Semi-Algebraic Function Rings and Reflectors of Partially Ordered Rings: SEMI-ALGEBRAIC FUNCTION RINGS by Niels SchwartzSemi-Algebraic Function Rings and Reflectors of Partially Ordered Rings: SEMI-ALGEBRAIC FUNCTION RINGS by Niels Schwartz

Semi-Algebraic Function Rings and Reflectors of Partially Ordered Rings: SEMI-ALGEBRAIC FUNCTION…

byNiels Schwartz, James J. Madden

Paperback | October 19, 1999

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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.
Title:Semi-Algebraic Function Rings and Reflectors of Partially Ordered Rings: SEMI-ALGEBRAIC FUNCTION…Format:PaperbackDimensions:312 pagesPublished:October 19, 1999Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540664602

ISBN - 13:9783540664604

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Table of Contents

Preface.- List of contents.- Introduction.- 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.- Bibliography.- List of categories.- Index.