%0 Journal Article
%T A note-question on partitions of semigroups
%A Igor Protasov
%A Ksenia Protasova
%J Mathematics
%D 2015
%I arXiv
%X Given a semigroup $S$ and an $n$-partition $\mathcal{P}$ of $S$, $n\in \mathbb{N}$, do there exist $A\in \mathcal{P}$ and a subset $F$ of $S$ such that $S=F ^{-1} \{x \in S: x A \bigcap A\neq\emptyset\}$ and $|F |\leq n$? We give an affirmative answer provided that either $S$ is finite or $n=2$.
%U http://arxiv.org/abs/1508.07133v1