LEADER 02884nam 2200625 450 001 996466858103316 005 20220911024248.0 010 $a3-540-39093-6 024 7 $a10.1007/BFb0101548 035 $a(CKB)1000000000437712 035 $a(SSID)ssj0000324366 035 $a(PQKBManifestationID)12080844 035 $a(PQKBTitleCode)TC0000324366 035 $a(PQKBWorkID)10313369 035 $a(PQKB)11057026 035 $a(DE-He213)978-3-540-39093-0 035 $a(MiAaPQ)EBC5576497 035 $a(Au-PeEL)EBL5576497 035 $a(OCoLC)1066191835 035 $a(MiAaPQ)EBC6842084 035 $a(Au-PeEL)EBL6842084 035 $a(OCoLC)793078864 035 $a(PPN)155220888 035 $a(EXLCZ)991000000000437712 100 $a20220911d1984 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on formally real fields /$fAlexander Prestel 205 $a1st ed. 1984. 210 1$aBerlin :$cSpringer-Verlag,$d[1984] 210 4$dİ1984 215 $a1 online resource (XI, 128 p.) 225 1 $aLecture notes in mathematics ;$v1093 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-13885-4 320 $aIncludes bibliographical references and index. 327 $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. 330 $aAbsolute values and their completions - like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization. In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge aquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1093. 606 $aFormally real fields 606 $aForms, Quadratic 615 0$aFormally real fields. 615 0$aForms, Quadratic. 676 $a512.3 700 $aPrestel$b A$g(Alexander),$f1941-$058277 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466858103316 996 $aLectures on formally real fields$978504 997 $aUNISA