On an extension of the Newton polygon test for polynomial reducibility


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




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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