Skip to main content
SpringerLink
Log in

On Double Basic Algebras and Pseudo-effect Algebras

  • Published:
Order Aims and scope Submit manuscript

Abstract

Double basic algebras are a counterpart of bounded lattices with order-antiautomorphisms on principal filters. In the paper, an independent axiomatization of double basic algebras is given and lattice pseudo-effect algebras are characterized in the setting of double basic 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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chajda, I.: Double basic algebras. Order 26, 149–162 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chajda, I., Halaš, R., Kühr, J.: Semilattice Structures. Heldermann Verlag, Lemgo (2007)

    MATH  Google Scholar 

  3. Chajda, I., Halaš, R., Kühr, J.: Many-valued quantum algebras. Algebra Univers. 60, 63–90 (2009)

    Article  MATH  Google Scholar 

  4. Chajda, I., Kühr, J.: GMV-algebras and meet-semilattices with sectionally antitone permutations. Math. Slovaca 56, 275–288 (2006)

    MathSciNet  MATH  Google Scholar 

  5. Chajda, I., Kühr, J.: Pseudo-effect algebras as total algebras. Int. J. Theor. Phys. doi:10.1007/s10773-009-0093-z

  6. Chajda, I., Kolařík, M.: Independence of axiom system of basic algebras. Soft Comput. 13, 41–43 (2009)

    Article  MATH  Google Scholar 

  7. Cignoli, R., Mundici, D., D’Ottaviano, I.: Algebraic Foundations of Many-valued Reasoning. Kluwer Acad. Publ., Dordrecht (1999)

    Google Scholar 

  8. Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer Acad. Publ., Dordrecht/Ister Science, Bratislava (2000)

    MATH  Google Scholar 

  9. Dvurečenskij, A., Vetterlein, T.: Pseudoeffect algebras I. Basic properties. Int. J. Theor. Phys. 40, 685–701 (2001)

    Article  MATH  Google Scholar 

  10. Dvurečenskij, A., Vetterlein, T.: Pseudoeffect algebras II. Basic properties. Int. J. Theor. Phys. 40, 703–726 (2001)

    Article  MATH  Google Scholar 

  11. Dvurečenskij, A., Vetterlein, T.: On pseudo-effect algebras which can be covered by pseudo MV-algebras. Demonstr. Math. 36, 261–282 (2003)

    MATH  Google Scholar 

  12. Georgescu, G., Iorgulescu, A.: Pseudo-MV algebras. Mult.-Valued Log. 6, 95–135 (2001)

    MathSciNet  MATH  Google Scholar 

  13. Rachůnek, J.: A non-commutative generalization of MV-algebras. Czechoslov. Math. J. 52, 255–273 (2002)

    Article  MATH  Google Scholar 

  14. Foulis, D., Bennett, M.K.: Effect algebras and unsharp quantum logics. Found. Phys. 24, 1331–1352 (1994)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Science, Palacký University at Olomouc, 17. listopadu 12, 77146, Olomouc, Czech Republic

    Ivan Chajda & Jan Kühr

  2. Department of Computer Science, Faculty of Science, Palacký University at Olomouc, 17. listopadu 12, 77146, Olomouc, Czech Republic

    Miroslav Kolařík

Authors
  1. Ivan Chajda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miroslav Kolařík
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jan Kühr
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jan Kühr.

Additional information

Supported by the Czech Government Research Project MSM6198959214, and partly by the Palacký University Grant PrF 2010 008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chajda, I., Kolařík, M. & Kühr, J. On Double Basic Algebras and Pseudo-effect Algebras. Order 28, 499–512 (2011). https://doi.org/10.1007/s11083-010-9187-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11083-010-9187-8

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation