| Description |
1 online resource (x, 205 pages) |
| Series |
Springer monographs in mathematics, 1439-7382 |
|
Springer monographs in mathematics. 1439-7382
|
| Contents |
Introduction; Absolute Values; Valuations; Extension of Valuations; Henselian Fields; Structure Theory; Applications of Valuation Theory |
| Summary |
Annotation Absolute values and their completions - 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 like in 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 of a standard course in algebra. The last chapter presents three applications of the general theory - as to Artin's Conjecture on the p-adic number fields - that could not be obtained by the use of absolute values only |
| Bibliography |
Includes bibliographical references (pages 199-200) and index |
| Notes |
English |
|
Print version record |
| In |
Springer e-books |
| Subject |
Valued fields.
|
|
Algebra.
|
|
algebra.
|
|
MATHEMATICS -- Number Theory.
|
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Valued fields.
|
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Álgebra
|
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Valued fields
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Corps valué
|
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Théorie des valuations.
|
| Form |
Electronic book
|
| Author |
Prestel, A. (Alexander), 1941-
|
| ISBN |
9783540300359 |
|
354030035X |
|
354024221X |
|
9783540242215 |
|
3642063454 |
|
9783642063459 |
|
1280413239 |
|
9781280413230 |
|
