Skip to main content
SpringerLink
Log in

A representation of m-algebraic lattices

  • Published:
algebra universalis Aims and scope Submit manuscript

Abstract

In this paper, we give a short proof of the following result of G. Grätzer and E. T. Schmidt: every m-algebraic lattice can be represented as the lattice of m-complete congruence relations of some m-complete modular 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. Freese, R., Lampe, W. A. andTaylor, W.,Congruence lattices of algebras of fixed similarity types. I., Indag. Math.82 (1) (1979), 59–68.

    Google Scholar 

  2. Grätzer, G.,On a family of certain subalgebras of a universal algebra, Indag. Math.68 (1965), 790–802.

    Google Scholar 

  3. Grätzer, G.,General Lattice Theory, Academic Press, New York, N.Y., Birkhäuser Verlag, Basel, Akademie Verlag, Berlin, 1978.

    Google Scholar 

  4. Grätzer, G.,Universal Algebra, Springer-Verlag, New York-Heidelberg-Berlin, second ed., 1979.

    Google Scholar 

  5. Grätzer, G.,The complete congruence lattice of a complete lattice, Lattices, Semigroups, and Universal Algebra, Proceedings of an international conference on lattices, semigroups, and universal algebra (Lisbon, 1988), Plenum Press, New York and London, 1990, pp. 81–88.

    Google Scholar 

  6. Grätzer, G. andSchmidt, E. T.,Algebraic lattices as congruence lattices: The m-complete case, Birkhoff Conference (Darmstadt, 1991), to appear.

  7. Reuter, K. andWille, R.,Complete congruence relations of complete lattices, Acta Sci. Math. (Szeged)51 (1987), 319–327.

    Google Scholar 

  8. Teo, S.-K.,Representing finite lattices as complete congruence lattices of complete lattices, Ann. Univ. Sci. Budapest. Eötvös Sect. Math.33 (1990), 177–182.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, R3T 2N2, Winnipeg, Man., Canada

    G. Grätzer, P. M. Johnson & E. T. Schmidt

  2. Transport Engineering Faculty Department of Mathematics, Technical University of Budapest, Müegyetem rkp. 9, 1111, Budapest, Hungary

    G. Grätzer, P. M. Johnson & E. T. Schmidt

Authors
  1. G. Grätzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. M. Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. T. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Bjarni Jonsson on his 70th birthday

The research of the first author was supported by the NSERC of Canada.

The research of the third author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grätzer, G., Johnson, P.M. & Schmidt, E.T. A representation of m-algebraic lattices. Algebra Universalis 32, 1–12 (1994). https://doi.org/10.1007/BF01190813

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01190813

Keywords

Search

Navigation