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 
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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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $|X|\ge3$.

[1] Klifford A., Preston G., Algebraicheskaya teoriya polugrupp, V 2 t., v. 1, Mir, M., 1972, 285 pp. | Zbl

[2] Zaretskii K. A., “Polugruppa binarnykh otnoshenii”, Mat. sb., 61(103):3 (1963), 291–305

[3] Gluskin L. M., “Polugruppy izotonnykh preobrazovanii”, Uspekhi mat. nauk, 16:5(101) (1961), 157–162 | MR | Zbl

[4] Aizenshtat A. Ya., “Regulyarnye polugruppy endomorfizmov uporyadochennykh mnozhestv”, Uchen. zap. Leningr. gos. ped. in-ta im. A. I. Gertsena, 387, 1968, 3–11 | MR

[5] Molchanov V. A., “Semigroups of mappings on graphs”, Semigroup Forum, 27 (1983), 155–199 | DOI | MR | Zbl

[6] Laradji A., Umar A., On certain finite semigroups of order-decreasing transformations, King Fahd Univ. Petroleum Minerals. Tech. Rep. Ser., 2003, 1–19 pp. | Zbl

[7] Huisheng P., Dingyu Z., “Green's equivalences on semigroups of transformations preserving order and an equivalence relation”, Semigroup Forum, 71 (2005), 241–251 | DOI | MR | Zbl

[8] Lyapin E. S., Polugruppy, Fizmatgiz, M., 1960, 592 pp. | MR | Zbl

[9] Shutov E. G., “Potentsialnaya delimost elementov v polugruppakh”, Uchen. zap. Leningr. gos. ped. in-ta im. Gertsena, 166, 1958, 75–103

[10] Vagner V. V., “Teoriya otnoshenii i algebra chastichnykh otobrazhenii”, Teoriya polugrupp i ee prilozheniya: Sb. nauch. tr., 1, Izd-vo Sarat. un-ta, Saratov, 1965, 3–178 | MR