Algebra Volume I: Fields and Galois Theory /

The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extens...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Lorenz, Falko (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: New York, NY : Springer New York : Imprint: Springer, 2006.
Edition:1st ed. 2006.
Series:Universitext,
Subjects:
Algebra.
Algebraic fields.
Polynomials.
Commutative algebra.
Commutative rings.
Number theory.
Field Theory and Polynomials.
Commutative Rings and Algebras.
Number Theory.
Online Access:Texto Completo
Table of Contents:
  • Constructibility with Ruler and Compass
  • Algebraic Extensions
  • Simple Extensions
  • Fundamentals of Divisibility
  • Prime Factorization in Polynomial Rings. Gauss's Theorem
  • Polynomial Splitting Fields
  • Separable Extensions
  • Galois Extensions
  • Finite Fields, Cyclic Groups and Roots of Unity
  • Group Actions
  • Applications of Galois Theory to Cyclotomic Fields
  • Further Steps into Galois Theory
  • Norm and Trace
  • Binomial Equations
  • Solvability of Equations
  • Integral Ring Extensions with Applications to Galois Theory
  • The Transcendence of ?
  • Fundamentals of Transcendental Field Extensions
  • Hilbert's Nullstellensatz.

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