---

＜電子ブック＞
Algebra : Volume I: Fields and Galois Theory / by Falko Lorenz
(Universitext. ISSN:21916675)

版	1st ed. 2006.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	VIII, 296 p. 6 illus : online resource
著者標目	*Lorenz, Falko author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic fields LCSH:Polynomials LCSH:Commutative algebra LCSH:Commutative rings LCSH:Number theory FREE:Algebra FREE:Field Theory and Polynomials FREE:Commutative Rings and Algebras FREE:Number Theory
一般注記	Constructibility with Ruler and Compass -- Algebraic Extensions -- Simple Extensions -- Fundamentals of Divisibility -- Prime Factorization in Polynomial Rings. Gauss’s Theorem -- Polynomial Splitting Fields -- Separable Extensions -- Galois Extensions -- Finite Fields, Cyclic Groups and Roots of Unity -- Group Actions -- Applications of Galois Theory to Cyclotomic Fields -- Further Steps into Galois Theory -- Norm and Trace -- Binomial Equations -- Solvability of Equations -- Integral Ring Extensions with Applications to Galois Theory -- The Transcendence of ? -- Fundamentals of Transcendental Field Extensions -- Hilbert’s Nullstellensatz 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 HTTP:URL=https://doi.org/10.1007/0-387-31608-6

 類似資料