Partition regularity of finite sets of homomorphisms

Document Type : Original Article

Authors

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Guilan, Iran

Abstract

‎In this paper‎, ‎we first establish a necessary and sufficient condition for a finite family of functions to be a Ramsey family‎. ‎More precisely‎, ‎we prove that a non-empty finite set $F$ of functions from $T$ to $S$ is a Ramsey family if and only if the system of equations‎‎ \[‎‎f^\beta(p) = y‎, ‎\qquad \forall f \in F‎‎\]‎ ‎takes equal values at some point $p \in \beta S$‎, ‎where $f^\beta‎: ‎\beta S \to \beta T$ is the unique continuous extension of $f‎: ‎S \to T$‎. ‎We then investigate monochromatic structures associated with homomorphisms‎. ‎Furthermore‎, ‎this paper generalizes Theorem 15.5 in [4] to homomorphisms on a commutative semigroup $S$‎.

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References

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Measure Algebras and Applications
Volume 3, Issue 2 - Serial Number 5
December 2025
Pages 82-92

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