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About this book
This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.
Authors and Affiliations
Bibliographic Information
Book Title: Commutative Algebra
Book Subtitle: Chapters 1-7
Authors: N. Bourbaki
Publisher: Springer Berlin, Heidelberg
Copyright Information: Springer-Verlag Berlin Heidelberg 1989
Softcover ISBN: 978-3-540-64239-8Published: 03 August 1998
Edition Number: 1
Number of Pages: XXIV, 625
Topics: Commutative Rings and Algebras