On an extension of the Newton polygon test for polynomial reducibility

Authors

  • Brahim Boudine Faculty of sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah university, Fez, Morocco

DOI:

https://doi.org/10.33044/revuma.2842

Abstract

Let $R$ be a commutative local principal ideal ring which is not integral, $f$ a polynomial in $R[x]$ such that $f(0) \neq 0$ and $N(f)$ its Newton polygon. If $N(f)$ contains $r$ sides of different slopes, we show that $f$ has at least $r$ different pure factors in $R[x]$. This generalizes the Newton polygon method over a ring which is not integral.

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Published

2024-02-21

Issue

Vol. 67 No. 1 (2024)

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Article

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Copyright (c) 2024 Brahim Boudine

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