A generalization of Dumas irreducibility criterion

TL;DR

This paper extends Dumas's classical irreducibility criterion for polynomials over discrete valuation domains by employing Newton polygons to establish a more general factorization result.

Contribution

It introduces a new irreducibility criterion that generalizes Dumas's classical result using Newton polygon techniques.

Findings

Established a new irreducibility criterion for polynomials over discrete valuation domains.

Provided a generalization of Dumas's classical irreducibility criterion.

Proved a key factorization result using Newton polygons.

Abstract

Using Newton polygons, a key factorization result for polynomials over discrete valuation domains is proved, which in particular yields new irreducibility criteria including a generalization of the classical irreducibility criterion of Dumas.