Generalized Loose Edge Factorization Theorems
Abstract
We extend a factorization theorem by Gwo\'zdziewicz and Hejmej from the ring of formal power series to any complete regular local ring R . More precisely, let f ∈ R and assume that its Newton polyhedron has a loose edge such that the initial formal of f along the latter is a product of two coprime polynomials, where one of them is not divided by any variable. Then this provides a factorization of f in R . As a consequence we obtain a factorization theorem for Weierstra polynomials with coefficients in R , which generalizes an earlier result by Rond and the author.
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