Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


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

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
10.08.2011
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Russian
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UDC: 
512.548 + 512.571

On Congruences of Partial n-ary Groupoids

Autors: 
Reshetnikov A. V., National Research University Moscow Institute of Electronic Technology
Abstract: 

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.

References: 
  1. Общая алгебра: в 2 т. Т. 2 / В. А. Артамонов, В. Н. Салий, Л. А. Скорняков и др.; под общ. ред. Л. А. Скорнякова. М.: Наука, Физматлит, 1991, (гл. Универсальные алгебры. С. 295–367).
  2. Кожухов И. Б., Решетников А. В. Алгебры, у которых все отношения эквивалентности являются конгруэнциями // Фундаментальная и прикладная математика. 2010. Т. 16, No 3. С. 161–192.
  3. Ляпин Е. С., Евсеев А. Е. Частичные алгебраические действия. СПб.: Образование, 1991. 163 с.