Articles liés à An Algebraic Introduction to K-Theory

An Algebraic Introduction to K-Theory - Couverture rigide

Livre 79 sur 188: Encyclopedia of Mathematics and its Applications

Magurn, Bruce A.

 
9780521800785: An Algebraic Introduction to K-Theory
Couverture rigide
ISBN 10 : 0521800781 ISBN 13 : 9780521800785
Editeur : Cambridge University Press, 2002

Synopsis

This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.

Revue de presse

Review of the hardback: '... this is a well written introduction to the theory of the algebraic K-groups Ko, K1 and K2; the author has done a wonderful job in presenting the material in a clear way that will be accessible to readers with a modest background in algebra.' Franz Lemmermeyer, Zentralblatt MATH

Review of the hardback: 'This is a fine introduction to algebraic K-theory, requiring only a basic preliminary knowledge of groups, rings and modules.' European Mathematical Society

Review of the hardback: '... a fine introduction to algebraic K-theory ...' EMS Newsletter

Review of the hardback: '... an excellent introduction to the algebraic K-theory.' Proceedings of the Edinburgh Mathematical Society

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2002
Langue
anglais
ISBN 10 
0521800781
ISBN 13 
9780521800785
Reliure
Relié
Nombre de pages
692
Coordonnées du fabricant
Cambridge University Press
https://www.cambridge.org/

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