A Field Guide to Algebra

• Main Author: Chambert-Loir, Antoine (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2005.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Algebra.; Commutative algebra.; Commutative rings.; Field theory (Physics).; Number theory.; Field Theory and Polynomials.; Number Theory.; Commutative Rings and Algebras.

This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will h...

Table of Contents:

• Field extensions
• Roots
• Galois theory
• A bit of group theory
• Applications
• Algebraic theory of differential equations.