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On the Embedding of the Free Lattice of Rank 3 in the Lattice Freely Generated by Three Distributive Type Elements

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Abstract

We prove the lattice freely generated by three distributive elements and the lattice freely generated by two distributive elements and one dually distributive element contain the free lattice of rank 3 as sublattice. We describe the lattice freely generated by two distributive elements and one both distributive and dually distributive element. It is infinite, but does not contain the free lattice of rank 3 as a sublattice.

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Acknowledgments

The authors thank the reviewer for useful observations and comments, without which Theorem 3 would not have appeared.

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Authors and Affiliations

  1. Algebra and Theoretical Computer Science, Ural Federal University, 19 Mira str., Ekaterinburg, 620002, Russia

    A. G. Gein & M. P. Shushpanov

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  1. A. G. Gein
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  2. M. P. Shushpanov
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Correspondence to M. P. Shushpanov.

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Supported through the Competitiveness Project (Agreement between the Ministry of Education and Science of the Russian Federation and the Ural Federal University No. 02.A03.21.0006, 27.08.2013).

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Gein, A.G., Shushpanov, M.P. On the Embedding of the Free Lattice of Rank 3 in the Lattice Freely Generated by Three Distributive Type Elements. Order 38, 203–210 (2021). https://doi.org/10.1007/s11083-020-09534-3

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  • DOI: https://doi.org/10.1007/s11083-020-09534-3

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