Syllabus
1. Noetherian and Artinian rings.
2. Prime and maximal ideals, the Jacobson radical and the nilradical, Nakayama's lemma.
3. Localization, flatness, integral extensions, going up and going down theorems.
4. Adic completion, the Artin-Rees lemma and the Krull's intersection theorem.
5. Dimension theory of rings and Krull's principal ideal theorem.
6. Regular sequences and Koszul complexes.
7. Basics on Regular, Gorenstein and Cohen-Macaulay rings.
8. Serre theorem about localization of regular rings.
Annotation
This is a Master level introductory course to a standard theory of commutative noetherian rings. In includes basics on lovalization and completion of rings, Krull dimension and homological conditions on rings.