000 03811nam a22005535i 4500
001 978-3-540-48284-0
003 DE-He213
005 20190213151432.0
007 cr nn 008mamaa
008 121227s1999 gw | s |||| 0|eng d
020 _a9783540482840
_9978-3-540-48284-0
024 7 _a10.1007/BFb0093968
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aSchwartz, Niels.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSemi-algebraic Function Rings and Reflectors of Partially Ordered Rings
_h[electronic resource] /
_cby Niels Schwartz, James J. Madden.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1999.
300 _aXIII, 279 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1712
505 0 _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.
520 _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.
650 0 _aAlgebra.
650 0 _aNumber theory.
650 0 _aGeometry.
650 0 _aGeometry, algebraic.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aNon-associative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11116
700 1 _aMadden, James J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662192412
776 0 8 _iPrinted edition:
_z9783540664604
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1712
856 4 0 _uhttps://doi.org/10.1007/BFb0093968
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10663
_d10663