An algebraic introduction to K-theory

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An algebraic introduction to K-theory / Bruce A. Magurn

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 2002
形態:: xiv, 676 p. ; 24 cm
シリーズ名:: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 87 <BA00064663>
著者名:: Magurn, Bruce A. <DA01278567>
ISBN:: 9780521800785 [0521800781]
書誌ID:: BA56729476

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注記:

Bibliography: p. 661-669
Includes index

主題:

K-theory

言語:

英語

目次情報:

Preface

Preliminaries / Chapter 0：

Groups of Modules: K[subscript 0] / Part I：

Free Modules / Chapter 1：

Bases / 1A：

Matrix Representations / 1B：

Absence of Dimension / 1C：

Projective Modules / Chapter 2：

Direct Summands / 2A：

Summands of Free Modules / 2B：

Grothendieck Groups / Chapter 3：

Semigroups of Isomorphism Classes / 3A：

Semigroups to Groups / 3B：

Resolutions / 3C：

Stability for Projective Modules / Chapter 4：

Adding Copies of R / 4A：

Stably Free Modules / 4B：

When Stably Free Modules Are Free / 4C：

Stable Rank / 4D：

Dimensions of a Ring / 4E：

Multiplying Modules / Chapter 5：

Semirings / 5A：

Burnside Rings / 5B：

Tensor Products of Modules / 5C：

Change of Rings / Chapter 6：

K[subscript 0] of Related Rings / 6A：

G[subscript 0] of Related Rings / 6B：

K[subscript 0] as a Functor / 6C：

The Jacobson Radical / 6D：

Localization / 6E：

Sources of K[subscript 0] / Part II：

Number Theory / Chapter 7：

Algebraic Integers / 7A：

Dedekind Domains / 7B：

Ideal Class Groups / 7C：

Extensions and Norms / 7D：

K[subscript 0] and G[subscript 0] of Dedekind Domains / 7E：

Group Representation Theory / Chapter 8：

Linear Representations / 8A：

Representing Finite Groups Over Fields / 8B：

Semisimple Rings / 8C：

Characters / 8D：

Groups of Matrices: K[subscript 1] / Part III：

Definition of K[subscript 1] / Chapter 9：

Elementary Matrices / 9A：

Commutators and K[subscript 1](R) / 9B：

Determinants / 9C：

The Bass K[subscript 1] of a Category / 9D：

Stability for K[subscript 1](R) / Chapter 10：

Surjective Stability / 10A：

Injective Stability / 10B：

Relative K[subscript 1] / Chapter 11：

Congruence Subgroups of GL[subscript n](R) / 11A：

Congruence Subgroups of SL[subscript n](R) / 11B：

Mennicke Symbols / 11C：

Relations Among Matrices: K[subscript 2] / Part IV：

K[subscript 2](R) and Steinberg Symbols / Chapter 12：

Definition and Properties of K[subscript 2](R) / 12A：

Elements of St(R) and K[subscript 2](R) / 12B：

Exact Sequences / Chapter 13：

The Relative Sequence / 13A：

Excision and the Mayer-Vietoris Sequence / 13B：

The Localization Sequence / 13C：

Universal Algebras / Chapter 14：

Presentation of Algebras / 14A：

Graded Rings / 14B：

The Tensor Algebra / 14C：

Symmetric and Exterior Algebras / 14D：

The Milnor Ring / 14E：

Tame Symbols / 14F：

Norms on Milnor K-Theory / 14G：

Matsumoto's Theorem / 14H：

Sources of K[subscript 2] / Part V：

Symbols in Arithmetic / Chapter 15：

Hilbert Symbols / 15A：

Metric Completion of Fields / 15B：

The p-Adic Numbers and Quadratic Reciprocity / 15C：

Local Fields and Norm Residue Symbols / 15D：

Brauer Groups / Chapter 16：

The Brauer Group of a Field / 16A：

Splitting Fields / 16B：

Twisted Group Rings / 16C：

The K[subscript 2] Connection / 16D：

Appendix

Sets, Classes, Functions / A：

Chain Conditions, Composition Series / B：

Special Symbols

References

Index

Preface

Preliminaries / Chapter 0：

Groups of Modules: K[subscript 0] / Part I：

Free Modules / Chapter 1：

Bases / 1A：

Matrix Representations / 1B：

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