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arXiv · 2511.21427

A generalized Dumas irreducibility criterion

Rishu Garg·Jitender Singh
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Abstract

As an extension of the classical irreducibility result of Dumas, a factorization result for polynomials over any valued field with a Krull valuation of arbitrary rank is proved. Further, among other results, a lower degree factor bound on factors of a given polynomial over a valued field with a Krull valuation is proved. These factorization results not only unify several known irreducibility results for polynomials over the said domains but also provide us sharp bounds on degrees of irreducible factors of the underlying polynomials.

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Rishu Garg, Jitender Singh. 2025-11-26. A generalized Dumas irreducibility criterion. https://arxiv.org/abs/2511.21427

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