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Lattices generated by modular element

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Abstract

We prove that the lattice generated by three modular elements is modular. For every n > 3 we construct a nonmodular lattice L generated by n elements each of which is modular in L.

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References

  1. Gein, A. G., Shushpanov, M. P. “Defining Relations of a Free Modular Lattice of Rank 3”, Russian Mathematics (Iz. VUZ) 57, No. 10, 59–61 (2013).

    MATH  MathSciNet  Google Scholar 

  2. Ore, O. “On the Theorem of Jordan–Hölder”, Trans. Amer.Math. Soc. 41, 266–275 (1937).

    MathSciNet  Google Scholar 

  3. Gein, A. G., Shushpanov, M. P. “On Sublattice Generated by Modular Elements”, in Proceedings of Internatational Algebraic Conference ‘Algebra and Linear Optimization’, Dedicated to Centennial of S. N. Chernikov, Yekaterinburg, May 14–19 2012 (“UMC-UPI”Publishers, Yekaterinburg, 2012), P. 47 [in Russian].

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  4. Shushpanov, M. P. “Nonmodular LatticesGenerated by Modular Elements”, in Proceedings of International Conference on Algebra Dedicated to 100-th Anniversary of S.M. Chernikov, Kyiv, Ukraine, August 20–26, 2012 (Dragomanov National Pedagogical University, Kyiv, 2012), P. 146 [in Russian].

    Google Scholar 

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Correspondence to M. P. Shushpanov.

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Original Russian Text © M.P. Shushpanov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 12, pp. 84–86.

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Shushpanov, M.P. Lattices generated by modular element. Russ Math. 59, 73–75 (2015). https://doi.org/10.3103/S1066369X15120075

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  • DOI: https://doi.org/10.3103/S1066369X15120075

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