Czechoslovak Mathematical Journal

, Volume 58, Issue 3, pp 725–740 | Cite as

A non commutative generalization of *-autonomous lattices

  • P. Emanovský
  • J. Rachůnek


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.


*-autonomous lattice pseudo *-autonomous lattice residuated lattice ideal normal ideal congruence 


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  1. [1]
    K. Blount, C. Tsinakis: The structure of residuated lattices. Int. J. Algebra Comput. 13 (2003), 437–461.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    S. Burris, H. P. Sankappanavar: A Course in Universal Algebra. Springer, Berlin-Heidelberg-New York, 1981.MATHGoogle Scholar
  3. [3]
    N. Galatos, C. Tsinakis: Generalized MV-algebras. J. Algebra 283 (2005), 254–291.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    G. Georgescu, A. Iorgulescu: Pseudo-MV algebras. Mult.-valued Logic 6 (2001), 95–135.MATHMathSciNetGoogle Scholar
  5. [5]
    J.-Y. Girard: Linear logic. Theor. Comput. Sci. 50 (1987), 1–102.MATHCrossRefMathSciNetGoogle Scholar
  6. [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. [7]
    I. Leustean: Non-commutative Lukasiewicz propositional logic. Arch. Math. Logic 45 (2006), 191–213.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    F. Paoli: Substructural Logic: A Primer. Kluwer, Dordrecht, 2002.MATHGoogle Scholar
  9. [9]
    F. Paoli: *-autonomous lattices. Stud. Log. 79 (2005), 283–304.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    F. Paoli: *-autonomous lattices and fuzzy sets. Soft Comput. 10 (2006), 607–617.MATHCrossRefGoogle Scholar
  11. [11]
    J. Rachůnek: A non-commutative generalization of MV-algebras. Czechoslovak Math. J. 52 (2002), 255–273.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    J. Rachůnek: Prime spectra of non-commutative generalizations of MV-algebras. Algebra Univers. 48 (2002), 151–169.MATHCrossRefGoogle Scholar
  13. [13]
    D. N. Yetter: Quantales and (noncommutative) linear logic. J. Symb. Log. 55 (1990), 41–64.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2008

Authors and Affiliations

  1. 1.Department of Algebra and GeometryPalacký University Olomouc, Fac. of SciOlomoucCzech Republic

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