<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The Eisenstein criterion is a particular case of the Schönemann’s irreducibility 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 will be given, too.</p>
</abstract>

The Eisenstein criterion is a particular case of the Schönemann’s irreducibility 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 will be given, too.

A Generalization of Eisenstein-Schönemann’s Irreducibility Criterion

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"A Generalization of Eisenstein-Schönemann\u2019s Irreducibility Criterion"}

The Eisenstein criterion is a particular case of the Schönemann’s irreducibility criterion stated in 1846. In 1906, based on Newton polygon techniques, Dumas...

A Generalization of Eisenstein-Schönemann’s Irreducibility Criterion

Published Online: Mar 07, 2023

Page range: 51 - 60

Received: Nov 12, 2022

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

Keywords
irreducibility criterion, irreducible factors, valued field, Henselian fields

© 2023 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Generalization of Eisenstein-Schönemann’s Irreducibility Criterion

Published Online: Mar 07, 2023

Page range: 51 - 60

Received: Nov 12, 2022

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

Keywordsirreducibility criterion, irreducible factors, valued field, Henselian fields

© 2023 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
irreducibility criterion, irreducible factors, valued field, Henselian fields