On the Factorization of Polynomials Over Discrete Valuation Domains

Abstract

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 ) = ∑ i = 0 d a i X d - i ∈ A [ X ] to deduce conditions on v(ai ) that allow us to find some information on the degree of the factors of F.