Skip to main content
SpringerLink
Log in

Annihilators in BCK-Algebras

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra \(\mathcal{A}\). We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice \({\mathcal{D}\left( \mathcal{A} \right)}\) of all deductive systems on \(\mathcal{A}\). Moreover, relative annihilators of \({C \in \mathcal{D}\left( \mathcal{A} \right)}\) with respect to \({B\;{\text{in}}\;\mathcal{D}\left( \mathcal{A} \right)}\) are introduced and serve as relative pseudocomplements of C w.r.t. B in \({\mathcal{D}\left( \mathcal{A} \right)}\).

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. H. A. S. Abujabal, M. A. Obaid and M. Aslam: On annihilators of BCK-algebras. Cze-choslovak Math. J. 45(120) (1995), 727–735.

    MathSciNet  Google Scholar 

  2. W. J. Blok and D. Pigozzi: Algebraizable Logics. Memoirs of the American Math. Soc., No 396, Providence, Rhode Island, 1989.

    Google Scholar 

  3. I. Chajda: The lattice of deductive systems on Hilbert algebras. Southeast Asian Bull. Math., To appear.

  4. I. Chajda and R. Halaš: Stabilizers in Hilbert algebras. Multiple Valued Logic 8 (2002), 139–148.

    MathSciNet  Google Scholar 

  5. A. Diego: Sur les algébres de Hilbert. Collection de Logique Math. Ser. A (Ed. Hermann) 21 (1967), 177–198.

  6. W. A. Dudek: On ideals and congruences in BCC-algebras. Czechoslovak Math. J. To appear.

  7. K. Iséki and S. Tanaka: An introduction to the theory of BCK-algebras. Math. Japon. 23 (1978), 1–26.

    MathSciNet  Google Scholar 

  8. K. Iséki and S. Tanaka: Ideal theory of BCK-algebras. Math. Japon. 21 (1976), 351–366.

    MathSciNet  Google Scholar 

  9. C. A. Meredith and A. N. Prior: Investigations into implicational S5. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 10 (1964), 203–220.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Radomír Halaš

Authors
  1. Radomír Halaš
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Halaš, R. Annihilators in BCK-Algebras. Czech Math J 53, 1001–1007 (2003). https://doi.org/10.1023/B:CMAJ.0000024536.04596.67

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:CMAJ.0000024536.04596.67

Search

Navigation