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Doctorate Algebra Syllabus

  M.S. Level Material
M.S. Algebra Syllabus
  Advanced Algebra
    Groups
    • Series of groups (Jordan-Holder Theorem), solvable and nilpotent groups
    • Representation theory (Maschke's Theorem)
    Rings
    • Modules
    • Division rings (Wedderburn's Theorem)
    • Noetherian rings (Hilbert Basis Theorem, power series rings), localization
    • Semi-simple rings (Density Theorem)
    • Gröbner Bases
    • Affine algebraic varieties
    Fields
    • Separable, inseparable and purely inseparable extensions, normal extensions
    • Transcendental extensions (transcendence bases)
    • Galois theory
  References
Dummit and Foote: Abstract Algebra
Hungerford: Algebra
Lang: Algebra
Rotman: Advanced Modern Algebra



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