论文标题
RADO功能和应用
Rado functionals and applications
论文作者
论文摘要
我们根据线性方程和不平等的混合系统的分区规律性研究了RADO功能和最大条件（首先由J. M. Barret等引入）。通过加强最大的RADO条件，我们为在给定换向环的某些无限子集上的多项式方程的分区规律提供了足够的条件。通过应用这些结果，我们得出了M. di Nasso和L. Luperi Baglini获得的先前结果的扩展，该分区在三个变量中定期进行定期不均匀多项式，以及对于$ h（xz^ρ，y）= 0 $的划分方程式的分区方程式的条件$ h \ in \ mathbb {z} [x，y] $是同质的多项式。
We study Rado functionals and the maximal condition (first introduced by J. M. Barret et al.) in terms of the partition regularity of mixed systems of linear equations and inequalities. By strengthening the maximal Rado condition, we provide a sufficient condition for the partition regularity of polynomial equations over some infinite subsets of a given commutative ring. By applying these results, we derive an extension of a previous result obtained by M. Di Nasso and L. Luperi Baglini concerning partition regular inhomogeneous polynomials in three variables and also conditions for the partition regularity of equations of the form $H(xz^ρ,y)=0$, where $ρ$ is a non-zero rational and $H\in\mathbb{Z}[x,y]$ is a homogeneous polynomial.
