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Algebra Logika, 2017, Volume 56, Number 1, Pages 3–19 (Mi al776)  

This article is cited in 3 scientific papers (total in 3 papers)

Modularity and distributivity of $3$-generated lattices with special elements among generators

A. G. Gein, M. P. Shushpanov

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

Abstract: We consider $3$-generated lattices whose generating elements possess properties that are, in a sense, close to modularity or distributivity. Those combinations of these properties are specified that are sufficient for a lattice to be modular, and even distributive.

Keywords: modular lattice, distributive lattice, left modular element, right modular element, distributive element, standard element.

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.2017.56.101

Full text: PDF file (920 kB)
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English version:
Algebra and Logic, 2017, 56:1, 1–12

Bibliographic databases:

UDC: 512.565
Received: 08.07.2015
Revised: 17.11.2015

Citation: A. G. Gein, M. P. Shushpanov, “Modularity and distributivity of $3$-generated lattices with special elements among generators”, Algebra Logika, 56:1 (2017), 3–19; Algebra and Logic, 56:1 (2017), 1–12

Citation in format AMSBIB
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\by A.~G.~Gein, M.~P.~Shushpanov
\paper Modularity and distributivity of $3$-generated lattices with special elements among generators
\jour Algebra Logika
\yr 2017
\vol 56
\issue 1
\pages 3--19
\mathnet{http://mi.mathnet.ru/al776}
\crossref{https://doi.org/10.17377/alglog.2017.56.101}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3731469}
\transl
\jour Algebra and Logic
\yr 2017
\vol 56
\issue 1
\pages 1--12
\crossref{https://doi.org/10.1007/s10469-017-9423-z}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85018752113}


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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, “Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators”, Algebra and Logic, 57:3 (2018), 237–247  mathnet  crossref  crossref  isi
    2. A. G. Gein, M. P. Shushpanov, “Free 3-Generated Lattices with Standard Element Among Generators”, Algebra and Logic, 57:6 (2019), 399–413  mathnet  crossref  crossref  isi
    3. M. P. Shushpanov, “Finiteness and infiniteness of $3$-generated lattices with distributive elements among generators”, Siberian Math. J., 60:4 (2019), 734–740  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
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