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. 
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     author = {M. Yu. Maksimovskiy},
     title = {Acts over semilattices},
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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/

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[2] Avdeyev A. Yu., Kozhukhov I. B., “Acts over completely 0-simple semigroups”, Acta Cybernet., 14:4 (2000), 523–531 | MR | Zbl

[3] Kilp M., Knauer U., Mikhalev A. V., Monoids, Acts and Categories, Walter de Gruyter, Berlin, 2000 | MR | Zbl