# Galois Fields and Galois Rings Made Easy

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- Author : Maurice Kibler
- Publisher : Elsevier
- Release : 22 September 2017
- ISBN : 9780081023518
- Page : 270 pages
- Rating : 4.5/5 from 103 voters

## Download Galois Fields and Galois Rings Made Easy in PDF, Epub and Kindle

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

### Galois Fields and Galois Rings Made Easy

- Author : Maurice Kibler
- Publisher : Elsevier
- Release Date : 2017-09-22
- ISBN : 9780081023518

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

### Computing in Communication Networks

- Author : Frank Fitzek,Fabrizio Granelli,Patrick Seeling
- Publisher : Academic Press
- Release Date : 2020-05-20
- ISBN : 9780128209042

Computing in Communication Networks: From Theory to Practice provides comprehensive details and practical implementation tactics on the novel concepts and enabling technologies at the core of the paradigm shift from store and forward (dumb) to compute and forward (intelligent) in future communication networks and systems. The book explains how to create virtualized large scale testbeds using well-established open source software, such as Mininet and Docker. It shows how and where to place disruptive techniques, such as machine learning, compressed sensing,

### Computer Algebra in Scientific Computing

- Author : Andreas Weber
- Publisher : MDPI
- Release Date : 2019-11-04
- ISBN : 9783039217304

Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors.

### Finite Commutative Rings and Their Applications

- Author : Gilberto Bini,Flaminio Flamini
- Publisher : Springer Science & Business Media
- Release Date : 2012-12-06
- ISBN : 9781461509578

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

### The Separable Galois Theory of Commutative Rings, Second Edition

- Author : Andy R. Magid
- Publisher : CRC Press
- Release Date : 2014-07-14
- ISBN : 9781482208054

The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a new chapter on the theory of separable algebras. The book develops the notion of commutative separable algebra over a given commutative ring and explains how to construct an equivalent category of

### Introduction to Coding Theory and Algebraic Geometry

- Author : J. van Lint,G. van der Geer
- Publisher : Birkhäuser
- Release Date : 2012-12-06
- ISBN : 9783034892865

These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas

### Galois Theory

- Author : Emil Artin
- Publisher : Courier Corporation
- Release Date : 2012-05-24
- ISBN : 9780486158259

Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

### Groups, Rings and Galois Theory

- Author : Victor P Snaith
- Publisher : World Scientific Publishing Company
- Release Date : 2003-09-29
- ISBN : 9789813102231

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

### Algebra for Secure and Reliable Communication Modeling

- Author : Mustapha Lahyane, Edgar Martínez-Moro
- Publisher : American Mathematical Soc.
- Release Date : 2015-06-23
- ISBN : 9781470410186

This volume contains the proceedings of the CIMPA Research School and Conference on Algebra for Secure and Reliable Communication Modeling, held from October 1-13, 2012, in Morelia, State of Michoacán, Mexico. The papers cover several aspects of the theory of coding theory and are gathered into three categories: general theory of linear codes, algebraic geometry and coding theory, and constacyclic codes over rings. The aim of this volume is to fill the gap between the theoretical part of algebraic geometry

### Field and Galois Theory

- Author : Patrick Morandi
- Publisher : Springer Science & Business Media
- Release Date : 2012-12-06
- ISBN : 9781461240402

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

### Galois Theory, Rings, Algebraic Groups and Their Applications

- Author : Simeon Ivanov
- Publisher : American Mathematical Soc.
- Release Date : 1992
- ISBN : 0821831402

This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic K—theory and some of their applications.

### Computations in Algebraic Geometry with Macaulay 2

- Author : David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
- Publisher : Springer Science & Business Media
- Release Date : 2013-03-14
- ISBN : 9783662048511

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

### Quadratic Forms Over Q and Galois Extensions of Commutative Rings

- Author : Frank DeMeyer,David Harrison,Rick Miranda
- Publisher : American Mathematical Soc.
- Release Date : 1989
- ISBN : 9780821824573

The object of the first two sections of this memoir is to give explicit descriptions of both the Witt ring of the rational numbers [bold]Q and the set of abelian extensions of [bold]Q. The third presents a discussion around a particular case of the Galois cubic extension, building on the general theory.

### Introduction to Abstract Algebra

- Author : Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger
- Publisher : JHU Press
- Release Date : 2014-07-01
- ISBN : 9781421411774

This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include:; Rings; Integral domains; The fundamental theorem of arithmetic; Fields; Groups; Lagrange's theorem; Isomorphism theorems for groups; Fundamental theorem of finite abelian groups; The simplicity of An for n5; Sylow theorems; The Jordan-Hölder theorem; Ring isomorphism theorems; Euclidean domains; Principal ideal domains; The fundamental theorem of algebra;

### Proceedings of the Conference on Algebra and Geometry

- Author : Anonim
- Publisher : Unknown
- Release Date : 1982
- ISBN : UOM:39015057368394