Commutative Algebra

Preface to New Typesetting
Preface
Preface to Second Edition
Conventions
Contents
I
	Elementary Results
		General Rings
		Noetherian Rings and Artinian Rings
	Flatness
		Flatness
		Faithful Flatness
		Going-up Theorem and Going-down Theorem
		Constructible Sets
	Associated Primes
		Ass(M)
		Primary Decomposition
		Homomorphisms and Ass
	Graded Rings
		Graded Rings and Modules
		Artin-Rees Theorem
	Dimension
		Dimension
		Homomorphisms and Dimension
		Finitely Generated Extensions
	Depth
		M-regular Sequences
		Cohen-Macaulay Rings
	Normal Rings and Regular Rings
		Classical Theory
		Homological Theory
		Unique Factorization
	Flatness II
		Local Criteria of Flatness
		Fibres of Flat Morphisms
		Theorems of Generic Flatness
	Completion
		Completion
		Zariski Rings
II
	Derivations
		Extension of Ring by a Module
		Derivations and Differentials
		Separability
	Formal Smoothness
		Formal Smoothness I
		Jacobian Criteria
		Formal Smoothness II
	Nagata Rings
		Nagata Rings
	Excellent Rings
		Closeness of Singular Locus
		Formal Fibres and G-Rings
		Excellent Rings
	Appendix
		Eakin's Theorem
		A Flatness Theorem
		Coefficient Rings
		p-Basis
		Cartier's Equality and Geometric Regularity
		Jacobian Criteria and Excellent Rings
		Krull Rings and Marot's Theorem
		Kunz' Theorems
		Complement
	bibliography
	Index