Galois Theory Through Exercises

1 Solving algebraic equations.- 2 Field extensions.- 3 Polynomials and irreducibility.- 4 Algebraic extensions.- 5 Splitting fields.- 6 Automorphism groups of fields.- 7 Normal extensions.- 8 Separable extensions.- 9 Galois extensions.- 10 Cyclotomic extensions.- 11 Galois modules.- 12 Solvable groups.- 13 Solvability of equations.- 14 Geometric constructions.- 15 Computing Galois groups.- 16 Supplementary problems.- 17 Proofs of the theorems.- 18 Hints and answers.- 19 Examples and selected solutions.- Appendix: Groups, rings and fields.- References.- List of notations.- Index.

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• Teoria dos números
• Álgebra
• Geometria algébrica
• Grupos e teoria do grupo

Galois theory;Galois theory exercises;Galois theory computer-assisted examples;cubic and quartic equations;finite fields;cyclotomic fields;Galois resolvents;lunes of Hippocrates;inverse Galois problem;solving algebraic equations of low degrees;field extensions;zeros of polynomials;algebraic field extensions;automorphism groups of fields;Galois groups of finite field extensions;Galois extensions;Galois modules;Solvability of equations