Algebraic number fields:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1996
|
| Edition: | 2. ed. |
| Series: | Graduate studies in mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 276 S. |
| ISBN: | 9780821804292 0821804294 |
Staff View
MARC
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| 245 | 1 | 0 | |a Algebraic number fields |c Gerald J. Janusz |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1996 | |
| 300 | |a X, 276 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 7 | |
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Record in the Search Index
| _version_ | 1805084140141281280 |
|---|---|
| adam_text |
Contents
Prefaces ix
Chapter I. Subrings of Fields 1
1. Localization 1
2. Integral Dependence 4
3. Discrete Valuation Rings and Dedekind Rings 7
4. Fractional Ideals and the Class Group 16
5. Norms and Traces 19
6. Extensions of Dedekind Rings 25
7. Ramification and the Discriminant 33
8. Norms of Ideals 42
9. Algebraic Integers 46
10. Cyclotomic Fields 52
11. Quadratic Reciprocity 59
12. Lattices in Real Vector Spaces 62
13. The Class Number and the Unit Theorem 67
Chapter II. Complete Fields 83
1. Valuations 83
2. Completions 90
3. Extensions of Nonarchimedean Valuations 100
4. Completions of Archimedean Valuations 108
5. The Topology of Completions of Number Fields 111
6. Local Norms and Traces and the Product Formula 114
Chapter III. Decomposition Groups and the Artin Map 121
1. Decomposition and Inertia Groups 121
2. The Frobenius Automorphism 125
3. The Artin Map for Abelian Extensions 130
Vli
viii CONTENTS
Chapter IV. Analytic Methods and Ray Classes 135
1. Moduli and Ray Classes 135
2. Dirichlet Series 141
3. Characters of Abelian Groups 154
4. L Series and Product Representations 156
5. The Frobenius Density Theorem 162
Chapter V. Class Field Theory 169
1. Cohomology of Cyclic Groups 169
2. Preparations for the Second Inequality 172
3. A Norm Index Computation 177
4. The Fundamental Equality for Cyclic Extensions 184
5. The Reciprocity Theorem 190
6. Ideal Groups, Conductors, and Class Fields 199
7. Reduction Steps toward the Existence Theorem 203
8. Kummer Extensions and the S unit Theorem 205
9. The Existence Theorem 208
10. Some Consequences of the Classification Theorem 215
11. Norm Residues and the Conductor 218
12. The Hilbert Class Field 228
Chapter VI. Quadratic Fields 233
1. The Conductor of Q(Vd) 233
2. Two Hilbert Class Fields 236
3. The Extended Class Group 241
4. The Class Number and L functions 249
Appendix 261
A. Normal Basis Theorem and Hilbert's Theorem 90 261
B. Modules over Principal Ideal Domains 263
C. Representation of Permutation Groups and Gauss Sums 266
References 273
Index 275 |
| any_adam_object | 1 |
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| classification_tum | MAT 125f |
| ctrlnum | (OCoLC)33162119 (DE-599)BVBBV010835824 |
| dewey-full | 512/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV010835824 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T07:59:43Z |
| institution | BVB |
| isbn | 9780821804292 0821804294 |
| language | English |
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| physical | X, 276 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Janusz, Gerald Joseph 1940- Verfasser (DE-588)1079363734 aut Algebraic number fields Gerald J. Janusz 2. ed. Providence, RI American Math. Soc. 1996 X, 276 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 7 CORPOS DE CLASSE larpcal Corps algébriques Corps de classe NÚMEROS ALGÉBRICOS larpcal TEORIA DOS NÚMEROS larpcal Algebraic fields Class field theory Klassenkörpertheorie (DE-588)4030951-4 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 s Klassenkörpertheorie (DE-588)4030951-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1141-1 Graduate studies in mathematics 7 (DE-604)BV009739289 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007242819&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Janusz, Gerald Joseph 1940- Algebraic number fields Graduate studies in mathematics CORPOS DE CLASSE larpcal Corps algébriques Corps de classe NÚMEROS ALGÉBRICOS larpcal TEORIA DOS NÚMEROS larpcal Algebraic fields Class field theory Klassenkörpertheorie (DE-588)4030951-4 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| subject_GND | (DE-588)4030951-4 (DE-588)4068537-8 |
| title | Algebraic number fields |
| title_auth | Algebraic number fields |
| title_exact_search | Algebraic number fields |
| title_full | Algebraic number fields Gerald J. Janusz |
| title_fullStr | Algebraic number fields Gerald J. Janusz |
| title_full_unstemmed | Algebraic number fields Gerald J. Janusz |
| title_short | Algebraic number fields |
| title_sort | algebraic number fields |
| topic | CORPOS DE CLASSE larpcal Corps algébriques Corps de classe NÚMEROS ALGÉBRICOS larpcal TEORIA DOS NÚMEROS larpcal Algebraic fields Class field theory Klassenkörpertheorie (DE-588)4030951-4 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| topic_facet | CORPOS DE CLASSE Corps algébriques Corps de classe NÚMEROS ALGÉBRICOS TEORIA DOS NÚMEROS Algebraic fields Class field theory Klassenkörpertheorie Algebraischer Zahlkörper |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007242819&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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