Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings

Niels Schwartz, James J. Madden (Autoren)

Buch | Softcover

XIII, 279 Seiten

1999
Springer Berlin (Verlag)
978-3-540-66460-4 (ISBN)

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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.

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.

Erscheint lt. Verlag	19.10.1999
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIII, 279 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	395 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • Algebraic Structure • formally real field • Funktion (Mathematik) • partially ordered ring • real spectrum • reflective subcategory • semi-algebraic functions
ISBN-10	3-540-66460-2 / 3540664602
ISBN-13	978-3-540-66460-4 / 9783540664604
Zustand	Neuware