A generalization of Eisenstein-Sch\"onemann's irreducibility criterion

Abstract

The Eisenstein criterion is a particular case of the Sch\"onemann'sirreducibility criterion stated in 1846. In 1906, based on Newton polygon techniques, Dumas gave a generalization of the Eisenstein criterion.In this paper, we extend this last generalization. Some applications on factorization of polynomials, and prime ideal factorization are given too.