Irreducibility criterion for quasi-ordinary polynomials

TL;DR

This paper introduces a new criterion for determining the irreducibility of quasi-ordinary polynomials using approximate roots and generalized Newton polygons.

Contribution

It provides a novel irreducibility criterion specifically for quasi-ordinary polynomials, enhancing existing algebraic tools.

Findings

New irreducibility criterion based on approximate roots

Utilizes generalized Newton polygons for analysis

Applicable to a broad class of quasi-ordinary polynomials

Abstract

We give a criterion for a quasi-ordinary polynomial to be irreducible. The criterion is based on the notion of approximate roots and that of generalized Newton polygons.