N. Bourbaki: Algebra | Buch

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Cover: 9783031192920 | Algebra | Chapter 8 | N. Bourbaki | Buch | HC runder Rücken kaschiert

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Sprache: Englisch

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Beschreibung

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.

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.

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.

Zusammenfassung

Translation of a completely revised edition

Introduces concepts absent in the previous editions

Historical note at the end of the volume

Inhaltsverzeichnis

Artinian Modules and Noetherian Modules.- The Structure of Modules of Finite Length.- Simple Modules.- Semisimple Modules.- Commutation.- Morita Equivalence of Modules and Algebras.- Simple Rings.- Semisimple Rings.- Radical.- Modules over an Artinian Ring.- Grothendieck Groups.- Tensor Products of Semisimple Modules.- Absolutely Semisimple Algebras.- Central Simple Algebras.- Brauer Groups.- Other Descriptions of the Brauer Group.- Reduced Norms and Traces.- Simple Algebras over a Finite Field.- Quaternion Algebras.- Linear Representations of Algebras.- Linear Representations of Finite Groups.- Algebras without Unit Element.- Determinants over a Noncommunitative Field.- Hilbert's Nullstellensatz.- Trace of an Endomorphism of Finite Rank.- Historical Note.- Bibliography.- Notation Index.- Terminology Index.

Details

Erscheinungsjahr:	2023
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	508
Inhalt:	xviii 490 S.
ISBN-13:	9783031192920
ISBN-10:	3031192923
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Bourbaki, N.
Übersetzung:	Erné, Reinie
Auflage:	2022
Hersteller:	Springer International Publishing Springer International Publishing AG
Maße:	241 x 160 x 33 mm
Von/Mit:	N. Bourbaki
Erscheinungsdatum:	16.03.2023
Gewicht:	0,922 kg