Geodesic
Acts over semilattices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 151-156

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In this paper, we consider acts over commutative semigroups of idempotents (semilattices). We prove that an act over a semilattice is a partially ordered set. We obtain a full description of acts over a finite chain and a necessary condition for a partially ordered set to be an act over some semilattice. 
@article{FPM_2008_14_7_a12,
     author = {M. Yu. Maksimovskiy},
     title = {Acts over semilattices},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {151--156},
     publisher = {mathdoc},
     volume = {14},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a12/}
}
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M. Yu. Maksimovskiy. Acts over semilattices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 151-156. http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a12/