Partition regularity of polynomial systems near zero

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