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Les Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.
Ce premier volume du Livre d'Algèbre, deuxième Livre des Éléments de mathématique, comprend les chapitres : Structures algébriques.
- Algèbre linéaire.
- Algèbres tensorielles, algèbres, extérieures, algèbres symétriques
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 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.
Ce premier volume du Livre d'Algèbre, deuxième Livre des Éléments de mathématique, comprend les chapitres : Structures algébriques.
- Algèbre linéaire.
- Algèbres tensorielles, algèbres, extérieures, algèbres symétriques
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 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.
From the reviews of the second edition:
"Thanks to a very republishing initiative launched by Springer Verlag ... this time as a complete collection of softcover editions at a reasonable price. ... The volume under review is the faithful and unabridged reprinting of the first three chapters, of Bourbaki's 'Algèbre' ... . Now as before, there is this legendary ample supply of complementing exercises and historical notes ... . Chapters 1-3 of Bourbaki's 'Algèbre' will persist as an indispensable source book of basic abstract algebra, also for future generations ... ." (Werner Kleinert, Zentralblatt MATH, Vol. 1111 (8), 2007)
"Thanks to a very republishing initiative launched by Springer Verlag ... this time as a complete collection of softcover editions at a reasonable price. ... The volume under review is the faithful and unabridged reprinting of the first three chapters, of Bourbaki's 'Algèbre' ... . Now as before, there is this legendary ample supply of complementing exercises and historical notes ... . Chapters 1-3 of Bourbaki's 'Algèbre' will persist as an indispensable source book of basic abstract algebra, also for future generations ... ." (Werner Kleinert, Zentralblatt MATH, Vol. 1111 (8), 2007)