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Algebra: Chapter 8

N. Bourbaki
Publisher: 
Springer
Publication Date: 
2023
Number of Pages: 
508
Format: 
Hardcover
Price: 
139.99
ISBN: 
978-3031192920
Category: 
Monograph
[Reviewed by
Benjamin Linowitz
, on
11/21/2023
]
This volume is an English translation of N. Bourbaki’s Algèbre: Chapitre 8: Modules et anneaux semi-simples, published in French in 2012 by Springer. The latter was a vast expansion of Bourbaki’s 1958 treatise of the same name, published by Hermann, and concerns the Morita equivalence of modules and algebras. The text has a very nice treatment of central simple algebras and the Brauer group and concludes with representation theoretic applications. Readers looking for a somewhat friendlier, and more number theoretic, exposition of some of this material are advised to consult John Voight’s Quaternion Algebras.

Benjamin Linowitz (benjamin.linowitz@oberlin.edu) is an Associate Professor of Mathematics at Oberlin College.