Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2011, Volume 11, Issue 3(2), Pages 46–51
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On congruences of partial $n$-ary groupoids
A. V. Reshetnikov
Moscow Institute of Electronic Technology, Chair of Higher Mathematics — 1
$R_i$-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.
partial groupoid, $n$-ary groupoid, congruence lattice, one-sided congruence lattice, equivalence relation lattice.
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A. V. Reshetnikov, “On congruences of partial $n$-ary groupoids”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 11:3(2) (2011), 46–51
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\paper On congruences of partial $n$-ary groupoids
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
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A. V. Reshetnikov, “O chastichnykh $n$-arnykh gruppoidakh, u kotorykh kazhdoe otnoshenie ekvivalentnosti yavlyaetsya kongruentsiei”, Chebyshevskii sb., 17:1 (2016), 232–239
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