Topological fields and near valuations
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1990
|
| Schriftenreihe: | Pure and applied mathematics
135 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102/MAT 127f 2001 A 31362 |
|---|---|
| DE-BY-TUM_katkey | 516837 |
| DE-BY-TUM_media_number | 040010661417 |
| _version_ | 1816711562641014784 |
| adam_text | Contents
PREFACE Hi
NOTATION ix
PART I: SURVEY OF TOPOLOGICAL FIELDS
1 INTRODUCTION 3
1.1 Neighborhood Bases at Zero 3
1.2 Alternate Axiomatizations 6
1.3 Basic Properties 8
2 VALUATIONS AND OTHER EXAMPLES 11
2.1 Prevaluations 11
2.2 Examples of Valued Fields 17
2.3 Other Examples 22
3 THE LATTICE OF RING TOPOLOGIES 30
3.1 Lattices of Topologies 30
3.2 Weakening Ring Topologies 32
3.3 Minimal Topologies 36
3.4 Independence 37
4 LOCALLY BOUNDED FIELDS 41
4.1 Bounded Sets 41
4.2 Locally Bounded Rings 43
4.3 Preorders 44
4.4 Preorders and Topologies 47
4.5 Lattice Results 54
4.6 Examples 60
vi
Contents vii
5 NORMED FIELDS 63
5.1 Norms 63
5.2 Nilpotence and Normability 65
6 COMPLETENESS 69
6.1 Completions of Rings 69
6.2 Completions of Fields 70
7 EMBEDDING AND EXTENSION 74
7.1 The Problem 74
7.2 The Product Topology Extension 74
8 EXISTENCE OF FIELD TOPOLOGIES 77
9 CONNECTED FIELDS 83
10 DISCONNECTED FIELDS 87
10.1 Extremally Disconnected Fields 87
10.2 Ultraregular Fields 89
11 LINEAR FIELDS 91
PART II: VALUED FIELDS
12 ABSOLUTE VALUES 97
12.1 Nonarchimedean Absolute Values 97
12.2 Absolute Values on PID s 100
12.3 Equivalent Absolute Values 105
12.4 Equivalent Valuations 107
12.5 Powers of Absolute Values 109
13 PLACES 112
14 VECTOR SPACES AND STRICTLY MINIMAL FIELDS . . .116
14.1 Strictly Minimal Fields 116
14.2 Completeness and Norms 121
14.3 Normed Algebras 125
viti Contents
15 EXTENSIONS OF VALUATIONS 132
15.1 Existence of Extensions 132
15.2 Archimedean Absolute Values 136
15.3 Complete and Algebraically Closed Fields 143
16 CHARACTERIZATIONS 147
16.1 Topologies Induced by Absolute Values 147
16.2 Archimedean Valuations 149
16.3 Type V Fields 151
16.4 Addiator Sequences 157
16.5 Topologies Induced by Valuations 161
APPENDIX A: TOPOLOGICAL GROUPS 164
A.I Fundamental Properties 164
A.2 Norms 168
A.3 Uniformity 170
APPENDIX B: ORDERED GROUPS AND FIELDS 176
B.I Ordered Sets 176
B.2 Partially Ordered Abelian Groups 185
B.3 Subgroups, Quotients, and Products 188
B.4 Extensions of Partial Orders 193
B.5 Totally Ordered Groups 197
B.6 Ordered Fields 202
B.7 Formal Power Series Fields 206
REFERENCES 211
INDEX 227
|
| any_adam_object | 1 |
| author | Shell, Niel |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Topologische Felder gnd |
| genre_facet | Topologische Felder |
| id | DE-604.BV004291477 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:10:36Z |
| institution | BVB |
| isbn | 082478412X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002669618 |
| oclc_num | 21523986 |
| open_access_boolean | |
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| physical | XIII, 233 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spellingShingle | Shell, Niel Topological fields and near valuations Pure and applied mathematics Corps ordonné Corps topologique Corps topologiques ram Corps valué Groupe ordonné Valuation Valuations, théorie des ram Topological fields Valuation theory Bewertungstheorie (DE-588)4122918-6 gnd Topologischer Körper (DE-588)4242582-7 gnd |
| subject_GND | (DE-588)4122918-6 (DE-588)4242582-7 |
| title | Topological fields and near valuations |
| title_auth | Topological fields and near valuations |
| title_exact_search | Topological fields and near valuations |
| title_full | Topological fields and near valuations Niel Shell |
| title_fullStr | Topological fields and near valuations Niel Shell |
| title_full_unstemmed | Topological fields and near valuations Niel Shell |
| title_short | Topological fields and near valuations |
| title_sort | topological fields and near valuations |
| topic | Corps ordonné Corps topologique Corps topologiques ram Corps valué Groupe ordonné Valuation Valuations, théorie des ram Topological fields Valuation theory Bewertungstheorie (DE-588)4122918-6 gnd Topologischer Körper (DE-588)4242582-7 gnd |
| topic_facet | Corps ordonné Corps topologique Corps topologiques Corps valué Groupe ordonné Valuation Valuations, théorie des Topological fields Valuation theory Bewertungstheorie Topologischer Körper Topologische Felder |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002669618&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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