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Through a set of related yet distinct texts, the author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions: Ideal- and valuation-theoretic aspects, L functions and class field theory, together with a presentation of algebraic foundations which are usually undersized in standard algebra courses.
List of contents
1 Field Extensions
2 Dedekind Theory
3 Algebraic Number Fields: Elementary and Geometric Methods
4 Elementary Analytic Theory
5 Valuation Theory
6 Algebraic Function Fields
Bibliography
Index
List of Symbols
About the author
Franz Halter-Koch studied at Universities of Graz and Hamburg under Helmut Hasse and Alexander Aigner. He has been an Assistant Professor at University of Cologne, and a Full Professor at University of Essen and University of Graz. He has 156 research articles published in various journals. His books include Ideal Systems (Marcel Dekker/CRC Press); Non-Unique Factorizations (Chapman&Hall/CRC), and Quadratic Irrationals, (Chapman&Hall/CRC).
Summary
Through a set of related yet distinct texts, the author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions: Ideal- and valuation-theoretic aspects, L functions and class field theory, together with a presentation of algebraic foundations which are usually undersized in standard algebra courses.
Additional text
"...Koch is extremely thorough, very incisive, and very careful --- all great pedagogical virtues, present in spades. He arranges his results very well, phrasing things carefully and explicitly, and his proofs are detailed. I tend to cover the margins of the books I read with everything from disputes and questions to proof sketches. Koch’s book would require only a minimum of this sort of polemics: it’s all there --- no guesswork. The additional blood, sweat, and tears attending learning mathematics well, i.e. doing problems, problems, problems, is represented by 20 problems attached to each of Koch’s six chapters. Scanning them, they look excellent to me: they should serve the reader very well indeed. And that’s true for the entire book: it’s excellent and is well worth using in order to learn this beautiful material. I look forward to Koch’s book of class field theory!"
- Michael Berg, Loyola Marymount University, Published in MAA
