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Related: Ring Theory

Overview

I am using Dummit's and Foote's 'Abstract Algebra', in particular the chapters that are dedicated to Field and Galois theory

Topics

• Field Extensions
  • Algebraic Field Extensions
    • Biquadratic Field Extensions
    • Classification of Simple Field Extensions
    • Algebraic Closure of a Field
  • Cyclotomic Polynomials and Extensions
• Automorphism Group of a Field Extension
  • Splitting Fields and Normal Field Extensions
    • Normal and Galois Closure of a Field Extension
    • Separable Field Extensions
      • Galois Field Extensions
        • Finite Fields
          • Berlekamp's Factorisation Algorithm
          • Artin-Schreier Extensions
        • Galois Groups of Polynomials
          • Solvable Polynomials and Radical Extensions
          • Kummer extensions
  • Composite Field Extensions
• Linear Algebraic Invariants in Field Theory
• Compass and Straightedge Constructions Using Field Theory
  • Compass and Ruler Constructions Using Field Theory
  • Origami Constructions Using Field Theory