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