Overview
- Translation of a completely revised edition
- Introduces concepts absent in the previous editions
- Historical note at the end of the volume
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Table of contents (1 chapter)
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Front Matter
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Back Matter
Keywords
About this book
It is devoted to the study of certain classes of rings and of modules, in particular to the notions of Noetherian or Artinian modules and rings, as well as that of radical.
This chapter studies Morita equivalence of module and algebras, it describes the structure of semisimple rings. Various Grothendieck groups are defined that play a universal role for module invariants.
The chapter also presents two particular cases of algebras over a field. The theory of central simple algebras is discussed in detail; their classification involves the Brauer group, of which several
descriptions are given. Finally, the chapter considers group algebras and applies the general theory to representations of finite groups.
At the end of the volume, a historical note taken from the previous edition recounts the evolution of many of the developed notions.
Authors and Affiliations
Bibliographic Information
Book Title: Algebra
Book Subtitle: Chapter 8
Authors: N. Bourbaki
Translated by: Reinie Erné
DOI: https://doi.org/10.1007/978-3-031-19293-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-19292-0Published: 16 March 2023
Softcover ISBN: 978-3-031-19295-1Published: 16 March 2024
eBook ISBN: 978-3-031-19293-7Published: 15 March 2023
Edition Number: 1
Number of Pages: XVIII, 490
Additional Information: Original Second French edition published by Springer, 2012
Topics: Algebra