Field extensions and Galois theory /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bastida, Julio R.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge [Cambridgeshire] ; New York, NY, USA : Cambridge University Press, ©1984.
Colección:Encyclopedia of mathematics and its applications ; v. 22.
Encyclopedia of mathematics and its applications. Section, Algebra.
Temas:
Field extensions (Mathematics)
Galois theory.
Extensions de corps (Mathématiques)
Théorie de Galois.
MATHEMATICS > Algebra > Intermediate.
Galois-Theorie
Körpererweiterung
Galois, Théorie de.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Editor's Statement; Foreword; Preface; Historical Introduction; Prerequisites; Notation; NOTATION PERTAINING TO THE THEORY OF FIELD EXTENSIONS AND GALOIS THEORY; Chapter 1 Preliminaries on Fields and Polynomials; 1.1. FIELDS OF FRACTIONS; PROBLEMS; 1.2. THE CHARACTERISTIC; 1.2.1. Examples; PROBLEMS; 1.3. PERFECT FIELDS AND PRIME FIELDS; PROBLEMS; 1.4. FIELD EXTENSIONS; 1.4.1. Examples; PROBLEMS; 1.5. FACTORIZATION OF POLYNOMIALS; 1.5.10. Examples; PROBLEMS; 1.6. SPLITTING OF POLYNOMIALS; 1.6.1. Examples; 1.6.2. Examples
  • 1.6.6. ExamplesPROBLEMS; 1.7. SEPARABLE POLYNOMIALS; 1.7.4. Examples; PROBLEMS; NOTES; Chapter 2 Algebraic Extensions; 2.1. ALGEBRAIC EXTENSIONS; 2.1.1. Examples; 2.1.7. Examples; PROBLEMS; 2.2. ALGEBRAICALLY CLOSED FIELDS; 2.2.8. Examples; PROBLEMS; 2.3. NORMAL EXTENSIONS; 2.3.1. Examples; 2.3.16. Examples; PROBLEMS; 2.4. PURELY INSEPARABLE EXTENSIONS; PROBLEMS; 2.5. SEPARABLE EXTENSIONS; PROBLEMS; NOTES; Chapter 3 Galois Theory; 3.1. SOME VECTOR SPACES OF MAPPINGS OF FIELDS; 3.1.4. Examples; PROBLEMS; 3.2. THE GENERAL GALOIS CORRESPONDENCES; 3.2.4. Examples; PROBLEMS; 3.3. GALOIS EXTENSIONS
  • PROBLEMS3.4. FINITE GALOIS THEORY; PROBLEMS; 3.5. ROOTS OF UNITY; PROBLEMS; 3.6. PRIMITIVE ELEMENTS; PROBLEMS; 3.7. SEPARABLE AND INSEPARABLE DEGREES; PROBLEMS; 3.8. NORMS AND TRACES; 3.8.1. Examples; PROBLEMS; 3.9. CYCLIC EXTENSIONS; PROBLEMS; 3.10. SOLVABILITY BY RADICALS; PROBLEMS; 3.11. FINITE FIELDS; 3.11.4. Examples; PROBLEMS; 3.12. INFINITE GALOIS THEORY; PROBLEMS; NOTES; Suggestions for further reading; Chapter 4 Transcendental Extensions; 4.1. DIMENSIONAL OPERATORS; 4.1.1. Examples; 4.1.2. Examples; PROBLEMS; 4.2. TRANSCENDENCE BASES AND TRANSCENDENCE DEGREE; PROBLEMS
  • 4.3. SPECIALIZATIONS AND PLACES OF FIELDS4.3.1. Examples; PROBLEMS; 4.4. SEPARABLE EXTENSIONS; PROBLEMS; 4.5. DERIVATIONS OF FIELDS; 4.5.1. Examples; 4.5.5. Examples; PROBLEMS; 4.6. DERIVATIONS OF ALGEBRAIC FUNCTION FIELDS; PROBLEMS; NOTES; Suggestions for further reading; References and Selected Bibliography; Bibliography; Of historical interest; Index

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