An algebraic introduction to K-theory /

"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

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Magurn, Bruce A.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, UK ; New York : Cambridge University Press, 2002.
Colección:Encyclopedia of mathematics and its applications ; v. 87.
Temas:
K-theory.
K-théorie.
MATHEMATICS > Algebra > Linear.
K-theory
Algebraische K-Theorie
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Part I Groups of Modules: K[subscript 0] 15
  • Chapter 1 Free Modules 17
  • 1A Bases 17
  • 1B Matrix Representations 26
  • 1C Absence of Dimension 38
  • Chapter 2 Projective Modules 43
  • 2A Direct Summands 43
  • 2B Summands of Free Modules 51
  • Chapter 3 Grothendieck Groups 57
  • 3A Semigroups of Isomorphism Classes 57
  • 3B Semigroups to Groups 71
  • 3C Grothendieck Groups 83
  • 3D Resolutions 95
  • Chapter 4 Stability for Projective Modules 104
  • 4A Adding Copies of R 104
  • 4B Stably Free Modules 108
  • 4C When Stably Free Modules Are Free 113
  • 4D Stable Rank 120
  • 4E Dimensions of a Ring 128
  • Chapter 5 Multiplying Modules 133
  • 5A Semirings 133
  • 5B Burnside Rings 135
  • 5C Tensor Products of Modules 141
  • Chapter 6 Change of Rings 160
  • 6A K[subscript 0] of Related Rings 160
  • 6B G[subscript 0] of Related Rings 169
  • 6C K[subscript 0] as a Functor 174
  • 6D The Jacobson Radical 178
  • 6E Localization 185
  • Part II Sources of K[subscript 0] 203
  • Chapter 7 Number Theory 205
  • 7A Algebraic Integers 205
  • 7B Dedekind Domains 212
  • 7C Ideal Class Groups 224
  • 7D Extensions and Norms 230
  • 7E K[subscript 0] and G[subscript 0] of Dedekind Domains 242
  • Chapter 8 Group Representation Theory 252
  • 8A Linear Representations 252
  • 8B Representing Finite Groups Over Fields 265
  • 8C Semisimple Rings 277
  • 8D Characters 300
  • Part III Groups of Matrices: K[subscript 1] 317
  • Chapter 9 Definition of K[subscript 1] 319
  • 9A Elementary Matrices 319
  • 9B Commutators and K[subscript 1](R) 322
  • 9C Determinants 328
  • 9D The Bass K[subscript 1] of a Category 333
  • Chapter 10 Stability for K[subscript 1](R) 342
  • 10A Surjective Stability 343
  • 10B Injective Stability 348
  • Chapter 11 Relative K[subscript 1] 357
  • 11A Congruence Subgroups of GL[subscript n](R) 357
  • 11B Congruence Subgroups of SL[subscript n](R) 369
  • 11C Mennicke Symbols 374
  • Part IV Relations Among Matrices: K[subscript 2] 399
  • Chapter 12 K[subscript 2](R) and Steinberg Symbols 401
  • 12A Definition and Properties of K[subscript 2](R) 401
  • 12B Elements of St(R) and K[subscript 2](R) 413
  • Chapter 13 Exact Sequences 430
  • 13A The Relative Sequence 431
  • 13B Excision and the Mayer-Vietoris Sequence 456
  • 13C The Localization Sequence 481
  • Chapter 14 Universal Algebras 488
  • 14A Presentation of Algebras 489
  • 14B Graded Rings 493
  • 14C The Tensor Algebra 497
  • 14D Symmetric and Exterior Algebras 505
  • 14E The Milnor Ring 518
  • 14F Tame Symbols 534
  • 14G Norms on Milnor K-Theory 547
  • 14H Matsumoto's Theorem 557
  • Part V Sources of K[subscript 2] 567
  • Chapter 15 Symbols in Arithmetic 569
  • 15A Hilbert Symbols 569
  • 15B Metric Completion of Fields 572
  • 15C The p-Adic Numbers and Quadratic Reciprocity 580
  • 15D Local Fields and Norm Residue Symbols 595
  • Chapter 16 Brauer Groups 610
  • 16A The Brauer Group of a Field 610
  • 16B Splitting Fields 623
  • 16C Twisted Group Rings 629
  • 16D The K[subscript 2] Connection 636
  • A Sets, Classes, Functions 645
  • B Chain Conditions, Composition Series 647.

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