Geodesic
Acts and partial acts over semilattices
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 1, pp. 3-7

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We consider the acts and the partial acts over semilattices. We obtain a necessary and sufficient condition to be a partially ordered set $X$ an act over a semilattice. The properties of partial acts are investigated and a sufficient condition is found for the expansion of partial act $X$ over a semilattice $S$ to a full $S$-act. 
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T. V. Apraksina; M. Yu. Maksimovskiy. Acts and partial acts over semilattices. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 1, pp. 3-7. http://geodesic.mathdoc.fr/item/ISU_2012_12_1_a0/