 $a Includes bibliographical references and index.
505 0 $a Front Cover; Dedication ; Galois Fields and Galois Rings Made Easy; Copyright ; Contents; Acknowledgments; Preface; List of Mathematical Symbols; Sets; Numbers; Matrices; Groups; Rings; Fields; 1. The Structures of Ring and Field; 1.1. Rings; 1.2. Fields; 2. Galois Fields; 2.1. Generalities; 2.2. Extension of a field: a typical example; 2.3. Extension of a field: the general case; 2.4. Sub-field of a Galois field; 2.5. Factorizations; 2.6. The application trace for a Galois field; 2.7. Bases of a Galois field; 2.8. Characters of a Galois field; 2.9. Gaussian sums over Galois fields.
505 8 $a 3. Galois Rings3.1. Generalities; 3.2. Construction of a Galois ring; 3.3. Examples and counter-examples of Galois rings; 3.4. The application trace for a Galois ring; 3.5. Characters of a Galois ring; 3.6. Gaussian sums over Galois rings; 4. Mutually Unbiased Bases; 4.1. Generalities; 4.2. Quantum angular momentum bases; 4.3. SU(2) approach to mutually unbiased bases; 4.4. Galois field approach to mutually unbiased bases; 4.5. Galois ring approach to mutually unbiased bases; 5. Appendix on Number Theory and Group Theory; 5.1. Elements of number theory; 5.2. Elements of group theory.
520 8 $a Annotation $b Presents physicists and theoretical chemists with discussions from the field of mathematics. The bodies and Galois rings are an important field of pure mathematics. In recent years, they have proven to be very useful in theoretical physics, especially in the field of the theory of quantum information. Unfortunately, the literature on body and Galois rings is primarily made for mathematicians and is difficult to access for physicists, hence the need for this timely book.
650 0 $a Galois theory. $3 523821
650 0 $a Rings (Algebra) $3 540500
650 7 $a MATHEMATICS $x Algebra $x Intermediate. $2 bisacsh $3 3508449
655 4 $a Electronic books. $2 lcsh $3 542853
856 4 0 $u https://www.sciencedirect.com/science/book/9781785482359