In this article, we give two different sufficient conditions for the irreducibility of a polynomial of more than one variable, over an algebraically closed field, 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.

中文翻译：

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多项式和的不可约性取决于不相交的变量集

在这篇文章中，我们给出了两个不同的充分条件，用于在代数闭域上一个以上变量的多项式不可约，可以写成两个多项式的和，这些多项式依赖于互不相交的变量集。这些条件是通过分析此类多项式的牛顿多面体，然后应用 Gao 引入的“不可约性准则”得出的。