An algebraic introduction to K-theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK
Cambridge University Press
2002
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
v. 87 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 661-669) and index "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 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 |
| Beschreibung: | 1 Online-Ressource (xiv, 676 p.) |
| ISBN: | 0521800781 1107089522 1107326001 9780521800785 9781107089525 9781107326002 |
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| 100 | 1 | |a Magurn, Bruce A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An algebraic introduction to K-theory |c Bruce A. Magurn |
| 264 | 1 | |a Cambridge, UK |b Cambridge University Press |c 2002 | |
| 300 | |a 1 Online-Ressource (xiv, 676 p.) | ||
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| 490 | 0 | |a Encyclopedia of mathematics and its applications |v v. 87 | |
| 500 | |a Includes bibliographical references (p. 661-669) and index | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |a Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year."--Jacket | ||
| 500 | |a 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 | ||
| 500 | |a - 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 | ||
| 500 | |a - 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 | ||
| 500 | |a - 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 | ||
| 650 | 4 | |a K-théorie | |
| 650 | 7 | |a Algebraische K-Theorie |2 swd | |
| 650 | 7 | |a MATHEMATICS / Algebra / Linear |2 bisacsh | |
| 650 | 7 | |a K-theory |2 fast | |
| 650 | 4 | |a K-theory | |
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Datensatz im Suchindex
| _version_ | 1804175473345822720 |
|---|---|
| any_adam_object | |
| author | Magurn, Bruce A. |
| author_facet | Magurn, Bruce A. |
| author_role | aut |
| author_sort | Magurn, Bruce A. |
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| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043081061 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:51Z |
| institution | BVB |
| isbn | 0521800781 1107089522 1107326001 9780521800785 9781107089525 9781107326002 |
| language | English |
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| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Magurn, Bruce A. Verfasser aut An algebraic introduction to K-theory Bruce A. Magurn Cambridge, UK Cambridge University Press 2002 1 Online-Ressource (xiv, 676 p.) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications v. 87 Includes bibliographical references (p. 661-669) and index "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 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 K-théorie Algebraische K-Theorie swd MATHEMATICS / Algebra / Linear bisacsh K-theory fast K-theory K-Theorie (DE-588)4033335-8 gnd rswk-swf K-Theorie (DE-588)4033335-8 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=569371 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Magurn, Bruce A. An algebraic introduction to K-theory K-théorie Algebraische K-Theorie swd MATHEMATICS / Algebra / Linear bisacsh K-theory fast K-theory K-Theorie (DE-588)4033335-8 gnd |
| subject_GND | (DE-588)4033335-8 |
| title | An algebraic introduction to K-theory |
| title_auth | An algebraic introduction to K-theory |
| title_exact_search | An algebraic introduction to K-theory |
| title_full | An algebraic introduction to K-theory Bruce A. Magurn |
| title_fullStr | An algebraic introduction to K-theory Bruce A. Magurn |
| title_full_unstemmed | An algebraic introduction to K-theory Bruce A. Magurn |
| title_short | An algebraic introduction to K-theory |
| title_sort | an algebraic introduction to k theory |
| topic | K-théorie Algebraische K-Theorie swd MATHEMATICS / Algebra / Linear bisacsh K-theory fast K-theory K-Theorie (DE-588)4033335-8 gnd |
| topic_facet | K-théorie Algebraische K-Theorie MATHEMATICS / Algebra / Linear K-theory K-Theorie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=569371 |
| work_keys_str_mv | AT magurnbrucea analgebraicintroductiontoktheory |