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: |