[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2009.46.5.845

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)

Publication Information

Bulletin of the Korean Mathematical Society / v.46, no.5, 2009 , pp. 845-856 More about this Journal

Abstract

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.

Keywords

orthomodular lattice; with finite sites; path-connected; non pathconnected; Boolean algebra;

Citations & Related Records

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