Logo - springer
Slogan - springer

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

Algebra

Volume II: Fields with Structure, Algebras and Advanced Topics

Series: Universitext

Volume package: Algebra

Lorenz, Falko

Translated by Levy, S.

2008

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$39.95

(net) price for USA

ISBN 978-0-387-72488-1

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$49.95

(net) price for USA

ISBN 978-0-387-72487-4

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • Superbly written and comprehensive survey of classical algebra
  • Includes unique collection of topics
  • Author provides enough detail to ensure that the only prerequisite is basic knowledge of algebra

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 extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry.

The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory.

Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students.

 

From Reviews of the German version:

This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the

framework of the development of carefully selected problems.

- Stefan Porubsky, Mathematical Reviews

Content Level » Graduate

Keywords » algebra - field - finite group - quadratic form

Related subjects » Algebra - Number Theory and Discrete Mathematics

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.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Algebra.