Skip to main content
SpringerLink
Log in

Free 3-Generated Lattices with Standard Element Among Generators

  • Published:
Algebra and Logic Aims and scope

We consider 3-generated lattices among generators of which there are elements of distributive and modular types, and one of the generators is necessarily standard. For each triple of such generators, we answer the question whether a lattice generated by that triple is finite.

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.

Similar content being viewed by others

References

  1. G. Grätzer, Lattice Theory: Foundation, Birkhäuser, Basel (2011).

    Book  MATH  Google Scholar 

  2. M. Stern, Semimodular Lattices. Theory and Applications, Encyclopedia Math. Appl., 73, Cambridge Univ. Press, Cambridge (1999).

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

    Article  MathSciNet  MATH  Google Scholar 

  4. S. P. Bhatta, “A characterization of neutral elements by the exclusion of sublattices,” Discr. Math., 309, No. 6, 1691-1702 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Grätzer, “Standard ideálok,” Magyar Tud. Akad. Mat. Fiz. Oszt. Közl, 9, 81-97 (1959).

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  7. A. G. Gein and M. P. Shushpanov, “Modularity and distributivity of 3-generated latticeswith special elements among generators,” Algebra and Logic, 56, No. 1, 1-12 (2017).

  8. A. G. Gein, “Lattices with modular and standard elements among generators,” Mal’tsev Readings (2016), p. 180; http://www.math.nsc.ru/conference/malmeet/16/malmeet16.pdf.

Download references

Author information

Authors and Affiliations

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

    A. G. Gein & M. P. Shushpanov

Authors
  1. A. G. Gein
    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. Gein.

Additional information

A. G. Gein and M. P. Shushpanov 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).

Translated from Algebra i Logika, Vol. 57, No. 6, pp. 619-638, November-December, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gein, A.G., Shushpanov, M.P. Free 3-Generated Lattices with Standard Element Among Generators. Algebra Logic 57, 399–413 (2019). https://doi.org/10.1007/s10469-019-09513-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-019-09513-7

Keywords

Search

Navigation