Skip to main content
  • Book
  • © 1996

Spaces of Orderings and Abstract Real Spectra

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1636)

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (9 chapters)

  1. Front Matter

    Pages I-VI
  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. The real spectrum of a ring

    • Murray A. Marshall
    Pages 83-97
  7. Abstract real spectra

    • Murray A. Marshall
    Pages 99-131
  8. Minimal generation of constructible sets

    • Murray A. Marshall
    Pages 133-150
  9. Structure results and realization results

    • Murray A. Marshall
    Pages 151-181
  10. Back Matter

    Pages 183-190

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.

Keywords

  • Lattice
  • algebra
  • orderings
  • quadratic forms
  • semi-algebraic sets
  • 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

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions