On Eisenstein–Dumas and generalized Schönemann polynomials

Bishnoi, Anuj ; Khanduja, Sudesh K. (2010) On Eisenstein–Dumas and generalized Schönemann polynomials Communications in Algebra, 38 (9). pp. 3163-3173. ISSN 0092-7872

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Official URL: http://www.tandfonline.com/doi/full/10.1080/009278...

Related URL: http://dx.doi.org/10.1080/00927870903164669

Abstract

Let v be a valuation of a field K having value group Z. It is known that a polynomial xn + an−1xn−1 + … +a0 satisfying v(ai)/n-i≥v(a0) > 0 with v(a0) coprime to n, is irreducible over K. Such a polynomial is referred to as an Eisenstein–Dumas polynomial with respect to v. In this article, we give necessary and sufficient conditions so that some translate g(x + a) of a given polynomial g(x) belonging to K[x] is an Eisenstein–Dumas polynomial with respect to v. In fact, an analogous problem is dealt with for a wider class of polynomials, viz. Generalized Schönemann polynomials with coefficients over valued fields of arbitrary rank.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Group.
Keywords:Field Theory and Polynomials; Non-Archimedean Valued Fields; Valued Fields
ID Code:112134
Deposited On:23 Jan 2018 12:19
Last Modified:23 Jan 2018 12:19

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