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Hardcover ISBN:  9780821849378 
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Hardcover ISBN:  9780821849378 
Product Code:  SURV/191 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470409968 
Product Code:  SURV/191.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821849378 
eBook ISBN:  9781470409968 
Product Code:  SURV/191.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 191; 2013; 276 ppMSC: Primary 12; Secondary 11; 16
Central simple algebras arise naturally in many areas of mathematics. They are closely connected with ring theory, but are also important in representation theory, algebraic geometry and number theory.
Recently, surprising applications of the theory of central simple algebras have arisen in the context of coding for wireless communication. The exposition in the book takes advantage of this serendipity, presenting an introduction to the theory of central simple algebras intertwined with its applications to coding theory. Many results or constructions from the standard theory are presented in classical form, but with a focus on explicit techniques and examples, often from coding theory.
Topics covered include quaternion algebras, splitting fields, the SkolemNoether Theorem, the Brauer group, crossed products, cyclic algebras and algebras with a unitary involution. Code constructions give the opportunity for many examples and explicit computations.
This book provides an introduction to the theory of central algebras accessible to graduate students, while also presenting topics in coding theory for wireless communication for a mathematical audience. It is also suitable for coding theorists interested in learning how division algebras may be useful for coding in wireless communication.
ReadershipGraduate students and research mathematicians interested in central simple algebras, coding theory, and wireless communications.

Table of Contents

Chapters

Introduction

1. Central simple algebras

2. Quaternion algebras

3. Fundamental results on central simple algebras

4. Splitting fields of central simple algebras

5. The Brauer group of a field

6. Crossed products

7. Cyclic algebras

8. Central simple algebras of degree 4

9. Central simple algebras with unitary involutions

Appendix A. Tensor products

Appendix B. A glimpse of number theory

Appendix C. Complex ideal lattices


Additional Material

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Central simple algebras arise naturally in many areas of mathematics. They are closely connected with ring theory, but are also important in representation theory, algebraic geometry and number theory.
Recently, surprising applications of the theory of central simple algebras have arisen in the context of coding for wireless communication. The exposition in the book takes advantage of this serendipity, presenting an introduction to the theory of central simple algebras intertwined with its applications to coding theory. Many results or constructions from the standard theory are presented in classical form, but with a focus on explicit techniques and examples, often from coding theory.
Topics covered include quaternion algebras, splitting fields, the SkolemNoether Theorem, the Brauer group, crossed products, cyclic algebras and algebras with a unitary involution. Code constructions give the opportunity for many examples and explicit computations.
This book provides an introduction to the theory of central algebras accessible to graduate students, while also presenting topics in coding theory for wireless communication for a mathematical audience. It is also suitable for coding theorists interested in learning how division algebras may be useful for coding in wireless communication.
Graduate students and research mathematicians interested in central simple algebras, coding theory, and wireless communications.

Chapters

Introduction

1. Central simple algebras

2. Quaternion algebras

3. Fundamental results on central simple algebras

4. Splitting fields of central simple algebras

5. The Brauer group of a field

6. Crossed products

7. Cyclic algebras

8. Central simple algebras of degree 4

9. Central simple algebras with unitary involutions

Appendix A. Tensor products

Appendix B. A glimpse of number theory

Appendix C. Complex ideal lattices