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 x^{n} + a_{n−1}x^{n−1} + … +a_{0} satisfying v(a_{i})/n-i≥v(a_{0}) > 0 with v(a_{0}) 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 |
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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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