On some properties of small orthomodular partial algebras (OMAs)
by
Peter Burmeister
Darmstadt University of Technology
Coauthors: Richard Holzer (Darmstadt University of Technology)

OMAs are the partial algebras corresponding to orthomodular posets (see P.Burmeister, M.Maczy\'nski. Orthomodular (partial) algebras and their representations. Dem. Math. XXVII, 1994, pp. 701-722.). A complete list of all 121 OMAs with up to 24 elements will be given by their Greechie diagrams (G.d.s), and their full embeddability into Boolean algebras will be discussed together with some other properties.

A computer program written by R.Holzer has computed all G.d.s of the OMAs with 26 (90 G.d.s), 28 (226 G.d.s) and 30 elements (628 G.d.s), for which every ``subdiagram'' also belongs to an OMA.

Moreover, while there exists a four generated infinite OMA, the epimorphic images of the free OMAs generated by two and three elements are classified and thus shown to be finite.

Date received: May 24, 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-66.