Capa do artigo Algebra
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Algebra eBook

Chapter 8

by N. Bourbaki
language: english
Publisher: Springer International Publishing, March of 2023 ‧
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This book is an English translation of an entirely revised version of the 1958 edition of the eighth chapter of the book Algebra, the second Book of the Elements of Mathematics.

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.

Algebra

Chapter 8

by N. Bourbaki

Property Description
ISBN: 9783031192937
Publisher: Springer International Publishing
Release Date: March of 2023
Language: English
Format: eBook
Collection: Mathematics And Statistics
Categories: eBooks in English > Science > Mathematics
EAN: 9783031192937

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