Vol. 19, No. 3, 1966

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Modular pairs in orthomodular lattices

Erik Andrew Schreiner

Vol. 19 (1966), No. 3, 519–528
Abstract

Call an orthomodular lattice L M-symmetric if M(e,f) implies M(f,e) for all e,f L and O-symmetric if M(e,f) implies M(f,e). To check for these properties it is sufficient to consider only those modular pairs in which the two elements are complements. Every O-symmetric lattice is M-symmetric. In an atomic orthomodular lattice, M-symmetry is equivalent to the atomic exchange property.

Mathematical Subject Classification
Primary: 06.40
Milestones
Received: 9 August 1965
Published: 1 December 1966
Authors
Erik Andrew Schreiner