Irreducibility of a sum of polynomials depending on disjoint sets of variables

Abstract

In this article, we give two different sufficient conditions for the irreducibility of a polynomial of more than one variable, over the field of complex numbers, that can be written as a sum of two polynomials which depend on mutually disjoint sets of variables. These conditions are derived from analyzing the Newton polytope of such a polynomial and then applying the `Irreducibility criterion' introduced by Gao.

arXiv comment10 pages, minor change in the statement of Proposition 1.4 and the proof of the same is rewritten for clarity, to appear in Indian Journal of Pure and Applied Mathematics