Factorization: unique and otherwise
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Ottawa, Ont
Canadian Mathematical Society/Société mathématique du Canada
2008
|
| Schriftenreihe: | CMS treatises in mathematics
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes index |
| Beschreibung: | X, 260 S. graph. Darst. |
| ISBN: | 9781568812410 |
Internformat
MARC
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| 020 | |a 9781568812410 |9 978-1-568-81241-0 | ||
| 035 | |a (OCoLC)845377469 | ||
| 035 | |a (DE-599)GBV571162703 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
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| 245 | 1 | 0 | |a Factorization |b unique and otherwise |c Steven H. Weintraub |
| 264 | 1 | |a Ottawa, Ont |b Canadian Mathematical Society/Société mathématique du Canada |c 2008 | |
| 300 | |a X, 260 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a CMS treatises in mathematics | |
| 500 | |a Includes index | ||
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018593848&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018593848 | ||
Datensatz im Suchindex
| _version_ | 1804140642882813952 |
|---|---|
| adam_text | Titel: Factorization
Autor: Weintraub, Steven H
Jahr: 2008
Contents
Preface ix
Introduction 1
1 Basic Notions 7
1.1 Integral Domains....................... 7
1.2 Quadratic Fields....................... 12
1.3 Exercises ........................... 16
2 Unique Factorization 19
2.1 Euclidean Domains...................... 20
2.2 The GCD-L Property and Euclid s Algorithm....... 31
2.3 Ideals and Principal Ideal Domains............. 45
2.4 Unique Factorization Domains ............... 51
2.5 Nonunique Factorization: The Case D 0......... 60
2.6 Nonunique Factorization: The Case D 0......... 67
2.7 Summing Up......................... 78
2.8 Exercises ........................... 80
3 The Gaussian Integers 91
3.1 Fermat s Theorem...................... 92
3.2 Factorization into Primes.................. 101
3.3 Exercises ........................... 105
4 Pell s Equation 111
4.1 Representations and Their Composition.......... 112
4.2 Solving Pell s Equation.................... 118
4.3 Numerical Examples and Further Results......... 127
4.4 Units in 0(^/D) ....................... 137
4.5 Exercises ........................... 139
viii Contents
5 Towards Algebraic Number Theory 143
5.1 Algebraic Numbers and Algebraic Integers......... 144
5.2 Ideal Theory ......................... 147
5.3 Dedekind Domains...................... 150
5.4 Algebraic Number Fields and Dedekind Domains..... 154
5.5 Prime Ideals in 0(y/D) ................... 158
5.6 Examples of Ideals in 0(773)................ 166
5.7 Behavior of Ideals in Algebraic Number Fields ...... 178
5.8 Ideal Elements........................ 180
5.9 Dirichlet s Unit Theorem .................. 182
5.10 Exercises ........................... 186
A Mathematical Induction 191
A.l Mathematical Induction and Its Equivalents........ 191
A.2 Consequences of Mathematical Induction ......... 196
A.3 Exercises ........................... 199
B Congruences 205
B.l The Notion of Congruence.................. 205
B.2 Linear Congruences...................... 211
B.3 Quadratic Congruences ................... 223
B.4 Proof of the Law of Quadratic Reciprocity......... 236
B.5 Primitive Roots........................ 241
B.6 Exercises ........................... 245
C Continuations from Chapter 2 251
C.l Continuation of the Proof of Theorem 2.8......... 251
C.2 Continuation of Example 2.26................ 255
C.3 Exercises ........................... 257
Index 259
|
| any_adam_object | 1 |
| author | Weintraub, Steven H. 1951- |
| author_GND | (DE-588)113001770 |
| author_facet | Weintraub, Steven H. 1951- |
| author_role | aut |
| author_sort | Weintraub, Steven H. 1951- |
| author_variant | s h w sh shw |
| building | Verbundindex |
| bvnumber | BV024621919 |
| classification_rvk | SK 180 SK 450 |
| ctrlnum | (OCoLC)845377469 (DE-599)GBV571162703 |
| dewey-full | 512.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.72 |
| dewey-search | 512.72 |
| dewey-sort | 3512.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV024621919 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:14Z |
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| isbn | 9781568812410 |
| language | English |
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| spelling | Weintraub, Steven H. 1951- Verfasser (DE-588)113001770 aut Factorization unique and otherwise Steven H. Weintraub Ottawa, Ont Canadian Mathematical Society/Société mathématique du Canada 2008 X, 260 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CMS treatises in mathematics Includes index HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018593848&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weintraub, Steven H. 1951- Factorization unique and otherwise |
| title | Factorization unique and otherwise |
| title_auth | Factorization unique and otherwise |
| title_exact_search | Factorization unique and otherwise |
| title_full | Factorization unique and otherwise Steven H. Weintraub |
| title_fullStr | Factorization unique and otherwise Steven H. Weintraub |
| title_full_unstemmed | Factorization unique and otherwise Steven H. Weintraub |
| title_short | Factorization |
| title_sort | factorization unique and otherwise |
| title_sub | unique and otherwise |
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