Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings

  • Authors
  • Niels Schwartz
  • James J. Madden

Part of the Lecture Notes in Mathematics book series (LNM, volume 1712)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Niels Schwartz, James J. Madden
    Pages 1-19
  3. Niels Schwartz, James J. Madden
    Pages 21-33
  4. Niels Schwartz, James J. Madden
    Pages 35-42
  5. Niels Schwartz, James J. Madden
    Pages 43-44
  6. Niels Schwartz, James J. Madden
    Pages 45-49
  7. Niels Schwartz, James J. Madden
    Pages 51-53
  8. Niels Schwartz, James J. Madden
    Pages 55-61
  9. Niels Schwartz, James J. Madden
    Pages 63-77
  10. Niels Schwartz, James J. Madden
    Pages 79-92
  11. Niels Schwartz, James J. Madden
    Pages 93-105
  12. Niels Schwartz, James J. Madden
    Pages 107-123
  13. Niels Schwartz, James J. Madden
    Pages 125-132
  14. Niels Schwartz, James J. Madden
    Pages 133-160
  15. Niels Schwartz, James J. Madden
    Pages 161-166
  16. Niels Schwartz, James J. Madden
    Pages 167-181
  17. Niels Schwartz, James J. Madden
    Pages 183-188
  18. Niels Schwartz, James J. Madden
    Pages 189-199
  19. Niels Schwartz, James J. Madden
    Pages 201-208
  20. Niels Schwartz, James J. Madden
    Pages 209-215

About this book

Introduction

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.

Keywords

Algebraic structure algebra formally real field partially ordered ring real spectrum reflective subcategory semi-algebraic functions

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093968
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66460-4
  • Online ISBN 978-3-540-48284-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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