Skip to main content
SpringerLink
Log in

Subdirectly irreducible sectionally pseudocomplemented semilattices

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.

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. S. Burris and H.P. Sankappanavar: A Course in Universal Algebra. Springer Verlag, New York, 1981.

    MATH  Google Scholar 

  2. I. Chajda: An extension of relative pseudocomplementation to non-distributive lattices. Acta Sci. Math. (Szeged) 69 (2003), 491–496.

    MATH  MathSciNet  Google Scholar 

  3. I. Chajda, G. Eigenthaler and H. Länger: Congruence Classes in Universal Algebra. Heldermann Verlag, Lemgo, 2003.

    MATH  Google Scholar 

  4. I. Chajda and R. Halaš: Sectionally pseudocomplemented lattices and semilattices. In: K.P. Shum (ed.) et al., Advances in Algebra. Proceedings of the ICM sattelite conference in algebra and related topics, Hong Kong, China, August 14–17, 2002. World Scientific, River Edge. 2003, pp. 282–290.

    Google Scholar 

  5. I. Chajda and S. Radeleczki: On varieties defined by pseudocomplemented nondistributive lattices. Publ. Math. Debrecen 63 (2003), 737–750.

    MATH  MathSciNet  Google Scholar 

  6. G. Grätzer: General Lattice Theory (2nd edition). Birkhäuser Verlag, Basel-Boston-Berlin, 1998.

    MATH  Google Scholar 

  7. P. Köler: Brouwerian semilattices. Trans. Amer. Math. Soc. 268 (1981), 103–126.

    Article  MathSciNet  Google Scholar 

  8. W. C. Nemitz: Implicative semi-lattices. Trans. Amer. Math. Soc. 117 (1965), 128–142.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. C. Varlet: A generalization of the notion of pseudo-complementedeness. Bull. Soc. Roy. Liège 37 (1968), 149–158.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Science, Palacký University, Tomkova 40, 779 00, Olomouc, Czech Republic

    R. Halaš & J. Kühr

Authors
  1. R. Halaš
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Kühr
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Council of the Czech Government, MSM 6198959214.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Halaš, R., Kühr, J. Subdirectly irreducible sectionally pseudocomplemented semilattices. Czech Math J 57, 725–735 (2007). https://doi.org/10.1007/s10587-007-0109-x

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-007-0109-x

Keywords

Search

Navigation