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- W756419981 abstract "Let K be a real function field over a real closed field F. Then there exists an F-place .phi.:K.rarw.F.cup.{.inf.}. This is Lang's Existence of Rational Place Theorem (6). There is an equivalent version of Lang's Theorem in (4). That is, if K is a function field over a field F, then, for any ordering P on F which extends to K, there exists an F-place .phi.: K.rarw.F'.cup.{.inf.} where F' is a real closure of (F, P). In [2], Knebusch pointed out the converse of the version of Lang's Theorem is also true. By a valuation theoretic approach to Lang's Theorem, we have found out the following generalization of Lang and Knebusch's Theorem. Let K be an arbitrary extension field of a field F. then an ordering P on F can be extended to an ordering P on K if there exists an F-place of K into some real closed field R containing F. Of course R.cap.F=P. The restriction K being a function field of F is vanished, though the codomain of the F-place is slightly varied. Therefore our theorem is a generalization of Lang and Knebusch's theorem." @default.
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- W756419981 date "1985-01-01" @default.
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- W756419981 title "SOME GENERALIZATION OF THE LANG'S EXISTENCE OF RATIONAL PLACE THEOREM" @default.
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