On a mild generalization of the Schönemann - Eisenstein - Dumas irreducibility criterion

Abstract

We state a mild generalization of the classical Schönemann and Eisenstein- Dumas irreducibility criterion in ℤ[x] and provide an elementary proof. In the end of the paper, we also provide a concrete example of a polynomial which is irreducible by the main result of the paper but whose irreducibility does not follow from existing criteria.