The Theory of Classical Valuations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1999
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In his studies of cyclotomic fields, in view of establishing his monumental theorem about Fermat's last theorem, Kummer introduced "local" methods. They are concerned with divisibility of "ideal numbers" of cyclotomic fields by lambda = 1 - psi where psi is a primitive p-th root of 1 (p any odd prime). Henssel developed Kummer's ideas, constructed the field of p-adic numbers and proved the fundamental theorem known today. Kurschak formally introduced the concept of a valuation of a field, as being real valued functions on the set of non-zero elements of the field satisfying certain properties, like the p-adic valuations. Ostrowski, Hasse, Schmidt and others developed this theory and collectively, these topics form the primary focus of this book |
| Beschreibung: | 1 Online-Ressource (XI, 403 p) |
| ISBN: | 9781461205517 9781461268147 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-1-4612-0551-7 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0551-7 |
| format | Electronic eBook |
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| id | DE-604.BV042419552 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461205517 9781461268147 |
| issn | 1439-7382 |
| language | English |
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| physical | 1 Online-Ressource (XI, 403 p) |
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| publishDate | 1999 |
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| spelling | Ribenboim, Paulo Verfasser aut The Theory of Classical Valuations by Paulo Ribenboim New York, NY Springer New York 1999 1 Online-Ressource (XI, 403 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 In his studies of cyclotomic fields, in view of establishing his monumental theorem about Fermat's last theorem, Kummer introduced "local" methods. They are concerned with divisibility of "ideal numbers" of cyclotomic fields by lambda = 1 - psi where psi is a primitive p-th root of 1 (p any odd prime). Henssel developed Kummer's ideas, constructed the field of p-adic numbers and proved the fundamental theorem known today. Kurschak formally introduced the concept of a valuation of a field, as being real valued functions on the set of non-zero elements of the field satisfying certain properties, like the p-adic valuations. Ostrowski, Hasse, Schmidt and others developed this theory and collectively, these topics form the primary focus of this book Mathematics K-theory K-Theory Mathematik Bewertungstheorie (DE-588)4122918-6 gnd rswk-swf Algebraischer Körper (DE-588)4141852-9 gnd rswk-swf Bewertungstheorie (DE-588)4122918-6 s Algebraischer Körper (DE-588)4141852-9 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-0551-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ribenboim, Paulo The Theory of Classical Valuations Mathematics K-theory K-Theory Mathematik Bewertungstheorie (DE-588)4122918-6 gnd Algebraischer Körper (DE-588)4141852-9 gnd |
| subject_GND | (DE-588)4122918-6 (DE-588)4141852-9 |
| title | The Theory of Classical Valuations |
| title_auth | The Theory of Classical Valuations |
| title_exact_search | The Theory of Classical Valuations |
| title_full | The Theory of Classical Valuations by Paulo Ribenboim |
| title_fullStr | The Theory of Classical Valuations by Paulo Ribenboim |
| title_full_unstemmed | The Theory of Classical Valuations by Paulo Ribenboim |
| title_short | The Theory of Classical Valuations |
| title_sort | the theory of classical valuations |
| topic | Mathematics K-theory K-Theory Mathematik Bewertungstheorie (DE-588)4122918-6 gnd Algebraischer Körper (DE-588)4141852-9 gnd |
| topic_facet | Mathematics K-theory K-Theory Mathematik Bewertungstheorie Algebraischer Körper |
| url | https://doi.org/10.1007/978-1-4612-0551-7 |
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