Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings

Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings by Niels Schwartz, James J. Madden.

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...

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Bibliographic Details
Main Authors: Schwartz, Niels (Author), Madden, James J. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
Edition:1st ed. 1999.
Series:Lecture Notes in Mathematics, 1712
Springer eBook Collection.
Subjects:
Algebra.
Number theory.
Geometry.
Algebraic geometry.
Nonassociative rings.
Rings (Algebra).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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