Field Theory

• Main Author: Roman, Steven (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2006.
• Edition: Second Edition.
• Series: Graduate Texts in Mathematics, 158
• Subjects: Mathematics.; Algebra.; Field theory (Physics).; Number theory.; Field Theory and Polynomials.; Number 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...

Table of Contents:

• 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.