A characterization of Krasner's Constant

Bhatia, Saurabh ; Khanduja, Sudesh K. (2002) A characterization of Krasner's Constant Communications in Algebra, 30 (6). pp. 2975-2991. ISSN 0092-7872

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Official URL: http://www.tandfonline.com/doi/abs/10.1081/AGB-120...

Related URL: http://dx.doi.org/10.1081/AGB-120004003


Let v be a henselian valuation of any rank of a eld K with value group G and υ- be its unique prolongation to a xed algebraic closure K- of K: For an element α of K-\K; which is separable over K; let ωK (α) denote the well known Krasner's constant given by max{υ-(α - α′)│α′ ≠ α runs over K conjugates of α. In 1946, Krasner proved that if β belonging to K- is such that υ-(α - β ) > ωK (α); then K(α) ⊆ K(β): In this paper, we investigate whether ωK (α) is the smallest among all the elements λ of the divisible closure of G which have the property that whenever υ-(α -β) > λ, β ∈ K-, then K(α) ⊆ K(β).

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