Recently, S. Kanti Patra and Md. Moid Shaikh proved the existence of monochromatic solutions to systems of polynomial equations near zero for particular dense subsemigroups \((S,+)\) of \((\mathbb {R}^{+},+)\). We extend their results to a much larger class of systems whilst weakening the requests on S, using solely basic results about ultrafilters.

中文翻译：

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多项式系统的分区正则性接近零

最近，S. Kanti帕特雷和MD。MOID谢赫证明单色解存在于多项式方程的系统接近零为特定密子半\（（S，+）\）的\（（\ mathbb {R} ^ {+} ，+）\）。我们仅使用有关超滤器的基本结果，即可将其结果扩展到更大范围的系统，同时减弱对S的要求。