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Partially ordered rings and semi-algebraic geometry /
The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
1979.
|
| Colección: | London Mathematical Society lecture note series ;
37. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 5.7. The Structure Sheaf, II
- The Sheaf Axioms for Basic Open Sets5.8. The Structure Sheaf, III
- Definition; CHAPTER VI
- POLYNOMIALS; 6.1. Polynomials as Functions; 6.2. Adjoining Roots; 6.3. A Universal Bound on the Roots of Polynomials; 6.4. A ""Going-Up"" Theorem for Semi-Integral Extensions; CHAPTER VII
- ORDERED FIELDS; 7.1. Basic Results; 7.2. Function Theoretic Properties of Polynomials; 7.3. Sturm's Theorem; 7.4. Dedekind Cuts; Archimedean and Non-Archimedean Extensions.; 7.5. Orders on Simple Field Extensions; 7.6. Total Orders and Signed Places; 7.7. Existence of Signed Places
- CHAPTER VIII
- AFFINE SEMT-ALGEBRAIC SETS8.1. Introduction and Notation; 8.2. Some Properties of RHJ-Algebras; 8.3. Real Curves; 8.4. Signed Places on Function Fields; 8.5. Characterization of Non-Negative Functions; 8.6. Derived Orders; 8.7. A Preliminary Inverse Function Theorem; 8.8. Algebraic Simple Points, Dimension, Codimension and Rank; 8.9. Stratification of Semi-Algebraic Sets; 8.10. Krull Dimension; 8.11. Orders on Function Fields; 8.12. Discussion of Total Orders on R(x, y); 8.13. Brief Discussion of Structure Sheaves; I
- The rational structure sheaf
- II
- The semi-algebraic structure sheaf