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Algebra Logika, 2018, Volume 57, Number 3, Pages 362–376 (Mi al854)  

This article is cited in 1 scientific paper (total in 1 paper)

Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators

M. P. Shushpanov

El'tsyn Ural Federal University, ul. Mira 19, Yekaterinburg, 620002 Russia

Abstract: It is known that a modular $3$-generated lattice is always finite and contains at most 28 elements. Lattices generated by three elements with certain modularity properties may no longer be modular but nevertheless remain finite. It is shown that a $3$-generated lattice among generating elements of which one is seminormal and another is coseminormal is finite and contains at most 45 elements. This estimate is stated to be sharp.

Keywords: left-modular element, right-modular element, seminormal element, defining relation.

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


DOI: https://doi.org/10.17377/alglog.2018.57.307

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English version:
Algebra and Logic, 2018, 57:3, 237–247

Bibliographic databases:

UDC: 512.565
Received: 25.11.2016
Revised: 23.02.2017

Citation: M. P. Shushpanov, “Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators”, Algebra Logika, 57:3 (2018), 362–376; Algebra and Logic, 57:3 (2018), 237–247

Citation in format AMSBIB
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\paper Finiteness of a~$3$-generated lattice with seminormal and coseminormal elements among generators
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\yr 2018
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. P. Shushpanov, “O konechnosti $3$-porozhdennoi reshetki s levomodulyarnym i razdelyayuschim elementami sredi porozhdayuschikh”, Izv. vuzov. Matem., 2019, no. 5, 92–94  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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