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010   $a3-540-48284-9
024 7 $a10.1007/BFb0093968
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035   $a(DE-He213)978-3-540-48284-0
035   $a(MiAaPQ)EBC5578287
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035   $a(OCoLC)1066179036
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100   $a20121227d1999      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aSemi-algebraic Function Rings and Reflectors of Partially Ordered Rings /$fby Niels Schwartz, James J. Madden
205   $a1st ed. 1999.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1999.
215   $a1 online resource (XIII, 279 p.) 
225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1712
300   $aBibliographic Level Mode of Issuance: Monograph
311 08$a3-540-66460-2 
327   $aPreordered 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.
330   $aThe book lays algebraic foundations for real geometry through a systematic investigation of partially ordered rings of semi-algebraic functions. Real spectra serve as primary geometric objects, the maps between them are determined by rings of functions associated with the spectra. The many different possible choices for these rings of functions are studied via reflections of partially ordered rings. Readers should feel comfortable using basic algebraic and categorical concepts. As motivational background some familiarity with real geometry will be helpful. The book aims at researchers and graduate students with an interest in real algebra and geometry, ordered algebraic structures, topology and rings of continuous functions.
410  0$aLecture Notes in Mathematics,$x1617-9692 ;$v1712
606   $aAlgebra
606   $aNumber theory
606   $aGeometry
606   $aGeometry, Algebraic
606   $aNonassociative rings
606   $aAlgebra
606   $aNumber Theory
606   $aGeometry
606   $aAlgebraic Geometry
606   $aNon-associative Rings and Algebras
615  0$aAlgebra.
615  0$aNumber theory.
615  0$aGeometry.
615  0$aGeometry, Algebraic.
615  0$aNonassociative rings.
615 14$aAlgebra.
615 24$aNumber Theory.
615 24$aGeometry.
615 24$aAlgebraic Geometry.
615 24$aNon-associative Rings and Algebras.
676   $a516.3
700   $aSchwartz$b Niels$f1950-$062483
702   $aMadden$b James J.
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910146310903321
996   $aSemi-algebraic function rings and reflectors of partially ordered rings$9262403
997   $aUNINA