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An Algebraic Introduction to K-Theory: 87 (Encyclopedia of Mathematics and its Applications, Series Number 87) - Hardcover
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.
"synopsis" may belong to another edition of this title.
Review
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
Book Description
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.
"About this title" may belong to another edition of this title.
- PublisherCambridge University Press
- Publication date2002
- ISBN 10 0521800781
- ISBN 13 9780521800785
- BindingHardcover
- LanguageEnglish
- Number of pages692
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An Algebraic Introduction to K-Theory (Encyclopedia of Mathematics and its Applications, Series Number 87)
Published by
Cambridge University Press, 2002
ISBN 10: 0521800781
ISBN 13: 9780521800785
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An Algebraic Introduction to K-Theory (Encyclopedia of Mathematics and its Applications, Series Number 87)
Published by
Cambridge University Press, 2002
ISBN 10: 0521800781
ISBN 13: 9780521800785
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An Algebraic Introduction to K-Theory (Hardcover)
Published by
Cambridge University Press, Cambridge, 2002
ISBN 10: 0521800781
ISBN 13: 9780521800785
New
Hardcover
Seller: CitiRetail, Stevenage, United Kingdom
Seller rating 5 out of 5 stars
Hardcover. Condition: new. Hardcover. 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 organizes 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, localization, Jacobson radical, chain conditions, Dedekind domains, semisimple 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. This book is both an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the clasical algebraic K-theory. On the other hand, K-theory is a natural organizing principle for the standard topics of a second course in algebra, and these topics are presented carefully here. The reader will not only learn algebraic K-theory, but also Dedekind domains, class groups, semisimple rings, character theory, quadratic forms, tensor products, localization, completion, tensor algebras, symmetric algebras, exterior algebras, central simple algebras, and Brauer groups. The presentation is self-contained, with all the necessary background and proofs, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. The prerequisites are minimal: just a first semester of algebra (including Galois theory and modules over a principal ideal domain). No experience with homological algebra, analysis, geometry, number theory, or topology is assumed. The author has successfuly used this text to teach algebra to first year graduate students. Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9780521800785
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An Algebraic Introduction to K-Theory (Hardcover)
Published by
Cambridge University Press, Cambridge, 2002
ISBN 10: 0521800781
ISBN 13: 9780521800785
New
Hardcover
Seller: AussieBookSeller, Truganina, VIC, Australia
Seller rating 3 out of 5 stars
Hardcover. Condition: new. Hardcover. 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 organizes 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, localization, Jacobson radical, chain conditions, Dedekind domains, semisimple 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. This book is both an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the clasical algebraic K-theory. On the other hand, K-theory is a natural organizing principle for the standard topics of a second course in algebra, and these topics are presented carefully here. The reader will not only learn algebraic K-theory, but also Dedekind domains, class groups, semisimple rings, character theory, quadratic forms, tensor products, localization, completion, tensor algebras, symmetric algebras, exterior algebras, central simple algebras, and Brauer groups. The presentation is self-contained, with all the necessary background and proofs, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. The prerequisites are minimal: just a first semester of algebra (including Galois theory and modules over a principal ideal domain). No experience with homological algebra, analysis, geometry, number theory, or topology is assumed. The author has successfuly used this text to teach algebra to first year graduate students. Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Seller Inventory # 9780521800785
Quantity: 1 available
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An Algebraic Introduction to K-Theory
Published by
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ISBN 10: 0521800781
ISBN 13: 9780521800785
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An Algebraic Introduction to K-Theory (Encyclopedia of Mathematics and its Applications, Series Number 87)
Published by
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ISBN 10: 0521800781
ISBN 13: 9780521800785
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An Algebraic Introduction to K-Theory
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ISBN 10: 0521800781
ISBN 13: 9780521800785
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Gebunden. Condition: New. 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. Seller Inventory # 446947659
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An Algebraic Introduction to K-Theory (Encyclopedia of Mathematics and its Applications, Series Number 87)
Published by
Cambridge University Press, 2002
ISBN 10: 0521800781
ISBN 13: 9780521800785
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An Algebraic Introduction to K-Theory (Hardcover)
Published by
Cambridge University Press, Cambridge, 2002
ISBN 10: 0521800781
ISBN 13: 9780521800785
New
Hardcover
Seller: Grand Eagle Retail, Fairfield, OH, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Condition: new. Hardcover. 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 organizes 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, localization, Jacobson radical, chain conditions, Dedekind domains, semisimple 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. This book is both an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the clasical algebraic K-theory. On the other hand, K-theory is a natural organizing principle for the standard topics of a second course in algebra, and these topics are presented carefully here. The reader will not only learn algebraic K-theory, but also Dedekind domains, class groups, semisimple rings, character theory, quadratic forms, tensor products, localization, completion, tensor algebras, symmetric algebras, exterior algebras, central simple algebras, and Brauer groups. The presentation is self-contained, with all the necessary background and proofs, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. The prerequisites are minimal: just a first semester of algebra (including Galois theory and modules over a principal ideal domain). No experience with homological algebra, analysis, geometry, number theory, or topology is assumed. The author has successfuly used this text to teach algebra to first year graduate students. Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521800785
Quantity: 1 available
Stock Image
An Algebraic Introduction to K-Theory
Published by
Cambridge University Press, 2002
ISBN 10: 0521800781
ISBN 13: 9780521800785
New
Hardcover
Seller: Revaluation Books, Exeter, United Kingdom
Seller rating 5 out of 5 stars
Hardcover. Condition: Brand New. 676 pages. 9.50x6.75x1.50 inches. In Stock. Seller Inventory # x-0521800781
Quantity: 2 available