Some Pólya-Type Irreducibility Criteria for Multivariate Polynomials

Abstract

We provide irreducibility criteria for multivariate polynomials with coefficients in an arbitrary field that extend a classical result of Pólya for polynomials with integer coefficients. In particular, we provide irreducibility conditions for polynomials of the form f(X)(Y − f ₁(X))…(Y − f _n (X)) + g(X), with f, f ₁, ⋅, f _n , g univariate polynomials over an arbitrary field.

Key Words:

• Irreducible multivariate polynomials
• Nonarchimedean absolute value

2010 Mathematics Subject Classification:

• Primary 11R09
• Secondary 11C08

ACKNOWLEDGMENTS

This work was supported by CNCSIS-UEFISCDI, project PNII-IDEI 443, code 1190/2008, and by a project LEA CNRS Franco-Roumain Math-Mode.

Notes

Communicated by T. Albu.