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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.)