Some factorization results for formal power series Article Swipe

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Rishu Garg , Jitender Singh · YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2501.05375

In this paper, we obtain some factorization results on formal power series over principle ideal domains with sharp bounds on number of irreducible factors. These factorization results correspondingly lead to irreducibility criteria for formal power series. The information about prime factorization of the constant term up to a unit and that of some higher order terms is utilized for the purpose. Further, using theory of Newton polygons for power series, we extend the classical Dumas irreducibility criterion to formal power series over discrete valuation domains, which in particular, yields several irreducibility criteria.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2501.05375

PDF

https://arxiv.org/pdf/2501.05375

OA Status

green

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