Introduction to Commutative Algebra

1. Rings and ideals (revisited and expanded).
2. Modules, exact sequences, tensor products.
3. Noetherian rings and modules over them.
4. Hilbert’s basis theorem.
5. Finitely generated modules over PID.
6. Hilbert’s Nullstellensatz.
7. Affine varieties.
8. Prime ideals and localization. Primary decomposition.
9. Discrete valuation rings.

Rings and ideals (revisited and expanded). Modules, exact sequences, tensor products. Noetherian rings and modules over them. Hilbert basis theorem. Finitely generated modules over PID. Hilbert Nullstellensatz. Affine varieties. Prime ideals and localization. Primary decomposition. Discrete valuation rings.