zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Elements of mathematics. Algebra I. Chapters 1–3. Transl. from the French. Softcover edition of the 2nd printing 1989. (English) Zbl 0904.00001
Berlin: Springer. xxiii, 709 p. DM 79.00; öS 577.00; sFr. 72.00; £30.50; $ 49.95 (1998).

It is a remarkable initiative undertaken by Springer-Verlag to have a new softcover edition of the English translation of the famous series “The elements of mathematics” by Nicolas Bourbaki. Several generations of mathematicians matured with the myth for a group of young mathematicians, their names covered with mysticism, who decided in a series of volumes to provide a solid foundation for the whole body of modern mathematics. More than 30 years have passed since the appearance of the French original of the first books but nevertheless “The Elements” are still vivid and are one of the main sources for references in many books and papers.

The present volume contains Chapters 1-3 of the second “numbered” book by Bourbaki (I. Theory of sets; II. Algebra; III. General topology; IV. Functions of real variable; V. Topological vector spaces; VI. Integration). Chapter 1 deals with algebraic structures (including monoids, groups, groups with operations, rings and fields). Chapter 2 is devoted to linear algebra (modules, vector spaces, affine and projective spaces, matrices, graded rings and modules). Chapter 3 contains the theory of algebras, graded algebras, tensor products, symmetric and exterior algebras, determinants, norms, traces and derivations, coalgebras (called in the text cogebras). Each chapter contains a long list of research exercises and historical notes.

Together with the other 6 chapters of Algebra and the books on Commutative algebra and Lie groups and Lie algebras (1998; Zbl 0904.17001), the text under review is of great value for any mathematician working in the field of algebra or some related topics.

[The 1989 ed. was reviewed in Zbl 0673.00001. For a review of Algebra II (Springer 1990), see Zbl 0719.12001].

00A05General mathematics
12-01Textbooks (field theory)
15-01Textbooks (linear algebra)
20-01Textbooks (group theory)
16-01Textbooks (associative rings and algebras)
17-01Textbooks (nonassociative rings and algebras)
15A69Multilinear algebra, tensor products
15A72Vector and tensor algebra, theory of invariants
15A75Exterior algebra, Grassmann algebras
15A78Other algebras built from modules
17D05Alternative rings
20E05Free nonabelian groups
20F16Solvable groups, supersolvable groups