Commutative algebra

Author(s)

• Bourbaki, Nicolas

Bibliographic Information

Commutative algebra

Nicolas Bourbaki

（Elements of mathematics / Nicolas Bourbaki）

Springer-Verlag, c1989

• ch. 1-7 : gw
• ch. 1-7 : gw : softcover
• ch. 1-7 : us

Other Title

Algèbre commutative

Note

Translation of: Algèbre commutative

Bibliography: p. 603-606

Includes index

Description and Table of Contents

Volume

ch. 1-7 : gw ISBN 9783540193715

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 'AlgA]bre 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.

Volume

ch. 1-7 : gw : softcover ISBN 9783540642398

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 '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.

Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BA06628568
• ISBN:
  • 3540193715
  • 3540642390
  • 0387193715
• LCCN: 88031138
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: fre
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: v.
• Size: 24 cm
• Classification:
  • LCC : QA251.3
  • DC19 : 512/.24
  • NDC7 : 410
  • NDC7 : 411.73
• Subject Headings:
  • LCSH : Commutative algebra
• Parent Bibliography ID:
  • BA01043035