Geodesic
On regularity of semigroups of maps that preserve a~binary relation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 225-240.

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We consider semigroups of full transformations, partial maps, and multi-value maps from a set $X$ to $X$, where every map preserves a binary relation $\sigma$ defined on $X$. We suggest several definitions for the preservation of $\sigma$ for partial maps and for multi-value maps. We review results about regularity of the semigroups mentioned above in the cases where $\sigma$ is a partial order, a quasi-order, an equivalence, or one of some special kinds of binary relations. Also we consider the question about regularity of the semigroup of full transformations that preserve a partial order and an equivalence simultaneously. 
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V. A. Yaroshevich. On regularity of semigroups of maps that preserve a~binary relation. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 225-240. http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a12/

[1] Aizenshtat A. Ya., “Opredelyayuschie sootnosheniya polugruppy endomorfizmov konechnogo lineinogo uporyadochennogo mnozhestva”, Sib. matem. zhurn., 3:2 (1962), 161–169 | Zbl

[2] Aizenshtat A. Ya., “Regulyarnye polugruppy endomorfizmov uporyadochennykh mnozhestv”, Uch. zap. Leningr. gos. ped. in-ta im. A. I. Gertsena, 387 (1968), 3–11

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

[4] Diasamidze Ya. I., Polnye polugruppy binarnykh otnoshenii, Adzhara, Batumi, 2000

[5] Zaretskii K. A., “Polugruppa binarnykh otnoshenii”, Matem. sb., 61:3(103) (1963), 291–305 | MR | Zbl

[6] Kim V. I., Kozhukhov I. B., “Usloviya regulyarnosti polugrupp izotonnykh preobrazovanii schetnykh tsepei”, Fundam. i prikl. matem., 12:8 (2006), 97–104

[7] Kim V. I., Kozhukhov I. B., Yaroshevich V. A., “Slabo regulyarnye polugruppy izotonnykh preobrazovanii”, Fundament. i prikl. matem., 17:4 (2012), 145–165

[8] Klifford A., Preston G., Algebraicheskaya teoriya polugrupp, v. 1, 2, Mir, M., 1972

[9] Kozhukhov I. B., Yaroshevich V. A., “Polugruppy otobrazhenii, sokhranyayuschikh binarnoe otnoshenie”, Fundament. i prikl. matem., 14:7 (2008), 129–135

[10] Lyapin E. S., “Abstraktnaya kharakteristika klassa polugrupp endomorfizmov sistem obschego vida”, Matem. sb., 70:2(112) (1966), 173–179

[11] Tvorogov A. V., Yaroshevich V. A., “O regulyarnosti polugruppy mnogoznachnykh preobrazovanii, sokhranyayuschikh zadannoe binarnoe otnoshenie”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya, Materialy XIII Mezhdunar. konf. (Tula, 2015), 135–137

[12] Yaroshevich V. A., “Otobrazheniya, soglasuyuschiesya s binarnymi otnosheniyami”, Matem. vestn. pedvuzov i un-tov Volgo-Vyatskogo regiona, 2009, no. 11, 135–142

[13] Yaroshevich V. A., “O svoistvakh polugrupp chastichnykh izotonnykh preobrazovanii kvaziuporyadochennykh mnozhestv”, Vestn. Moskovskoi gos. akad. del. admin. Ser. Filosof., sots. i estestv. nauki, 2011, no. 3, 139–144

[14] Yaroshevich V. A., “Regulyarnye polugruppy izotonnykh preobrazovanii chastichno uporyadochennykh mnozhestv spetsialnogo vida”, Informatsionno-upravlyayuschie vychislitelnye sistemy: algoritmy, apparatnye i programmnye sredstva, MIET, M., 2011, 84–97

[15] Yaroshevich V. A., “Regulyarnye otnosheniya, sokhranyayuschie odnovremenno chastichnyi poryadok i otnoshenie ekvivalentnosti”, Sb. nauchn. tr. MIET, MIET, M., 2016, 121–126

[16] Adams M. E., Gould M., “Posets whose monoids of order-preserving maps are regular”, Order, 1989, no. 6, 195–201 | MR | Zbl

[17] Bötcher M., Knauer U., “Endomorphism spectra of graphs”, Discrete Math., 109 (1992), 45–57 | MR

[18] Deng Lun-Zhi, Zeng Ji-Wen, You Tai-Jie, “Green's relations and regularity for semigroups of transformations that preserve order and a double direction equivalence”, Semigroup Forum, 84 (2012), 59–68 | MR | Zbl

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

[20] Laradji A., Umar A., Combinatorial results for semigroups of order-preserving partial transformations, Technical Report Ser., King Fahd Univ. of Petroleum and Minerals (Saudi Arabia), Dept. Math. Sci., 2004 | MR

[21] Lei Sun, Hui Sheng Pei, “Green's relations on semigroups of transformations preserving two equivalence relations”, J. Math. Res. Expos., 29:3 (2009), 415–422 | MR | Zbl

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