Galois Theory and Applications: Solved Exercises and Problems By: Mohamed Ayad

Author: Mohamed Ayad

The book provides exercises and problems with solutions in Galois Theory and its applications, which include finite fields, permutation polynomials, derivations and algebraic number theory.

It will be useful to the audience below:

Students who want to learn the material around the arithmetic of polynomials and field extensions.

Teachers who want to work on problems with their students.

Researchers who require a reference book. The book contains some useful results generally known by specialists, but for which a detailed proof is not always in the literature.
Contents:
Polynomials, Fields, Generalities
Algebraic Extention, Algebraic Closure
Separability, Inseparability
Normal Extensions
Galois Extensions, Galois Groups
Finite Fields
Permutation Polynomials
Transcendental Extensions, Linearly Disjoint Extensions, Luroth’s Theorem
Multivariate Polynomials
Integral Elements, Algebraic Number Theory
Derivations

Readership: Undergraduate and graduate students in Galois group theory.
Keywords: Galois Theory;Number Theory;Finite Fields;Permutation Polynomials;Derivations;Polynomials;Field ExtensionsReview: Key Features: There is no competing book to the present one

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