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 |