Geodesic
Semigroups over which all acts are residually finite
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 4, pp. 1335-1344 
I. B. Kozhukhov. Semigroups over which all acts are residually finite. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 4, pp. 1335-1344. http://geodesic.mathdoc.fr/item/FPM_1998_4_4_a11/
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     author = {I. B. Kozhukhov},
     title = {Semigroups over which all acts are residually finite},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1335--1344},
     year = {1998},
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     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_4_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The properties ($*$) and ($**$) of semigroup $S$ are investigated, namely: ($*$) every subdirectly irreducible right $S$-act is finite; ($**$) the cardinalities of subdirectly irreducible right $S$ acts are bounded by a natural number. We prove that if $S$ is a nilsemigroup then then these conditions are equivalent to each other and to finiteness of $S$. We characterize the commutative semigroups satisfying ($**$).