Geodesic
On the regularity of some subsemigroups of equivalence relation's endomorphism monoid
Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 5-11.

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

For the set of halfstrong (locally strong, quasi-strong) endomorphisms of an equivalence relation graph, the conditions to form a semigroup are found. Thus the answer to the question put by M. Böttcher and U. Knauer's is given. The conditions for regularity of such semigroups are found too.
Keywords: regularity, semigroup
Mots-clés : endomorphism, equivalence. 
@article{PDM_2014_3_a0,
     author = {E. A. Bondar},
     title = {On the regularity of some subsemigroups of equivalence relation's endomorphism monoid},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {5--11},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_3_a0/}
}
TY  - JOUR
AU  - E. A. Bondar
TI  - On the regularity of some subsemigroups of equivalence relation's endomorphism monoid
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2014
SP  - 5
EP  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2014_3_a0/
LA  - ru
ID  - PDM_2014_3_a0
ER  - 
%0 Journal Article
%A E. A. Bondar
%T On the regularity of some subsemigroups of equivalence relation's endomorphism monoid
%J Prikladnaâ diskretnaâ matematika
%D 2014
%P 5-11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2014_3_a0/
%G ru
%F PDM_2014_3_a0
E. A. Bondar. On the regularity of some subsemigroups of equivalence relation's endomorphism monoid. Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 5-11. http://geodesic.mathdoc.fr/item/PDM_2014_3_a0/

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

[2] Shneperman L. B., “Polugruppy endomorfizmov kvaziuporyadochennykh mnozhestv”, Uchënye zapiski LGPI im. A. I. Gertsena, 238, 1962, 21–37 | Zbl

[3] Vazhenin Yu. M., “Ob elementarnoi opredelyaemosti i elementarnoi kharakterizuemosti klassov refleksivnykh grafov”, Izv. vuzov. Matematika, 1972, no. 7, 3–11 | MR | Zbl

[4] Popov B. V., “Polugruppy endomorfizmov refleksivnykh binarnykh otnoshenii”, Uchënye zapiski LGPI im. A. I. Gertsena, 302, 1967, 116–123 | MR | Zbl

[5] Araújo J., Konieczny J., “Dense relations are determined by their endomorphism monoids”, Semigroup Forum, 70 (2005), 302–306 | DOI | MR | Zbl

[6] Kozhukhov I. B., Yaroshevich V. A., “Polugruppy otobrazhenii, sokhranyayuschikh binarnoe otnoshenie”, Fundamentalnaya i prikladnaya matematika, 14:7 (2008), 129–135 | MR

[7] Aizenshtat A. Ya., “Regulyarnye polugruppy endomorfizmov uporyadochennykh mnozhestv”, Uchënye zapiski LGPI im. A. I. Gertsena, 387, 1968, 3–11 | MR

[8] Kim V. I., Kozhukhov I. B., “Usloviya regulyarnosti polugrupp izotonnykh preobrazovanii schetnykh tsepei”, Fundamentalnaya i prikladnaya matematika, 12:8 (2006), 97–104 | MR | Zbl

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

[10] Böttcher M., Knauer U., “Endomorphism spectra of graphs”, Discrete Mathematics, 109 (1992), 45–57 | DOI | MR | Zbl

[11] Böttcher M., Knauer U., “Postscript: Endomorphism spectra of graphs”, Discrete Mathematics, 270 (2003), 329–331 | DOI | MR | Zbl

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

[13] Ma M., You T., Luo S., et al., “Regularity and Green's relations for finite E-order-preserving transformations semigroups”, Semigroup Forum, 80 (2010), 164–173 | DOI | MR | Zbl

[14] Deng L., Zeng J., You T., “Green's relations and regularity for semigroups of transformations that preserve reverse direction equivalence”, Semigroup Forum, 83 (2011), 489–498 | DOI | MR | Zbl

[15] Deng L., Zeng J., Xu B., “Green's relations and regularity for semigroups of transformations that preserve double direction equivalence”, Semigroup Forum, 80 (2010), 416–425 | DOI | MR | Zbl

[16] Deng L., Zeng J., You T., “Green's relations and regularity for semigroups of transformations that preserve order and a double direction equivalence”, Semigroup Forum, 84 (2012), 59–68 | DOI | MR | Zbl

[17] Zhuchok Yu. V., “Endomorfizmi vidnoshen ekvivalentnosti”, Visn. Kiiv. univ. Ser. Fiz.-mat. nauki, 3 (2007), 22–26 | Zbl

[18] Zhuchok Yu. V., “Polugruppy endomorfizmov 2-nilpotentnykh binarnykh otnoshenii”, Fundamentalnaya i prikladnaya matematika, 14:6 (2008), 75–83 | MR

[19] Novikov F. A., Diskretnaya matematika, Standart tretego pokoleniya, 2-e izd., Piter, SPb., 2013, 432 pp.

[20] Knauer U., Nieporte M., “Endomorphisms of graphs. I. The monoid of strong endomorphisms”, Arch. Math., 52 (1989), 607–614 | DOI | MR | Zbl

[21] Fan S., “Graphs whose strong endomorphism monoids are regular”, Arch. Math., 73 (1999), 419–421 | DOI | MR | Zbl