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Loose edges and factorization theorems


Authors: Janusz Gwoździewicz, Beata Gryszka and Bernd Schober
Journal: Proc. Amer. Math. Soc. 149 (2021), 2265-2278
MSC (2020): Primary 13F25, 12E05, 14B05
DOI: https://doi.org/10.1090/proc/14720
Published electronically: March 23, 2021
MathSciNet review: 4246781
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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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Additional Information

Janusz Gwoździewicz
Affiliation: Institute of Mathematics, Pedagogical University of Cracow, Podchora̧\accent95 zych 2, PL-30-084 Cracow, Poland
Email: janusz.gwozdziewicz@up.krakow.pl

Beata Gryszka
Affiliation: Institute of Mathematics, Pedagogical University of Cracow, Podchora̧\accent95 zych 2, PL-30-084 Cracow, Poland
MR Author ID: 1233841
Email: bhejmej1f@gmail.com

Bernd Schober
Affiliation: Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany
MR Author ID: 1218416
ORCID: 0000-0003-0315-0656
Email: schober.math@gmail.com; bernd.schober@uni-oldenburg.de

Keywords: Irreducibility, formal power series, Newton polyhedron.
Received by editor(s): December 6, 2018
Received by editor(s) in revised form: April 8, 2019
Published electronically: March 23, 2021
Additional Notes: The third author was supported by the DFG-project “Order zeta functions and resolutions of singularities” (DFG project number: 373111162).
Communicated by: Rachel Pries
Article copyright: © Copyright 2021 American Mathematical Society