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.
Categories: math.AG math.AC