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ISBN 10: 354024221X
ISBN 13: 978-3540242215
Author: Antonio Engler, Alexander Prestel
Absolute values and their completions -like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization.
In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge acquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -for instance to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values alone.
Chapter1 : Introduction
Chapter 2: Content
Chapter 3: Conclusion
Chapter 4: Appendices
Chapter 5: Glossary
Chapter 6: References
Chapter 7: Index
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