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Les formalismes fondamentaux de l’algèbre commutative. (Fundamental formalisms of commutative algebra). Nouv. éd. Nouv. éd. (Les formalismes fondamentaux de l’algèbre commutative.) (French) Zbl 0907.13002
Collection Enseignement des Sciences. 20. Paris: Hermann. xii, 260 p. (1998).
The first edition of this textbook appeared in 1974, under the same title and in the same series of treatises in mathematics and natural sciences (see Zbl 0301.13001). The present edition of this well-proved book, which is among the long-standing standard texts on commutative algebra used at French universities since more than twenty years, appears as an entirely unchanged reprint of the first edition, although this fact is nowhere indicated here. Even the bibliography has not been up-dated, in the meantime, but all this does not belittle the enduringly outstanding role of this excellent textbook in the relevant literature.
The main features of the author’s approach to teaching commutative algebra, which consist in stressing the categorical and functorial aspects of the subject, exhibiting a Bourbaki-style elegance, rigor, systematic representation, generality and economy, providing a wealth of challenging and further-leading exercises, as well as in touching upon various other topics in algebra and geometry, remain nearly unchallenged in the textbook literature on commutative algebra. Now as before, this 25-years-old text is a brilliant guide for advanced, ambitious students in the field.

MSC:
13-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra
13Dxx Homological methods in commutative ring theory
13-02 Research exposition (monographs, survey articles) pertaining to commutative algebra
13Axx General commutative ring theory
13Cxx Theory of modules and ideals in commutative rings
15-XX Linear and multilinear algebra; matrix theory
18Gxx Homological algebra in category theory, derived categories and functors
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