대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제46권5호
  • /
  • Pages.845-856
  • /
  • 2009
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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PATH-CONNECTED AND NON PATH-CONNECTED ORTHOMODULAR LATTICES

  • Park, Eun-Soon (DEPARTMENT OF MATHEMATICS SOONGSIL UNIVERSITY) ;
  • Song, Won-Hee (DEPARTMENT OF MATHEMATICS GRADUATE SCHOOL SOONGSIL UNIVERSITY)
  • 발행 : 2009.09.30
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초록

A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A $\cap$ B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A $\cap$ B| < $\infty$ for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [ComL]$\vee$ generated by the commutators of L is finite, then L is pathconnected.

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참고문헌

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