Skip to main content
Log in

Congruence lattices of pseudocomplemented semilattices

  • Published:
algebra universalis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. R. Balbes andA. Horn,Stone lattices, Duke Math. J.37 (1970), 537–546.

    Article  MATH  MathSciNet  Google Scholar 

  2. G. Birkhoff,Lattice Theory, 2nd ed. American Mathematical Society, 1948.

  3. G. Birkhoff,Lattice Theory, 3rd ed. American Mathematical Society, 1967.

  4. R. A. Dean andR. H. Oehmke,Idempotent semigroups with distributive right congruence lattices, Pacific J. Math.14 (1964), 1187–1209.

    MATH  MathSciNet  Google Scholar 

  5. R. Freese andJ. B. Nation,Congruence lattices of semilattices, Pacific J. Math.49 (1973), 51–58.

    MATH  MathSciNet  Google Scholar 

  6. O. Frink,Representations of Boolean algebras, Bull. Amer. Math. Soc.47 (1941), 755–756.

    Article  MATH  MathSciNet  Google Scholar 

  7. O. Frink,Pseudocomplements in semilattices, Duke Math. J.29 (1962), 505–514.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Grätzer,Universal Algebra, Van Nostrand, 1968.

  9. G. Grätzer,Lattice Theory, W. H. Freeman and Company, 1971.

  10. G. Grätzer andH. Lakser,The structure of pseudocomplemented distributive lattices II. Congruence extension and amalgamation, Trans. Amer. Math. Soc.156 (1971), 343–358.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Grätzer andE. T. Schmidt,Ideals and Congruence relations in lattices, Acta Math. Acad. Sci. Hungar.9 (1958), 137–175.

    Article  MATH  MathSciNet  Google Scholar 

  12. T. E. Hall,On the lattice of congruences on a semilattice, J. Austral. Math. Soc.12 (1971), 456–460.

    Article  MATH  MathSciNet  Google Scholar 

  13. L. Henkin, J. D. Monk andA. Tarski,Cylindric Algebras. Part I., North Holland, 1971.

  14. J. T. Jones,Pseudocomplemented semilattices, Ph.D. Dissertation, U.C.L.A., 1972.

  15. J. T. Jones,Projective pseudocomplemented semilattices, Pacific J. of Mathematics52 (1974), 443–456.

    MATH  Google Scholar 

  16. B. Jónsson,Topics in Universal Algebra, Springer-Verlag, 1972.

  17. T. Katrinák,Pseudocomplementare Halbverbände, Mat. Casopis Sloven. Akad. Vied.18 (1968), 121–143.

    MATH  MathSciNet  Google Scholar 

  18. L. Nachbin,On a characterization of the lattice of all ideals of a Boolean ring, Fund. Math.36 (1949), 137–142.

    MATH  MathSciNet  Google Scholar 

  19. D. Papert,Congruence relations in semilattices, J. London Math. Soc.39 (1964), 723–729.

    MATH  MathSciNet  Google Scholar 

  20. H. Rasiowa andR. Sikorski,The Mathematics of Metamathematics, Monog. Mat. Vol. 41, Warsaw, 1963.

  21. H. P. Sankappanavar,A study of congruence lattices of pseudocomplemented semilattices, Ph. D. Thesis, University of Waterloo, 1974.

  22. J. Varlet,Congruence dans les demi-lattis, Bull. Soc. Roy. Sci. Liége,34 (1965), 231–240.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sankappanavar, H.P. Congruence lattices of pseudocomplemented semilattices. Algebra Universalis 9, 304–316 (1979). https://doi.org/10.1007/BF02488042

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02488042

Keywords

Navigation