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Book Categories |
Ch. 1 | Valuation Rings | 1 |
1.1 | Valuation Rings and Valuations of Fields | 1 |
1.2 | Valuation Rings in Algebraic Extensions | 11 |
1.3 | Henselian Valuation Rings | 20 |
1.4 | Alebgraic Extensions of Valued Fields | 31 |
1.5 | Immediate Extensions | 46 |
1.6 | Density | 65 |
1.7 | Constructions | 71 |
Ch. 2 | Multi-Valued Fields | 85 |
2.1 | Prufer Rings | 85 |
2.2 | The Zariski Topology and the Restriction Mapping | 94 |
2.3 | Affine Families of Valuation Rings | 100 |
2.4 | Weakly Boolean Families and Boolean Families of Valuation Rings | 111 |
2.5 | Near Boolean Families of Valuation Rings | 123 |
2.6 | Independence | 130 |
Ch. 3 | Local-Global Properties of Near Boolean Families | 141 |
3.1 | Rational Points over Henselian Fields | 141 |
3.2 | Arithmetic Local-Global Principle | 151 |
3.3 | Equivalent Forms of Property LG[subscript A] | 158 |
3.4 | Preservation of Property LG[subscript A] under Algebraic Separable Extensions | 167 |
3.5 | Geometric Local-Global Principle | 174 |
3.6 | Existence of Families with Property LG[subscript A] | 184 |
Ch. 4 | Model-Theoretic Properties of Multi-Valued Fields | 195 |
4.1 | Embedding Theorems | 195 |
4.2 | The Robinson Theorem | 204 |
4.3 | Valued Fields | 207 |
4.4 | Finitely Multi-Valued Fields | 216 |
4.5 | Multi-Valued Fields with Boolean Families | 226 |
4.6 | Multi-Valued Fields with Near Boolean Families | 246 |
Bibliographical and Historical Remarks | 259 | |
References | 263 | |
Subject Index | 269 |
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Add Multi-Valued Fields, The book deals with the theory of valued fields and multi-valued fields. The theory of Prufer rings is discussed from the geometric point of view. The author shows that by introducing the Zariski topology on families of valuation rings, it is possible t, Multi-Valued Fields to the inventory that you are selling on WonderClubX
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Add Multi-Valued Fields, The book deals with the theory of valued fields and multi-valued fields. The theory of Prufer rings is discussed from the geometric point of view. The author shows that by introducing the Zariski topology on families of valuation rings, it is possible t, Multi-Valued Fields to your collection on WonderClub |