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