Algebra I Prelim topics


  • Group theory: Isomorphism theorems, direct and semi-direct product, Orbit-Stabilizer Theorem, Sylow theorems, Jordan-Holder theorem, solvable and nilpotent groups, generators and relations.

  • Ring theory: Isomorphism theorems, UFD, PID, Euclidean domains, ring of fractions, local rings.

  • Modules: Isomorphism theorems, direct sums and free modules, Fundamental theorem of finitely generated modules over a PID (and its group theory analogue), Noetherian, Artinian modules.

Main References

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