Geodesic
Potentially right simple finite semigroups
Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 120-123

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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. 
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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/