Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings

• Main Authors: Schwartz, Niels (Author, http://id.loc.gov/vocabulary/relators/aut), Madden, James J. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Edition: 1st ed. 1999.
• Series: Lecture Notes in Mathematics, 1712
• Subjects: Algebra.; Number theory.; Geometry.; Algebraic geometry.; Nonassociative rings.; Rings (Algebra).; Number Theory.; Algebraic Geometry.; Non-associative Rings and Algebras.

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...

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.