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Bourbaki

Commutative Algebra

Chapters 1-7
Softcover edition
1st ed. 1989. 2nd printing 1998. Buch. xxiv, 625 S.: Bibliographien. Softcover
Springer ISBN 978-3-540-64239-8
Format (B x L): 15,5 x 23,5 cm
Gewicht: 2090 g
In englischer Sprache
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.
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