Lorenz / Levy Algebra

Volume I: Fields and Galois Theory
2006
ISBN: 978-0-387-31608-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 304 Seiten, eBook

Reihe: Universitext

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."

Zielgruppe

Graduate

Autoren/Hrsg.

Lorenz, Falko

Levy, Silvio

Weitere Mitwirkende

Levy, Silvio

Inhaltsverzeichnis

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.