Elements of Mathematics: Elements of Mathematics. 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 '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.

List of contents

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

Product details

• Authors: N Bourbaki, N. Bourbaki, Nicolas Bourbaki
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.1998
• EAN: 9783540642398
• ISBN: 978-3-540-64239-8
• No. of pages: 625
• Weight: 858 g
• Sets: Elements of Mathematics; Elements of Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, Geometrie / Algebraische Geometrie, Algebraische Geometrie, MATHEMATICS / Algebra / General, Kommutation - kommutativ