Eléments de mathématique, : algèbre, Chapitre 3, algèbre multilinéaire / N. Bourbaki

N. Bourbaki's imposing work “Éléments de Mathématique” is a monumental treatise of more than seven thousand pages, which must be seen as the perhaps most influential and sweeping mathematical opus of the 20th century. The first volume was published in 1939 and the most recent one in 1998, which amounts to a period of publishing activity of about sixty years, with varying thematic topics and different groups of (secret) authors. Through their fundamental treatise, the Bourbaki groups brought a totally new vision of pure mathematics, mainly by means of its profound reorganization, conceptual clarification, and terminological systematization. Until now, N. Bourbaki's “Éléments de Mathématique” consists of ten books covering the foundations of some of the most important areas in modern pure mathematics. Book II of the entire treatise is devoted to the basics of the theory of algebraic structures, in its most abstract setting, and it is simply titled “Algebra”. Book II encompasses ten chapters,which were successively published between 1943 and 1980, originally in French. Chapter 3 treats general algebras, examples of concrete algebras, graded algebras, tensor algebras, symmetric algebras, exterior algebras, norms and traces, derivations in algebras, coalgebras, and their geometric applications (p-vectors and Grassmannians). Now as before, there is this legendary ample supply of complementing exercises and historical notes adding up to the everlasting value of this particular volume. (Zentralblatt)

Bibliogr. p.[155]-156. Index