Commutative Algebra

Commutative Algebra, Hideyuki Matsumura,1st ed, 1970, 262p, W. A. Benjamin, 978-0805370249
	A Note from the Publisher
	Preface
	Conventions
	Contents
	Index
Part I
	Chapter 1. ELEMENTARY RESULTS
		1. General Rings
		2. Noetherian Rings and Artinian Rings
	Chapter 2. FLATNESS
		3. Flatness
		4. Faithful Flatness
		5. Going-up and Going-down
		6. Constructable Sets
	Chapter 3. ASSOCIATED PRIMES
		7. Ass(M)
		8. Primary Decomposition
		9. Homomorphisms and Ass
	Chapter 4. GRADED RINGS
		10. Graded Rings and Modules
		11. Artin-Rees Theorem
	Chanpter 5. DIMENSION
		12. Dimension
		13. Homomorphism and Dimension
		14. Finitely Generated Extensions
	Chapter 6. DEPTH
		15. M-regular Sequences
		16. Cohen-Macaulay Rings
	Chapter 7. NORMAL RINGS and REGULAR RINGS
		17. Classical Theory
		18. Homological Theory
		19. Unique Factorization
	Chapter 8. FLATNESS II
		20. Local Criteria of Flatness
		21. Fibres of Flat Morphisms
		22. Theorem of Generic Flatness
	Chapter 9. COMPLETION
		23. completion
		24. Zariski Rings
PART II
	Chapter 10. DERIVATION
		25. Extension of a Ring by a Module
		26. Derivations and DifferentiaIs
		27. Separability
	Chapter 11. FORMAL SMOOTHNESS
		28. Formal Smoothness I
		29. Jacobian Criteria
		30. FormaI Smoothness II
	Chapter 12. NAGATA RINGS
		31. Nagata Rings
	Chapter 13. EXCELLENT RINGS
		32. Closedness of the Singular Locus
		33. FormaI Fibres and G-Rings
		34. Excellent Rings