From Math Reviews: "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. Thus, for instance, the transformation of the classical geometrical problems on constructions with ruler and compass in their algebraic setting in the first chapter introduces the reader spontaneously to such fundamental algebraic notions as field extension, the degree of an extension, etc... The book ends with an appendix containing exercises and notes on the previous parts of the book. However, brief historical comments and suggestions for further reading are also scattered through the text."
Author(s): Falko Lorenz, Silvio Levy
Series: Universitext
Edition: 1
Publisher: Springer
Year: 2005
Language: English
Pages: 292
algebra.jpg......Page 1
front-matter......Page 2
1Constructibility with Ruler and Compass......Page 8
2Algebraic Extensions......Page 21
3Simple Extensions......Page 27
4Fundamentals of Divisibility......Page 39
5Prime Factorization in Polynomial Rings. Gauss’s Theorem......Page 50
6Polynomial Splitting Fields......Page 59
7Separable Extensions......Page 69
8Galois Extensions......Page 78
9Finite Fields, Cyclic Groups and Roots of Unity......Page 86
10Group Actions......Page 96
11Applications of Galois Theory to Cyclotomic Fields......Page 105
12Further Steps into Galois Theory......Page 116
13Norm and Trace......Page 133
14Binomial Equations......Page 142
15Solvability of Equations......Page 164
16Integral Ring Extensions with Applications to Galois Theory......Page 190
17The Transcendence of π......Page 202
18Fundamentals of Transcendental Field Extensions......Page 208
19Hilbert’s Nullstellensatz......Page 216
back-matter......Page 230
