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Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings

  • Book
  • © 1999

Overview

Authors:
  1. Niels Schwartz
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  2. James J. Madden
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1712)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Niels Schwartz, James J. Madden
    Pages 1-19

  3. Preordered and partially ordered rings

    • Niels Schwartz, James J. Madden
    Pages 21-33

  4. Reflective subcategories

    • Niels Schwartz, James J. Madden
    Pages 35-42

  5. Totally ordered and real closed fields

    • Niels Schwartz, James J. Madden
    Pages 43-44

  6. Real spectra of preordered rings

    • Niels Schwartz, James J. Madden
    Pages 45-49

  7. Epimorphisms of reduced porings

    • Niels Schwartz, James J. Madden
    Pages 51-53

  8. Functions and representable porings

    • Niels Schwartz, James J. Madden
    Pages 55-61

  9. Semi-algebraic functions

    • Niels Schwartz, James J. Madden
    Pages 63-77

  10. Comparing reflectors

    • Niels Schwartz, James J. Madden
    Pages 79-92

  11. Constructing reflectors

    • Niels Schwartz, James J. Madden
    Pages 93-105

  12. H-closed epireflectors

    • Niels Schwartz, James J. Madden
    Pages 107-123

  13. Quotient-closed reflectors

    • Niels Schwartz, James J. Madden
    Pages 125-132

  14. The real closure reflector

    • Niels Schwartz, James J. Madden
    Pages 133-160

  15. Arities of reflectors and approximations by H-closed reflectors

    • Niels Schwartz, James J. Madden
    Pages 161-166

  16. Epimorphic extensions of reduced porings

    • Niels Schwartz, James J. Madden
    Pages 167-181

  17. Essential monoreflectors

    • Niels Schwartz, James J. Madden
    Pages 183-188

  18. Reflections of totally ordered fields

    • Niels Schwartz, James J. Madden
    Pages 189-199

  19. von Neumann regular f-rings

    • Niels Schwartz, James J. Madden
    Pages 201-208

  20. Totally ordered domains

    • Niels Schwartz, James J. Madden
    Pages 209-215
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Keywords

About this book

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 possible choices for these rings of functions are studied via reflections of partially ordered rings. Readers should feel comfortable using basic algebraic and categorical concepts. As motivational background some familiarity with real geometry will be helpful. The book aims at researchers and graduate students with an interest in real algebra and geometry, ordered algebraic structures, topology and rings of continuous functions.

Bibliographic Information

  • Book Title: Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings

  • Authors: Niels Schwartz, James J. Madden

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093968

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-66460-4Published: 19 October 1999

  • eBook ISBN: 978-3-540-48284-0Published: 13 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIII, 279

  • Topics: Algebra, Number Theory, Geometry, Algebraic Geometry, Non-associative Rings and Algebras

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