Skip to main content
Log in

Alan Day's doubling construction

  • 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. Adaricheva, K. V.,A characterization of finite lattices of subsemilattices (in Russian), Algebra i Logica30 (1991), 385–404.

    Google Scholar 

  2. Adaricheva, K. V. andGorbunov, V. A.,The structure of finite atomistic lattices of quasivarieties, Soviet Math. Dokl.41 (1990), 80–82.

    Google Scholar 

  3. Adaricheva, K. V., Dziobiak, W. andGorbunov, V. A.,Finite atomistic lattices that can be represented as lattices of quasivarieties, Fund. Math.142 (1993), 19–43.

    Google Scholar 

  4. Day, A.,A simple solution of the word problem for lattices, Canad. Math. Bull.13 (1970), 253–254.

    Google Scholar 

  5. Day, A.,p-modularity implies modularity in equational classes, Algebra Universalis3 (1973), 398–399.

    Google Scholar 

  6. Day, A.,Splitting lattices generate all lattices, Algebra Universalis7 (1977), 163–170.

    Google Scholar 

  7. Day, A.,Splitting lattices and congruence-modularity, Contributions to universal algebra, Proceedings of the Colloquium held in Szeged, 1975. Colloq. Math. Soc. János Bolyai, vol. 17, North Holland Publishing Co., Amsterdam, 1977, 57–71.

    Google Scholar 

  8. Day, A.,Characterizations of finite lattices that are bounded-homomorphic images or sublattices of free lattices, Canad. J. Math.31 (1979), 69–78.

    Google Scholar 

  9. Day, A.,Congruence normality: the characterization of the doubling class of convex sets, Appendix by J. B. Nation, Algebra Universalis31 (1994), 397–406.

    Google Scholar 

  10. Day, A.,Doubling constructions in lattice theory, Canad. J. Math.44 (1992), 252–269.

    Google Scholar 

  11. Day, A. andFreese, R.,A characterization of identities implying congruence modularity, I, Canad. J. Math.32 (1980), 1140–1167.

    Google Scholar 

  12. Day, A. andNation, J. B.,Congruence normal covers of finitely generated lattice varieties, Canad. Math. Bull.35 (1992), 311–320.

    Google Scholar 

  13. Freese, R.,Finitely presented lattices: canonical forms and the covering relation, Trans. Amer. Math. Soc.312 (1989), 841–860.

    Google Scholar 

  14. Freese, R.,Finitely presented lattices: continuity and semidistributivity, Lattices, Semigroups, and Universal Algebra (J. Almeida, G. Bordalo, and Philip Dwinger, eds), Proceedings of the Lisbon Conference, 1988, Plenum Press, New York, 1990, 67–70.

    Google Scholar 

  15. Freese, R.,Free and finitely presented lattices, Proceedings of the International Conference on Algebra honoring A. Maltsev (L. A. Bokut, Yu. L. Ershov, and A. I. Kostríkin, eds.), vosibirsk, USSR, August 21–26, 1989. Contemporary Math., vol.131 (Part 3), 1992, 85–97.

  16. Freese, R.,Weak atomicity in finitely presented lattices: an example, preprint.

  17. Freese, R.,Alan Day's early work: congruence identities, Algebra Universalis34 (1995), 4–23.

    Google Scholar 

  18. Freese, R. andNation, J. B.,3-3 lattice inclusions imply congruence modularity, Algebra Universalis7 (1977), 191–194.

    Google Scholar 

  19. Freese, R., Kearnes, K. andNation, J. B.,Congruence lattices of congruence semidistributive algebras, Proceedings of the Internation Conference Honoring Garrett Birkhoff (K. Baker, E. T. Schmidt and R. Wille, eds.), Darmstadt, Germany, June 13–17, 1991. Springer-Verlag, New York (to appear).

    Google Scholar 

  20. Geyer, W.,The generalized doubling construction and formal concept analysis, Algebra Universalis32 (1994), 341–367.

    Google Scholar 

  21. Geyer, W.,On Tamari lattices, Discrete Math, (to appear).

  22. Gorbunov, V. A.,The structure of lattices of quasivarieties, Algebra Universalis32 (1994), 493–530.

    Google Scholar 

  23. Grãtzer, G.,Chapter on Universal algebra, Trends in lattice theory, edited by J. C. Abbott, Van Nostrand Reinhold, New York (1970).

    Google Scholar 

  24. Grãtzer, G.,A property of transferable lattices, Proc. Amer. Math. Soc.43 (1974), 269–271.

    Google Scholar 

  25. Jónsson, B.,Relatively free lattices, Coll. Math.21 (1970), 191–196.

    Google Scholar 

  26. McKenzle, R.,Equational bases and non-modular lattice varieties, Trans. Amer. Math. Soc.174 (1972), 1–43.

    Google Scholar 

  27. Nation, J. B.,Varieties whose congruences satisfy certain lattice identities, Algebra Universalis4 (1974), 78–88.

    Google Scholar 

  28. Nation, J. B.,An approach to lattice varieties of finite height. Algebra Universalis27 (1990), 521–543.

    Google Scholar 

  29. Repnitskii, V. B.,On finite lattices which are emheddable in subsemigroup lattices, preprint (1992).

  30. Repnitskii, V. B.,On sublattices of subsemigroup lattices, preprint (1992).

  31. Skolem, T.,Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit und Beweisbarkeit mathematischen Sätze nebst einem Theoreme über dichte Mengen, Videnskapsselskapets skrifter I. Mathematisk-naturvidenskabelig klasse, Videnskabsakademiet i Kristiania4 (1920), 1–36.

    Google Scholar 

  32. Skolem, T.,Select Works in Logic, Scandinavian University Books, Oslo, 1979.

    Google Scholar 

  33. Slavík, V.,Lattices with finite W-covers, Algebra Universalis (to appear).

  34. Ph. M. Whitman,Free lattices, Ann. of Math. (2)42 (1941), 325–330.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported in part by NSF Grant DMS 91-22011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nation, J.B. Alan Day's doubling construction. Algebra Universalis 34, 24–34 (1995). https://doi.org/10.1007/BF01200488

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01200488

Keywords

Navigation