The binary quasiorder on  semigroups

Taras Banakh, Olena Hryniv


Given two elements x,y of a semigroup X we write xy if for every homomorphism χ:X{0,1} we have χ(x)χ(y). The quasiorder is called the binary quasiorder on X. It induces the equivalence relation 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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