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