Skip to main content
SpringerLink
Log in

A non commutative generalization of *-autonomous lattices

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

Pseudo *-autonomous lattices are non-commutative generalizations of *-autonomous lattices. It is proved that the class of pseudo *-autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo *-autonomous lattices can be described as their normal ideals.

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. K. Blount, C. Tsinakis: The structure of residuated lattices. Int. J. Algebra Comput. 13 (2003), 437–461.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Burris, H. P. Sankappanavar: A Course in Universal Algebra. Springer, Berlin-Heidelberg-New York, 1981.

    MATH  Google Scholar 

  3. N. Galatos, C. Tsinakis: Generalized MV-algebras. J. Algebra 283 (2005), 254–291.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Georgescu, A. Iorgulescu: Pseudo-MV algebras. Mult.-valued Logic 6 (2001), 95–135.

    MATH  MathSciNet  Google Scholar 

  5. J.-Y. Girard: Linear logic. Theor. Comput. Sci. 50 (1987), 1–102.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Jipsen, C. Tsinakis: A survey of residuated lattices. In: Ordered Algebraic Structures (J. Martinez, ed.). Kluwer, Dordrecht, 2002, pp. 19–56.

    Google Scholar 

  7. I. Leustean: Non-commutative Lukasiewicz propositional logic. Arch. Math. Logic 45 (2006), 191–213.

    Article  MATH  MathSciNet  Google Scholar 

  8. F. Paoli: Substructural Logic: A Primer. Kluwer, Dordrecht, 2002.

    MATH  Google Scholar 

  9. F. Paoli: *-autonomous lattices. Stud. Log. 79 (2005), 283–304.

    Article  MATH  MathSciNet  Google Scholar 

  10. F. Paoli: *-autonomous lattices and fuzzy sets. Soft Comput. 10 (2006), 607–617.

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Rachůnek: Prime spectra of non-commutative generalizations of MV-algebras. Algebra Univers. 48 (2002), 151–169.

    Article  MATH  Google Scholar 

  13. D. N. Yetter: Quantales and (noncommutative) linear logic. J. Symb. Log. 55 (1990), 41–64.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    P. Emanovský & J. Rachůnek

Authors
  1. P. Emanovský
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Rachůnek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Emanovský.

Additional information

The work on the paper was supported by grant of Czech Government MSM 6198959214.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Emanovský, P., Rachůnek, J. A non commutative generalization of *-autonomous lattices. Czech Math J 58, 725–740 (2008). https://doi.org/10.1007/s10587-008-0047-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-008-0047-2

Keywords

Search

Navigation