Abstract Algebra Applications to Galois Theory Algebraic Geometry and Cryptography

Abstract Algebra Applications to Galois Theory, Algebraic Geometry and Cryptography

Abstract Algebra: Applications to Galois Theory, Algebraic Geometry and Cryptography by Gerhard Rosenberger & Benjamin Fine & Celine Carstensen

Contents of Abstract Algebra

  • Groups, Rings and Fields
  • Maximal and Prime Ideals
  • Prime Elements and Unique Factorization Domains
  • Polynomials and Polynomial Rings
  • Field Extensions
  • Field Extensions and Compass and Straightedge Constructions
  • Kronecker’s Theorem and Algebraic Closures
  • Splitting Fields and Normal Extensions
  • Groups, Subgroups and Examples
  • Normal Subgroups, Factor Groups and Direct Products
  • Symmetric and Alternating Groups
  • Solvable Groups
  • Groups Actions and the Sylow Theorems
  • Free Groups and Group Presentations
  • Finite Galois Extensions
  • Separable Field Extensions
  • Applications of Galois Theory
  • The Theory of Modules
  • Finitely Generated Abelian Groups
  • Integral and Transcendental Extensions
  • The Hilbert Basis Theorem and the Nullstellensatz
  • Algebraic Cryptography

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