Universitext
Universitext.
New York
Galois theory
Lorenz
Falko
Falko Lorenz
Algebra
9780387724881
0387724885
Galois, Théorie de
Algebraic fields
9780387316086
0387316086
2006-2008
Corps algébriques
Levy
Silvio
Silvio Levy
Springer
Einführung in die Algebra.
de
Algebra
Algebra.
Print version:
Algèbre
Einführung in die Algebra.
2016-08-09
nyu
209914197
en
Algebra
Textbooks
209914197
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, diophantine dimensions 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.
2006/2008