Produktbild: Classical Galois Theory

Classical Galois Theory

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

17.07.2012

Verlag

John Wiley & Sons Inc

Seitenzahl

296

Maße (L/B/H)

24/16,1/2,1 cm

Gewicht

616 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-09139-5

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

17.07.2012

Verlag

John Wiley & Sons Inc

Seitenzahl

296

Maße (L/B/H)

24/16,1/2,1 cm

Gewicht

616 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-09139-5

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: GPSR Kontakt

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  • Produktbild: Classical Galois Theory
  • PREFACE xi
     
    1 CLASSICAL FORMULAS 1
     
    1.1 Quadratic Polynomials / 3
     
    1.2 Cubic Polynomials / 5
     
    1.3 Quartic Polynomials / 11
     
    2 POLYNOMIALS AND FIELD THEORY 15
     
    2.1 Divisibility / 16
     
    2.2 Algebraic Extensions / 24
     
    2.3 Degree of Extensions / 25
     
    2.4 Derivatives / 29
     
    2.5 Primitive Element Theorem / 30
     
    2.6 Isomorphism Extension Theorem and Splitting Fields / 35
     
    3 FUNDAMENTAL THEOREM ON SYMMETRIC POLYNOMIALS AND DISCRIMINANTS 41
     
    3.1 Fundamental Theorem on Symmetric Polynomials / 41
     
    3.2 Fundamental Theorem on Symmetric Rational Functions / 48
     
    3.3 Some Identities Based on Elementary Symmetric Polynomials / 50
     
    3.4 Discriminants / 53
     
    3.5 Discriminants and Subfields of the Real Numbers / 60
     
    4 IRREDUCIBILITY AND FACTORIZATION 65
     
    4.1 Irreducibility Over the Rational Numbers / 65
     
    4.2 Irreducibility and Splitting Fields / 69
     
    4.3 Factorization and Adjunction / 72
     
    5 ROOTS OF UNITY AND CYCLOTOMIC POLYNOMIALS 80
     
    5.1 Roots of Unity / 80
     
    5.2 Cyclotomic Polynomials / 82
     
    6 RADICAL EXTENSIONS AND SOLVABILITY BY RADICALS 89
     
    6.1 Basic Results on Radical Extensions / 89
     
    6.2 Gauss's Theorem on Cyclotomic Polynomials / 93
     
    6.3 Abel's Theorem on Radical Extensions / 104
     
    6.4 Polynomials of Prime Degree / 109
     
    7 GENERAL POLYNOMIALS AND THE BEGINNINGS OF GALOIS THEORY 117
     
    7.1 General Polynomials / 117
     
    7.2 The Beginnings of Galois Theory / 124
     
    8 CLASSICAL GALOIS THEORY ACCORDING TO GALOIS 135
     
    9 MODERN GALOIS THEORY 151
     
    9.1 Galois Theory and Finite Extensions / 152
     
    9.2 Galois Theory and Splitting Fields / 156
     
    10 CYCLIC EXTENSIONS AND CYCLOTOMIC FIELDS 171
     
    10.1 Cyclic Extensions / 171
     
    10.2 Cyclotomic Fields / 179
     
    11 GALOIS'S CRITERION FOR SOLVABILITY OF POLYNOMIALS BY RADICALS 185
     
    12 POLYNOMIALS OF PRIME DEGREE 192
     
    13 PERIODS OF ROOTS OF UNITY 200
     
    14 DENESTING RADICALS 225
     
    15 CLASSICAL FORMULAS REVISITED 231
     
    15.1 General Quadratic Polynomial / 231
     
    15.2 General Cubic Polynomial / 233
     
    15.3 General Quartic Polynomial / 236
     
    APPENDIX A COSETS AND GROUP ACTIONS 245
     
    APPENDIX B CYCLIC GROUPS 249
     
    APPENDIX C SOLVABLE GROUPS 254
     
    APPENDIX D PERMUTATION GROUPS 261
     
    APPENDIX E FINITE FIELDS AND NUMBER THEORY 270
     
    APPENDIX F FURTHER READING 274
     
    REFERENCES 277
     
    INDEX 281