Commutative Algebra (2020 spring & summer)

The main reference is Introduction to commutative algebra written by M. E. Atiyah and I. G. Macdonald.

Chapter 1, Rings and Ideals. note

Chapter 2, Modules. note

Chpater 3, Rings and Modules of Fractions. note1 note2

Chapter 4, Primary Decomposition. note

Chapter 5, Integral Dependence. note

Buffer 5+1/2, Valuations, Noether's Normalization Lemma, and Hilbert's Nullstellensatz. note

Chapter 6, Chain Conditions. note

Chapter 7, Noetherian Rings. note

Chapter 8, Artin Rings. note

Chapter 9, Discrete Valuation Rings and Dedekind Domains. note

Chapter 10, Completions. note

Chapter 11, Dimension Theory. note