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On hyperlattices: congruence relations, ideals and homomorphism

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Dschang, BP 67, Dschang, Cameroon

    B. B. N. Koguep & C. Lele

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  1. B. B. N. Koguep
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  2. C. Lele
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Correspondence to B. B. N. Koguep.

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Koguep, B.B.N., Lele, C. On hyperlattices: congruence relations, ideals and homomorphism. Afr. Mat. 30, 101–111 (2019). https://doi.org/10.1007/s13370-018-0630-0

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  • DOI: https://doi.org/10.1007/s13370-018-0630-0

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