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001 978-3-540-39093-0
003 DE-He213
005 20190213151322.0
007 cr nn 008mamaa
008 121227s1984 gw | s |||| 0|eng d
020 _a9783540390930
_9978-3-540-39093-0
024 7 _a10.1007/BFb0101548
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aPrestel, Alexander.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLectures on Formally Real Fields
_h[electronic resource] /
_cby Alexander Prestel.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1984.
300 _aXI, 128 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 ;
_v1093
505 0 _aOrderings and semiorderings of fields -- Quadratic forms over formally real fields -- Real algebraic closures -- Some notions from model theory -- The transfer-principle for real closed fields -- The space of orderings and semiorderings -- Real places -- Real henselian fields -- SAP-fields -- Quadratic forms over formally real fields.
520 _aAbsolute values and their completions - like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization. In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge aquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.
650 0 _aAlgebra.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aMathematical Logic and Foundations.
_0http://scigraph.springernature.com/things/product-market-codes/M24005
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662207390
776 0 8 _iPrinted edition:
_z9783540138853
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1093
856 4 0 _uhttps://doi.org/10.1007/BFb0101548
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10261
_d10261