Geodesic
Congruence lattice of S-acts
Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 1, pp. 107-115.

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In this work we give the necessary and sufficient conditions for modularity and distributivity of the congruence lattice of disconnected S-acts. 
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A. A. Stepanova; D. O. Ptahov. Congruence lattice of S-acts. Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 1, pp. 107-115. http://geodesic.mathdoc.fr/item/DVMG_2013_13_1_a9/

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[2] D. P. Egorova, “Struktura kongruentsii unarnoi algebry”, Uporyadochennye mnozhestva i reshetki, Mezhvuzovskii nauchnyi sbornik, v. 5, 1978, 11–44 | MR | Zbl

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