Geodesic
On congruences of partial $n$-ary groupoids
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 46-51

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$R_i$-congruence is defined for partial $n$-ary groupoids as a generalization of right congruence of a full binary groupoid. It is proved that for any $i$ the $R_i$-congruences of a partial $n$-ary groupoid $G$ form a lattice, where the congruence lattice of $G$ is not necessary a sublattice. An example is given, demonstrating that the congruence lattice of a partial $n$-ary groupoid is not always a sublattice of the equivalence relations lattice of $G$. The partial $n$-ary groupoids $G$ are characterized such that for some $i$, all the equivalence relations on $G$ are its $R_i$-congruences. 
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     author = {A. V. Reshetnikov},
     title = {On congruences of partial $n$-ary groupoids},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {46--51},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2011_11_3_a6/}
}
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A. V. Reshetnikov. On congruences of partial $n$-ary groupoids. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 46-51. http://geodesic.mathdoc.fr/item/ISU_2011_11_3_a6/