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

Lhoussain El Fadil


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.

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DOI: https://doi.org/10.2478/tmmp-2023-0005