The binary quasiorder on semigroups

Taras Banakh, Olena Hryniv

Given two elements $x,y$ of a semigroup $X$ we write $x\lesssim y$ if for every homomorphism $\chi :X\to \{0,1\}$ we have $\chi (x)\le \chi (y)$. The quasiorder $\lesssim$ is called the $binary$…