Franklin

Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings [electronic resource] / by Niels Schwartz, James J. Madden.

Author/Creator:
Schwartz, Niels. author., Author,
Publication:
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
Format/Description:
Book
1 online resource (XIII, 279 pages)
Series:
Lecture Notes in Mathematics, 0075-8434 ; 1712
Lecture Notes in Mathematics, 0075-8434 ; 1712
Contained In:
Springer eBooks
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Details

Subjects:
Algebra.
Number theory.
Geometry.
Geometry, algebraic.
Local subjects:
Algebra. (search)
Number Theory. (search)
Geometry. (search)
Algebraic Geometry. (search)
Non-associative Rings and Algebras. (search)
System Details:
text file PDF
Summary:
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.
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.
Contributor:
Madden, James J. author., Author,
SpringerLink (Online service)
Other format:
Printed edition:
Printed edition:
ISBN:
9783540482840
Publisher Number:
10.1007/BFb0093968 doi
Access Restriction:
Restricted for use by site license.