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Published online by Cambridge University Press: 26 February 2010
Let where a0≠0, m≥2, n = e1 + … + em and the ξi(1≤i≤m) are the distinct zeros of f in some algebraic closure of the p-adic field
. Then K =
(ξ1, ξ2, …, ξm) is a finite separable extension of
and we denote by “ord” the unique extension of the (additive) p-adic valuation on
to K, normalized with ord p = 1.