An algebraic introduction to K-theory / (Record no. 518024)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 05626nam a22003618i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9781107326002 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160235.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 130129s2002||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781107326002 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521800785 (hardback) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521106580 (paperback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA612.33 |
| Item number | .M34 2002 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512/.55 |
| Edition number | 21 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Magurn, Bruce A., |
| Relator term | author. |
| 245 13 - TITLE STATEMENT | |
| Title | An algebraic introduction to K-theory / |
| Statement of responsibility, etc | Bruce A. Magurn. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2002. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xiv, 676 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | Encyclopedia of mathematics and its applications ; |
| Volume number/sequential designation | volume 87 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Miscellaneous information | Part I |
| Title | Groups of Modules: K[subscript 0] |
| Miscellaneous information | 15 -- |
| -- | Chapter 1 |
| Title | Free Modules |
| Miscellaneous information | 17 -- |
| -- | 1A |
| Title | Bases |
| Miscellaneous information | 17 -- |
| -- | 1B |
| Title | Matrix Representations |
| Miscellaneous information | 26 -- |
| -- | 1C |
| Title | Absence of Dimension |
| Miscellaneous information | 38 -- |
| -- | Chapter 2 |
| Title | Projective Modules |
| Miscellaneous information | 43 -- |
| -- | 2A |
| Title | Direct Summands |
| Miscellaneous information | 43 -- |
| -- | 2B |
| Title | Summands of Free Modules |
| Miscellaneous information | 51 -- |
| -- | Chapter 3 |
| Title | Grothendieck Groups |
| Miscellaneous information | 57 -- |
| -- | 3A |
| Title | Semigroups of Isomorphism Classes |
| Miscellaneous information | 57 -- |
| -- | 3B |
| Title | Semigroups to Groups |
| Miscellaneous information | 71 -- |
| -- | 3C |
| Title | Grothendieck Groups |
| Miscellaneous information | 83 -- |
| -- | 3D |
| Title | Resolutions |
| Miscellaneous information | 95 -- |
| -- | Chapter 4 |
| Title | Stability for Projective Modules |
| Miscellaneous information | 104 -- |
| -- | 4A |
| Title | Adding Copies of R |
| Miscellaneous information | 104 -- |
| -- | 4B |
| Title | Stably Free Modules |
| Miscellaneous information | 108 -- |
| -- | 4C |
| Title | When Stably Free Modules Are Free |
| Miscellaneous information | 113 -- |
| -- | 4D |
| Title | Stable Rank |
| Miscellaneous information | 120 -- |
| -- | 4E |
| Title | Dimensions of a Ring |
| Miscellaneous information | 128 -- |
| -- | Chapter 5 |
| Title | Multiplying Modules |
| Miscellaneous information | 133 -- |
| -- | 5A |
| Title | Semirings |
| Miscellaneous information | 133 -- |
| -- | 5B |
| Title | Burnside Rings |
| Miscellaneous information | 135 -- |
| -- | 5C |
| Title | Tensor Products of Modules |
| Miscellaneous information | 141 -- |
| -- | Chapter 6 |
| Title | Change of Rings |
| Miscellaneous information | 160 -- |
| -- | 6A |
| Title | K[subscript 0] of Related Rings |
| Miscellaneous information | 160 -- |
| -- | 6B |
| Title | G[subscript 0] of Related Rings |
| Miscellaneous information | 169 -- |
| -- | 6C |
| Title | K[subscript 0] as a Functor |
| Miscellaneous information | 174 -- |
| -- | 6D |
| Title | The Jacobson Radical |
| Miscellaneous information | 178 -- |
| -- | 6E |
| Title | Localization |
| Miscellaneous information | 185 -- |
| -- | Part II |
| Title | Sources of K[subscript 0] |
| Miscellaneous information | 203 -- |
| -- | Chapter 7 |
| Title | Number Theory |
| Miscellaneous information | 205 -- |
| -- | 7A |
| Title | Algebraic Integers |
| Miscellaneous information | 205 -- |
| -- | 7B |
| Title | Dedekind Domains |
| Miscellaneous information | 212 -- |
| -- | 7C |
| Title | Ideal Class Groups |
| Miscellaneous information | 224 -- |
| -- | 7D |
| Title | Extensions and Norms |
| Miscellaneous information | 230 -- |
| -- | 7E |
| Title | K[subscript 0] and G[subscript 0] of Dedekind Domains |
| Miscellaneous information | 242 -- |
| -- | Chapter 8 |
| Title | Group Representation Theory |
| Miscellaneous information | 252 -- |
| -- | 8A |
| Title | Linear Representations |
| Miscellaneous information | 252 -- |
| -- | 8B |
| Title | Representing Finite Groups Over Fields |
| Miscellaneous information | 265 -- |
| -- | 8C |
| Title | Semisimple Rings |
| Miscellaneous information | 277 -- |
| -- | 8D |
| Title | Characters |
| Miscellaneous information | 300 -- |
| -- | Part III |
| Title | Groups of Matrices: K[subscript 1] |
| Miscellaneous information | 317 -- |
| -- | Chapter 9 |
| Title | Definition of K[subscript 1] |
| Miscellaneous information | 319 -- |
| -- | 9A |
| Title | Elementary Matrices |
| Miscellaneous information | 319 -- |
| -- | 9B |
| Title | Commutators and K[subscript 1](R) |
| Miscellaneous information | 322 -- |
| -- | 9C |
| Title | Determinants |
| Miscellaneous information | 328 -- |
| -- | 9D |
| Title | The Bass K[subscript 1] of a Category |
| Miscellaneous information | 333 -- |
| -- | Chapter 10 |
| Title | Stability for K[subscript 1](R) |
| Miscellaneous information | 342 -- |
| -- | 10A |
| Title | Surjective Stability |
| Miscellaneous information | 343 -- |
| -- | 10B |
| Title | Injective Stability |
| Miscellaneous information | 348 -- |
| -- | Chapter 11 |
| Title | Relative K[subscript 1] |
| Miscellaneous information | 357 -- |
| -- | 11A |
| Title | Congruence Subgroups of GL[subscript n](R) |
| Miscellaneous information | 357 -- |
| -- | 11B |
| Title | Congruence Subgroups of SL[subscript n](R) |
| Miscellaneous information | 369 -- |
| -- | 11C |
| Title | Mennicke Symbols |
| Miscellaneous information | 374 -- |
| -- | Part IV |
| Title | Relations Among Matrices: K[subscript 2] |
| Miscellaneous information | 399 -- |
| -- | Chapter 12 |
| Title | K[subscript 2](R) and Steinberg Symbols |
| Miscellaneous information | 401 -- |
| -- | 12A |
| Title | Definition and Properties of K[subscript 2](R) |
| Miscellaneous information | 401 -- |
| -- | 12B |
| Title | Elements of St(R) and K[subscript 2](R) |
| Miscellaneous information | 413 -- |
| -- | Chapter 13 |
| Title | Exact Sequences |
| Miscellaneous information | 430 -- |
| -- | 13A |
| Title | The Relative Sequence |
| Miscellaneous information | 431 -- |
| -- | 13B |
| Title | Excision and the Mayer-Vietoris Sequence |
| Miscellaneous information | 456 -- |
| -- | 13C |
| Title | The Localization Sequence |
| Miscellaneous information | 481 -- |
| -- | Chapter 14 |
| Title | Universal Algebras |
| Miscellaneous information | 488 -- |
| -- | 14A |
| Title | Presentation of Algebras |
| Miscellaneous information | 489 -- |
| -- | 14B |
| Title | Graded Rings |
| Miscellaneous information | 493 -- |
| -- | 14C |
| Title | The Tensor Algebra |
| Miscellaneous information | 497 -- |
| -- | 14D |
| Title | Symmetric and Exterior Algebras |
| Miscellaneous information | 505 -- |
| -- | 14E |
| Title | The Milnor Ring |
| Miscellaneous information | 518 -- |
| -- | 14F |
| Title | Tame Symbols |
| Miscellaneous information | 534 -- |
| -- | 14G |
| Title | Norms on Milnor K-Theory |
| Miscellaneous information | 547 -- |
| -- | 14H |
| Title | Matsumoto's Theorem |
| Miscellaneous information | 557 -- |
| -- | Part V |
| Title | Sources of K[subscript 2] |
| Miscellaneous information | 567 -- |
| -- | Chapter 15 |
| Title | Symbols in Arithmetic |
| Miscellaneous information | 569 -- |
| -- | 15A |
| Title | Hilbert Symbols |
| Miscellaneous information | 569 -- |
| -- | 15B |
| Title | Metric Completion of Fields |
| Miscellaneous information | 572 -- |
| -- | 15C |
| Title | The p-Adic Numbers and Quadratic Reciprocity |
| Miscellaneous information | 580 -- |
| -- | 15D |
| Title | Local Fields and Norm Residue Symbols |
| Miscellaneous information | 595 -- |
| -- | Chapter 16 |
| Title | Brauer Groups |
| Miscellaneous information | 610 -- |
| -- | 16A |
| Title | The Brauer Group of a Field |
| Miscellaneous information | 610 -- |
| -- | 16B |
| Title | Splitting Fields |
| Miscellaneous information | 623 -- |
| -- | 16C |
| Title | Twisted Group Rings |
| Miscellaneous information | 629 -- |
| -- | 16D |
| Title | The K[subscript 2] Connection |
| Miscellaneous information | 636 -- |
| Title | A Sets, Classes, Functions |
| Miscellaneous information | 645 -- |
| -- | B |
| Title | Chain Conditions, Composition Series |
| Miscellaneous information | 647. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | K-theory. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521800785 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Encyclopedia of mathematics and its applications ; |
| Volume number/sequential designation | v. 87. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9781107326002">https://doi.org/10.1017/CBO9781107326002</a> |
No items available.