Algebra: Volume II: Fields with Structure, Algebras and Advanced Topics (Universitext) - Softcover

Lorenz, Falko

Softcover

ISBN 10: 0387724877 ISBN 13: 9780387724874

Publisher: Springer, 2007

Synopsis

This is Volume II of a two-volume introductory text in classical algebra. The text moves methodically with numerous examples and details so that readers with some basic knowledge of algebra can read it without difficulty. It is recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume are the theory of ordered fields and Nullstellen Theorems. Known researcher Lorenz also includes the fundamentals of the theory of quadratic forms, of valuations, local fields and modules. What’s more, the book contains some lesser known or nontraditional results – for instance, Tsen's results on the solubility of systems of polynomial equations with a sufficiently large number of indeterminates.

About this title

About the Author

Prof. Dr. Falko Lorenz lehrt an der Universität Münster Mathematik und ist auswärtiges Mitglied der Akademie gemeinnütziger Wissenschaften zu Erfurt.

From the Back Cover

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

Edition details

• Publisher: Springer
• Publication date: 2007
• Language: English
• ISBN 10: 0387724877
• ISBN 13: 9780387724874
• Binding: Paperback
• Number of pages: 340