Matsumura H. Commutative ring theory

New York: Cambridge University Press, 1986. — xii + 320 p. — (Cambridge Studies in Advanced Mathematics 8). — ISBN: 978-0-521-36764-6.In publishing this English edition I have tried to make a rather extensive revision. Most of the mistakes and insufficiencies in the original edition have, I hope, been corrected, and some theorems have been improved. Some topics have been added in the form of Appendices to individual sections. Only Appendices A, B and C are from the original. The final section, §33, of the original edition was entitled 'Kurtz' Theorems' and did not substantially differ from a section in the second edition of my previous book Commutative Algebra (Benjamin, 2nd dn 1980), so I have replaced it by the present §33.
The bibliography at the end of the book has been considerably enlarged, although it is obviously impossible to do justice to all of the ever-increasing literature.Commutative rings and modules.
Prime ideals.
Properties of extension rings.
Valuation rings.
Dimension theory.
Regular sequences.
Regular rings.
Flatness revisited.
Derivations.
I-smoothness.
Applications of complete local rings.