Elements of mathematics. Algebra I. Chapters 1–3. Transl. from the French. 2nd printing. (English) Zbl 0673.00001

Bourbaki, Nicolas

Berlin etc.: Springer-Verlag. xxiii, 709 p. (1989).

It is not easy for the reviewer to give a review of this book. Who could give a review of any translation of the Bible in an unchanged edition after nearly twenty years of research? [For a review of the first edition of the English translation (1974) see Zbl 0281.00006.]
On the other side I don’t know if it is nowadays possible to get students acquainted with this “mercilessly abstract presentation” [E. Artin in his review of Bourbaki’s “Algèbre” in Bull. Am. Math. Soc. 59, 474-479 (1953); reprinted in Collected Papers (1965), pp. 534-538 - who suggested an English translation], if it isn’t accompanied with coloured cubes or fractals.
Twenty years ago the reviewer was forced to learn some French (because it was a prerequisite to actually understand any lecture, e.g. in algebra) - and he knows till now the definition of a Cartesian product, and of the tensor product, and their difference to a direct sum. He had forgotten the notion of “gamut” which appears now in texts of computer science on formal languages (or was it “magma”?). Some light in the darkness? - Take and read!

Reviewer: B.Richter

MSC:

00A05

Mathematics in general

Keywords:

algebraic structures; linear algebra; tensor algebra

Citations:

Zbl 0211.024; Zbl 0281.00006