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Algebra Logika, 2013, Volume 52, Number 6, Pages 657–666 (Mi al612)  

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

Finitely generated lattices with completely modular elements among generators

A. G. Gein, M. P. Shushpanov

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

Abstract: We look at the concept of a completely modular element of a lattice, which is the modular analog of the well-known concept of a neutral element of a lattice. It is proved that a lattice is modular if it is generated by three elements of which two are completely modular. Also it is shown that a lattice generated by $n$, $n>3$, completely modular elements must not necessarily be modular.

Keywords: modular lattices, free lattices, modular elements.

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English version:
Algebra and Logic, 2014, 52:6, 435–441

Bibliographic databases:

UDC: 512.565
Received: 17.08.2013
Revised: 28.11.2013

Citation: A. G. Gein, M. P. Shushpanov, “Finitely generated lattices with completely modular elements among generators”, Algebra Logika, 52:6 (2013), 657–666; Algebra and Logic, 52:6 (2014), 435–441

Citation in format AMSBIB
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\vol 52
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\pages 657--666
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\pages 435--441
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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. A. G. Geǐn, M. P. Shushpanov, “Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type”, Siberian Math. J., 56:4 (2015), 631–636  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. A. G. Gein, “Finitely generated lattices with $M$-standard elements among generators”, Russian Math. (Iz. VUZ), 60:3 (2016), 14–17  mathnet  crossref  isi
    3. M. P. Shushpanov, “O beskonechnosti svobodnoi $3$-porozhdennoi reshetki s odnim levomodulyarnym porozhdayuschim”, Sib. elektron. matem. izv., 14 (2017), 528–532  mathnet  crossref
    4. 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
    5. 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
    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, “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
  • Алгебра и логика Algebra and Logic
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