A Characterization of Finite Tame Extensions | Zendy

Khanduja Sudesh K. | Zendy

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A Characterization of Finite Tame Extensions

Author(s) -

Khanduja Sudesh K.

Publication year - 2000

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609300007219

Subject(s) - mathematics , mathematics subject classification , residue field , valuation (finance) , discrete valuation , pure mathematics , extension (predicate logic) , finite field , discrete mathematics , field (mathematics) , combinatorics , finance , computer science , economics , programming language

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 (Tr K ′/ 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). 1991 Mathematics Subject Classification 12J10, 12J25, 13A18.

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