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
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York :
Cambridge University Press,
2002.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 87. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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 |
| Beschreibung: | 1 online resource (xiv, 676 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 661-669) and index. |
| ISBN: | 9781107089525 1107089522 9781107326002 1107326001 9781107095830 1107095832 1107085594 9781107085596 1139882937 9781139882934 1107103916 9781107103917 1107101417 9781107101418 9780521106580 0521106583 |
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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 | ||
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| 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. |
| 588 | 0 | |a Print version record. | |
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Datensatz im Suchindex
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| adam_text | |
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| author | Magurn, Bruce A. |
| author_facet | Magurn, Bruce A. |
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| contents | Groups of Modules: K[subscript 0] Free Modules Bases Matrix Representations Absence of Dimension Projective Modules Direct Summands Summands of Free Modules Grothendieck Groups Semigroups of Isomorphism Classes Semigroups to Groups Resolutions Stability for Projective Modules Adding Copies of R Stably Free Modules When Stably Free Modules Are Free Stable Rank Dimensions of a Ring Multiplying Modules Semirings Burnside Rings Tensor Products of Modules Change of Rings K[subscript 0] of Related Rings G[subscript 0] of Related Rings K[subscript 0] as a Functor The Jacobson Radical Localization Sources of K[subscript 0] Number Theory Algebraic Integers Dedekind Domains Ideal Class Groups Extensions and Norms K[subscript 0] and G[subscript 0] of Dedekind Domains Group Representation Theory Linear Representations Representing Finite Groups Over Fields Semisimple Rings Characters Groups of Matrices: K[subscript 1] Definition of K[subscript 1] Elementary Matrices Commutators and K[subscript 1](R) Determinants The Bass K[subscript 1] of a Category Stability for K[subscript 1](R) Surjective Stability Injective Stability Relative K[subscript 1] Congruence Subgroups of GL[subscript n](R) Congruence Subgroups of SL[subscript n](R) Mennicke Symbols Relations Among Matrices: K[subscript 2] K[subscript 2](R) and Steinberg Symbols Definition and Properties of K[subscript 2](R) Elements of St(R) and K[subscript 2](R) Exact Sequences The Relative Sequence Excision and the Mayer-Vietoris Sequence The Localization Sequence Universal Algebras Presentation of Algebras Graded Rings The Tensor Algebra Symmetric and Exterior Algebras The Milnor Ring Tame Symbols Norms on Milnor K-Theory Matsumoto's Theorem Sources of K[subscript 2] Symbols in Arithmetic Hilbert Symbols Metric Completion of Fields The p-Adic Numbers and Quadratic Reciprocity Local Fields and Norm Residue Symbols Brauer Groups The Brauer Group of a Field Splitting Fields Twisted Group Rings The K[subscript 2] Connection A Sets, Classes, Functions Chain Conditions, Composition Series |
| ctrlnum | (OCoLC)847527208 |
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| 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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--</subfield><subfield code="g">2A</subfield><subfield code="t">Direct Summands</subfield><subfield code="g">43 --</subfield><subfield code="g">2B</subfield><subfield code="t">Summands of Free Modules</subfield><subfield code="g">51 --</subfield><subfield code="g">Chapter 3</subfield><subfield code="t">Grothendieck Groups</subfield><subfield code="g">57 --</subfield><subfield code="g">3A</subfield><subfield code="t">Semigroups of Isomorphism Classes</subfield><subfield code="g">57 --</subfield><subfield code="g">3B</subfield><subfield code="t">Semigroups to Groups</subfield><subfield code="g">71 --</subfield><subfield code="g">3C</subfield><subfield code="t">Grothendieck Groups</subfield><subfield code="g">83 --</subfield><subfield code="g">3D</subfield><subfield code="t">Resolutions</subfield><subfield code="g">95 --</subfield><subfield code="g">Chapter 4</subfield><subfield code="t">Stability for Projective Modules</subfield><subfield code="g">104 --</subfield><subfield code="g">4A</subfield><subfield code="t">Adding Copies of R</subfield><subfield code="g">104 --</subfield><subfield code="g">4B</subfield><subfield code="t">Stably Free Modules</subfield><subfield code="g">108 --</subfield><subfield code="g">4C</subfield><subfield code="t">When Stably Free Modules Are Free</subfield><subfield code="g">113 --</subfield><subfield code="g">4D</subfield><subfield code="t">Stable Rank</subfield><subfield code="g">120 --</subfield><subfield code="g">4E</subfield><subfield code="t">Dimensions of a Ring</subfield><subfield code="g">128 --</subfield><subfield code="g">Chapter 5</subfield><subfield code="t">Multiplying Modules</subfield><subfield code="g">133 --</subfield><subfield code="g">5A</subfield><subfield code="t">Semirings</subfield><subfield code="g">133 --</subfield><subfield code="g">5B</subfield><subfield code="t">Burnside Rings</subfield><subfield code="g">135 --</subfield><subfield code="g">5C</subfield><subfield code="t">Tensor Products of 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Theory</subfield><subfield code="g">205 --</subfield><subfield code="g">7A</subfield><subfield code="t">Algebraic Integers</subfield><subfield code="g">205 --</subfield><subfield code="g">7B</subfield><subfield code="t">Dedekind Domains</subfield><subfield code="g">212 --</subfield><subfield code="g">7C</subfield><subfield code="t">Ideal Class Groups</subfield><subfield code="g">224 --</subfield><subfield code="g">7D</subfield><subfield code="t">Extensions and Norms</subfield><subfield code="g">230 --</subfield><subfield code="g">7E</subfield><subfield code="t">K[subscript 0] and G[subscript 0] of Dedekind Domains</subfield><subfield code="g">242 --</subfield><subfield code="g">Chapter 8</subfield><subfield code="t">Group Representation Theory</subfield><subfield code="g">252 --</subfield><subfield code="g">8A</subfield><subfield code="t">Linear Representations</subfield><subfield code="g">252 --</subfield><subfield code="g">8B</subfield><subfield code="t">Representing Finite Groups Over Fields</subfield><subfield code="g">265 --</subfield><subfield code="g">8C</subfield><subfield code="t">Semisimple Rings</subfield><subfield code="g">277 --</subfield><subfield code="g">8D</subfield><subfield code="t">Characters</subfield><subfield code="g">300 --</subfield><subfield code="g">Part III</subfield><subfield code="t">Groups of Matrices: K[subscript 1]</subfield><subfield code="g">317 --</subfield><subfield code="g">Chapter 9</subfield><subfield code="t">Definition of K[subscript 1]</subfield><subfield code="g">319 --</subfield><subfield code="g">9A</subfield><subfield code="t">Elementary Matrices</subfield><subfield code="g">319 --</subfield><subfield code="g">9B</subfield><subfield code="t">Commutators and K[subscript 1](R)</subfield><subfield code="g">322 --</subfield><subfield code="g">9C</subfield><subfield code="t">Determinants</subfield><subfield code="g">328 --</subfield><subfield code="g">9D</subfield><subfield code="t">The Bass K[subscript 1] of a Category</subfield><subfield code="g">333 --</subfield><subfield code="g">Chapter 10</subfield><subfield code="t">Stability for K[subscript 1](R)</subfield><subfield code="g">342 --</subfield><subfield code="g">10A</subfield><subfield code="t">Surjective Stability</subfield><subfield code="g">343 --</subfield><subfield code="g">10B</subfield><subfield code="t">Injective Stability</subfield><subfield code="g">348 --</subfield><subfield code="g">Chapter 11</subfield><subfield code="t">Relative K[subscript 1]</subfield><subfield code="g">357 --</subfield><subfield code="g">11A</subfield><subfield code="t">Congruence Subgroups of GL[subscript n](R)</subfield><subfield code="g">357 --</subfield><subfield code="g">11B</subfield><subfield code="t">Congruence Subgroups of SL[subscript n](R)</subfield><subfield code="g">369 --</subfield><subfield code="g">11C</subfield><subfield code="t">Mennicke Symbols</subfield><subfield code="g">374 --</subfield><subfield code="g">Part IV</subfield><subfield code="t">Relations Among Matrices: K[subscript 2]</subfield><subfield code="g">399 --</subfield><subfield code="g">Chapter 12</subfield><subfield code="t">K[subscript 2](R) and Steinberg Symbols</subfield><subfield code="g">401 --</subfield><subfield code="g">12A</subfield><subfield code="t">Definition and Properties of K[subscript 2](R)</subfield><subfield code="g">401 --</subfield><subfield code="g">12B</subfield><subfield code="t">Elements of St(R) and K[subscript 2](R)</subfield><subfield code="g">413 --</subfield><subfield code="g">Chapter 13</subfield><subfield code="t">Exact Sequences</subfield><subfield code="g">430 --</subfield><subfield code="g">13A</subfield><subfield code="t">The Relative Sequence</subfield><subfield code="g">431 --</subfield><subfield code="g">13B</subfield><subfield code="t">Excision and the Mayer-Vietoris Sequence</subfield><subfield code="g">456 --</subfield><subfield code="g">13C</subfield><subfield code="t">The Localization Sequence</subfield><subfield code="g">481 --</subfield><subfield code="g">Chapter 14</subfield><subfield code="t">Universal Algebras</subfield><subfield code="g">488 --</subfield><subfield code="g">14A</subfield><subfield code="t">Presentation of Algebras</subfield><subfield code="g">489 --</subfield><subfield code="g">14B</subfield><subfield code="t">Graded Rings</subfield><subfield code="g">493 --</subfield><subfield code="g">14C</subfield><subfield code="t">The Tensor Algebra</subfield><subfield code="g">497 --</subfield><subfield code="g">14D</subfield><subfield code="t">Symmetric and Exterior Algebras</subfield><subfield code="g">505 --</subfield><subfield code="g">14E</subfield><subfield code="t">The Milnor Ring</subfield><subfield code="g">518 --</subfield><subfield code="g">14F</subfield><subfield code="t">Tame Symbols</subfield><subfield code="g">534 --</subfield><subfield code="g">14G</subfield><subfield code="t">Norms on Milnor K-Theory</subfield><subfield code="g">547 --</subfield><subfield code="g">14H</subfield><subfield code="t">Matsumoto's Theorem</subfield><subfield code="g">557 --</subfield><subfield code="g">Part V</subfield><subfield code="t">Sources of K[subscript 2]</subfield><subfield code="g">567 --</subfield><subfield code="g">Chapter 15</subfield><subfield code="t">Symbols in Arithmetic</subfield><subfield code="g">569 --</subfield><subfield code="g">15A</subfield><subfield code="t">Hilbert Symbols</subfield><subfield code="g">569 --</subfield><subfield code="g">15B</subfield><subfield code="t">Metric Completion of Fields</subfield><subfield code="g">572 --</subfield><subfield code="g">15C</subfield><subfield code="t">The p-Adic Numbers and Quadratic Reciprocity</subfield><subfield code="g">580 --</subfield><subfield code="g">15D</subfield><subfield code="t">Local Fields and Norm Residue Symbols</subfield><subfield code="g">595 --</subfield><subfield code="g">Chapter 16</subfield><subfield code="t">Brauer Groups</subfield><subfield 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| id | ZDB-4-EBA-ocn847527208 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:23Z |
| institution | BVB |
| isbn | 9781107089525 1107089522 9781107326002 1107326001 9781107095830 1107095832 1107085594 9781107085596 1139882937 9781139882934 1107103916 9781107103917 1107101417 9781107101418 9780521106580 0521106583 |
| language | English |
| oclc_num | 847527208 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 676 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Magurn, Bruce A. An algebraic introduction to K-theory / Bruce A. Magurn. Cambridge, UK ; New York : Cambridge University Press, 2002. 1 online resource (xiv, 676 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 87 Includes bibliographical references (pages 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. Print version record. English. K-theory. http://id.loc.gov/authorities/subjects/sh85071200 K-théorie. MATHEMATICS Algebra Linear. bisacsh K-theory fast Algebraische K-Theorie gnd http://d-nb.info/gnd/4141839-6 Print version: Magurn, Bruce A. Algebraic introduction to K-theory. Cambridge, UK ; New York : Cambridge University Press, 2002 0521800781 (DLC) 2001043552 (OCoLC)47863216 Encyclopedia of mathematics and its applications ; v. 87. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569371 Volltext |
| spellingShingle | Magurn, Bruce A. An algebraic introduction to K-theory / Encyclopedia of mathematics and its applications ; Groups of Modules: K[subscript 0] Free Modules Bases Matrix Representations Absence of Dimension Projective Modules Direct Summands Summands of Free Modules Grothendieck Groups Semigroups of Isomorphism Classes Semigroups to Groups Resolutions Stability for Projective Modules Adding Copies of R Stably Free Modules When Stably Free Modules Are Free Stable Rank Dimensions of a Ring Multiplying Modules Semirings Burnside Rings Tensor Products of Modules Change of Rings K[subscript 0] of Related Rings G[subscript 0] of Related Rings K[subscript 0] as a Functor The Jacobson Radical Localization Sources of K[subscript 0] Number Theory Algebraic Integers Dedekind Domains Ideal Class Groups Extensions and Norms K[subscript 0] and G[subscript 0] of Dedekind Domains Group Representation Theory Linear Representations Representing Finite Groups Over Fields Semisimple Rings Characters Groups of Matrices: K[subscript 1] Definition of K[subscript 1] Elementary Matrices Commutators and K[subscript 1](R) Determinants The Bass K[subscript 1] of a Category Stability for K[subscript 1](R) Surjective Stability Injective Stability Relative K[subscript 1] Congruence Subgroups of GL[subscript n](R) Congruence Subgroups of SL[subscript n](R) Mennicke Symbols Relations Among Matrices: K[subscript 2] K[subscript 2](R) and Steinberg Symbols Definition and Properties of K[subscript 2](R) Elements of St(R) and K[subscript 2](R) Exact Sequences The Relative Sequence Excision and the Mayer-Vietoris Sequence The Localization Sequence Universal Algebras Presentation of Algebras Graded Rings The Tensor Algebra Symmetric and Exterior Algebras The Milnor Ring Tame Symbols Norms on Milnor K-Theory Matsumoto's Theorem Sources of K[subscript 2] Symbols in Arithmetic Hilbert Symbols Metric Completion of Fields The p-Adic Numbers and Quadratic Reciprocity Local Fields and Norm Residue Symbols Brauer Groups The Brauer Group of a Field Splitting Fields Twisted Group Rings The K[subscript 2] Connection A Sets, Classes, Functions Chain Conditions, Composition Series K-theory. http://id.loc.gov/authorities/subjects/sh85071200 K-théorie. MATHEMATICS Algebra Linear. bisacsh K-theory fast Algebraische K-Theorie gnd http://d-nb.info/gnd/4141839-6 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85071200 http://d-nb.info/gnd/4141839-6 |
| title | An algebraic introduction to K-theory / |
| title_alt | Groups of Modules: K[subscript 0] Free Modules Bases Matrix Representations Absence of Dimension Projective Modules Direct Summands Summands of Free Modules Grothendieck Groups Semigroups of Isomorphism Classes Semigroups to Groups Resolutions Stability for Projective Modules Adding Copies of R Stably Free Modules When Stably Free Modules Are Free Stable Rank Dimensions of a Ring Multiplying Modules Semirings Burnside Rings Tensor Products of Modules Change of Rings K[subscript 0] of Related Rings G[subscript 0] of Related Rings K[subscript 0] as a Functor The Jacobson Radical Localization Sources of K[subscript 0] Number Theory Algebraic Integers Dedekind Domains Ideal Class Groups Extensions and Norms K[subscript 0] and G[subscript 0] of Dedekind Domains Group Representation Theory Linear Representations Representing Finite Groups Over Fields Semisimple Rings Characters Groups of Matrices: K[subscript 1] Definition of K[subscript 1] Elementary Matrices Commutators and K[subscript 1](R) Determinants The Bass K[subscript 1] of a Category Stability for K[subscript 1](R) Surjective Stability Injective Stability Relative K[subscript 1] Congruence Subgroups of GL[subscript n](R) Congruence Subgroups of SL[subscript n](R) Mennicke Symbols Relations Among Matrices: K[subscript 2] K[subscript 2](R) and Steinberg Symbols Definition and Properties of K[subscript 2](R) Elements of St(R) and K[subscript 2](R) Exact Sequences The Relative Sequence Excision and the Mayer-Vietoris Sequence The Localization Sequence Universal Algebras Presentation of Algebras Graded Rings The Tensor Algebra Symmetric and Exterior Algebras The Milnor Ring Tame Symbols Norms on Milnor K-Theory Matsumoto's Theorem Sources of K[subscript 2] Symbols in Arithmetic Hilbert Symbols Metric Completion of Fields The p-Adic Numbers and Quadratic Reciprocity Local Fields and Norm Residue Symbols Brauer Groups The Brauer Group of a Field Splitting Fields Twisted Group Rings The K[subscript 2] Connection A Sets, Classes, Functions Chain Conditions, Composition Series |
| 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 | algebraic introduction to k theory |
| topic | K-theory. http://id.loc.gov/authorities/subjects/sh85071200 K-théorie. MATHEMATICS Algebra Linear. bisacsh K-theory fast Algebraische K-Theorie gnd http://d-nb.info/gnd/4141839-6 |
| topic_facet | K-theory. K-théorie. MATHEMATICS Algebra Linear. K-theory Algebraische K-Theorie |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569371 |
| work_keys_str_mv | AT magurnbrucea analgebraicintroductiontoktheory AT magurnbrucea algebraicintroductiontoktheory |