Factorization of polynomials over valued fields based on graded polynomials

Year, pages: 2020, 807 - 814

In this paper, we develop a new method based on Newton polygon and graded polynomials, similar to the known one based on Newton polygon and residual polynomials. This new method allows us the factorization of any monic polynomial in any henselian valued field. As applications, we give a new proof of Hensel's lemma and a theorem on prime ideal factorization.

Fadil, L. 2020. Factorization of polynomials over valued fields based on graded polynomials. In Mathematica Slovaca, vol. 70, no.4, pp. 807-814. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0393

Fadil, L. (2020). Factorization of polynomials over valued fields based on graded polynomials. Mathematica Slovaca, 70(4), 807-814. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0393

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava