On Krasner's constant

Abstract

Let v be a henselian valuation of any rank of a field K and v ̄be the extension of v to a fixed algebraic closure K̄ of K. Let α ∈ K̄\K be separable over K. In this paper the author investigates the condition under which Krasner's constant ω_K(α) given by max{v̄(α − α′)|α′ ≠ α runs over K-conjugates of α}, is equal to min{v̄(α − α′): α′ runs over K-conjugates of α}; this is the condition for α to be equidistant from all of its K-conjugates.