Grechie diagrams of orthomodular algebras
by
Richard Holzer
TU Darmstadt

A Greechie diagram can be seen as a special hypergraph. The interpretation of a hypergraph is defined as a partial algebra of type (2, 1, 0). 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.

Date received: May 22, 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 # caee-50.