For citation:
Reshetnikov A. V. On Congruences of Partial n-ary Groupoids. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 3, pp. 46-51. DOI: 10.18500/1816-9791-2011-11-3-2-46-51
On Congruences of Partial n-ary Groupoids
Ri-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 Ri-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 Ri-congruences.
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