Commutative Algebra: Chapters 1-7 by N. Bourbaki (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐For some reason, I got this idea in my head that I didn’t need any algebra books besides Atiyah & Macdonald, Lang and maybe Eisenbud. Not true. I think this is considered to be one of the “good” Bourbaki books. Anyway, if you “do algebra”, you will probably find this book worth having eventually. The font is fine, perhaps a point small for my taste, and the printing is clear, not like those hack photocopy jobs that some of the publishers use for old books (I’m looking at you Addison-Wesley)

⭐good

⭐thanks

⭐A fantastic introduction to commutative algebra written in the style of Russell and Whitehead but with the pragmatism of Martin Gardiner. This book is an essential to anyone who thinks they are a mathematician.

⭐This book is a most important reference about Commutative Algebra. This book is written according to the abstract Bourbaki style.

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