Topological rings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
North-Holland
1993
|
| Schriftenreihe: | North-Holland mathematics studies
178 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 498 S. |
| ISBN: | 0444894462 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804122597582962688 |
|---|---|
| adam_text | CONTENTS
Preface vii
Chapter I. Topological Rings and Modules 1
1 Examples of Topological Rings 1
2 Topological Modules, Vector Spaces, and Algebras 11
3 Neighborhoods of Zero 18
4 Subrings, Ideals, Submodules, and Subgroups 23
5 Quotients and Projective Limits of Rings and Modules 32
Chapter II. Metrizability and Completeness 44
6 Metrizable Groups 44
7 Completions of Commutative Hausdorff Groups 55
8 Completions of Topological Rings and Modules 64
9 Baire Spaces 68
10 Summability 71
11 Continuity of Inversion and Ad version 80
Chapter III. Local Boundedness 88
12 Locally Bounded Modules and Rings 88
13 Locally Retrobounded Division Rings 94
14 Norms and Absolute Values 102
15 Finite dimensional Vector Spaces 112
16 Topological Division Rings 120
Chapter IV. Real Valuations 134
17 Real Valuations and Valuation Rings 134
18 Discrete Valuations 141
19 Extensions of Real Valuations 152
Chapter V. Complete Local Rings 166
20 Noetherian Modules and Rings 166
21 Cohen Subrings of Complete Local Rings 173
22 Complete Discretely Valued Fields 186
23 Complete Local Noetherian Rings 192
24 Complete Semilocal Noetherian Rings 197
ix
x PREFACE
Chapter VI. Primitive and Semisimple Rings 206
25 Primitive Rings 206
26 The Radical of a Ring 216
27 Artinian Modules and Rings 226
Chapter VII. Linear Compactness and Semisim
plicity 232
28 Linearly Compact Rings and Modules 232
29 Linearly Compact Semisimple Rings 241
30 Strongly Linearly Compact Modules 251
31 Locally Linearly Compact Semisimple Rings 256
32 Locally Compact Semisimple Rings 267
Chapter VIII. Linear Compactness in Rings with
Radical 283
33 Linear Compactness in Rings with Radical 283
34 Lifting Idempotents 295
35 Locally Compact Rings 317
36 The Radical Topology 330
Chapter IX. Complete Local Noetherian Rings 359
37 The Principal Ideal Theorem 359
38 Krull Dimension and Regular Local Rings 368
39 Complete Regular Local Rings 377
40 The Japanese Property 391
Chapter X. Locally Centrally Linearly Compact
Rings 398
41 Complete Discretely Valued Fields and Division Rings 398
42 Finite dimensional Algebras 406
43 Locally Centrally Linearly Compact Rings 414
Chapter XI. Historical Notes 424
44 Topologies on Commutative Rings 424
45 Locally and Linearly Compact Rings 428
46 Category, Duality, and Existence Theorems 435
Bibliography 440
Errata 487
Index of Names 489
Index of Symbols and Definitions 492
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV008211560 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:16:24Z |
| institution | BVB |
| isbn | 0444894462 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005420049 |
| oclc_num | 246656903 |
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| physical | X, 498 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland mathematics studies |
| series2 | North-Holland mathematics studies |
| spelling | Warner, Seth Verfasser aut Topological rings Seth Warner Amsterdam [u.a.] North-Holland 1993 X, 498 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematics studies 178 Topologischer Ring Topologischer Ring (DE-588)4311180-4 gnd rswk-swf Topologischer Ring (DE-588)4311180-4 s DE-604 North-Holland mathematics studies 178 (DE-604)BV000003247 178 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005420049&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Warner, Seth Topological rings North-Holland mathematics studies Topologischer Ring Topologischer Ring (DE-588)4311180-4 gnd |
| subject_GND | (DE-588)4311180-4 |
| title | Topological rings |
| title_auth | Topological rings |
| title_exact_search | Topological rings |
| title_full | Topological rings Seth Warner |
| title_fullStr | Topological rings Seth Warner |
| title_full_unstemmed | Topological rings Seth Warner |
| title_short | Topological rings |
| title_sort | topological rings |
| topic | Topologischer Ring Topologischer Ring (DE-588)4311180-4 gnd |
| topic_facet | Topologischer Ring |
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