Geodesic
Variants of the lattice of partitions of a countable set
Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 8-18

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In this paper we consider the ordered by inclusion lattice $\operatorname{Part}(M)$ of all partitions of a countable set $M$. The lattice $\operatorname{Part}(M)$ is a semigroup with respect to the operation $\wedge$ which maps two partitions to their greatest lower bound. We obtain necessary and sufficiency conditions for isomorphism of two variants of the semigroup $\operatorname{Part}(M)$.
Keywords: sandwich-semigroup, lattice of partitions.
Mots-clés : variant 
@article{ADM_2018_26_1_a2,
     author = {Oleksandra O. Desiateryk and Olexandr G. Ganyushkin},
     title = {Variants of the lattice of partitions of a countable set},
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     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_26_1_a2/}
}
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Oleksandra O. Desiateryk; Olexandr G. Ganyushkin. Variants of the lattice of partitions of a countable set. Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 8-18. http://geodesic.mathdoc.fr/item/ADM_2018_26_1_a2/