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Orthomodular partial algebras
by
Richard Holzer
TU-Darmstadt
An orthomodular partial algebra (OMA) is a partial algebra of type (2, 1, 0) which can be used as an algrebraic representation of an orthomodular poset. Such orthomodular partial algebras can be described by the interpretation of a Greechie diagram, where a Greechie diagram can be seen as a special hypergraph. A hypergraph is an OMA-diagramm if the interpretation is an orthomodular partial algebra in which the interpretation of each line is a block and the interpretation of each point is an atom of the algebra. There exists a canonical bijection (up to isomorphism) between all nontrivial OMAs in which each block is finite and all complete (i.e. each block is induced by a line) OMA-diagrams with finite lines. Two such OMAs are isomorphic iff the corresponding diagrams are isomorphic. There exists an algorithm to check wether a hypergraph is an OMA diagram without computing the interpretation of the hypergraph. There exists an infinite number of subdirectly irreducible OMAs.
Date received: December 21, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafo-35.