Elements of mathematics. Commutative algebra. Chapters 1–7. Transl. from the French. Softcover edition of the 2nd printing 1989. (English) Zbl 0902.13001

Bourbaki, Nicolas

Berlin: Springer. xxiv, 625 p. (1998).

The first seven chapters of N. Bourbaki’s “Commutative algebra”, which numbers among the later volumes within the entire series “Elements of mathematics”, have appeared between 1961 and 1965. Two more chapters (chapter 8 and 9) were then added in 1983 (Zbl 0579.13001). Ever since its first appearance, this volume has been considered one of the most complete, systematic and elegant reference books on modern commutative algebra. Without any doubt, this prominent role of Bourbaki’s “Commutative algebra” is wholly persisting, up to these days.
The English translation of the French original was made available in 1972 (Zbl 0279.13001). The present edition of N. Bourbaki’s “Commutative algebra. Chapters 1-7” is the accurate reprint of this first and only English translation in softcover form. Having been sold out for the past few years, yet being subject to undiminishedly strong demand, this outstanding reference book is now purchasable again, this time even so as a much less expensive softcover.

Reviewer: W.Kleinert (Berlin)

MSC:

13-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra
13Cxx	Theory of modules and ideals in commutative rings
13-02	Research exposition (monographs, survey articles) pertaining to commutative algebra
01A75	Collected or selected works; reprintings or translations of classics
13Jxx	Topological rings and modules
13A15	Ideals and multiplicative ideal theory in commutative rings
13A18	Valuations and their generalizations for commutative rings
14C20	Divisors, linear systems, invertible sheaves

Keywords:

localization; graduate rings; flat modules; primary decomposition; ring extensions; valuations; completion; commutative algebra