Holdings: An algebraic introduction to K-Theory

An algebraic introduction to K-Theory:

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Bibliographic Details
Main Author:	Magurn, Bruce A. (Author)
Format:	Book
Language:	English
Published:	Cambridge Univ. Press 2002
Edition:	1.publ.
Series:	Encyclopedia of mathematics and its applications 87
Subjects:	K-Theorie
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XIV, 676 S.
ISBN:	0521800781 9780521800785 9780521106580

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MARC


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adam_text	ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS AN ALGEBRAIC INTRODUCTION TO K-THEORY BRUCE A. MAGURN MIAMI UNIVERSITY, OHIO CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE XI CHAPTER 0 PRELIMINARIES 1 PART I GROUPS OF MODULES: KQ 15 CHAPTER 1 FREE MODULES 17 1A BASES 17 IB 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 5 A SEMIRINGS 133 5B BURNSIDE RINGS 135 5C TENSOR PRODUCTS OF MODULES 141 CHAPTER 6 CHANGE OF RINGS 160 6A KQ OF RELATED RINGS 160 6B G O OF RELATED RINGS 169 6C K O AS A FUNCTOR 174 CONTENTS 6D THE JACOBSON RADICAL 178 6E LOCALIZATION 185 PART II SOURCES OF K O 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 KO AND GQ OF DEDEKIND DOMAINS 24 2 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 T 317 CHAPTER 9 DEFINITION OF K X 319 9A ELEMENTARY MATRICES 319 9B COMMUTATORS AND K X (R) , 322 9C DETERMINANTS . 328 9D THE BASS K X OF A CATEGORY 333 CHAPTER 10 STABILITY FOR K X (R) .. 342 * 10A SURJECTIVE STABILITY 343 10B INJECTIVE STABILITY 348 CHAPTER 11 RELATIVE K X 357 11A CONGRUENCE SUBGROUPS OF GL N (R) 357 11B CONGRUENCE SUBGROUPS OF SL N (R) 369 LLC MENNICKE SYMBOLS 374 PART IV RELATIONS AMONG MATRICES: K? 399 CHAPTER 12 K 2 (R) AND STEINBERG SYMBOLS 401 12A DEFINITION AND PROPERTIES OF K 2 (R) 401 12B ELEMENTS OF ST(R) AND K 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 CONTENTS 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 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 2 CONNECTION 636 APPENDIX 645 A SETS, CLASSES, FUNCTIONS 645 B CHAIN CONDITIONS, COMPOSITION SERIES 647 SPECIAL SYMBOLS 657 REFERENCES 661 INDEX 671
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spelling	Magurn, Bruce A. Verfasser aut An algebraic introduction to K-Theory Bruce A. Magurn 1.publ. Cambridge Univ. Press 2002 XIV, 676 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 87 Hier auch später erschienene, unveränderte Nachdrucke K-Theorie (DE-588)4033335-8 gnd rswk-swf K-Theorie (DE-588)4033335-8 s DE-604 Encyclopedia of mathematics and its applications 87 (DE-604)BV000903719 87 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009818174&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Magurn, Bruce A. An algebraic introduction to K-Theory Encyclopedia of mathematics and its applications 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-Theorie (DE-588)4033335-8 gnd
topic_facet	K-Theorie
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