TY  - BOOK
AU  - Kibler,Maurice
TI  - Galois fields and Galois rings made easy
SN  - 9780081023518
AV  - QA214 
U1  - 512.32 23
PY  - 2017///
CY  - Amsterdam
PB  - Elsevier
KW  - Galois theory
KW  - Rings (Algebra)
N1  - 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; 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
N2  - Annotation; 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
UR  - https://www.sciencedirect.com/science/book/9781785482359
ER  -