This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.

Leseprobe

Foreword.- Constructibility with Ruler and Compass.- Algebraic Extensions.- Simple Extensions.-Fundamentals of Divisibility.- Prime Factorization in Polynomial Rings. Gauss''s Theorem.- Polynomial Splittin Fields.- SeparableExtensions.- Galois Extensions.-Finite fields, Cyclic Groups and Roots of Unity.- GroupActions.- Applications of Galois Theory to Cyclotomic Fields.- Further Steps into Galois theory.- Norm and Trace.- Binomial Equations.- Solvability of Equations.- Integral Ring Extensions.- The Transcendence of pi.- Transcendental Field Extensions.- Hilbert''s Nullstellensatz.- Appendix: Problems and Remarks.- Index of Notation.- Index.

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Springer Verlag GmbH
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