Algebraic number theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Chapman and Hall
1987
|
| Edition: | 2. ed. |
| Series: | Chapman and Hall mathematics series.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 3. Aufl. u.d.T.: Stewart, Ian: Algebraic number theory and Fermat's last theorem |
| Physical Description: | XIX, 262 S. |
| ISBN: | 0412298708 041229690X |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804116660603322368 |
|---|---|
| adam_text | Algebraic
Number
Theory
IAN STEWART
DAVID TALL
Mathematics Institute
University of Warwick
Coventry
SECOND EDITION
LONDON NEW YORK
CHAPMAN AND HALL
Contents
Preface
Readers guide
Index of notation
The origins of algebraic number theory
PARTI ALGEBRAIC METHODS
Algebraic background
1 1 Rings and fields
1 2 Factorization of polynomials
1 3 Field extensions
1 4 Symmetric polynomials
1 5 Modules
1 6 Free abelian groups
Algebraic numbers
2 1 Algebraic numbers
2 2 Conjugates and discriminants
2 3 Algebraic integers
2 4 Integral bases
2 5 Norms and traces
2 6 Rings of integers
page xi
XV
xvii
vii
viii CONTENTS
3 Quadratic and cyclotomic fields 66
3 1 Quadratic fields 66
3 2 Cyclotomic fields 69
4 Factorization into irreducibles 78
4 1 Historical background 79
4 2 Trivial factorizations 81
4 3 Factorization into irreducibles 85
4 4 Examples of non-unique factorization into
irreducibles 89
4 5 Prime factorization 94
4 6 Euclidean domains 97
4 7 Euclidean quadratic fields 99
4 8 Consequences of unique factorization 102
4 9 The Ramanujan-Nagell theorem 104
5 Ideals 110
5 1 Historical background 111
5 2 Prime factorization of ideals 114
5 3 The norm of an ideal 125
5 4 Nonunique factorization in cyclotomic fields 133
PART II GEOMETRIC METHODS
6 Lattices 141
6 1 Lattices 141
6 2 The quotient torus 144
7 Minkowski s theorem 151
7 1 Minkowski s theorem 151
7 2 The two-squares theorem 154
7 3 The four-squares theorem 155
8 Geometric representation of algebraic numbers 158
8 1 The space L 158
9 Class-group and class-number 164
9 1 The class-group 164
9 2 An existence theorem 166
9 3 Finiteness of the class-group 171
9 4 How to make an ideal principal 172
9 5 Unique factorization of elements in an
extension ring 176
CONTENTS ix
PART HI NUMBER-THEORETIC APPLICATIONS
10 Computational methods 185
10 1 Factorization of a rational prime 185
10 2 Minkowski s constants 189
10 3 Some class-number calculations 193
10 4 Tables 196
11 Fermat s Last Theorem 199
11 1 Some history 199
11 2 Elementary considerations 202
11 3 Kummer s lemma 205
11 4 Kummer s Theorem 210
11 5 Regular primes 214
12 Dirichlet s Units Theorem 219
12 1 Introduction 219
12 2 Logarithmic space 220
12 3 Embedding the unit group in logarithmic space 221
12 4 Dirichlet s theorem 223
Appendix Quadratic Residues 231
A I Quadratic equations in Zm 232
A 2 The units of Zm 234
A 3 Quadratic Residues 240
References 253
Index 257
|
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| classification_tum | MAT 120f |
| ctrlnum | (OCoLC)14967078 (DE-599)BVBBV002205581 |
| 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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| indexdate | 2024-07-09T15:42:02Z |
| institution | BVB |
| isbn | 0412298708 041229690X |
| language | English |
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| physical | XIX, 262 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Chapman and Hall |
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| series2 | Chapman and Hall mathematics series. |
| spelling | Stewart, Ian 1945- Verfasser (DE-588)124091598 aut Algebraic number theory Ian Stewart ; David Tall 2. ed. London u.a. Chapman and Hall 1987 XIX, 262 S. txt rdacontent n rdamedia nc rdacarrier Chapman and Hall mathematics series. 3. Aufl. u.d.T.: Stewart, Ian: Algebraic number theory and Fermat's last theorem Nombres algébriques, Théorie des Nombres algébriques, théorie des ram Algebraic number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Fermatsche Vermutung (DE-588)4154012-8 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s Fermatsche Vermutung (DE-588)4154012-8 s 1\p DE-604 Zahlentheorie (DE-588)4067277-3 s 2\p DE-604 Tall, David Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001448913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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 |
| spellingShingle | Stewart, Ian 1945- Tall, David Algebraic number theory Nombres algébriques, Théorie des Nombres algébriques, théorie des ram Algebraic number theory Zahlentheorie (DE-588)4067277-3 gnd Fermatsche Vermutung (DE-588)4154012-8 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4154012-8 (DE-588)4001170-7 |
| title | Algebraic number theory |
| title_auth | Algebraic number theory |
| title_exact_search | Algebraic number theory |
| title_full | Algebraic number theory Ian Stewart ; David Tall |
| title_fullStr | Algebraic number theory Ian Stewart ; David Tall |
| title_full_unstemmed | Algebraic number theory Ian Stewart ; David Tall |
| title_short | Algebraic number theory |
| title_sort | algebraic number theory |
| topic | Nombres algébriques, Théorie des Nombres algébriques, théorie des ram Algebraic number theory Zahlentheorie (DE-588)4067277-3 gnd Fermatsche Vermutung (DE-588)4154012-8 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Nombres algébriques, Théorie des Nombres algébriques, théorie des Algebraic number theory Zahlentheorie Fermatsche Vermutung Algebraische Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001448913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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