Afrika Matematika

, Volume 30, Issue 1–2, pp 101–111 | Cite as

On hyperlattices: congruence relations, ideals and homomorphism

  • B. B. N. KoguepEmail author
  • C. Lele


We introduce the notion of congruences in hyperlattices. We prove that a quotient of a hyperlattice by a congruence is a “weak-hyperlattice” and not a hyperlattice in general. We explore the connections between congruences, ideals and homomorphism of hyperlattices. In particular, we establish necessary and sufficient conditions for a zero-congruence class to be an ideal of a hyperlattice.


Hyperlattice Ideal Congruence Homomorphism 

Mathematics Subject Classification

06B10 06B75 08A72 



The authors would like to thank the anonymous referees for their careful reading of the paper and useful suggestions to clarify this work.


  1. 1.
    Cabrera, I.P., Cordero, P., Gutiérrez, G., Martínez, J., Ojeda-Aciego, M.: Congruence relations on some hyperstructures. Ann. Math. Artif. Intell. 56(3–4), 361–370 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Corsini, P., Leoreanu, V.: Application of Hyperstructure Theory. Advances in Mathematics, vol. 5. Kluwer Academic Publishers, Boston (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)CrossRefzbMATHGoogle Scholar
  4. 4.
    Koguep, B.B.N., Lele, C., Nganou, J.B.: Normal hyperlattices and pure 448 ideals of hyperlattices. Asian Eur. J. Math. 9(1), 1650020 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Koguep, B.B.N., Nkuimi, C., Lele, C.: On fuzzy ideals of hyperlattice. Int. J. Algebra 2(15), 739–750 (2008)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Konstantinidou, M., Mittas, J.: An introduction to the theory of hyperlattices. Mathematica Balcanica 7(23), 187–193 (1997)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Marty, F.: Sur une généralisation de la notion de groupe. In: \(8^{i\grave{e}me}\) Congrès des Mathématiciens Scandinaves, pp. 45–49. Stockhlom (1934)Google Scholar
  8. 8.
    Rahnamai-Barghi, A.: The prime ideal theorem for distributive hyperlattices. Ital. J. Pure Appl. Math. 10, 75–78 (2001)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Rahnamai-Barghi, A.: The prime ideal theorem and semiprime ideals in meethyperlattices. Ital. J. Pure Appl. Math. 5, 53–60 (1999)zbMATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of DschangDschangCameroon

Personalised recommendations