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.
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Received July 22, 2004; accepted in final form February 1, 2007.
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Holzer, R. Greechie diagrams of orthomodular partial algebras. Algebra univers. 57, 419–453 (2007). https://doi.org/10.1007/s00012-007-2051-z
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DOI: https://doi.org/10.1007/s00012-007-2051-z