On the Factorization of Polynomials Over Discrete Valuation Domains

Ştefănescu, Doru

doi:10.2478/auom-2014-0023

Abstract

We study some factorization properties for univariate polynomials with coefficients in a discrete valuation domain (A,v). We use some properties of the Newton index of a polynomial $F (X) = \sum_{i = 0}^{d} a_{i} X^{d - i} \in A [X]$ to deduce conditions on v(a_i) that allow us to find some information on the degree of the factors of F.

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On the Factorization of Polynomials Over Discrete Valuation Domains

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