Introduction to Galois Theory

1 Invitation to Galois Theory.- 2 Basic Concepts of Group Theory.- 3 Basic Concepts of Ring Theory.- 4 Basic Concepts of Algebras Over a Field.- 5 Finite Fields, Perfect Fields.- 6 The Galois Correspondence.- 7 Addendum: Infinite Galois Correspondence.- 8 Cyclotomy and Constructibility.- 9 Solvability by Radicals.- 10 Reduction Modulo p.- 11 Complements.- 12 Review Exercises.- 13 Solutions to Exercises.

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

textbook on Galois theory;ruler and compass constructions;ring theory;field extensions;finite fields;perfect fields;Galois correspondence;cyclotomic fields;solvability by radicals;reduction modulo p;Chebotarev density theorem;solvable groups;Frobenius element;transcendence of e and pi