Greechie diagrams of orthomodular partial algebras |
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Authors: | Richard Holzer |
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Institution: | (1) Faculty of Informatics and Mathematics, University of Passau, Innstr. 43, 94032 Passau, Germany |
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Abstract: | Greechie diagrams are well known graphical representations of orthomodular partial algebras, orthomodular posets and orthomodular
lattices. For each hypergraph D a partial algebra ⟦D⟧ = (A; ⊕, ′, 0) of type (2,1,0) can be defined. A Greechie diagram can be seen as a special hypergraph: different points of the
hypergraph have different interpretations in the corresponding partial algebra ⟦D⟧, and each line in the hypergraph has a maximal Boolean subalgebra as interpretation, in which the points are the atoms.
This paper gives some generalisations of the characterisations in K83] and D84] of diagrams which represent orthomodular
partial algebras (= OMAs), and we give an algorithm how to check whether a given hypergraph D is an OMA-diagram whose maximal Boolean subalgebras are induced by the lines of the hypergraph.
Received July 22, 2004; accepted in final form February 1, 2007. |
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Keywords: | Primary: 08A55 Secondary: 06F99 |
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