Tame fields and tame extensions

Khanduja, Sudesh K. (1998) Tame fields and tame extensions Journal of Algebra, 201 (2). pp. 647-655. ISSN 0021-8693

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1006/jabr.1997.7298

Abstract

Let V be a henselian valuation of any rank of a field K and let V̅ be the extension of V to a fixed algebraic closure K̅ of K. In this paper, it is proved that (K, V) is a tame field, i.e., every finite extension of (K, V) is tamely ramified, if and only if, to each α ∈ K̅\K, there correspondsa ∈ K for which V̅(α − a) ≥ ΔK(α), where ΔK(α) = min{V̅(α′ − α)|α′ runs over all K-conjugates of α}. A special case of the previous result, when K is a perfect field of nonzero characteristic was proved in 1995, with the purpose of completing a result of James Ax [S. K. Khanduja,J. Algebra172(1995), 147–151].

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Valued Fields; Valuations and their Generalizations
ID Code:69882
Deposited On:19 Nov 2011 10:25
Last Modified:19 Nov 2011 10:25

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