List of Abstract Algebra Topics - Field Theory

Field Theory

Basic concepts
  • Field (mathematics)
  • Subfield (mathematics)
    • Multiplicative group
      • Primitive element (field theory)
  • Field extension
    • Algebraic extension
      • Splitting field
      • Algebraically closed field
        • Algebraic element
        • Algebraic closure
    • Separable extension
      • Separable polynomial
    • Normal extension
    • Galois extension
    • Abelian extension
    • Transcendence degree
  • Field norm
  • Field trace
  • Conjugate element (field theory)
  • Tensor product of fields
Types
  • Algebraic number field
  • Global field
  • Local field
  • Finite field
  • Symmetric function
  • Formally real field
  • Real closed field
Applications
  • Galois theory
    • Galois group
    • Inverse Galois problem
  • Kummer theory

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