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

Voir la notice de l'article provenant de la source Math-Net.Ru

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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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/

[1] Yu. L. Ershov, Kratno normirovannye polya, Sib. shkola algebry i logiki, Nauch. kniga, Novosibirsk, 2000

[2] Yu. L. Ershov, “Separant proizvolnogo mnogochlena”, Algebra i logika, 53:6 (2014), 704–709

[3] D. Brink, “New light on Hensel's lemma”, Expo. Math., 24:4 (2006), 291–306 | DOI | MR | Zbl

[4] Yu. L. Ershov, “Rasshireniya Lyubina–Teita (elementarnyi podkhod)”, Izv. RAN. Ser. matem., 71:6 (2007), 3–28 | DOI | MR | Zbl

[5] Yu. L. Ershov, “Obobscheniya lemmy Genzelya i metod blizhaishego kornya”, Algebra i logika, 50:6 (2011), 701–706 | MR | Zbl

[6] Yu. L. Ershov, “Separanty nekotorykh mnogochlenov”, Sib. matem. zh., 52:5 (2011), 1053–1057 | MR | Zbl

[7] S. S. Goncharov, Yu. L. Ershov, Konstruktivnye modeli, Sibirskaya shkola algebry i logiki, Nauchnaya kniga, Novosibirsk, 1999

[8] B. L. Van der Varden, Algebra, Nauka, M., 1976 | MR

[9] Yu. L. Ershov, “Teorema o normakh kornei i koeffitsientov”, Dokl. RAN, 417:5 (2007), 589–591 | MR | Zbl