Algebra: Fields and Galois Theory (Repost)
Algebra: Fields and Galois Theory by Falko Lorenz
English | PDF | 2006 | 292 Pages | ISBN : 0387289305 | 2.4 MB
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.
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