Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-20T00:36:05.426Z Has data issue: false hasContentIssue false
  • English
  • Français

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: skhand@panjabuniv.chd.nic.in
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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