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＜電子ブック＞
Constructible Sets in Real Geometry / by Carlos Andradas, Ludwig Bröcker, Jesus M. Ruiz
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 33)

版	1st ed. 1996.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1996
本文言語	英語
大きさ	IX, 270 p : online resource
著者標目	*Andradas, Carlos author Bröcker, Ludwig author Ruiz, Jesus M author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry FREE:Algebraic Geometry
一般注記	I. A First Look at Semialgebraic Geometry -- 1. Real Closed Fields and Transfer Principles -- 2. What is Semialgebraic Geometry? -- 3. Real Spaces -- 4. Examples -- II. Real Algebra -- 1. The Real Spectrum of a Ring -- 2. Specializations, Zero Sets and Real Ideals -- 3. Real Valuations -- 4. Real Going-Up and Real Going-Down -- 5. Abstract Semialgebraic Functions -- 6. Cylindrical Decomposition -- 7. Real Strict Localization -- Notes -- III. Spaces of Signs -- 1. The Axioms -- 2. Forms -- 3. SAP-Spaces and Fans -- 4. Local Spaces of Signs -- 5. The Space of Signs of a Ring -- 6. Subspaces -- Notes -- IV. Spaces of Orderings -- 1. The Axioms Revisited -- 2. Basic Constructions -- 3. Spaces of Finite Type -- 4. Spaces of Finite Chain Length -- 5. Finite Type = Finite Chain Length -- 6. Local-Global Principles -- 7. Representation Theorem and Invariants -- Notes -- V. The Main Results -- 1. Stability Formulae -- 2. Complexity of Constructible Sets -- 3. Separation -- 4. Real Divisors -- 5. The Artin-Lang Property -- Notes -- VI. Spaces of Signs of Rings -- 1. Fans and Valuations -- 2. Field Extensions: Upper Bounds -- 3. Field Extensions: Lower Bounds -- 4. Algebras -- 5. Algebras Finitely Generated over Fields -- 6. Archimedean Rings -- 7. Coming Back to Geometry -- Notes -- VII. Real Algebra of Excellent Rings -- 1. Regular Homomorphisms -- 2. Excellent Rings -- 3. Extension of Orderings Under Completion -- 4. Curve Selection Lemma -- 5. Dimension, Valuations and Fans -- 6. Closures of Constructible Sets -- 7. Real Going-down for Regular Homomorphisms -- 8. Connected Components of Constructible Sets -- Notes -- VIII. Real Analytic Geometry -- 1. Semianalytic Sets -- 2. Semianalytic Set Germs -- 3. Cylindrical Decomposition of Germs -- 4. Rings of Global Analytic Functions -- 5. Hilbert’s 17th Problem and Real Nullstellensatz -- 6.Minimal Generation of Global Semianalytic Sets -- 7. Topology of Global Semianalytic Sets -- 8. Germs at Compact Sets -- Notes HTTP:URL=https://doi.org/10.1007/978-3-642-80024-5

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