Generalized Loose Edge Factorization Theorems
英文摘要：
We extend a factorization theorem by Gwoździewicz and Hejmej from the ring of formal power series to any complete regular local ring $ R $. More precisely, let $ f \in 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 Weierstraß polynomials with coefficients in $ R $, which generalizes an earlier result by Rond and the author.
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