Algebra Fields with Structure, Algebras and Advanced Topics /

• Main Author: Lorenz, Falko (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2008.
• Subjects: Mathematics.; Algebra.; Commutative algebra.; Commutative rings.; Field theory (Physics).; Matrix theory.; Number theory.; Commutative Rings and Algebras.; Field Theory and Polynomials.; Linear and Multilinear Algebras, Matrix Theory.; Number 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...

Table of Contents:

• Ordered Fields and Real Fields
• Hilbert's Seventeenth Problem and the Real Nullstellensatz
• Orders and Quadratic Forms
• Absolute Values on Fields
• Residue Class Degree and Ramification Index
• Local Fields
• Witt Vectors
• The Tsen Rank of a Field
• Fundamentals of Modules
• Wedderburn Theory
• Crossed Products
• The Brauer Group of a Local Field
• Local Class Field Theory
• Semisimple Representations of Finite Groups
• The Schur Group of a Field.