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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
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2002.
|
| Colección: | Encyclopedia of mathematics and its applications ;
v. 87. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Magurn, Bruce A. | |
| 245 | 1 | 3 | |a An algebraic introduction to K-theory / |c Bruce A. Magurn. |
| 260 | |a Cambridge, UK ; |a New York : |b Cambridge University Press, |c 2002. | ||
| 300 | |a 1 online resource (xiv, 676 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v v. 87 | |
| 504 | |a Includes bibliographical references (pages 661-669) and index. | ||
| 520 | 1 | |a "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 | |
| 520 | 8 | |a 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. | |
| 520 | 8 | |a Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year."--Jacket | |
| 505 | 0 | 0 | |g Part I |t Groups of Modules: K[subscript 0] |g 15 -- |g Chapter 1 |t Free Modules |g 17 -- |g 1A |t Bases |g 17 -- |g 1B |t Matrix Representations |g 26 -- |g 1C |t Absence of Dimension |g 38 -- |g Chapter 2 |t Projective Modules |g 43 -- |g 2A |t Direct Summands |g 43 -- |g 2B |t Summands of Free Modules |g 51 -- |g Chapter 3 |t Grothendieck Groups |g 57 -- |g 3A |t Semigroups of Isomorphism Classes |g 57 -- |g 3B |t Semigroups to Groups |g 71 -- |g 3C |t Grothendieck Groups |g 83 -- |g 3D |t Resolutions |g 95 -- |g Chapter 4 |t Stability for Projective Modules |g 104 -- |g 4A |t Adding Copies of R |g 104 -- |g 4B |t Stably Free Modules |g 108 -- |g 4C |t When Stably Free Modules Are Free |g 113 -- |g 4D |t Stable Rank |g 120 -- |g 4E |t Dimensions of a Ring |g 128 -- |g Chapter 5 |t Multiplying Modules |g 133 -- |g 5A |t Semirings |g 133 -- |g 5B |t Burnside Rings |g 135 -- |g 5C |t Tensor Products of Modules |g 141 -- |g Chapter 6 |t Change of Rings |g 160 -- |g 6A |t K[subscript 0] of Related Rings |g 160 -- |g 6B |t G[subscript 0] of Related Rings |g 169 -- |g 6C |t K[subscript 0] as a Functor |g 174 -- |g 6D |t The Jacobson Radical |g 178 -- |g 6E |t Localization |g 185 -- |g Part II |t Sources of K[subscript 0] |g 203 -- |g Chapter 7 |t Number Theory |g 205 -- |g 7A |t Algebraic Integers |g 205 -- |g 7B |t Dedekind Domains |g 212 -- |g 7C |t Ideal Class Groups |g 224 -- |g 7D |t Extensions and Norms |g 230 -- |g 7E |t K[subscript 0] and G[subscript 0] of Dedekind Domains |g 242 -- |g Chapter 8 |t Group Representation Theory |g 252 -- |g 8A |t Linear Representations |g 252 -- |g 8B |t Representing Finite Groups Over Fields |g 265 -- |g 8C |t Semisimple Rings |g 277 -- |g 8D |t Characters |g 300 -- |g Part III |t Groups of Matrices: K[subscript 1] |g 317 -- |g Chapter 9 |t Definition of K[subscript 1] |g 319 -- |g 9A |t Elementary Matrices |g 319 -- |g 9B |t Commutators and K[subscript 1](R) |g 322 -- |g 9C |t Determinants |g 328 -- |g 9D |t The Bass K[subscript 1] of a Category |g 333 -- |g Chapter 10 |t Stability for K[subscript 1](R) |g 342 -- |g 10A |t Surjective Stability |g 343 -- |g 10B |t Injective Stability |g 348 -- |g Chapter 11 |t Relative K[subscript 1] |g 357 -- |g 11A |t Congruence Subgroups of GL[subscript n](R) |g 357 -- |g 11B |t Congruence Subgroups of SL[subscript n](R) |g 369 -- |g 11C |t Mennicke Symbols |g 374 -- |g Part IV |t Relations Among Matrices: K[subscript 2] |g 399 -- |g Chapter 12 |t K[subscript 2](R) and Steinberg Symbols |g 401 -- |g 12A |t Definition and Properties of K[subscript 2](R) |g 401 -- |g 12B |t Elements of St(R) and K[subscript 2](R) |g 413 -- |g Chapter 13 |t Exact Sequences |g 430 -- |g 13A |t The Relative Sequence |g 431 -- |g 13B |t Excision and the Mayer-Vietoris Sequence |g 456 -- |g 13C |t The Localization Sequence |g 481 -- |g Chapter 14 |t Universal Algebras |g 488 -- |g 14A |t Presentation of Algebras |g 489 -- |g 14B |t Graded Rings |g 493 -- |g 14C |t The Tensor Algebra |g 497 -- |g 14D |t Symmetric and Exterior Algebras |g 505 -- |g 14E |t The Milnor Ring |g 518 -- |g 14F |t Tame Symbols |g 534 -- |g 14G |t Norms on Milnor K-Theory |g 547 -- |g 14H |t Matsumoto's Theorem |g 557 -- |g Part V |t Sources of K[subscript 2] |g 567 -- |g Chapter 15 |t Symbols in Arithmetic |g 569 -- |g 15A |t Hilbert Symbols |g 569 -- |g 15B |t Metric Completion of Fields |g 572 -- |g 15C |t The p-Adic Numbers and Quadratic Reciprocity |g 580 -- |g 15D |t Local Fields and Norm Residue Symbols |g 595 -- |g Chapter 16 |t Brauer Groups |g 610 -- |g 16A |t The Brauer Group of a Field |g 610 -- |g 16B |t Splitting Fields |g 623 -- |g 16C |t Twisted Group Rings |g 629 -- |g 16D |t The K[subscript 2] Connection |g 636 -- |t A Sets, Classes, Functions |g 645 -- |g B |t Chain Conditions, Composition Series |g 647. |
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| 650 | 0 | |a K-theory. | |
| 650 | 6 | |a K-théorie. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a K-theory |2 fast | |
| 650 | 7 | |a Algebraische K-Theorie |2 gnd | |
| 776 | 0 | 8 | |i Print version: |a Magurn, Bruce A. |t Algebraic introduction to K-theory. |d Cambridge, UK ; New York : Cambridge University Press, 2002 |z 0521800781 |w (DLC) 2001043552 |w (OCoLC)47863216 |
| 830 | 0 | |a Encyclopedia of mathematics and its applications ; |v v. 87. | |
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