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Finitely generated lattices with M-standard elements among generators

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Abstract

We prove that a lattice is modular if it is generated by three elements, two of which are M-standard. We also show that a lattice generated by n, n > 3, M-standard elements should not necessarily be modular.

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Authors and Affiliations

  1. Ural Federal University, ul. Mira 19, Ekaterinburg, 620002, Russia

    A. G. Gein

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  1. A. G. Gein
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Correspondence to A. G. Gein.

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Original Russian Text © A.G. Gein, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 3, pp. 18–22.

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Gein, A.G. Finitely generated lattices with M-standard elements among generators. Russ Math. 60, 14–17 (2016). https://doi.org/10.3103/S1066369X16030026

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  • DOI: https://doi.org/10.3103/S1066369X16030026

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