Algebra

Fields with Structure, Algebras and Advanced Topics

  • Falko Lorenz

Table of contents

About this book

Introduction

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

Keywords

algebra field finite group quadratic form

Authors and affiliations

  • Falko Lorenz
    • 1
  1. 1.University Mü nster48149Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-72488-1
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-72487-4
  • Online ISBN 978-0-387-72488-1
  • About this book