Loose edges and factorization theorems

Gwoździewicz, Janusz; Gryszka, Beata; Schober, Bernd

doi:10.1090/proc/14720

Loose edges and factorization theorems
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by Janusz Gwoździewicz, Beata Gryszka and Bernd Schober PDF

Proc. Amer. Math. Soc. 149 (2021), 2265-2278 Request permission

Abstract:

Let $R$ be a regular local ring with maximal ideal $\mathfrak {m}$. We consider elements $f \in R$ such that their Newton polyhedron has a loose edge. We show that if the symbolic restriction of $f$ to such an edge is a product of two coprime polynomials, then $f$ factorizes in the $\mathfrak {m}$-adic completion.

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