Skip to main content
SpringerLink
Log in

Small non-Arguesian lattices

  • 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Camillo, V. P.,Inducing lattice maps by semilinear isomorphisms, Rocky Mountain J. of Math.14 (1984), 475–486.

    Google Scholar 

  2. Day, A. andHerrmann, Ch.,Gluings of modular lattices, Order5 (1988), 85–101.

    Google Scholar 

  3. Day, A. andJónsson, B.,The structure of non-Arguesian lattices, Bull. Amer. Math. Soc.13 (1985), 157–159.

    Google Scholar 

  4. Day, A. andJónsson, B.,A structural characterization of non-Arguesian lattices, Order2 (1986), 335–350.

    Google Scholar 

  5. Day, A. andJónsson, B.,Non-Arguesian configurations in a modular lattice, Acta Sci. Math. (Szeged)51 (1987), 309–318.

    Google Scholar 

  6. Day, A. andJónsson, B.,Non-Arguesian configurations and gluings of modular lattices, Algebra Universalis26 (1989), 208–215.

    Google Scholar 

  7. Day, A. andPickering, D.,A note on the Arguesian lattice identity, Proc. Visegrad Conference on Universal Algebra (1982).

  8. Freese, R.,The variety of modular lattices is not generated by its finite members, Trans. Amer. Math. Soc.255 (1979), 277–300.

    Google Scholar 

  9. Graczynska, E.,On the sums of double systems of lattices, Contributions to Universal Algebra, Colloq. Math. Soc. J. Bolyai, vol. 17, 1977, pp. 161–166.

    Google Scholar 

  10. Haiman, M.,Two notes on the Arguesian identity, Algebra Universalis21 (1985), 167–171.

    Google Scholar 

  11. Haiman, M.,Arguesian lattices which are not type-1, Algebra Universalis28 (1991), 128–137.

    Google Scholar 

  12. Hall, M. andDilworth, R. P.,The imbedding problem for modular lattices, Ann. of Math.45 (1944), 450–456.

    Google Scholar 

  13. Herrmann, Ch.,S-Verklebte Summen von Verbänden, Math. Z.130 (1973, 225–274.

    Google Scholar 

  14. Herrmann, Ch.,Quasiplanare Verbände, Archiv. Math.24 (1973), 240–246.

    Google Scholar 

  15. Herrmann, Ch.,Modulare Verbände von Länge n≤6, Proc. Houston Lattice Theory Conference, 1973, pp. 119–146.

  16. Herrmann, Ch. andHuhn, A. P.,Lattices of normal subgroups generated by frames, Colloq. Math. Society János Bolyai, vol.14, 1976, pp. 97–136.

    Google Scholar 

  17. Herrmann, Ch., Pickering, D. andRoddy, M.,Geometric description of modular lattices, to appear in Algebra Universalis.

  18. Jónsson, B.,Modular lattices and Desargues theorem, Math. Scand.2 (1954), 295–314.

    Google Scholar 

  19. Jónsson, B.,Arguesian lattices of dimension n≤4, Math. Scand.7 (1959), 133–145.

    Google Scholar 

  20. Jónsson, B.,The class of Arguesian lattices is selfdual, Algebra Universalis2 (1972), 396–396.

    Google Scholar 

  21. Jónsson, B. andNation, J. B.,Representation of 2-distributivemodular lattices of finite length, Acta Sci. Math.51 (1987), 123–128.

    Google Scholar 

  22. Nation, J. B. andPickering, D.,Arguesian lattices whose skeleton is a chain, Algebra Universalis24 (1987), 91–100.

    Google Scholar 

  23. von Neumann, J.,Continuous Geometry, Princeton University Press, Princeton, N.J., 1960.

    Google Scholar 

  24. Pickering, D.,Minimal non-Arguesian lattices, Ph.D. Thesis, University of Hawaii, 1984.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Lakehead University, P7B 5E1, Thunder Bay, Ontario, Canada

    Alan Day, Christian Herrmann, Bjarni Jónsson, J. B. Nation & Doug Pickering

  2. Technische Hochschule Darmstadt, FB4 AGI, 6100, Darmstadt, Germany

    Alan Day, Christian Herrmann, Bjarni Jónsson, J. B. Nation & Doug Pickering

  3. Department of Mathematics, Vanderbilt University, 37235, Nashville, TN, USA

    Alan Day, Christian Herrmann, Bjarni Jónsson, J. B. Nation & Doug Pickering

  4. Department of Mathematics, University of Hawaii, 96822, Honolulu, HI, USA

    Alan Day, Christian Herrmann, Bjarni Jónsson, J. B. Nation & Doug Pickering

  5. Department of Mathematics, Brandon University, R7A 6A9, Brandon, Manitoba, Canada

    Alan Day, Christian Herrmann, Bjarni Jónsson, J. B. Nation & Doug Pickering

Authors
  1. Alan Day
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Herrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bjarni Jónsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. B. Nation
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Doug Pickering
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was partially supported by NSERC Grants A-8190 (Day) and A-7884 (Pickering), and NSF Grants DMS 88-00290 (Jónsson) and DMS 87-03540 (Nation).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Day, A., Herrmann, C., Jónsson, B. et al. Small non-Arguesian lattices. Algebra Universalis 31, 66–94 (1994). https://doi.org/10.1007/BF01188180

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01188180

Search

Navigation