Potentially right simple finite semigroups
Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 120-123
Yu. I. Kozhukhova. Potentially right simple finite semigroups. Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 120-123. http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a8/
@article{CHEB_2011_12_1_a8,
     author = {Yu. I. Kozhukhova},
     title = {Potentially right simple finite semigroups},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {120--123},
     year = {2011},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a8/}
}
TY  - JOUR
AU  - Yu. I. Kozhukhova
TI  - Potentially right simple finite semigroups
JO  - Čebyševskij sbornik
PY  - 2011
SP  - 120
EP  - 123
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a8/
LA  - ru
ID  - CHEB_2011_12_1_a8
ER  - 
%0 Journal Article
%A Yu. I. Kozhukhova
%T Potentially right simple finite semigroups
%J Čebyševskij sbornik
%D 2011
%P 120-123
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a8/
%G ru
%F CHEB_2011_12_1_a8

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

It is proved that in any finite semigroup, if every element is divided by every one on the right in potential sense then every element is divided by every one in usual sense too.

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

[2] Lyapin E. S., Polugruppy, Fizmatlit, M., 1960 | MR | Zbl

[3] Fountain J. B., “Abundant semigroups”, Proc. London Math. Soc., 44:3 (1982), 103–129 | DOI | MR | Zbl

[4] Kozhukhov I. B., Yaroshevich V. A., “O potentsialnoi delimosti matrits nad distributivnymi reshetkami”, Diskret. matem., 22:2 (2010), 148–159 | DOI | MR | Zbl