Algebra II Prelim topics


  • Field theory: Field extensions, splitting fields, separable and normal extensions, finite fields, cyclotomic fields.

  • Galois theory: Fundamental theorem of Galois theory, solvability by radicals, computing some Galois groups.

  • Topics from Algebraic number theory: fractional ideals, unique factorization in a Dedekind domain.

  • Topics from Algebraic geometry: Hilbert basis theorem, nullstellensatz, tensor products.

  • Topics from Homological Algebra: categories, functors, exact sequences, projective and injective modules, flatness, direct and inverse limits.

Main References

  • Dummit and Foote: Abstract Algebra, 3rd Edition
  • Hungeford: Algebra
  • Lang: Algebra, 3rd Edition