On the factorization of polynomials over discrete valuation domains. (English) Zbl 1340.11085
Summary: 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 \(F(X)=\sum^d_{i=0} a_i X^{d-i}\in A[X]\) to deduce conditions on \(v(a_i)\) that allow us to find some information on the degree of the factors of \(F\).
MSC:
11R09 | Polynomials (irreducibility, etc.) |