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arXiv · 2201.10786

The binary quasiorder on semigroups

Taras Banakh·Olena Hryniv
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Abstract

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 $binary$ $quasiorder$ on $X$. It induces the equivalence relation $\Updownarrow$ that coincides with the least semilattice congruence on $X$. In the paper we discuss some known and new properties of the binary quasiorder on semigroups.

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Taras Banakh, Olena Hryniv. 2022-01-26. The binary quasiorder on semigroups. https://arxiv.org/abs/2201.10786

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