Commutative Algebra : Chapters 1-7

This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algebre 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.