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arXiv · 1804.05366

On Abhyankar's irreducibility criterion for quasi-ordinary polynomials

Janusz Gwoździewicz·Beata Hejmej
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Abstract

Let $f$ and $g$ be Weierstrass polynomials with coefficients in the ring of formal power series over an algebraically closed field of characteristic zero. Assume that $f$ is irreducible and quasi-ordinary. We show that if degree of $g$ is small enough and all monomials appearing in the resultant of $f$ and $g$ have orders big enough, then $g$ is irreducible and quasi-ordinary, generalizing Abhyankar's irreducibility criterion for plane analytic curves.

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Janusz Gwoździewicz, Beata Hejmej. 2018-04-15. On Abhyankar's irreducibility criterion for quasi-ordinary polynomials. https://arxiv.org/abs/1804.05366

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