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catalog abstract ""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. Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year."--Jacket.".
catalog contributor b12547049.
catalog created "2002.".
catalog date "2002".
catalog date "2002.".
catalog dateCopyrighted "2002.".
catalog description ""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.".
catalog description "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".
catalog description "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.".
catalog description "Includes bibliographical references (p. 661-669) and index.".
catalog description "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".
catalog description "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".
catalog description "Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year."--Jacket.".
catalog description "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.".
catalog extent "xiv, 676 p. :".
catalog identifier "0521800781 (hardback)".
catalog isPartOf "Encyclopedia of mathematics and its applications ; v. 87".
catalog issued "2002".
catalog issued "2002.".
catalog language "eng".
catalog publisher "Cambridge, UK ; New York : Cambridge University Press,".
catalog subject "512/.55 21".
catalog subject "K-theory.".
catalog subject "QA612.33 .M34 2002".
catalog tableOfContents "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".
catalog tableOfContents "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.".
catalog tableOfContents "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".
catalog tableOfContents "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".
catalog title "An algebraic introduction to K-theory / Bruce A. Magurn.".
catalog type "text".