Partition regularity of polynomial systems near zero

Abstract

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