Algebra

by Nicolas Bourbaki

This is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Algèbre'. It gives a thorough exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic groups, actions, rings, fields. The second chapter studies the properties of modules and linear maps, especially with respect to the tensor product and duality constructions. The third chapter investigates algebras, in particular tensor algebras. Determinants, norms, traces and derivations are also studied.

709 pages, Hardcover

First published December 1, 1973

About the author

Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality. Their work led to the discovery of several concepts and terminologies still discussed.
Bourbaki congress, 1938.

While Nicolas Bourbaki is an invented personage, the Bourbaki group is officially known as the Association des collaborateurs de Nicolas Bourbaki (Association of Collaborators of Nicolas Bourbaki), which has an office at the École Normale Supérieure in Paris.