A generalization of Dumas irreducibility criterion
Number Theory
2026-05-19 v3 Commutative Algebra
Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2505.08549,
title = {A generalization of Dumas irreducibility criterion},
author = {Jitender Singh},
journal= {arXiv preprint arXiv:2505.08549},
year = {2026}
}
Comments
10 pages; The statement and proof of Lemma 8 have been revised and corrected, Proof of Theorem 1 is rewritten