Field Theory

This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Roman, Steven (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2006.
Edición:2nd ed. 2006.
Colección:Graduate Texts in Mathematics, 158
Temas:
Algebra.
Algebraic fields.
Polynomials.
Number theory.
Field Theory and Polynomials.
Number Theory.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Preliminaries
  • Preliminaries
  • Field Extensions
  • Polynomials
  • Field Extensions
  • Embeddings and Separability
  • Algebraic Independence
  • Galois Theory
  • Galois Theory I: An Historical Perspective
  • Galois Theory II: The Theory
  • Galois Theory III: The Galois Group of a Polynomial
  • A Field Extension as a Vector Space
  • Finite Fields I: Basic Properties
  • Finite Fields II: Additional Properties
  • The Roots of Unity
  • Cyclic Extensions
  • Solvable Extensions
  • The Theory of Binomials
  • Binomials
  • Families of Binomials.

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