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On an operation with regular elements

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Abstract

In this paper, we prove that the class of meet-complemented lattices expanded with the greatest regular below, which is right adjoint to the double meet-complement, is an equational class satisfying the Stone equality. It is also the case that the class of distributive meet-complemented lattices with the greatest regular below is the same as the class of Stone distributive meet-complemented lattices with the greatest Boolean below.

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Acknowledgements

The author thanks two anonymous referees for their help in substantially improving the general presentation of this paper. Special thanks are due to the referee who has also been very helpful in correcting linguistic errors. Finally, the author is grateful to José Luis Castiglioni for his comments on a previous version.

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Authors and Affiliations

  1. Universidade Estadual de Campinas (UNICAMP), R. Sérgio Buarque de Holanda, 251 Cidade Universitária, Campinas, SP, 13083-859, Brazil

    Rodolfo C. Ertola-Biraben

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  1. Rodolfo C. Ertola-Biraben
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Correspondence to Rodolfo C. Ertola-Biraben.

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Communicated by C. Noguera.

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Ertola-Biraben, R.C. On an operation with regular elements. Soft Comput 23, 2271–2278 (2019). https://doi.org/10.1007/s00500-018-3572-4

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