Skip to main content
SpringerLink
Log in

A non-finitely based quasi-variety of De Morgan algebras

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

In this paper we exhibit a non-finitely based, finitely generated quasi-variety of De Morgan algebras and determine the bottom of the lattices of sub-quasi-varieties of Kleene and De Morgan algebras.

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. Adams, M. E., and W. Dziobiak, ‘Lattices of quasivarieties of 3-element algebras’, J. of Algebra 166:181–210, 1994.

    Google Scholar 

  2. Burris, S., and H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, 1981.

  3. Cornish, W., and P. R. Fowler, ‘Coproducts of Kleene algebras’, J. Austral. Math. Soc. (Series A) 27:209–220, 1979.

    Google Scholar 

  4. Dziobiak, W., ‘Finitely generated congruence distributive quasivarieties of algebras’, Fund. Math. 133:47–57, 1989.

    Google Scholar 

  5. Dziobiak, W., ‘Finite bases for finitely generated, relatively congruence distributive quasi-varieties’, Algebra Universalis 28:303–323, 1991.

    Google Scholar 

  6. Gaitán, H., ‘Quasivarieties of De Morgan algebras: RCEP’, Revista Colombiana de Matemáticas 27:203–208, 1993.

    Google Scholar 

  7. Kalman, J. A., ‘Lattices with involution’, Trans. Amer. Math. Soc. 87: 485–491, 1958.

    Google Scholar 

  8. Pynko, A. P., ‘Implicational classes of De Morgan lattices’, Discrete Math. 205:171–181, 1999.

    Google Scholar 

  9. Sankappanavar, H. P., ‘A characterization of principal congruences of de Morgan algebras and its applications’, in A. I. Arruda, R. Chuaqui and N.C.A. da Costa, (eds.), Mathematical Logic in Latin America, North-Holland, Amsterdam, 1980, pp. 341–349

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matmáticas, Universidad Nacional de Colombia Ciudad Universitaria, Bogotá, Colombia

    Hernando Gaitán

  2. Departamento de Matemáticas y Física, Universidad Tecnológica del Chocó, ‘Diego Luis Córdoba’, Quibdó, Chocó, Colombia

    Milton H. Perea

Authors
  1. Hernando Gaitán
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Milton H. Perea
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by Vicerrectoría Académica de la Facultad de Ciencias and by División de Investigación, Sede Bogotá of the Universidad Nacional de Colombia.

Special issue of Studia Logica: “Algebraic Theory of Quasivarieties” Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaitán, H., Perea, M.H. A non-finitely based quasi-variety of De Morgan algebras. Stud Logica 78, 237–248 (2004). https://doi.org/10.1007/s11225-005-7248-6

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-005-7248-6

Keywords

Search

Navigation