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Spaces of Orderings and Abstract Real Spectra

  • Book
  • © 1996

Overview

Authors:
  1. Murray A. Marshall
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1636)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    • Murray A. Marshall
    Pages 1-4

  3. Orderings on fields

    • Murray A. Marshall
    Pages 5-17

  4. Spaces of orderings

    • Murray A. Marshall
    Pages 19-35

  5. Fans and the representation theorem

    • Murray A. Marshall
    Pages 37-59

  6. P-structures, connected components and 0 the isotropy theorem

    • Murray A. Marshall
    Pages 61-82

  7. The real spectrum of a ring

    • Murray A. Marshall
    Pages 83-97

  8. Abstract real spectra

    • Murray A. Marshall
    Pages 99-131

  9. Minimal generation of constructible sets

    • Murray A. Marshall
    Pages 133-150

  10. Structure results and realization results

    • Murray A. Marshall
    Pages 151-181

  11. Back Matter

    Pages 183-190
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Keywords

About this book

This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.

Bibliographic Information

  • Book Title: Spaces of Orderings and Abstract Real Spectra

  • Authors: Murray A. Marshall

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0092696

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1996

  • Softcover ISBN: 978-3-540-61729-7Published: 02 October 1996

  • eBook ISBN: 978-3-540-69996-5Published: 17 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 198

  • Topics: Algebraic Geometry, Order, Lattices, Ordered Algebraic Structures

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