Spaces of orderings and abstract real spectra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1996
|
| Schriftenreihe: | Lecture notes in mathematics
1636 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 190 S. |
| ISBN: | 3540617299 |
Internformat
MARC
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| 100 | 1 | |a Marshall, Murray A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Spaces of orderings and abstract real spectra |c Murray A. Marshall |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a VI, 190 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1636 | |
| 650 | 4 | |a Corps ordonnés | |
| 650 | 4 | |a Formes quadratiques | |
| 650 | 7 | |a Lichamen (wiskunde) |2 gtt | |
| 650 | 7 | |a Ordening |2 gtt | |
| 650 | 7 | |a Spectraaltheorie |2 gtt | |
| 650 | 4 | |a Valuations, Théorie des | |
| 650 | 4 | |a Forms, Quadratic | |
| 650 | 4 | |a Ordered fields | |
| 650 | 4 | |a Valuation theory | |
| 650 | 0 | 7 | |a Spektrum |g Mathematik |0 (DE-588)4182180-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ordnung |g Mathematik |0 (DE-588)4043745-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1805082794996531200 |
|---|---|
| adam_text |
Table of Contents
Introduction 1
1. Orderings on Fields
1.1 Lang's homomorphism theorem 5
1.2 Characters on groups of exponent 2 8
1.3 Orderings and real places 11
1.4 Examples 14
2. Spaces of Orderings
2.1 Axioms for spaces of orderings 19
2.2 Quadratic forms and the Witt ring 24
2.3 Pfister's local global principle 30
2.4 Subspaces and preorderings 32
3. Fans and the Representation Theorem
3.1 Fans 37
3.2 The representation theorem 40
3.3 SAP spaces 44
3.4 The stability index 47
3.5 Fans and real places 50
3.6 Trivialization theorem for fans 54
4. P Structures, Connected Components and the Isotropy
Theorem
4.1 Two constructions 61
4.2 Spaces of orderings of finite chain length 65
4.3 The isotropy theorem 67
4.4 Proofs in the field case 70
4.5 Lemmas concerning the subspaces Xt, t £ x(G) 73
4.6 Connected components and P structures 76
4.7 The chain length theorem 80
VI Table of Contents
5. The Real Spectrum of a Ring
5.1 Orderings on rings 83
5.2 Examples 86
5.3 Constructible sets and semi algebraic sets 89
5.4 Nullstellensatz and Positivstellensatz 91
5.5 Value sets of quadratic forms 95
6. Abstract Real Spectra
6.1 Axioms for abstract real spectra . 99
6.2 Properties of value sets 105
6.3 The spectral topology 110
6.4 More on specialization 114
6.5 Zariski topology and ideals 117
6.6 Subspaces and preorderings 121
6.7 Brocker's weak local global principle 127
6.8 Hormander Lojasiewicz inequality 129
7. Minimal Generation of Constructible Sets
7.1 Basic sets 133
7.2 Minimal generation of basic open sets 134
7.3 Dimension 138
7.4 Minimal generation of basic closed sets 140
7.5 More on basic sets 142
7.6 Zero dimensional case 144
7.7 Separating families, etc 146
8. Structure Results and Realization Results
8.1 Semi local case 151
8.2 Brocker's Axioms 155
8.3 Representation theorems 160
8.4 Behaviour of fans under specialization 163
8.5 Classification of abstract real spectra of finite chain length . 164
8.6 Real places and P structures 168
8.7 Realizing abstract real spectra of finite chain length 172
8.8 Real closed abstract real spectra 176
8.9 Classification of zero dimensional abstract real spectra . 179
References 183
Subject Index 187
Symbol Index 189 |
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| author | Marshall, Murray A. |
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| id | DE-604.BV011001484 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T07:38:19Z |
| institution | BVB |
| isbn | 3540617299 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007365366 |
| oclc_num | 246274306 |
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| physical | VI, 190 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Marshall, Murray A. Verfasser aut Spaces of orderings and abstract real spectra Murray A. Marshall Berlin [u.a.] Springer 1996 VI, 190 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1636 Corps ordonnés Formes quadratiques Lichamen (wiskunde) gtt Ordening gtt Spectraaltheorie gtt Valuations, Théorie des Forms, Quadratic Ordered fields Valuation theory Spektrum Mathematik (DE-588)4182180-4 gnd rswk-swf Ordnung Mathematik (DE-588)4043745-0 gnd rswk-swf Körper Algebra (DE-588)4308063-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s DE-604 Körper Algebra (DE-588)4308063-7 s Ordnung Mathematik (DE-588)4043745-0 s Spektrum Mathematik (DE-588)4182180-4 s Lecture notes in mathematics 1636 (DE-604)BV000676446 1636 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007365366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marshall, Murray A. Spaces of orderings and abstract real spectra Lecture notes in mathematics Corps ordonnés Formes quadratiques Lichamen (wiskunde) gtt Ordening gtt Spectraaltheorie gtt Valuations, Théorie des Forms, Quadratic Ordered fields Valuation theory Spektrum Mathematik (DE-588)4182180-4 gnd Ordnung Mathematik (DE-588)4043745-0 gnd Körper Algebra (DE-588)4308063-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4182180-4 (DE-588)4043745-0 (DE-588)4308063-7 (DE-588)4001161-6 |
| title | Spaces of orderings and abstract real spectra |
| title_auth | Spaces of orderings and abstract real spectra |
| title_exact_search | Spaces of orderings and abstract real spectra |
| title_full | Spaces of orderings and abstract real spectra Murray A. Marshall |
| title_fullStr | Spaces of orderings and abstract real spectra Murray A. Marshall |
| title_full_unstemmed | Spaces of orderings and abstract real spectra Murray A. Marshall |
| title_short | Spaces of orderings and abstract real spectra |
| title_sort | spaces of orderings and abstract real spectra |
| topic | Corps ordonnés Formes quadratiques Lichamen (wiskunde) gtt Ordening gtt Spectraaltheorie gtt Valuations, Théorie des Forms, Quadratic Ordered fields Valuation theory Spektrum Mathematik (DE-588)4182180-4 gnd Ordnung Mathematik (DE-588)4043745-0 gnd Körper Algebra (DE-588)4308063-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Corps ordonnés Formes quadratiques Lichamen (wiskunde) Ordening Spectraaltheorie Valuations, Théorie des Forms, Quadratic Ordered fields Valuation theory Spektrum Mathematik Ordnung Mathematik Körper Algebra Algebraische Geometrie |
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