Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings
The book lays algebraic foundations for real geometry through a systematic investigation of partially ordered rings of semi-algebraic functions. Real spectra serve as primary geometric objects, the maps between them are determined by rings of functions associated with the spectra. The many different...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1999, 1999
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| Edition: | 1st ed. 1999 |
| Series: | Lecture Notes in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Preordered and partially ordered rings
- Reflective subcategories
- Totally ordered and real closed fields
- Real spectra of preordered rings
- Epimorphisms of reduced porings
- Functions and representable porings
- Semi-algebraic functions
- Comparing reflectors
- Constructing reflectors
- H-closed epireflectors
- Quotient-closed reflectors
- The real closure reflector
- Arities of reflectors and approximations by H-closed reflectors
- Epimorphic extensions of reduced porings
- Essential monoreflectors
- Reflections of totally ordered fields
- von Neumann regular f-rings
- Totally ordered domains
- Reduced f-rings
- Rings of continuous piecewise polynomial functions
- Rings of continuous piecewise rational functions
- Discontinuous semi-algebraic functions
- The lattice of H-closed monoreflectors