Geodesic
The Green's relations and the generalized Green's relations on certain transformation semigroups
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 3, pp. 33-37.

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We investigate the Green's relations $\mathscr L$, $\mathscr R$ on the semigroups of isotone transformations of the partially ordered sets, and also the generalized Green's relations $\mathscr L^*$, $\mathscr R^*$ on the semigroup $B(X)$ of binary relations on a set $X$. It is proved that $\mathscr L=\mathscr L^*$, $\mathscr R=\mathscr R^*$ in the semigroup $B(X)$ though this semigroup is non-regular for $|X|\ge3$. 
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I. B. Kozhukhov; V. A. Yaroshevich. The Green's relations and the generalized Green's relations on certain transformation semigroups. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 3, pp. 33-37. http://geodesic.mathdoc.fr/item/ISU_2009_9_3_a5/

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