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Coverings of [Mon] and Minimal Orthomodular Lattices

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Abstract

A finite, nonmodular orthomodular lattice (OML)T is called minimal if all its proper subOMLs aremodular. For a finite, nonmodular OML T, T minimal isequivalent to the equational class [T], generated by T, covers the equational class [MOn] forsome n. The main result of this paper is that thereexist infinitely many minimal OMLs. They are obtainedfrom quadratic spaces on finite fields. The automorphism groups of such OMLs are given.

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REFERENCES

  • Carréga, J. C. (1995). Minimal orthomodular lattices, International Journal of Theoretical Physics, 34, 1265–1270.

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Authors
  1. J. C. Carrega
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Carrega, J.C. Coverings of [Mon] and Minimal Orthomodular Lattices. International Journal of Theoretical Physics 37, 11–16 (1998). https://doi.org/10.1023/A:1026696718992

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  • DOI: https://doi.org/10.1023/A:1026696718992

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