Algebra Volume II: Fields with Structure, Algebras and Advanced Topics

Algebra Volume II: Fields with Structure, Algebras and Advanced Topics / by Falko Lorenz.

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
Main Author: Lorenz, Falko (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2008.
Edition:1st ed. 2008.
Series:Universitext,
Springer eBook Collection.
Subjects:
Algebra.
Commutative algebra.
Commutative rings.
Field theory (Physics).
Matrix theory.
Number theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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