Overview

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.

Full Product Details

Author:   Niels Schwartz ,  James J. Madden
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1999 ed.
Volume:   1712
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   0.940kg
ISBN:  

9783540664604

ISBN 10:   3540664602
Pages:   279
Publication Date:   19 October 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Preordered and partially ordered rings.- Reflective subcategories.- Totally ordered and real closed fields.- Real spectra of preordered rings.- Epimorphisms of reduced porings.- Functions and representable porings.- Semi-algebraic functions.- Comparing reflectors.- Constructing reflectors.- H-closed epireflectors.- Quotient-closed reflectors.- The real closure reflector.- Arities of reflectors and approximations by H-closed reflectors.- Epimorphic extensions of reduced porings.- Essential monoreflectors.- Reflections of totally ordered fields.- von Neumann regular f-rings.- Totally ordered domains.- Reduced f-rings.- Rings of continuous piecewise polynomial functions.- Rings of continuous piecewise rational functions.- Discontinuous semi-algebraic functions.- The lattice of H-closed monoreflectors.

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