On the Factorization of Polynomials Over Discrete Valuation Domains

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

Keywords

• irreducible polynomials
• valuation
• newton polygon