PATH-CONNECTED AND NON PATH-CONNECTED ORTHOMODULAR LATTICES

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 5, 2009, pp.845-856
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.5.845

Title & Authors

PATH-CONNECTED AND NON PATH-CONNECTED ORTHOMODULAR LATTICES

Park, Eun-Soon; Song, Won-Hee;

Park, Eun-Soon; Song, Won-Hee;

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 B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A B| < 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] generated by the commutators of L is finite, then L is pathconnected.

Keywords

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

Language

English

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