Elements of Mathematics. Commutative Algebra. Chapters 1 - 7, Band Chapt.1-7

Seitenzahl:

625

Gewicht:

986 g

Auflage:

2. Printing

Erschienen bei:

Springer

Kurzbeschreibung

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

Beschreibung

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.

Mehr über...

Mehr über:  Algebra, algebraic geometry, Algebraische Geometrie, geometry, Geometrie / Algebraische Geometrie, Kommutation - kommutativ, kommutativ ( Kommutation ), Kommutative Algebra, commutative algebra, arithmetical, divisors, Mathematik; Handbuch/Lehrbuch, Mathematics / Algebra / General

Mehr von: 

Mehr von:  Nicolas Bourbaki, Springer-Verlag GmbH