Advertisement

Siberian Mathematical Journal

, Volume 30, Issue 6, pp 831–849 | Cite as

Equational closure operator and forbidden semidistributive lattices

  • K. V. Adaricheva
  • V. A. Gorbunov
Article

Keywords

Closure Operator Equational Closure Semidistributive Lattice 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    A. I. Mal'tsev, “On some boundary problems of algebra and mathematical logic,” in: Proceedings of the International Congress of Mathematicians, Moscow, 1966 [in Russian], Mir, Moscow (1968), pp. 217–231.Google Scholar
  2. 2.
    G. Birkhoff, “Universal algebra,” in: Proceedings of the First Canadian Math. Congress, Montreal, 1945, The University of Toronto Press (1946), pp. 310–326.Google Scholar
  3. 3.
    V. A. Gorbunov, “On lattices of quasivarieties,” Algebra Logika,15, No. 4, 436–457 (1976).Google Scholar
  4. 4.
    V. A. Gorbunov and V. I. Tumanov, “The structure of lattices of quasivarieties,” Trudy Inst. Mat., Akad. Nauk SSSR. Sib. Otdel.,2, 12–44 (1982).Google Scholar
  5. 5.
    W. Dziobiak, “On atoms in the lattice of quasivarieties,” Algebra Univ.,24, 32–35 (1987).Google Scholar
  6. 6.
    W. Lampe, “A property of the lattice of equational theories,” Algebra Univ.,23, 61–69 (1986).Google Scholar
  7. 7.
    R. McKenzie, “Finite forbidden lattices,” in: Proceedings of the Fourth Int. Conf. on Univ. Algebra and Lattice Theory, Puebla, 1982, Springer-Verlag (1983), pp. 176–205.Google Scholar
  8. 8.
    G. Birkhoff, Lattice Theory [Russian translation], Nauka, Moscow (1984).Google Scholar
  9. 9.
    G. Grätzer, General Lattice Theory [Russian translation], Mir, Moscow (1982).Google Scholar
  10. 10.
    P. Crawley and R. Dilworth, Algebraic Theory of Lattices, Prentice-Hall, New Jersey (1973).Google Scholar
  11. 11.
    A. I. Mal'tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).Google Scholar
  12. 12.
    V. A. Gorbunov and V. I. Tumanov, “On one class of lattices of quasivarieties,” Algebra Logika19, No. 1, 59–80 (1980).Google Scholar
  13. 13.
    L. A. Skornyakov, Elements of Lattice Theory [in Russian], Nauka, Moscow (1982).Google Scholar
  14. 14.
    O. Ore, “On the foundation of abstract algebra. I,” Ann. Math.,36, 406–437 (1935).Google Scholar
  15. 15.
    J. Jezek and V. Slavik, “Primitive lattices,” Czechoslovak Math. J.,29, 595–634 (1979).Google Scholar
  16. 16.
    A. I. Budkin and V. A. Gorbunov, “To the theory of quasivarieties of algebraic systems,” Algebra Logika,14, No. 2, 123–142 (1975).Google Scholar
  17. 17.
    V. A. Gorbunov, “Coverings in lattices of quasivarieties and independent axiomatizability,” Algebra Logika,14, No. 2, 123–142 (1975).Google Scholar
  18. 18.
    V. A. Gorbunov and D. M. Smirnov, “Finite algebras and the general theory of quasivarieties,” Colloq. Math. Soc. Janos Bolyai,28, 325–332 (1979).Google Scholar
  19. 19.
    G. Birkhoff and M. K. Bennett, “The convexity lattice of poset,” Order,2, 223–242 (1985).Google Scholar
  20. 20.
    V. I. Tumanov, “Finite distributive lattices of quasivarieties,” Algebra Logika,22, No. 2, 168–171 (1983).Google Scholar
  21. 21.
    A. A. Vinogradov, “Quasivarieties of abelian groups,” Algebra Logika,4, No. 6, 15–19 (1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • K. V. Adaricheva
  • V. A. Gorbunov

There are no affiliations available

Personalised recommendations