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Congruence relations on some hyperstructures

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Abstract

In this work we study the structure of the set of congruences on several hyperstructures with one and two (hyper-)operations. On the one hand, we show sufficient conditions guaranteeing that the set of congruences of an nd-groupoid forms a complete lattice (which, in turn, is a sublattice of the lattice of equivalence relations on the nd-groupoid). On the other hand, we focus on the study of the congruences on a multilattice; specifically, we prove that the set of congruences on an m-distributive multilattice forms a complete lattice and, moreover, show that the classical relationship between homomorphisms and congruences can be adequately adapted to work with multilattices under suitable restrictions.

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Authors and Affiliations

  1. Dpto. Matemática Aplicada, E.T.S.I. Informática, Universidad de Málaga, Málaga, Spain

    Inma P. Cabrera, Pablo Cordero, Gloria Gutiérrez, Javier Martínez & Manuel Ojeda-Aciego

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  1. Inma P. Cabrera
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  2. Pablo Cordero
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  3. Gloria Gutiérrez
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  4. Javier Martínez
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  5. Manuel Ojeda-Aciego
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Corresponding author

Correspondence to Inma P. Cabrera.

Additional information

Partially supported by projects TIN2006-15455-C03-01, TIN2007-65819 (Science Ministry of Spain) and P06-FQM-02049 (Junta de Andalucía).

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Cabrera, I.P., Cordero, P., Gutiérrez, G. et al. Congruence relations on some hyperstructures. Ann Math Artif Intell 56, 361–370 (2009). https://doi.org/10.1007/s10472-009-9146-5

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  • DOI: https://doi.org/10.1007/s10472-009-9146-5

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