Skip to main content

Unary operations on completely distributive complete lattices

  • 504 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1149)

Keywords

  • Distributive Lattice
  • Complete Lattice
  • Unary Operation
  • Dual Argument
  • Irreducible Element

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Balbes and Ph. Dwinger, Distributive lattices. University of Missouri Press, 1974.

    Google Scholar 

  2. B. Banaschewski and G. Bruns, Categorical characterization of the MacNeil completion, Archiv der Math. XVIII (1967), Fasc. 4, 369–377.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. H.J. Bandelt, On complete distributivity and maximal d-intervals. Coll. Math. Soc., Janos Bolay: 14 Lattice Theory, Szeged, 1974, 29–43.

    Google Scholar 

  4. H.J. Bandelt, Regularity and complete distributivity. Semigroup Forum 19 (1980), 123–126.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. H.J. Bandelt, M-distributive lattices. Arch. der Math., 39 (1982), Fasc. 5, 436–441.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. H.J. Bandelt, On regularity classes of binary relations. Universal Algebra and applications Banach Center Publications, Vol. G, PWN-Pol. Sci. Publ., Warsaw, 1982, 329–333.

    Google Scholar 

  7. H.J. Bandelt and M. Erne, The category of Z-continuous posets. J.Pure Appl. Algebra 30 (1983), no. 3, 219–226.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. T.S. Blyth and M.F. Janowitz, Residuation theory. Pergamon Press, Oxford, 1972.

    MATH  Google Scholar 

  9. B.A. Davey, On the lattice of subvarieties. Houston J. of Math., Vol. 5, 2, 1979, 183–192.

    MathSciNet  MATH  Google Scholar 

  10. Ph. Dwinger, Classes of completely distributive complete lattices. Indag. Math. 41 (1979), no. 4, 411–423.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Ph. Dwinger, Structure of completely distributive complete lattices. Indag. Math. 43 (1981), no. 4, 361–373.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Ph. Dwinger, Characterization of the complete homomorphic images of a complete distributive lattice I. Indag. Math. 44, (1982), no. 4, 403–414.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Ph. Dwinger, Characterization of the complete homomorphic images of a complete distributive lattice II. Indag. Math. 45, (1983), no. 1, 43–49.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. L. Geisinger and W. Graves, The category of complete algebraic lattices. J. of Comb. Theory, 13, no. 3, 1972, 332–338.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, D.S. Scott, A compendium of continuous lattices. Springer Verlag, Berlin-Heidelberg-New York, 1980.

    CrossRef  MATH  Google Scholar 

  16. G. Gratzer, General lattice theory, Birkhauser Verlag, Basel-Stuttgart, 1978.

    CrossRef  MATH  Google Scholar 

  17. G. Markowsky, Free completely distributive lattices. Proc. Amer. Math. Soc. 74 (1979), 227–228.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. G.N. Raney, A subdirect-union representation for completely distributive complete lattices. Proc. Amer. Math. Soc., 97 (1953), 518–522.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. G.N. Raney, Tight Galois connections and complete distributivity, Trans. Amer. Math. Soc., 97 (1960), 418–426.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Dwinger, P. (1985). Unary operations on completely distributive complete lattices. In: Comer, S.D. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098455

Download citation

  • DOI: https://doi.org/10.1007/BFb0098455

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15691-8

  • Online ISBN: 978-3-540-39638-3

  • eBook Packages: Springer Book Archive