Elements of Mathematics: Algebra, Pt.1 (Actualites scientifiques et industrielles)

This is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Alg?bre'. It gives a thorough exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects: 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. Algebra is essentially concerned with calculating, that is, performing, on elements of a set, "algebraic operations", the most well-known example of which is provided by the "four rules" of elementary arithmetic.