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Small orthomodular partial algebras

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Abstract

Orthomodular partial algebras (OMAs) can be seen as the algebraic representation of orthomodular posets. We use Greechie diagrams for the graphical representation of OMAs and investigate characterizations for the strong embeddability of a given OMA into a Boolean OMA. We present a complete list of the Greechie diagrams of OMAs up to 24 elements, and we show that there exists an infinite OMA that is generated by 4 elements.

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Authors and Affiliations

  1. OFFIS, R&D Division Transportation, Escherweg 2, 26121, Oldenburg, Germany

    Richard Holzer

  2. Department of Mathematics, AG 1, Darmstadt University of Technology, Schloßgartenstr. 7, D-64289, Darmstadt, Germany

    Peter Burmeister

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  1. Richard Holzer
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  2. Peter Burmeister
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Correspondence to Richard Holzer.

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Presented by S. Pulmannova.

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Holzer, R., Burmeister, P. Small orthomodular partial algebras. Algebra Univers. 73, 157–178 (2015). https://doi.org/10.1007/s00012-015-0318-3

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  • DOI: https://doi.org/10.1007/s00012-015-0318-3

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