Loose edges and factorization theorems

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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