Elementary and Analytic Theory of Algebraic Numbers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Ausgabe: | Third Edition |
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this book is to present an exposition of the theory of algebraic numbers, excluding class-field theory and its consequences. There are many ways to develop this subject; the latest trend is to neglect the classical Dedekind theory of ideals in favour of local methods. However, for numerical computations, necessary for applications of algebraic numbers to other areas of number theory, the old approach seems more suitable, although its exposition is obviously longer. On the other hand the local approach is more powerful for analytical purposes, as demonstrated in Tate's thesis. Thus the author has tried to reconcile the two approaches, presenting a self-contained exposition of the classical standpoint in the first four chapters, and then turning to local methods. In the first chapter we present the necessary tools from the theory of Dedekind domains and valuation theory, including the structure of finitely generated modules over Dedekind domains. In Chapters 2, 3 and 4 the classical theory of algebraic numbers is developed. Chapter 5 contains the fundamental notions of the theory of p-adic fields, and Chapter 6 brings their applications to the study of algebraic number fields. We include here Shafarevich's proof of the Kronecker-Weber theorem, and also the main properties of adeles and ideles |
| Beschreibung: | 1 Online-Ressource (XI, 712 p) |
| ISBN: | 9783662070017 9783642060106 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-07001-7 |
Internformat
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Datensatz im Suchindex
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| author | Narkiewicz, Władysław |
| author_facet | Narkiewicz, Władysław |
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| author_sort | Narkiewicz, Władysław |
| author_variant | w n wn |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-07001-7 |
| edition | Third Edition |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662070017 9783642060106 |
| issn | 1439-7382 |
| language | English |
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| physical | 1 Online-Ressource (XI, 712 p) |
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| spelling | Narkiewicz, Władysław Verfasser aut Elementary and Analytic Theory of Algebraic Numbers by Władysław Narkiewicz Third Edition Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XI, 712 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 The aim of this book is to present an exposition of the theory of algebraic numbers, excluding class-field theory and its consequences. There are many ways to develop this subject; the latest trend is to neglect the classical Dedekind theory of ideals in favour of local methods. However, for numerical computations, necessary for applications of algebraic numbers to other areas of number theory, the old approach seems more suitable, although its exposition is obviously longer. On the other hand the local approach is more powerful for analytical purposes, as demonstrated in Tate's thesis. Thus the author has tried to reconcile the two approaches, presenting a self-contained exposition of the classical standpoint in the first four chapters, and then turning to local methods. In the first chapter we present the necessary tools from the theory of Dedekind domains and valuation theory, including the structure of finitely generated modules over Dedekind domains. In Chapters 2, 3 and 4 the classical theory of algebraic numbers is developed. Chapter 5 contains the fundamental notions of the theory of p-adic fields, and Chapter 6 brings their applications to the study of algebraic number fields. We include here Shafarevich's proof of the Kronecker-Weber theorem, and also the main properties of adeles and ideles Mathematics Algebra Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Algebraische Zahl (DE-588)4141847-5 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s 1\p DE-604 Algebraische Zahl (DE-588)4141847-5 s 2\p DE-604 Analytische Zahlentheorie (DE-588)4001870-2 s 3\p DE-604 Zahlentheorie (DE-588)4067277-3 s 4\p DE-604 https://doi.org/10.1007/978-3-662-07001-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Narkiewicz, Władysław Elementary and Analytic Theory of Algebraic Numbers Mathematics Algebra Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd Algebraische Zahl (DE-588)4141847-5 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4001870-2 (DE-588)4141847-5 (DE-588)4001170-7 (DE-588)4067277-3 |
| title | Elementary and Analytic Theory of Algebraic Numbers |
| title_auth | Elementary and Analytic Theory of Algebraic Numbers |
| title_exact_search | Elementary and Analytic Theory of Algebraic Numbers |
| title_full | Elementary and Analytic Theory of Algebraic Numbers by Władysław Narkiewicz |
| title_fullStr | Elementary and Analytic Theory of Algebraic Numbers by Władysław Narkiewicz |
| title_full_unstemmed | Elementary and Analytic Theory of Algebraic Numbers by Władysław Narkiewicz |
| title_short | Elementary and Analytic Theory of Algebraic Numbers |
| title_sort | elementary and analytic theory of algebraic numbers |
| topic | Mathematics Algebra Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd Algebraische Zahl (DE-588)4141847-5 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Mathematics Algebra Mathematik Analytische Zahlentheorie Algebraische Zahl Algebraische Zahlentheorie Zahlentheorie |
| url | https://doi.org/10.1007/978-3-662-07001-7 |
| work_keys_str_mv | AT narkiewiczwładysław elementaryandanalytictheoryofalgebraicnumbers |