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A CHARACTERIZATION OF FINITE TAME EXTENSIONS

Published online by Cambridge University Press:  23 October 2000

SUDESH K. KHANDUJA
SUDESH K. KHANDUJA
Affiliation:
Department of Mathematics, Panjab University, Chandigarh 160014, India; e-mail: [email protected]
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Abstract

Let v be a henselian valuation of a field K. In this paper it is proved that any finite extension (K′, v′) of (K, v) is tame if and only if there exists α ≠ 0 in K′ such that v′(α) = v(TrK′/K(α)) using elementary results of valuation theory. A special case of this result, when the characteristic of the residue field of v is p > 0 and (K′, v′)/(K, v) is an extension of degree p, was proved in 1990 by J. P. Tignol (J. Reine Angew. Math. 404 (1990) 1–38).

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 5 , September 2000 , pp. 551 - 554
Copyright
© The London Mathematical Society 2000

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Footnotes

Research partially supported by CSIR vide grant no. 25(0095)/97/EMR-II.