In a recent paper, Kanti Patra and Moid Shaik proved the existence of monochromatic solutions to certain systems of polynomial equations near zero for particulars dense subsemigroups $S$ of $((0,infty),+)$. We extend their results to a much larger class of equations, whilst weakening the requests on $S$. Recently, S. Kanti Patra and Md. Moid Shaikh proved the existence of monochromatic solutions to systems of polynomial equations near zero for particular dense subsemi-groups (S, +) of (R+, +). We extend their results to a much larger class of systems whilst weakening the requests on S, using solely basic results about ultrafilters.

Partition regularity of polynomial systems near 0 / L. Luperi Baglini. - In: SEMIGROUP FORUM. - ISSN 0037-1912. - 103:1(2021 Aug), pp. 191-208. [10.1007/s00233-021-10179-w]

Partition regularity of polynomial systems near 0

L. Luperi Baglini
2021

Abstract

In a recent paper, Kanti Patra and Moid Shaik proved the existence of monochromatic solutions to certain systems of polynomial equations near zero for particulars dense subsemigroups $S$ of $((0,infty),+)$. We extend their results to a much larger class of equations, whilst weakening the requests on $S$. Recently, S. Kanti Patra and Md. Moid Shaikh proved the existence of monochromatic solutions to systems of polynomial equations near zero for particular dense subsemi-groups (S, +) of (R+, +). We extend their results to a much larger class of systems whilst weakening the requests on S, using solely basic results about ultrafilters.
partition regularity, ultrafilters, semigroups, infinitesimals;
Settore MAT/01 - Logica Matematica
30-mar-2021
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/829844
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