Categories and modules: with K-theory in view
Berrick, A. J.
Categories and modules: with K-theory in view - Cambridge: Cambridge University Press, 2000. - xvii, 361 p. : ill. ; hb. ; 24 cm. - Cambridge studies in advanced mathematics ; 67 .
Includes bibliographical references (p. 344-349) and index.
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.
9780521632768
Modules (Algebra)
Categories (Mathematics)
K-theory
The Morita theory
Localisation
511.3 / BER
Categories and modules: with K-theory in view - Cambridge: Cambridge University Press, 2000. - xvii, 361 p. : ill. ; hb. ; 24 cm. - Cambridge studies in advanced mathematics ; 67 .
Includes bibliographical references (p. 344-349) and index.
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.
9780521632768
Modules (Algebra)
Categories (Mathematics)
K-theory
The Morita theory
Localisation
511.3 / BER
