Algebra

Falko Lorenz, Silvio Levy0387289305, 9780387289304, 9780387724874, 9780387724881

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.”

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Table of contents :
front-matter……Page 1
1Constructibility with Ruler and Compass……Page 7
2Algebraic Extensions……Page 20
3Simple Extensions……Page 26
4Fundamentals of Divisibility……Page 38
5Prime Factorization in Polynomial Rings. Gauss’s Theorem……Page 49
6Polynomial Splitting Fields……Page 58
7Separable Extensions……Page 68
8Galois Extensions……Page 77
9Finite Fields, Cyclic Groups and Roots of Unity……Page 85
10Group Actions……Page 95
11Applications of Galois Theory to Cyclotomic Fields……Page 104
12Further Steps into Galois Theory……Page 115
13Norm and Trace……Page 132
14Binomial Equations……Page 141
15Solvability of Equations……Page 163
16Integral Ring Extensions with Applications to Galois Theory……Page 189
17The Transcendence of π……Page 201
18Fundamentals of Transcendental Field Extensions……Page 207
19Hilbert’s Nullstellensatz……Page 215
back-matter……Page 229