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Sibirsk. Mat. Zh., 2015, Volume 56, Number 4, Pages 798–804 (Mi smj2679)  

This article is cited in 7 scientific papers (total in 7 papers)

Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type

A. G. Geĭn, M. P. Shushpanov

Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg, Russia

Abstract: We consider the $3$-generated lattices whose generators enjoy some properties that are close to modularity in a sense, including left modularity, right modularity, and dual right modularity. We find all combinations of these properties that suffice for the modularity of the lattice.

Keywords: modular lattice, modular element.

DOI: https://doi.org/10.17377/smzh.2015.56.407

Full text: PDF file (312 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2015, 56:4, 631–636

Bibliographic databases:

UDC: 512.565
Received: 06.11.2014

Citation: A. G. Geǐn, M. P. Shushpanov, “Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type”, Sibirsk. Mat. Zh., 56:4 (2015), 798–804; Siberian Math. J., 56:4 (2015), 631–636

Citation in format AMSBIB
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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 beskonechnosti svobodnoi $3$-porozhdennoi reshetki s odnim levomodulyarnym porozhdayuschim”, Sib. elektron. matem. izv., 14 (2017), 528–532  mathnet  crossref
    2. A. G. Gein, M. P. Shushpanov, “Modularity and distributivity of $3$-generated lattices with special elements among generators”, Algebra and Logic, 56:1 (2017), 1–12  mathnet  crossref  crossref  mathscinet  isi
    3. M. P. Shushpanov, “On the embedding of the free lattice of rank $3$ in the lattice freely generated by three completely right modular elements”, Sib. elektron. matem. izv., 14 (2017), 1215–1219  mathnet  crossref
    4. M. P. Shushpanov, “On $3$-generated lattices with a completely modular element among generators”, Algebr. Universalis, 78:3 (2017), 377–387  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. A. G. Gein, M. P. Shushpanov, “Free 3-generated lattices with two semi-normal generators”, Order-J. Theory Ordered Sets Appl., 35:2 (2018), 247–252  crossref  mathscinet  zmath  isi  scopus
    7. 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
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