Springer
New York
Galois theory
Algebra. Vol. 2, Fields with structure, algebras, and advanced topics.
Print version:
Lorenz
Falko
Falko Lorenz
Algebra
9780387724881
0387724885
Algebraic fields
Galois theory
Einführung in die Algebra.
de
Algebraic fields
2017-07-09
Algebra
Levy
Silvio
Silvio Levy
Einführung in die Algebra.
nyu
Universitext
Universitext.
Algebra. Vol. 2, Fields with structure, algebras, and advanced topics
Electronic books
en
308295908
Problems and exercises
Textbooks
Fields with structure, algebras, and advanced topics
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
2008
2008
Foreword -- 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 -- Appendix: problems and remarks -- Index
308295908