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Minimal orthomodular lattices

Abstract

The lattices calledminimal orthomodular (MOL) arise in a special exclusion problem concerning the class of all orthomodular lattices (OML) and the subclass of all modular orthocomplemented lattices. This problem was given in G. Kalmbach's book,Orthomodular Lattices. We prove that an exclusion system necessarily must contain an infinite lattice. We prove that, except one, all the finite, irreducible MOLs have only blocks with eight elements. We characterize finite MOLs by a covering property related to equational classes generated by the modular ortholattices MOn.

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References

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Carrega, J.C. Minimal orthomodular lattices. Int J Theor Phys 34, 1265–1270 (1995). https://doi.org/10.1007/BF00676237

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Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Equational Classis
  • Orthomodular Lattice