Galois Module Structure of Algebraic Integers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1983
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, A Series of Modern Surveys in Mathematics
1 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools |
| Beschreibung: | 1 Online-Ressource (X, 266 p) |
| ISBN: | 9783642688164 9783642688188 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-68816-4 |
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Datensatz im Suchindex
| _version_ | 1804153098008002560 |
|---|---|
| any_adam_object | |
| author | Fröhlich, Albrecht |
| author_facet | Fröhlich, Albrecht |
| author_role | aut |
| author_sort | Fröhlich, Albrecht |
| author_variant | a f af |
| building | Verbundindex |
| bvnumber | BV042422933 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-68816-4 |
| format | Electronic eBook |
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| id | DE-604.BV042422933 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642688164 9783642688188 |
| issn | 0071-1136 |
| language | English |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, A Series of Modern Surveys in Mathematics |
| spelling | Fröhlich, Albrecht Verfasser aut Galois Module Structure of Algebraic Integers by Albrecht Fröhlich Berlin, Heidelberg Springer Berlin Heidelberg 1983 1 Online-Ressource (X, 266 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, A Series of Modern Surveys in Mathematics 1 0071-1136 In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools Mathematics Field theory (Physics) Number theory Number Theory Field Theory and Polynomials Mathematik Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Integral (DE-588)4131477-3 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s Integraldarstellung (DE-588)4127585-8 s 1\p DE-604 Galois-Theorie (DE-588)4155901-0 s 2\p DE-604 Integral (DE-588)4131477-3 s 3\p DE-604 https://doi.org/10.1007/978-3-642-68816-4 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 |
| spellingShingle | Fröhlich, Albrecht Galois Module Structure of Algebraic Integers Mathematics Field theory (Physics) Number theory Number Theory Field Theory and Polynomials Mathematik Galois-Theorie (DE-588)4155901-0 gnd Integral (DE-588)4131477-3 gnd Integraldarstellung (DE-588)4127585-8 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4155901-0 (DE-588)4131477-3 (DE-588)4127585-8 (DE-588)4001170-7 |
| title | Galois Module Structure of Algebraic Integers |
| title_auth | Galois Module Structure of Algebraic Integers |
| title_exact_search | Galois Module Structure of Algebraic Integers |
| title_full | Galois Module Structure of Algebraic Integers by Albrecht Fröhlich |
| title_fullStr | Galois Module Structure of Algebraic Integers by Albrecht Fröhlich |
| title_full_unstemmed | Galois Module Structure of Algebraic Integers by Albrecht Fröhlich |
| title_short | Galois Module Structure of Algebraic Integers |
| title_sort | galois module structure of algebraic integers |
| topic | Mathematics Field theory (Physics) Number theory Number Theory Field Theory and Polynomials Mathematik Galois-Theorie (DE-588)4155901-0 gnd Integral (DE-588)4131477-3 gnd Integraldarstellung (DE-588)4127585-8 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Mathematics Field theory (Physics) Number theory Number Theory Field Theory and Polynomials Mathematik Galois-Theorie Integral Integraldarstellung Algebraische Zahlentheorie |
| url | https://doi.org/10.1007/978-3-642-68816-4 |
| work_keys_str_mv | AT frohlichalbrecht galoismodulestructureofalgebraicintegers |