This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'AlgA]bre 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.
- ISBN10 3540193715
- ISBN13 9783540193715
- Publish Date 22 December 1988
- Publish Status Out of Print
- Out of Print 11 November 2010
- Publish Country DE
- Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Edition 1972. 2nd Printing ed.
- Format Hardcover
- Pages 656
- Language English