Verfügbarkeit: Galois theory

Galois theory:

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1. Verfasser:	Stewart, Ian 1945- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2015]
Ausgabe:	Fourth edition
Schriftenreihe:	A Chapman & Hall book
Schlagworte:	Galois theory Algebraische Gleichung Galois-Theorie Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Previous edition, 2004. - Includes bibliographical references (pages 309-314) and index
Beschreibung:	xxii, 321 Seiten Illustrationen, Diagramme 24 cm
ISBN:	9781482245820

Internformat

MARC


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Datensatz im Suchindex

_version_	1804176105694822400
adam_text	CONTENTS ACKNOWLEDGEMENTS PREFACE TO THE FIRST EDITION PREFACE TO THE SECOND EDITION PREFACE TO THE THIRD EDITION PREFACE TO THE FOURTH EDITION HISTORICAL INTRODUCTION %1 XLLL XV XVLL XXI 1 1 CLASSICAL ALGEBRA 17 1.1 COMPLEX NUMBERS .................. ........ 18 1.2 SUBFIELDS AND SUBRINGS OF THE COMPLEX NUMBERS .......... 18 1.3 SOLVING EQUATIONS .......................... 22 1.4 SOLUTION BY RADICALS . ..... ... . .... ........... 24 2 THE FUNDAMENTAL THEOREM OF ALGEBRA 35 2.1 POLYNOMIALS ............................. 35 2.2 FUNDAMENTAL THEOREM OF ALGEBRA .................. 39 2.3 IMPLICATIONS ............................. 42 3 FACTORISATION OF POLYNOMIALS 47 3.1 THE EUCLIDEAN ALGORITHM ...................... 47 3.2 IRREDUCIBILITY ............................. 51 3.3 GAUSS S LEMMA ............................ 54 3.4 EISENSTEIN S CRITERION ......................... 55 3.5 REDUCTION MODULO P......................... 57 3.6 ZEROS OF POLYNOMIALS ....................... 58 4 FIELD EXTENSIONS 63 4.1 FIELD EXTENSIONS ........... ............. .. 63 4.2 RATIONAL EXPRESSIONS ......................... 66 4.3 SIMPLE EXTENSIONS ........................ .. 67 VII $ BIIOTHEK DEUTSCHES MUSEUM T? HLUENCHE A VIII CONTENTS 5 SIMPLE EXTENSIONS 71 5.1 ALGEBRAIC AND TRANSCENDENTAL EXTENSIONS ....... ....... 71 5.2 THE MINIMAL POLYNOMIAL .................. ..... 72 5.3 SIMPLE ALGEBRAIC EXTENSIONS ...... .... ........... 73 5.4 CLASSIFYING SIMPLE EXTENSIONS . ... ................ 75 6 THE DEGREE OF AN EXTENSION 79 6.1 DEFINITION OF THE DEGREE ........ ............. .. 79 6.2 THE TOWER LAW ............... ...... ....... 80 7 RULER-AND-COMPASS CONSTRUCTIONS 87 7.1 APPROXIMATE CONSTRUCTIONS AND MORE GENERAL INSTRUMENTS ..... 89 7.2 CONSTRUCTIONS IN C........... ............... 90 7.3 SPECIFIC CONSTRUCTIONS . ............... ....... 94 7.4 IMPOSSIBILITY PROOFS ......... ................ 99 7.5 CONSTRUCTION FROM A GIVEN SET OF POINTS .......... .... 101 8 THE IDEA BEHIND GALOIS THEORY 107 8.1 A FIRST LOOK AT GALOIS THEORY .................... 108 8.2 GALOIS GROUPS ACCORDING TO GALOIS ............ ..... 108 8.3 HOW TO USE THE GALOIS GROUP ....... ............. 110 8.4 THE ABSTRACT SETTING .......... .......... ..... 111 8.5 POLYNOMIALS AND EXTENSIONS ...... ...... ......... 112 8.6 THE GALOIS CORRESPONDENCE ..... . ............... 114 8.7 DIET GALOIS ... ....... ........... ..... .... 116 8.8 NATURAL IRRATIONALITIES ...... ............ ....... 121 9 NORMALITY AND SEPARABILITY 129 9.1 SPLITTING FIELDS ............ ........... ..... 129 9.2 NORMALITY ................... ......... 132 9.3 SEPARABILITY ...... ............. .......... . 133 10 COUNTING PRINCIPLES 137 10.1 LINEAR INDEPENDENCE OF MONOMORPHISMS .............. 137 11 FIELD AUTOMORPHISMS 145 11.1 K-MONOMORPHISMS .......... ................ 145 11.2 NORMAL CLOSURES ............ ............... 146 12 THE GAELOIS CORRESPONDENCE 151 12.1 THE FUNDAMENTAL THEOREM OF GALOIS THEORY ........ .... 151 13 A WORKED EXAMPLE 155 CONTENTS IX 14 SOLUBILITY AND SIMPLICITY 161 14.1 SOLUBLE GROUPS ........................ .... 161 14.2 SIMPLE GROUPS ............ .... ..... . ...... 164 14.3 CAUCHY S THEOREM .... ................ .... 166 15 SOLUTION BY RADICALS 171 15.1 RADICAL EXTENSIONS ....... ........ ........... 171 15.2 AN INSOLUBLE QUINTIC ..... ..... .... ........... 176 15.3 OTHER METHODS ........ ......... . .......... 178 16 ABSTRACT RINGS AND FIELDS 181 16.1 RINGS AND FIELDS ........................... 181 16.2 GENERAL PROPERTIES OF RINGS AND FIELDS ............. .. 184 16.3 POLYNOMIALS OVER GENERAL RINGS ............. . .... 186 16.4 THE CHARACTERISTIC OF A FIELD ................... .. 187 16.5 INTEGRAL DOMAINS . ... .... ................... 188 17 ABSTRACT FIELD EXTENSIONS 193 17.1 MINIMAL POLYNOMIALS ......... ..... .... ....... 193 17.2 SIMPLE ALGEBRAIC EXTENSIONS ...... .... .... ....... 194 17.3 SPLITTING FIELDS ...... ... .... .... .... ....... 195 17.4 NORMALITY .............. ................. 197 17.5 SEPARABILITY .... .... ... ............... .... 197 17.6 GALOIS THEORY FOR ABSTRACT FIELDS ... ............... 202 18 THE GENERAL POLYNOMIAL EQUATION 205 18.1 TRANSCENDENCE DEGREE ....... .... ...... ... .... 205 18.2 ELEMENTARY SYMMETRIC POLYNOMIALS ................. 208 18.3 THE GENERAL POLYNOMIAL ...................... 209 18.4 CYCLIC EXTENSIONS .... . ..................... 211 18.5 SOLVING EQUATIONS OF DEGREE FOUR OR LESS ............ .. 214 19 FINITE FIELDS 221 19.1 STRUCTURE OF FINITE FIELDS . ............... ....... 221 19.2 THE MULTIPLICATIVE GROUP .................. .... 222 19.3 APPLICATION TO SOLITAIRE ........................ 224 20 REGULAR POLYGONS 227 20.1 WHAT EUCLID KNEW ............... . ... ..... .. 227 20.2 WHICH CONSTRUCTIONS ARE POSSIBLE? ................. 230 20.3 REGULAR POLYGONS ........................... 231 20.4 FERMAT NUMBERS ........................... 235 20.5 HOW TO DRAW A REGULAR 17-GON ................... 235 X CONTENTS 21 CIRCLE DIVISION 243 21.1 GENUINE RADICALS ........................... 244 21.2 FIFTH ROOTS REVISITED ...... .... ... . ....... .... 246 21.3 VANDERMONDE REVISITED ....................... 249 21.4 THE GENERAL CASE . .... ... . .......... . ... .... 250 21.5 CYCLOTOMIC POLYNOMIALS ....................... 253 21.6 GALOIS GROUP OF Q(Y) :Q...................... 255 21.7 THE TECHNICAL LEMMA ........................ 256 21.8 MORE ON CYCLOTOMIC POLYNOMIALS .................. 257 21.9 CONSTRUCTIONS USING A TRISECTOR ................... 259 22 CALCULATING GALOIS GROUPS 267 22.1 TRANSITIVE SUBGROUPS ......................... 267 22.2 BARE HANDS ON THE CUBIC ....................... 268 22.3 THE DISCRIMINANT ........................... 271 22.4 GENERAL ALGORITHM FOR THE GALOIS GROUP .... ....... .... 272 23 ALGEBRAICALLY CLOSED FIELDS 277 23.1 ORDERED FIELDS AND THEIR EXTENSIONS ................ 277 23.2 SYLOW S THEOREM . ... .... .... ............... 279 23.3 THE ALGEBRAIC PROOF ......................... 281 24 TRANSCENDENTAL NUMBERS 285 24.1 IRRATIONALITY .............................. 286 24.2 TRANSCENDENCE OF E ... ....................... 288 24.3 TRANSCENDENCE OF 7R ......................... 289 25 WHAT DID GALOIS DO OR KNOW? 295 25.1 LIST OF THE RELEVANT MATERIAL ..................... 296 25.2 THE FIRST MEMOIR .......................... 296 25.3 WHAT GALOIS PROVED ... ..... ......... . ... ... . 297 25.4 WHAT IS GALOIS UP TO? ..... ... ..... ... . ... .... 299 25.5 ALTERNATING GROUPS, ESPECIALLY A5 .................. 301 25.6 SIMPLE GROUPS KNOWN TO GALOIS ................... 302 25.7 SPECULATIONS ABOUT PROOFS ...................... 303 REFERENCES 309 INDEX . 315
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spelling	Stewart, Ian 1945- (DE-588)124091598 aut Galois theory Ian Stewart, University of Warwick, Coventry, UK Fourth edition Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2015] © 2015 xxii, 321 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Previous edition, 2004. - Includes bibliographical references (pages 309-314) and index Galois theory Algebraische Gleichung (DE-588)4001162-8 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Lehrbuch gnd rswk-swf Galois-Theorie (DE-588)4155901-0 s Lehrbuch f DE-604 Algebraische Gleichung (DE-588)4001162-8 s 1\p DE-604 Digitalisierung Deutsches Museum application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028898867&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Stewart, Ian 1945- Galois theory Galois theory Algebraische Gleichung (DE-588)4001162-8 gnd Galois-Theorie (DE-588)4155901-0 gnd
subject_GND	(DE-588)4001162-8 (DE-588)4155901-0
title	Galois theory
title_auth	Galois theory
title_exact_search	Galois theory
title_full	Galois theory Ian Stewart, University of Warwick, Coventry, UK
title_fullStr	Galois theory Ian Stewart, University of Warwick, Coventry, UK
title_full_unstemmed	Galois theory Ian Stewart, University of Warwick, Coventry, UK
title_short	Galois theory
title_sort	galois theory
topic	Galois theory Algebraische Gleichung (DE-588)4001162-8 gnd Galois-Theorie (DE-588)4155901-0 gnd
topic_facet	Galois theory Algebraische Gleichung Galois-Theorie Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028898867&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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