Algebra universalis

, Volume 73, Issue 2, pp 157–178 | Cite as

Small orthomodular partial algebras

  • Richard Holzer
  • Peter Burmeister


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.

Key words and phrases

orthomodular partial algebra orthomodular poset Greechie diagram 

2010 Mathematics Subject Classification

Primary: 08A55 Secondary: 06F99 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.OFFIS, R&D Division TransportationOldenburgGermany
  2. 2.Department of Mathematics, AG 1Darmstadt University of TechnologyDarmstadtGermany

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