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