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Author:   N. Bourbaki ,  Nicolas Bourbaki
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2ème éd. 2012
Dimensions:   Width: 15.50cm , Height: 2.80cm , Length: 23.50cm
Weight:   0.759kg
ISBN:  

9783540353157

ISBN 10:   3540353151
Pages:   489
Publication Date:   14 January 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Language:   French

Table of Contents

Introduction.- Chapitre VIII. Modules et anneaux semi-simples.- 1. Modules artiniens et modules noethériens.- 2. Structure des modules de longueur finie.- 3. Modules simples.- 4. Modules semi-simples.- 5. Commutation.- 6. Équivalence de Morita des modules et des algèbres.- 7. Anneaux simples.- 8. Anneaux semi-simples.- 9. Radical.- 10. Modules sur un anneau artinien.- 11. Groupes de Grothendieck.- 12. Produit tensoriel de modules semi-simples.- 13. Algèbres absolument semi-simples.- 14. Algèbres centrales et simples.- 15. Groupes de Brauer.- 16. Autres descriptions du groupe de Brauer.- 17. Normes et traces réduites.- 18. Algèbres simples sur un corps fini.- 20. Représentations linéaires des algèbres.- 21. Représentations linéaires des groupes finis.- Appendice 1. Algèbres sans élément unité.- Appendice 2. Déterminants sur un corps non commutatif.- Appendice 3. Le théorème des zéros de Hilbert.- Appendice 4. Trace d’un endomorphisme de rang fini.- Note Historique.- Bibliographie.- Index des notations.- Index terminologique

Reviews

<p>From the reviews of the second edition: <p> This book is intended as a comprehensive exposition of the theory of semi-simple rings and modules, with special emphasis on the Noetherian and Artinian cases. Each section ends with a large collection of related exercises in the typical Bourbaki-style . Certainly, it has been both a splendid idea and a great undertaking to rewrite N. Bourbaki s classic Chapter 8 of Book II of the Elements of Mathematics in such excellent a manner, very much so to the benefit of further generations of mathematicians. (Werner Kleinert, Zentralblatt MATH, Vol. 1245, 2012)

From the reviews of the second edition: “This book is intended as a comprehensive exposition of the theory of semi-simple rings and modules, with special emphasis on the Noetherian and Artinian cases. … Each section ends with a large collection of related exercises in the typical Bourbaki-style … . Certainly, it has been both a splendid idea and a great undertaking to rewrite N. Bourbaki’s classic Chapter 8 of Book II of the ‘Elements of Mathematics’ in such excellent a manner, very much so to the benefit of further generations of mathematicians.” (Werner Kleinert, Zentralblatt MATH, Vol. 1245, 2012)

From the reviews of the second edition: </p> This book is intended as a comprehensive exposition of the theory of semi-simple rings and modules, with special emphasis on the Noetherian and Artinian cases. Each section ends with a large collection of related exercises in the typical Bourbaki-style . Certainly, it has been both a splendid idea and a great undertaking to rewrite N. Bourbaki s classic Chapter 8 of Book II of the Elements of Mathematics in such excellent a manner, very much so to the benefit of further generations of mathematicians. (Werner Kleinert, Zentralblatt MATH, Vol. 1245, 2012)</p>

From the reviews of the second edition: This book is intended as a comprehensive exposition of the theory of semi-simple rings and modules, with special emphasis on the Noetherian and Artinian cases. Each section ends with a large collection of related exercises in the typical Bourbaki-style . Certainly, it has been both a splendid idea and a great undertaking to rewrite N. Bourbaki s classic Chapter 8 of Book II of the Elements of Mathematics in such excellent a manner, very much so to the benefit of further generations of mathematicians. (Werner Kleinert, Zentralblatt MATH, Vol. 1245, 2012)

From the reviews of the second edition: This book is intended as a comprehensive exposition of the theory of semi-simple rings and modules, with special emphasis on the Noetherian and Artinian cases. Each section ends with a large collection of related exercises in the typical Bourbaki-style . Certainly, it has been both a splendid idea and a great undertaking to rewrite N. Bourbaki s classic Chapter 8 of Book II of the Elements of Mathematics in such excellent a manner, very much so to the benefit of further generations of mathematicians. (Werner Kleinert, Zentralblatt MATH, Vol. 1245, 2012)

From the reviews of the second edition: This book is intended as a comprehensive exposition of the theory of semi-simple rings and modules, with special emphasis on the Noetherian and Artinian cases. ... Each section ends with a large collection of related exercises in the typical Bourbaki-style ... . Certainly, it has been both a splendid idea and a great undertaking to rewrite N. Bourbaki's classic Chapter 8 of Book II of the 'Elements of Mathematics' in such excellent a manner, very much so to the benefit of further generations of mathematicians. (Werner Kleinert, Zentralblatt MATH, Vol. 1245, 2012)

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