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Elements of Mathematics. Algebra I. Chapters 1 - 3.
ISBN 3540642439 / 9783540642435 / 3-540-64243-9
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This is the softcover reprint of the English translation of 1974 available from Springer since 1989 of the first 3 chapters of Bourbaki's 'Algbre'. 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. TOCAlgebraic Structures.- Linear Algebra.- Tensor Algebras, Exterior Algebras.- Symmetric Algebras.- Historical Notes. [via]