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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 |
MARC
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| 100 | 1 | |a Brumfiel, Gregory W. | |
| 245 | 1 | 0 | |a Partially ordered rings and semi-algebraic geometry / |c Gregory W. Brumfiel. |
| 260 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c 1979. | ||
| 300 | |a 1 online resource (280 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series ; |v 37 | |
| 504 | |a Includes bibliographical references (pages 273-277) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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 the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance. | ||
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a II -- The semi-algebraic structure sheaf | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Commutative rings. | |
| 650 | 0 | |a Categories (Mathematics) | |
| 650 | 0 | |a Geometry, Algebraic. | |
| 650 | 6 | |a Anneaux commutatifs. | |
| 650 | 6 | |a Catégories (Mathématiques) | |
| 650 | 6 | |a Géométrie algébrique. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Geometry, Algebraic. |2 fast |0 (OCoLC)fst00940902 | |
| 650 | 7 | |a Categories (Mathematics) |2 fast |0 (OCoLC)fst00849000 | |
| 650 | 7 | |a Commutative rings. |2 fast |0 (OCoLC)fst00871205 | |
| 650 | 7 | |a Geordneter Ring |2 gnd | |
| 650 | 7 | |a Semialgebraischer Raum |2 gnd | |
| 650 | 1 | 7 | |a Algebraïsche meetkunde. |2 gtt |
| 650 | 0 | 7 | |a Semi-algebraischer Raum. |2 swd |
| 655 | 4 | |a Semi-algebraische Geometrie. | |
| 655 | 7 | |a Semi-algebraische Geometrie. |2 swd | |
| 776 | 0 | 8 | |i Print version: |a Brumfiel, Gregory W. |t Partially ordered rings and semi-algebraic geometry. |d Cambridge [Eng.] ; New York : Cambridge University Press, 1979 |z 052122845X |w (DLC) 80469087 |w (OCoLC)6022756 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 37. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552504 |z Texto completo |
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