A NOTE ON WEAKLY PATH-CONNECTED ORTHOMODULAR LATTICES

  • Published : 1997.07.01

Abstract

We show that each orthomodular lattice containing only atomic nonpath-connected blocks is a full subalgebra of an irreducible path-connected orthomodular lattice and there is a path-connected orthomodualr lattice L containing a weakly path-connected full subalgebra C(x) for some element x in L.

Keywords

References

  1. Can. J. Math. v.31 Block-finite Orthomodular Lattices Bruns, G.
  2. Algebra Universalis v.27 Block and Commutators in Orthomodular Lattices Bruns, G.;Greechie, R.
  3. J. of Combinatorial Theory v.4 On the Structure of Orthomodular Lattices Satisfying the Chain Condition Greechie, R.
  4. Order v.1 Commutator-finite Orthomodular Lattices Greechie, R.;Herman, L.
  5. Orthomodular Lattices Kalmbach, G.
  6. Kansas State University Ph. D. Thesis Path-connected Orthomodular Lattices Park, E.
  7. Bull. of Korean Math. Soc. v.31 A Note on Relatively Path-connected Orthomodular Lattices Park, E.
  8. Comm. of Korean Math. Soc. v.10 Note on Nonpath-connected Orthomodular Lattices Park, E.