Lecture Notes in Mathematics

Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings

Authors: Schwartz, Niels, Madden, James J.

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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.

Table of contents (24 chapters)

  • Introduction

    Schwartz, Niels (et al.)

    Pages 1-19

  • Preordered and partially ordered rings

    Schwartz, Niels (et al.)

    Pages 21-33

  • Reflective subcategories

    Schwartz, Niels (et al.)

    Pages 35-42

  • Totally ordered and real closed fields

    Schwartz, Niels (et al.)

    Pages 43-44

  • Real spectra of preordered rings

    Schwartz, Niels (et al.)

    Pages 45-49

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-48284-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-540-66460-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1712
Copyright
1999
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-48284-0
DOI
10.1007/BFb0093968
Softcover ISBN
978-3-540-66460-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 279
Topics