Skip to main content
SpringerLink
Log in

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

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Grätzer G. and Schmidt E. T., “Standard ideals in lattices,” Acta Math. Acad. Sci. Hungar., 12, 17–86 (1961).

    Article  MathSciNet  MATH  Google Scholar 

  2. Bhatta S. P., “A characterization of neutral elements by the exclusion of sublattices,” Discrete Math., 309, 1691–1702 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  3. Ore O., “On the theorem of Jordan–Holder,” Trans. Amer. Math. Soc., 41, 266–275 (1937).

    MathSciNet  Google Scholar 

  4. Stern M., Semimodular Lattices. Theory and Applications, Cambridge Univ. Press, Cambridge (1999).

    Book  MATH  Google Scholar 

  5. Gein A. G. and Shushpanov M. P., “Finitely generated lattices with completely modular elements among generators,” Algebra and Logic, 52, No. 6, 435–441 (2014).

    Article  MathSciNet  Google Scholar 

  6. Gein A. G. and Shushpanov M. P., “Defining relations of a free modular lattice of rank 3,” Russian Math. (Iz. VUZ), 57, No. 10, 59–61 (2013).

    MathSciNet  MATH  Google Scholar 

  7. Gein A. G. and Shushpanov M. P., “On a sublattice that generated by modular elements,” in: Abstracts: International Conference “Algebra and Linear Optimization” Dedicated to S. N. Chernikov on the Occasion of His 100 Birthday (Ekaterinburg, May 14–19, 2012), Izdat. UMTS-UPI, Ekaterinburg, 2012, p. 47.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ural Federal University, Ekaterinburg, Russia

    A. G. Geĭn & M. P. Shushpanov

Authors
  1. A. G. Geĭn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. P. Shushpanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. G. Geĭn.

Additional information

Original Russian Text Copyright © 2015 Geĭn A.G. and Shushpanov M.P.

The authors were supported under Agreement No. 02.A03.21.0006 of 27.08.2013 between the Ministry of Education and Science of the Russian Federation and Ural Federal University.

Ekaterinburg. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 4, pp. 798–804, July–August, 2015; DOI: 10.17377/smzh.2015.56.407.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Geĭn, A.G., Shushpanov, M.P. Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type. Sib Math J 56, 631–636 (2015). https://doi.org/10.1134/S0037446615040072

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446615040072

Keywords

Search

Navigation