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Minimal Orthomodular Lattices from Quadratic Spaces over Finite Fields
Authors:J. C. Carréga  R. J. Greechie  R. Mayet
Affiliation:(1) Institut Girard Desargues, UPRES-A 5028 du CNRS, Universiteé Lyon 1, 69622 Villeurbanne Cedex, France;(2) Louisiana Tech University, Ruston, Louisiana, 71272
Abstract:If T is a finite, nonmodular, orthomodular lattice (OML), T is called minimal ifall its proper subOMLs are modular. In this paper we give a new infinite list ofminimal OMLs. They are obtained from quadratic spaces over a finite field Kof cardinality q equiv 3 (mod 4). Their Greechie diagrams for q = 7 and q = 11are presented in a new way.
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