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Beschreibung
This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.
This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.
Inhaltsverzeichnis
1. Categories; 2. Categories and exact sequences; 3. Change of rings; 4. The Morita theory; 5. Limits in categories; 6. Localisation; 7. Local-global methods.
Details
Erscheinungsjahr: 2012
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Buch
ISBN-13: 9780521632768
ISBN-10: 0521632765
Sprache: Englisch
Einband: Gebunden
Autor: Berrick, A. J.
Keating, M. E.
Redaktion: Bollobas, Bela
Hersteller: Cambridge University Press
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 235 x 157 x 27 mm
Von/Mit: A. J. Berrick (u. a.)
Erscheinungsdatum: 25.05.2012
Gewicht: 0,766 kg
Artikel-ID: 102551605

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