Roots of Irreducible Polynomials in Tame Henselian Extension Fields |
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| Authors: | Ron Brown |
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| Institution: | 1. Department of Mathematics , University of Hawaii , Honolulu , Hawaii , USA ron@math.hawaii.edu |
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| Abstract: | A class of irreducible polynomials 𝒫 over a valued field (F, v) is introduced, which is the set of all monic irreducible polynomials over F when (F, v) is maximally complete. A “best-possible” criterion is given for when the existence of an approximate root in a tamely ramified Henselian extension K of F of a polynomial f in 𝒫 guarantees the existence of an exact root of f in K. |
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| Keywords: | Henselian field Irreducible polynomial Root of a polynomial Tame ramification |
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