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Algebra Logika, 2015, Volume 54, Number 2, Pages 236–242 (Mi al689)  

How to find (compute) a separant

Yu. L. Ershovab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: 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.

DOI: https://doi.org/10.17377/alglog.2015.54.206

Full text: PDF file (127 kB)
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English version:
Algebra and Logic, 2015, 54:2, 155–160

Bibliographic databases:

UDC: 512.623.4
Received: 02.04.2015

Citation: Yu. L. Ershov, “How to find (compute) a separant”, Algebra Logika, 54:2 (2015), 236–242; Algebra and Logic, 54:2 (2015), 155–160

Citation in format AMSBIB
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