A characterization of finite tame extensions

Khanduja, Sudesh K. (2000) A characterization of finite tame extensions Bulletin of the London Mathematical Society, 32 (5). pp. 551-554. ISSN 0024-6093

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Official URL: http://blms.oxfordjournals.org/content/32/5/551.sh...

Related URL: http://dx.doi.org/10.1112/S0024609300007219


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 ρ > 0 and (K′, v′)/(K, v) is an extension of degree ρ, was proved in 1990 by J. P. Tignol (J. Reine Angew. Math. 404 (1990) 1–38). 1991 Mathematics Subject Classification 12J10, 12J25, 13A18.

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