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Minimal Orthomodular Lattices from Quadratic Spaces over Finite Fields

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Abstract

If T is a finite, nonmodular, orthomodular lattice (OML), T is called minimal ifall its proper subOMLs are modular. In this paper we give a new infinite list ofminimal OMLs. They are obtained from quadratic spaces over a finite field Kof cardinality q ≡ 3 (mod 4). Their Greechie diagrams for q = 7 and q = 11are presented in a new way.

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REFERENCES

  • Artin, E. (1967). Algébre Geométrique, Gauthier-Villars, Paris.

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  • Carréga, J. C. (1998). Coverings of [Mon] and minimal orthomodular Lattices, Int. J. Theor. Phys. 37, 11-16.

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Authors and Affiliations

  1. Institut Girard Desargues, UPRES-A 5028 du CNRS, Universiteé Lyon 1, 69622, Villeurbanne Cedex, France

    J. C. Carréga & R. Mayet

  2. Louisiana Tech University, Ruston, Louisiana, 71272

    R. J. Greechie

Authors
  1. J. C. Carréga
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  2. R. J. Greechie
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  3. R. Mayet
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Carréga, J.C., Greechie, R.J. & Mayet, R. Minimal Orthomodular Lattices from Quadratic Spaces over Finite Fields. International Journal of Theoretical Physics 39, 517–524 (2000). https://doi.org/10.1023/A:1003665116019

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  • DOI: https://doi.org/10.1023/A:1003665116019

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