Geodesic
How to find (compute) a separant
Algebra i logika, Tome 54 (2015) no. 2, pp. 236-242

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Let $f$ be an arbitrary (unitary) polynomial over a valued field $\mathbb F=\langle F,R\rangle$. In [Algebra i Logika, 53, No. 6, 704–709 (2014)], a separant $\sigma_f$ of such a polynomial was defined to be an element of a value group $\Gamma_{R_0}$ for any algebraically closed extension $\mathbb F_0=\langle F_0,R_0\rangle\ge\mathbb F$. Specifically, the separant was used to obtain a generalization of Hensel's lemma. We show a more algebraic way (compared to the previous) for finding a separant.
Keywords: valued field, separant, Hensel's lemma. 
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     author = {Yu. L. Ershov},
     title = {How to find (compute) a~separant},
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Yu. L. Ershov. How to find (compute) a separant. Algebra i logika, Tome 54 (2015) no. 2, pp. 236-242. http://geodesic.mathdoc.fr/item/AL_2015_54_2_a5/