Commutative Algebra: Chapters 1-7

ISBN-13: 9783540642398 / Angielski / Miękka / 1998 / 625 str.

N. Bourbaki; Nicolas Bourbaki

Opis

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.

Spis treści

Flat Modules; Localization; Graduations, Filtrations and Topologies; Associated Prime Ideals and Primary Decomposition, Integers, Valuations, Divisors, Exercises