Czechoslovak Mathematical Journal

, Volume 52, Issue 2, pp 255–273 | Cite as

A non-commutative generalization of MV-algebras

  • Jiří Rachůnek


Differential Equation Mathematical Modeling Ordinary Differential Equation Industrial Mathematic Discrete Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    V.D. Belousov: Foundations of the Theory of Quasigroups and Loops. Nauka, Moscow, 1967. (In Russian.)Google Scholar
  2. [2]
    A. Bigard, K. Keimel and S. Wolfenstein: Groupes et Anneaux Réticulés. Springer-Verlag, Berlin-Heidelberg-New York, 1977.Google Scholar
  3. [3]
    S. Burris and H.P. Sankappanavar: A Course in Universal Algebra. Springer-Verlag, Berlin-Heidelberg-New York, 1981.Google Scholar
  4. [4]
    C. C. Chang: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467–490.Google Scholar
  5. [5]
    C. C. Chang: A new proof of the completeness of the Lukasiewicz axioms. Trans. Amer. Math. Soc. 93 (1959), 74–80.Google Scholar
  6. [6]
    R. Cignoli: Free lattice-ordered abelian groups and varieties of MV -algebras. Proc. IX. Latin. Amer. Symp. Math. Log., Part 1, Not. Log. Mat. 38 (1993), 113–118.Google Scholar
  7. [7]
    Lattice-Ordered Groups (Advances and Techniques) (A.M.W. Glass and W. Charles Holland, eds.). Kluwer Acad. Publ., Dordrecht-Boston-London, 1989.Google Scholar
  8. [8]
    C. S. Hoo: MV-algebras, ideals and semisimplicity. Math. Japon. 34 (1989), 563–583.Google Scholar
  9. [9]
    V. M. Kopytov and N. Ya. Medvedev: The Theory of Lattice Ordered Groups. Kluwer Acad. Publ., Dordrecht-Boston-London, 1994.Google Scholar
  10. [10]
    T. Kovář: A general theory of dually residuated lattice ordered monoids. Thesis, Palacký University Olomouc, 1996.Google Scholar
  11. [11]
    D. Mundici: Interpretation of AFC *-algebras in Lukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15–63.Google Scholar
  12. [12]
    D. Mundici: MV-algebras are categorically equivalent to bounded commutative BCK-algebras. Math. Japon. 31 (1986), 889–894.Google Scholar
  13. [13]
    J. Rachůnek: DRl-semigroups and MV -algebras. Czechoslovak Math. J. 48(123) (1998), 365–372.Google Scholar
  14. [14]
    J. Rachůnek: MV-algebras are categorically equivalent to a class of DRl1(i)-semigroups. Math. Bohem. 123 (1998), 437–441.Google Scholar
  15. [15]
    K. L. N. Swamy: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105–114.Google Scholar
  16. [16]
    K. L. N. Swamy: Dually residuated lattice ordered semigroups II. Math. Ann. 160 (1965), 64–71.Google Scholar
  17. [17]
    K. L. N. Swamy: Dually residuated lattice ordered semigroups III. Math. Ann. 167 (1966), 71–74.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2002

Authors and Affiliations

  • Jiří Rachůnek
    • 1
  1. 1.Department of Algebra and Geometry, Faculty of SciencesPalacký UniversityOlomoucCzech Republic

Personalised recommendations